TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60008 ms.

The following DP Processors were used


Problem 1 was processed with processor DependencyGraph (0ms).
 | – Problem 2 was processed with processor SubtermCriterion (0ms).
 | – Problem 3 was processed with processor BackwardsNarrowing (11ms).
 |    | – Problem 5 was processed with processor BackwardsNarrowing (13ms).
 |    |    | – Problem 6 was processed with processor BackwardsNarrowing (19ms).
 |    |    |    | – Problem 7 was processed with processor BackwardsNarrowing (26ms).
 |    |    |    |    | – Problem 8 was processed with processor BackwardsNarrowing (34ms).
 |    |    |    |    |    | – Problem 9 was processed with processor BackwardsNarrowing (76ms).
 |    |    |    |    |    |    | – Problem 10 was processed with processor BackwardsNarrowing (80ms).
 |    |    |    |    |    |    |    | – Problem 11 was processed with processor BackwardsNarrowing (92ms).
 |    |    |    |    |    |    |    |    | – Problem 12 was processed with processor BackwardsNarrowing (50ms).
 |    |    |    |    |    |    |    |    |    | – Problem 13 was processed with processor BackwardsNarrowing (117ms).
 |    |    |    |    |    |    |    |    |    |    | – Problem 14 was processed with processor BackwardsNarrowing (129ms).
 |    |    |    |    |    |    |    |    |    |    |    | – Problem 15 was processed with processor BackwardsNarrowing (72ms).
 |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 16 was processed with processor BackwardsNarrowing (73ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 17 was processed with processor BackwardsNarrowing (88ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 18 was processed with processor BackwardsNarrowing (83ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 19 was processed with processor BackwardsNarrowing (225ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 20 was processed with processor BackwardsNarrowing (107ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 21 was processed with processor BackwardsNarrowing (280ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 22 was processed with processor BackwardsNarrowing (128ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 23 was processed with processor BackwardsNarrowing (133ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 24 remains open; application of the following processors failed [BackwardsNarrowing (296ms), BackwardsNarrowing (111ms), BackwardsNarrowing (115ms), BackwardsNarrowing (350ms), BackwardsNarrowing (160ms), BackwardsNarrowing (185ms), BackwardsNarrowing (448ms), BackwardsNarrowing (211ms), BackwardsNarrowing (280ms), BackwardsNarrowing (534ms), BackwardsNarrowing (314ms), BackwardsNarrowing (527ms), BackwardsNarrowing (201ms), BackwardsNarrowing (581ms), BackwardsNarrowing (333ms), BackwardsNarrowing (358ms), BackwardsNarrowing (388ms), BackwardsNarrowing (424ms), BackwardsNarrowing (655ms), BackwardsNarrowing (364ms), BackwardsNarrowing (712ms), BackwardsNarrowing (304ms), BackwardsNarrowing (784ms), BackwardsNarrowing (471ms)].
 | – Problem 4 was processed with processor SubtermCriterion (0ms).

The following open problems remain:

Open Dependency Pair Problem 3

Dependency Pairs

f#(s(x), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Rewrite Rules

min(0, y) → 0min(x, 0) → 0
min(s(x), s(y)) → s(min(x, y))max(0, y) → y
max(x, 0) → xmax(s(x), s(y)) → s(max(x, y))
p(s(x)) → xf(s(x), s(y), s(z)) → f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f(0, y, z) → max(y, z)f(x, 0, z) → max(x, z)
f(x, y, 0) → max(x, y)

Original Signature

Termination of terms over the following signature is verified: min, f, 0, max, s, p

Problem 1: DependencyGraph

Dependency Pair Problem

Dependency Pairs

f#(s(x), s(y), s(z)) → max#(s(y), s(z))f#(s(x), s(y), s(z)) → min#(s(x), max(s(y), s(z)))
f#(x, y, 0) → max#(x, y)min#(s(x), s(y)) → min#(x, y)
f#(s(x), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), s(z)) → p#(min(s(x), max(s(y), s(z))))
f#(0, y, z) → max#(y, z)f#(s(x), s(y), s(z)) → min#(s(y), s(z))
f#(s(x), s(y), s(z)) → max#(s(x), max(s(y), s(z)))f#(s(x), s(y), s(z)) → min#(s(x), min(s(y), s(z)))
max#(s(x), s(y)) → max#(x, y)f#(x, 0, z) → max#(x, z)

Rewrite Rules

min(0, y) → 0min(x, 0) → 0
min(s(x), s(y)) → s(min(x, y))max(0, y) → y
max(x, 0) → xmax(s(x), s(y)) → s(max(x, y))
p(s(x)) → xf(s(x), s(y), s(z)) → f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f(0, y, z) → max(y, z)f(x, 0, z) → max(x, z)
f(x, y, 0) → max(x, y)

Original Signature

Termination of terms over the following signature is verified: min, f, 0, max, s, p

Strategy

The following SCCs where found

min#(s(x), s(y)) → min#(x, y)
f#(s(x), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
max#(s(x), s(y)) → max#(x, y)

Problem 2: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

max#(s(x), s(y)) → max#(x, y)

Rewrite Rules

min(0, y) → 0min(x, 0) → 0
min(s(x), s(y)) → s(min(x, y))max(0, y) → y
max(x, 0) → xmax(s(x), s(y)) → s(max(x, y))
p(s(x)) → xf(s(x), s(y), s(z)) → f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f(0, y, z) → max(y, z)f(x, 0, z) → max(x, z)
f(x, y, 0) → max(x, y)

Original Signature

Termination of terms over the following signature is verified: min, f, 0, max, s, p

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

max#(s(x), s(y)) → max#(x, y)

Problem 3: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(s(x), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Rewrite Rules

min(0, y) → 0min(x, 0) → 0
min(s(x), s(y)) → s(min(x, y))max(0, y) → y
max(x, 0) → xmax(s(x), s(y)) → s(max(x, y))
p(s(x)) → xf(s(x), s(y), s(z)) → f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f(0, y, z) → max(y, z)f(x, 0, z) → max(x, z)
f(x, y, 0) → max(x, y)

Original Signature

Termination of terms over the following signature is verified: f, min, max, 0, s, p

Strategy

The left-hand side of the rule f#(s(x), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(s(x), s(y), max(s(z), 0)) 
f#(s(x), s(y), min(s(_x42), s(_x41))) 
f#(p(s(s(x))), s(y), s(z)) 
f#(s(x), s(y), max(s(_x42), s(_x41))) 
f#(s(x), p(s(s(y))), s(z)) 
f#(s(x), max(s(_x32), s(_x31)), s(z)) 
f#(s(x), s(y), p(s(s(z)))) 
f#(s(x), max(0, s(y)), s(z)) 
f#(s(x), s(y), max(0, s(z))) 
f#(max(s(_x22), s(_x21)), s(y), s(z)) 
f#(max(s(x), 0), s(y), s(z)) 
f#(min(s(_x22), s(_x21)), s(y), s(z)) 
f#(s(x), max(s(y), 0), s(z)) 
f#(max(0, s(x)), s(y), s(z)) 
f#(s(x), min(s(_x32), s(_x31)), s(z)) 
Thus, the rule f#(s(x), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is replaced by the following rules:
f#(s(x), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(0, s(y)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))f#(min(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))
f#(s(x), s(y), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(s(x))), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(0, s(x)), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(s(x), min(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(min(_x32, _x31)), s(z))), p(min(s(x), max(s(min(_x32, _x31)), s(z)))), min(s(x), min(s(min(_x32, _x31)), s(z))))
f#(s(x), max(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(max(_x32, _x31)), s(z))), p(min(s(x), max(s(max(_x32, _x31)), s(z)))), min(s(x), min(s(max(_x32, _x31)), s(z))))f#(s(x), p(s(s(y))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(x), 0), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Problem 5: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(s(x), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(0, s(y)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))f#(min(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))
f#(s(x), s(y), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(s(x))), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(0, s(x)), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(s(x), min(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(min(_x32, _x31)), s(z))), p(min(s(x), max(s(min(_x32, _x31)), s(z)))), min(s(x), min(s(min(_x32, _x31)), s(z))))
f#(s(x), max(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(max(_x32, _x31)), s(z))), p(min(s(x), max(s(max(_x32, _x31)), s(z)))), min(s(x), min(s(max(_x32, _x31)), s(z))))f#(s(x), p(s(s(y))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(x), 0), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Rewrite Rules

min(0, y) → 0min(x, 0) → 0
min(s(x), s(y)) → s(min(x, y))max(0, y) → y
max(x, 0) → xmax(s(x), s(y)) → s(max(x, y))
p(s(x)) → xf(s(x), s(y), s(z)) → f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f(0, y, z) → max(y, z)f(x, 0, z) → max(x, z)
f(x, y, 0) → max(x, y)

Original Signature

Termination of terms over the following signature is verified: min, f, 0, max, s, p

Strategy

The left-hand side of the rule f#(s(x), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(s(x), f(s(y), 0, 0), s(z)) 
f#(max(s(_x22), s(_x21)), max(s(y), 0), s(z)) 
f#(s(x), max(p(s(s(y))), 0), s(z)) 
f#(s(x), max(s(y), min(_x51, 0)), s(z)) 
f#(s(x), max(s(y), p(s(0))), s(z)) 
f#(s(x), max(s(y), 0), p(s(s(z)))) 
f#(s(x), max(s(y), min(0, _x51)), s(z)) 
f#(min(s(_x22), s(_x21)), max(s(y), 0), s(z)) 
f#(s(x), max(s(y), 0), max(s(z), 0)) 
f#(s(x), max(s(y), 0), min(s(_x42), s(_x41))) 
f#(s(x), f(0, s(y), 0), s(z)) 
f#(p(s(s(x))), max(s(y), 0), s(z)) 
f#(s(x), p(s(max(s(y), 0))), s(z)) 
f#(s(x), max(s(y), 0), max(0, s(z))) 
f#(s(x), max(min(s(_x42), s(_x41)), 0), s(z)) 
f#(s(x), max(0, max(s(y), 0)), s(z)) 
f#(s(x), max(max(s(_x42), s(_x41)), 0), s(z)) 
f#(s(x), max(s(y), 0), max(s(_x42), s(_x41))) 
f#(s(x), max(max(0, s(y)), 0), s(z)) 
f#(s(x), max(s(y), max(0, 0)), s(z)) 
f#(max(0, s(x)), max(s(y), 0), s(z)) 
f#(s(x), max(max(s(y), 0), 0), s(z)) 
f#(max(s(x), 0), max(s(y), 0), s(z)) 
Thus, the rule f#(s(x), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is replaced by the following rules:
f#(max(0, s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(s(x), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(s(x), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))
f#(max(s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(min(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))
f#(s(x), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(s(x), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(p(s(s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Problem 6: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(max(0, s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(0, s(y)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(s(x), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(max(s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(min(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))
f#(s(x), s(y), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(s(x), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(min(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))f#(s(x), s(y), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(s(x), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), min(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(min(_x32, _x31)), s(z))), p(min(s(x), max(s(min(_x32, _x31)), s(z)))), min(s(x), min(s(min(_x32, _x31)), s(z))))
f#(s(x), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(s(x), p(s(s(y))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))f#(max(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))
f#(s(x), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(s(x))), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(s(x), max(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(max(_x32, _x31)), s(z))), p(min(s(x), max(s(max(_x32, _x31)), s(z)))), min(s(x), min(s(max(_x32, _x31)), s(z))))f#(max(s(x), 0), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Rewrite Rules

min(0, y) → 0min(x, 0) → 0
min(s(x), s(y)) → s(min(x, y))max(0, y) → y
max(x, 0) → xmax(s(x), s(y)) → s(max(x, y))
p(s(x)) → xf(s(x), s(y), s(z)) → f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f(0, y, z) → max(y, z)f(x, 0, z) → max(x, z)
f(x, y, 0) → max(x, y)

Original Signature

Termination of terms over the following signature is verified: f, min, max, 0, s, p

Strategy

The left-hand side of the rule f#(max(0, s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), s(z)) 
f#(max(0, s(x)), f(s(y), 0, 0), s(z)) 
f#(max(0, s(x)), max(0, max(s(y), 0)), s(z)) 
f#(max(0, s(x)), p(s(max(s(y), 0))), s(z)) 
f#(max(0, s(x)), f(0, s(y), 0), s(z)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), s(z)) 
f#(max(0, s(x)), max(s(y), 0), min(s(_x42), s(_x41))) 
f#(max(0, s(x)), max(s(y), 0), max(0, s(z))) 
f#(max(max(0, 0), s(x)), max(s(y), 0), s(z)) 
f#(max(p(s(0)), s(x)), max(s(y), 0), s(z)) 
f#(f(0, 0, s(x)), max(s(y), 0), s(z)) 
f#(max(0, s(x)), max(max(s(y), 0), 0), s(z)) 
f#(max(0, s(x)), max(max(0, s(y)), 0), s(z)) 
f#(max(0, s(x)), max(s(y), 0), max(s(z), 0)) 
f#(max(min(0, _x31), s(x)), max(s(y), 0), s(z)) 
f#(p(s(max(0, s(x)))), max(s(y), 0), s(z)) 
f#(max(0, s(x)), max(s(y), min(_x51, 0)), s(z)) 
f#(f(0, s(x), 0), max(s(y), 0), s(z)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), s(z)) 
f#(max(0, s(x)), max(s(y), 0), p(s(s(z)))) 
f#(max(0, s(x)), max(s(y), 0), max(s(_x42), s(_x41))) 
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), s(z)) 
f#(max(0, max(0, s(x))), max(s(y), 0), s(z)) 
f#(max(0, s(x)), max(s(y), min(0, _x51)), s(z)) 
f#(max(0, max(s(x), 0)), max(s(y), 0), s(z)) 
f#(max(0, s(x)), max(p(s(s(y))), 0), s(z)) 
f#(max(max(0, s(x)), 0), max(s(y), 0), s(z)) 
f#(max(min(_x31, 0), s(x)), max(s(y), 0), s(z)) 
f#(max(0, s(x)), max(s(y), p(s(0))), s(z)) 
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), s(z)) 
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), s(z)) 
Thus, the rule f#(max(0, s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is replaced by the following rules:
f#(max(0, s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(max(0, s(x)), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(max(0, s(x)), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Problem 7: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(max(0, s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(min(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))f#(s(x), s(y), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(min(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))
f#(s(x), s(y), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(s(x), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), p(s(s(y))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))f#(s(x), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(s(x))), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(s(x), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(max(_x32, _x31)), s(z))), p(min(s(x), max(s(max(_x32, _x31)), s(z)))), min(s(x), min(s(max(_x32, _x31)), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(0, s(y)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(s(x), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), min(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(min(_x32, _x31)), s(z))), p(min(s(x), max(s(min(_x32, _x31)), s(z)))), min(s(x), min(s(min(_x32, _x31)), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(0, s(x)), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(s(x), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(max(0, s(x)), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(s(x), 0), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Rewrite Rules

min(0, y) → 0min(x, 0) → 0
min(s(x), s(y)) → s(min(x, y))max(0, y) → y
max(x, 0) → xmax(s(x), s(y)) → s(max(x, y))
p(s(x)) → xf(s(x), s(y), s(z)) → f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f(0, y, z) → max(y, z)f(x, 0, z) → max(x, z)
f(x, y, 0) → max(x, y)

Original Signature

Termination of terms over the following signature is verified: min, f, 0, max, s, p

Strategy

The left-hand side of the rule f#(max(0, s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(max(0, s(x)), max(s(y), max(0, 0)), max(s(z), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(s(z), min(_x61, 0))) 
f#(max(0, s(x)), max(s(y), 0), f(s(z), 0, 0)) 
f#(max(0, s(x)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(0, max(s(z), 0))) 
f#(max(max(0, 0), s(x)), max(s(y), 0), max(s(z), 0)) 
f#(p(s(max(0, s(x)))), max(s(y), 0), max(s(z), 0)) 
f#(max(0, s(x)), max(max(0, s(y)), 0), max(s(z), 0)) 
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(p(s(s(z))), 0)) 
f#(max(0, s(x)), max(s(y), p(s(0))), max(s(z), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), max(s(z), 0)) 
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) 
f#(max(0, s(x)), max(max(s(y), 0), 0), max(s(z), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), max(s(z), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(s(z), max(0, 0))) 
f#(max(0, s(x)), max(s(y), 0), p(s(max(s(z), 0)))) 
f#(max(0, s(x)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(s(z), p(s(0)))) 
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(s(z), 0)) 
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(s(z), 0)) 
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(s(z), min(0, _x61))) 
f#(max(0, s(x)), max(s(y), 0), f(0, s(z), 0)) 
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(s(z), 0)) 
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), 0)) 
f#(f(0, s(x), 0), max(s(y), 0), max(s(z), 0)) 
f#(max(0, s(x)), f(s(y), 0, 0), max(s(z), 0)) 
f#(max(0, s(x)), p(s(max(s(y), 0))), max(s(z), 0)) 
f#(max(0, s(x)), f(0, s(y), 0), max(s(z), 0)) 
f#(max(0, max(0, s(x))), max(s(y), 0), max(s(z), 0)) 
f#(max(max(0, s(x)), 0), max(s(y), 0), max(s(z), 0)) 
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) 
f#(max(0, s(x)), max(0, max(s(y), 0)), max(s(z), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), 0), max(s(z), 0)) 
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(s(z), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(max(0, s(z)), 0)) 
f#(max(p(s(0)), s(x)), max(s(y), 0), max(s(z), 0)) 
Thus, the rule f#(max(0, s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is replaced by the following rules:
f#(max(0, s(x)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(f(0, s(x), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Problem 8: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(min(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))f#(s(x), s(y), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(min(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))
f#(s(x), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(s(x), max(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(max(_x32, _x31)), s(z))), p(min(s(x), max(s(max(_x32, _x31)), s(z)))), min(s(x), min(s(max(_x32, _x31)), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(0, s(x)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))
f#(s(x), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(x), 0), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(s(x), s(y), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), p(s(s(y))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(p(s(s(x))), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(0, s(y)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(s(x), min(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(min(_x32, _x31)), s(z))), p(min(s(x), max(s(min(_x32, _x31)), s(z)))), min(s(x), min(s(min(_x32, _x31)), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))f#(s(x), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(s(x), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Rewrite Rules

min(0, y) → 0min(x, 0) → 0
min(s(x), s(y)) → s(min(x, y))max(0, y) → y
max(x, 0) → xmax(s(x), s(y)) → s(max(x, y))
p(s(x)) → xf(s(x), s(y), s(z)) → f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f(0, y, z) → max(y, z)f(x, 0, z) → max(x, z)
f(x, y, 0) → max(x, y)

Original Signature

Termination of terms over the following signature is verified: f, min, max, 0, s, p

Strategy

The left-hand side of the rule f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(max(0, max(s(x), 0)), max(s(y), 0), max(p(s(s(z))), 0)) 
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), p(s(0)))) 
f#(max(0, max(s(x), min(_x61, 0))), max(s(y), 0), max(s(z), 0)) 
f#(max(0, max(max(0, s(x)), 0)), max(s(y), 0), max(s(z), 0)) 
f#(max(0, max(p(s(s(x))), 0)), max(s(y), 0), max(s(z), 0)) 
f#(max(p(s(0)), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) 
f#(max(0, max(s(x), p(s(0)))), max(s(y), 0), max(s(z), 0)) 
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(0, s(z)), 0)) 
f#(max(0, max(s(x), 0)), max(s(y), 0), p(s(max(s(z), 0)))) 
f#(p(s(max(0, max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) 
f#(max(min(0, _x31), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) 
f#(max(0, max(s(x), 0)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) 
f#(max(0, max(s(x), 0)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) 
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(_x61, 0))) 
f#(max(0, p(s(max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) 
f#(max(0, max(s(x), 0)), max(s(y), 0), f(0, s(z), 0)) 
f#(max(0, max(s(x), 0)), max(0, max(s(y), 0)), max(s(z), 0)) 
f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(s(z), 0)) 
f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(s(z), 0)) 
f#(max(0, max(s(x), 0)), f(0, s(y), 0), max(s(z), 0)) 
f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(s(z), 0))) 
f#(max(0, f(0, s(x), 0)), max(s(y), 0), max(s(z), 0)) 
f#(max(0, f(s(x), 0, 0)), max(s(y), 0), max(s(z), 0)) 
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), max(0, 0))) 
f#(max(0, max(max(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) 
f#(max(0, max(s(x), max(0, 0))), max(s(y), 0), max(s(z), 0)) 
f#(max(max(0, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) 
f#(max(0, max(0, max(s(x), 0))), max(s(y), 0), max(s(z), 0)) 
f#(max(max(0, max(s(x), 0)), 0), max(s(y), 0), max(s(z), 0)) 
f#(max(min(_x31, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) 
f#(f(0, max(s(x), 0), 0), max(s(y), 0), max(s(z), 0)) 
f#(max(0, max(s(x), 0)), max(s(y), min(_x51, 0)), max(s(z), 0)) 
f#(max(0, max(s(x), 0)), f(s(y), 0, 0), max(s(z), 0)) 
f#(max(0, max(s(x), 0)), max(max(0, s(y)), 0), max(s(z), 0)) 
f#(max(0, max(s(x), 0)), max(s(y), min(0, _x51)), max(s(z), 0)) 
f#(max(0, max(s(x), 0)), p(s(max(s(y), 0))), max(s(z), 0)) 
f#(max(0, max(s(x), 0)), max(s(y), 0), f(s(z), 0, 0)) 
f#(max(0, max(s(x), 0)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) 
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(0, _x61))) 
f#(max(0, max(s(x), 0)), max(max(s(y), 0), 0), max(s(z), 0)) 
f#(max(0, max(s(x), min(0, _x61))), max(s(y), 0), max(s(z), 0)) 
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(max(0, max(s(x), 0)), max(s(y), p(s(0))), max(s(z), 0)) 
f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), max(s(z), 0)) 
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) 
f#(max(0, max(max(s(x), 0), 0)), max(s(y), 0), max(s(z), 0)) 
f#(max(0, max(min(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) 
Thus, the rule f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is replaced by the following rules:
f#(max(0, max(max(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))f#(max(0, max(max(0, s(x)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, max(s(x), 0), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), min(0, _x61))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), min(_x61, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))
f#(max(0, max(p(s(s(x))), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), max(0, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(max(s(x), 0), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, f(s(x), 0, 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, f(0, s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(p(s(0)), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), p(s(0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))f#(max(max(0, max(s(x), 0)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, max(s(x), 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(min(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))

Problem 9: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(max(0, s(x)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), min(0, _x61))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(min(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))f#(s(x), s(y), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(min(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))
f#(max(max(0, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), max(0, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(max(s(x), 0), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), p(s(0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))
f#(max(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(s(x), max(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(max(_x32, _x31)), s(z))), p(min(s(x), max(s(max(_x32, _x31)), s(z)))), min(s(x), min(s(max(_x32, _x31)), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(s(x), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(0, s(x)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(p(s(s(x))), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, f(s(x), 0, 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, max(s(x), 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))
f#(s(x), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(x), 0), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(max(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))f#(max(0, max(s(x), min(_x61, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(s(x), s(y), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(max(0, max(s(x), 0)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), p(s(s(y))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, max(s(x), 0)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(s(x))), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(min(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(0, s(y)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(max(0, s(x)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, max(s(x), 0), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), min(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(min(_x32, _x31)), s(z))), p(min(s(x), max(s(min(_x32, _x31)), s(z)))), min(s(x), min(s(min(_x32, _x31)), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(max(0, s(x)), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))f#(max(0, max(s(x), 0)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, f(0, s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Rewrite Rules

min(0, y) → 0min(x, 0) → 0
min(s(x), s(y)) → s(min(x, y))max(0, y) → y
max(x, 0) → xmax(s(x), s(y)) → s(max(x, y))
p(s(x)) → xf(s(x), s(y), s(z)) → f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f(0, y, z) → max(y, z)f(x, 0, z) → max(x, z)
f(x, y, 0) → max(x, y)

Original Signature

Termination of terms over the following signature is verified: min, f, 0, max, s, p

Strategy

The left-hand side of the rule f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(max(0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) 
f#(max(p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) 
f#(max(0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) 
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) 
f#(f(0, s(x), 0), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) 
f#(max(max(0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) 
f#(max(0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) 
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) 
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(max(0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) 
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) 
f#(max(0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) 
f#(max(max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(p(s(max(0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) 
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) 
f#(max(0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) 
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) 
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) 
Thus, the rule f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is replaced by the following rules:
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))f#(max(0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Problem 10: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(min(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(max(s(x), 0), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))f#(p(s(max(0, max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), p(s(0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(s(x), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(s(x), max(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(max(_x32, _x31)), s(z))), p(min(s(x), max(s(max(_x32, _x31)), s(z)))), min(s(x), min(s(max(_x32, _x31)), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(0, s(x)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(p(s(s(x))), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, f(s(x), 0, 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(max(0, s(x)), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, max(s(x), 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(max(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), p(s(s(y))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, max(s(x), 0)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(s(x))), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(min(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(max(0, s(x)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, max(s(x), 0), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), min(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(min(_x32, _x31)), s(z))), p(min(s(x), max(s(min(_x32, _x31)), s(z)))), min(s(x), min(s(min(_x32, _x31)), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(max(0, s(x)), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))f#(s(x), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, f(0, s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), min(0, _x61))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(min(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))f#(max(0, max(s(x), max(0, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))
f#(f(0, s(x), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))
f#(max(0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(s(x), 0), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), min(_x61, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(max(0, s(x)), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(min(_x31, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(0, s(y)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Rewrite Rules

min(0, y) → 0min(x, 0) → 0
min(s(x), s(y)) → s(min(x, y))max(0, y) → y
max(x, 0) → xmax(s(x), s(y)) → s(max(x, y))
p(s(x)) → xf(s(x), s(y), s(z)) → f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f(0, y, z) → max(y, z)f(x, 0, z) → max(x, z)
f(x, y, 0) → max(x, y)

Original Signature

Termination of terms over the following signature is verified: f, min, max, 0, s, p

Strategy

The left-hand side of the rule f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(p(s(max(0, s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, max(0, s(x))), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(max(0, f(0, s(z), 0)), 0)) 
f#(f(0, s(x), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, s(x)), max(max(0, s(y)), 0), max(f(0, s(z), 0), 0)) 
f#(max(max(0, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(_x81, 0)), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) 
f#(max(p(s(0)), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(max(f(0, s(z), 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(z), 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(0, _x81)), 0)) 
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), max(0, 0)), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), p(s(0)))) 
f#(max(0, s(x)), max(s(y), 0), max(f(max(0, 0), s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(p(s(f(0, s(z), 0))), 0)) 
f#(max(0, s(x)), max(0, max(s(y), 0)), max(f(0, s(z), 0), 0)) 
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, s(x)), f(0, s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, s(x)), f(s(y), 0, 0), max(f(0, s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(f(p(s(0)), s(z), 0), 0)) 
f#(max(0, s(x)), max(max(s(y), 0), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), max(0, 0))) 
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(f(0, s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(f(0, min(s(_x72), s(_x71)), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(f(0, p(s(s(z))), 0), 0)) 
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), max(f(0, s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(f(0, max(0, s(z)), 0), 0)) 
f#(max(0, s(x)), max(s(y), p(s(0))), max(f(0, s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), p(s(max(f(0, s(z), 0), 0)))) 
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), p(s(0))), 0)) 
f#(max(max(0, s(x)), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(0, max(f(0, s(z), 0), 0))) 
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(f(0, s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(f(min(0, _x61), s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(f(min(_x61, 0), s(z), 0), 0)) 
f#(max(0, s(x)), p(s(max(s(y), 0))), max(f(0, s(z), 0), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(0, _x61))) 
f#(max(0, max(s(x), 0)), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(_x72), s(_x71)), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(_x61, 0))) 
f#(max(0, s(x)), max(s(y), 0), f(0, f(0, s(z), 0), 0)) 
Thus, the rule f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is replaced by the following rules:
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, f(0, s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(p(s(0)), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(max(0, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, min(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(min(0, _x61), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(min(_x61, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(f(0, s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(f(0, s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(f(0, s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(f(0, s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Problem 11: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(min(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(max(s(x), 0), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))f#(f(0, 0, s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(p(s(0)), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), p(s(0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(s(x), max(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(max(_x32, _x31)), s(z))), p(min(s(x), max(s(max(_x32, _x31)), s(z)))), min(s(x), min(s(max(_x32, _x31)), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(max(0, s(x)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(p(s(s(x))), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(f(0, s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, f(s(x), 0, 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(max(0, s(x)), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(0, max(s(x), 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(max(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(p(s(0)), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), p(s(s(y))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, max(s(x), 0)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(s(x))), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(min(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(max(0, s(x)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, max(s(x), 0), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), min(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(min(_x32, _x31)), s(z))), p(min(s(x), max(s(min(_x32, _x31)), s(z)))), min(s(x), min(s(min(_x32, _x31)), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(0, s(x)), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))
f#(s(x), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, f(0, s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(f(0, s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, f(0, s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), min(0, _x61))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(0, s(x)), max(s(y), 0), max(f(0, max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(min(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))f#(max(0, max(s(x), max(0, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(max(0, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))
f#(max(0, s(x)), max(max(0, s(y)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(min(0, _x61), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(f(0, s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))f#(max(0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(f(0, s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(x), 0), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), min(_x61, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(max(0, max(s(x), 0)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(0, s(y)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, min(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(min(_x61, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Rewrite Rules

min(0, y) → 0min(x, 0) → 0
min(s(x), s(y)) → s(min(x, y))max(0, y) → y
max(x, 0) → xmax(s(x), s(y)) → s(max(x, y))
p(s(x)) → xf(s(x), s(y), s(z)) → f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f(0, y, z) → max(y, z)f(x, 0, z) → max(x, z)
f(x, y, 0) → max(x, y)

Original Signature

Termination of terms over the following signature is verified: min, f, 0, max, s, p

Strategy

The left-hand side of the rule f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), 0, 0)) 
f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(0, _x71))) 
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), 0, 0)) 
f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), 0, 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, p(s(0)))) 
f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), 0, 0)))) 
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), 0, 0))) 
f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) 
f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), 0, 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), 0, 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), 0, 0)) 
f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), 0, 0)) 
f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(0)), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) 
f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(0, _x61), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, max(0, 0))) 
f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), 0, 0)) 
f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(_x71, 0))) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(_x61, 0), 0)) 
f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) 
Thus, the rule f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is replaced by the following rules:
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Problem 12: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(min(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(max(s(x), 0), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(f(0, 0, s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(p(s(0)), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), p(s(0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(s(x), max(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(max(_x32, _x31)), s(z))), p(min(s(x), max(s(max(_x32, _x31)), s(z)))), min(s(x), min(s(max(_x32, _x31)), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(0, max(0, s(x))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(p(s(s(x))), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(f(0, s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, f(s(x), 0, 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, max(s(x), 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(max(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))
f#(max(0, s(x)), max(s(y), 0), max(f(p(s(0)), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(s(x), p(s(s(y))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, max(s(x), 0)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(s(x))), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(min(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(max(0, s(x)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, max(s(x), 0), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), min(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(min(_x32, _x31)), s(z))), p(min(s(x), max(s(min(_x32, _x31)), s(z)))), min(s(x), min(s(min(_x32, _x31)), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(max(0, s(x)), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, f(0, s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(f(0, s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, f(0, s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), min(0, _x61))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(min(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))
f#(max(0, max(s(x), max(0, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(max(0, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(min(0, _x61), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(f(0, s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))
f#(max(0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(f(0, s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(s(x), 0), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), min(_x61, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(max(0, s(x)), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(min(_x31, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(0, s(y)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, min(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(max(0, s(x)), max(s(y), 0), max(f(min(_x61, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Rewrite Rules

min(0, y) → 0min(x, 0) → 0
min(s(x), s(y)) → s(min(x, y))max(0, y) → y
max(x, 0) → xmax(s(x), s(y)) → s(max(x, y))
p(s(x)) → xf(s(x), s(y), s(z)) → f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f(0, y, z) → max(y, z)f(x, 0, z) → max(x, z)
f(x, y, 0) → max(x, y)

Original Signature

Termination of terms over the following signature is verified: f, min, max, 0, s, p

Strategy

The left-hand side of the rule f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(f(0, 0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) 
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(f(0, 0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(min(_x31, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(max(f(0, 0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) 
f#(f(0, max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) 
f#(p(s(f(0, 0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, min(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) 
f#(f(0, 0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) 
f#(f(0, 0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) 
f#(max(0, f(0, 0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) 
f#(f(max(0, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) 
f#(f(0, 0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) 
f#(f(0, 0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) 
f#(f(p(s(0)), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) 
f#(f(0, 0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) 
f#(f(0, min(0, _x41), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) 
f#(f(0, 0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) 
f#(f(min(0, _x31), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) 
f#(f(0, min(_x41, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) 
f#(f(0, 0, max(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) 
f#(f(0, 0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) 
f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) 
f#(f(0, 0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) 
Thus, the rule f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is replaced by the following rules:
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, min(_x41, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))f#(f(0, 0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(p(s(0)), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(max(0, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(f(0, 0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))f#(f(0, 0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, min(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))
f#(max(0, f(0, 0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(f(0, 0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(min(_x31, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(min(0, _x31), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))
f#(f(0, min(0, _x41), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Problem 13: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(min(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(max(s(x), 0), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(f(0, 0, s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(f(0, 0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(p(s(0)), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), p(s(0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(s(x), max(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(max(_x32, _x31)), s(z))), p(min(s(x), max(s(max(_x32, _x31)), s(z)))), min(s(x), min(s(max(_x32, _x31)), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, min(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(f(0, 0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(f(0, 0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(p(s(s(x))), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(f(0, s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, f(s(x), 0, 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(max(0, s(x)), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(f(0, 0, max(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))
f#(max(0, max(0, max(s(x), 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(max(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))
f#(f(p(s(0)), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(p(s(0)), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, max(s(x), 0)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(s(x), p(s(s(y))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, max(s(x), 0)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(s(x))), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(min(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))f#(max(0, f(0, 0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(max(0, s(x)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, max(s(x), 0), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), min(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(min(_x32, _x31)), s(z))), p(min(s(x), max(s(min(_x32, _x31)), s(z)))), min(s(x), min(s(min(_x32, _x31)), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(max(0, s(x)), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, f(0, s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(f(0, s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, f(0, s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), min(0, _x61))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, min(_x41, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))f#(s(x), s(y), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(f(0, 0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(min(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), max(0, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(max(0, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(max(0, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(f(0, 0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(min(0, _x61), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(min(0, _x31), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(f(0, s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))f#(max(0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(f(0, s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(s(x), 0), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), min(_x61, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(max(0, max(s(x), 0)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(0, s(y)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, min(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))f#(f(min(_x31, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(min(_x61, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, min(0, _x41), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Rewrite Rules

min(0, y) → 0min(x, 0) → 0
min(s(x), s(y)) → s(min(x, y))max(0, y) → y
max(x, 0) → xmax(s(x), s(y)) → s(max(x, y))
p(s(x)) → xf(s(x), s(y), s(z)) → f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f(0, y, z) → max(y, z)f(x, 0, z) → max(x, z)
f(x, y, 0) → max(x, y)

Original Signature

Termination of terms over the following signature is verified: min, f, 0, max, s, p

Strategy

The left-hand side of the rule f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(p(s(s(z))), 0), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), max(0, 0)), 0)) 
f#(max(0, s(x)), max(p(s(max(s(_x62), s(_x61)))), 0), max(max(s(z), 0), 0)) 
f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) 
f#(max(min(_x31, 0), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), min(_x51, 0)), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(p(max(s(s(y)), 0)), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(p(max(0, s(s(y)))), 0), max(max(s(z), 0), 0)) 
f#(max(p(s(0)), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) 
f#(max(max(0, s(x)), 0), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), 0), p(s(max(max(s(z), 0), 0)))) 
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), max(0, 0))) 
f#(max(0, min(s(_x42), s(_x41))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), p(s(max(p(s(s(y))), 0))), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(max(p(s(s(y))), 0), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(s(z), 0, 0), 0)) 
f#(max(0, s(x)), max(p(p(s(s(s(y))))), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(0, max(p(s(s(y))), 0)), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), p(s(0))), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(0, max(s(z), 0)), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(s(z), 0), 0), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), min(_x61, 0))) 
f#(max(0, s(x)), max(p(s(s(y))), 0), max(p(s(max(s(z), 0))), 0)) 
f#(max(0, s(x)), max(p(s(max(0, s(y)))), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), max(0, 0)), max(max(s(z), 0), 0)) 
f#(max(0, max(0, s(x))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), min(_x71, 0)), 0)) 
f#(max(0, p(s(s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), min(0, _x51)), max(max(s(z), 0), 0)) 
f#(max(min(0, _x31), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), min(0, _x61))) 
f#(max(0, s(x)), f(p(s(s(y))), 0, 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(p(s(max(s(y), 0))), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), 0), f(max(s(z), 0), 0, 0)) 
f#(max(max(0, 0), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), 0), f(0, max(s(z), 0), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), p(s(0))), max(max(s(z), 0), 0)) 
f#(max(0, max(s(_x42), s(_x41))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), p(s(0)))) 
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), min(0, _x71)), 0)) 
f#(max(0, s(x)), max(p(s(min(s(_x62), s(_x61)))), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), 0), max(0, max(max(s(z), 0), 0))) 
f#(max(0, s(x)), max(max(0, p(s(s(y)))), 0), max(max(s(z), 0), 0)) 
f#(p(s(max(0, s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, s(x)), max(p(s(p(s(s(y))))), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), f(0, p(s(s(y))), 0), max(max(s(z), 0), 0)) 
f#(f(0, s(x), 0), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(0, s(z)), 0), 0)) 
Thus, the rule f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is replaced by the following rules:
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(p(s(s(y))), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(p(s(s(y))), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(max(s(s(y)), 0)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(p(s(s(y))))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(p(s(s(y))), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(min(s(_x62), s(_x61)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x62, _x61)), s(z))), p(min(s(x), max(s(min(_x62, _x61)), s(z)))), min(s(x), min(s(min(_x62, _x61)), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(max(s(y), 0))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))f#(max(max(0, s(x)), 0), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(max(0, s(s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(max(s(_x62), s(_x61)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x62, _x61)), s(z))), p(min(s(x), max(s(max(_x62, _x61)), s(z)))), min(s(x), min(s(max(_x62, _x61)), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, p(s(s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(p(s(s(s(y))))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(max(0, s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(p(s(s(y))), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Problem 14: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(max(s(x), 0), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(min(s(_x62), s(_x61)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x62, _x61)), s(z))), p(min(s(x), max(s(min(_x62, _x61)), s(z)))), min(s(x), min(s(min(_x62, _x61)), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(s(x), max(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(max(_x32, _x31)), s(z))), p(min(s(x), max(s(max(_x32, _x31)), s(z)))), min(s(x), min(s(max(_x32, _x31)), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, min(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(f(0, 0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(f(0, s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, f(s(x), 0, 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))
f#(max(0, max(s(x), 0)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(p(s(s(y))), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(max(s(s(y)), 0)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(s(x))), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), min(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(min(_x32, _x31)), s(z))), p(min(s(x), max(s(min(_x32, _x31)), s(z)))), min(s(x), min(s(min(_x32, _x31)), s(z))))
f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))
f#(max(0, f(0, s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), min(0, _x61))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, min(_x41, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(f(0, 0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(p(s(s(y))))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))
f#(f(0, s(x), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(p(s(s(y))), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(min(0, _x31), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(max(s(y), 0))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(0, s(y)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, min(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, p(s(s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(min(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))f#(max(0, s(x)), max(max(p(s(s(y))), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(max(0, max(s(x), p(s(0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))f#(f(0, 0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(0, max(0, s(x))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(p(s(s(x))), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(max(0, s(s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(0, max(s(x), 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(max(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(p(s(s(y))), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(p(s(0)), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(p(s(0)), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(s(x), p(s(s(y))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, max(s(x), 0)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(min(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))
f#(max(0, f(0, 0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(f(0, 0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, max(max(0, s(x)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, max(s(x), 0), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(p(s(s(s(y))))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(max(0, s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(f(0, s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, f(0, s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))
f#(s(x), s(y), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(min(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))f#(max(0, max(s(x), max(0, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(max(0, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(max(0, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(f(0, 0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(min(0, _x61), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(f(0, s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(max(s(_x62), s(_x61)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x62, _x61)), s(z))), p(min(s(x), max(s(max(_x62, _x61)), s(z)))), min(s(x), min(s(max(_x62, _x61)), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))
f#(max(0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(f(0, s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(s(x), 0), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), min(_x61, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(f(min(_x31, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(min(_x61, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, min(0, _x41), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Rewrite Rules

min(0, y) → 0min(x, 0) → 0
min(s(x), s(y)) → s(min(x, y))max(0, y) → y
max(x, 0) → xmax(s(x), s(y)) → s(max(x, y))
p(s(x)) → xf(s(x), s(y), s(z)) → f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f(0, y, z) → max(y, z)f(x, 0, z) → max(x, z)
f(x, y, 0) → max(x, y)

Original Signature

Termination of terms over the following signature is verified: f, min, max, 0, s, p

Strategy

The left-hand side of the rule f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(max(0, p(s(s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) 
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), min(_x91, 0)), 0))) 
f#(max(p(s(0)), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) 
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) 
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), p(s(0))), 0))) 
f#(max(0, s(x)), max(s(y), 0), max(0, max(f(s(z), 0, 0), 0))) 
f#(max(0, s(x)), max(s(y), 0), f(0, max(max(s(z), 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), max(0, max(max(s(z), 0), 0))) 
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), max(0, 0)))) 
f#(max(0, s(x)), max(s(y), 0), max(max(0, 0), max(max(s(z), 0), 0))) 
f#(max(0, s(x)), max(s(y), 0), max(0, f(max(s(z), 0), 0, 0))) 
f#(max(0, s(x)), max(s(y), 0), max(p(s(0)), max(max(s(z), 0), 0))) 
f#(max(0, s(x)), max(s(y), p(s(0))), max(0, max(max(s(z), 0), 0))) 
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), p(s(0))))) 
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(0, max(max(s(z), 0), 0))) 
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(0, max(max(s(z), 0), 0))) 
f#(max(0, s(x)), max(s(y), 0), max(min(_x51, 0), max(max(s(z), 0), 0))) 
f#(f(0, s(x), 0), max(s(y), 0), max(0, max(max(s(z), 0), 0))) 
f#(max(max(0, 0), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) 
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), max(0, 0)), 0))) 
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(0, s(z)), 0), 0))) 
f#(max(0, s(x)), max(s(y), 0), max(0, max(0, max(max(s(z), 0), 0)))) 
f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) 
f#(max(0, s(x)), max(s(y), 0), max(0, p(s(max(max(s(z), 0), 0))))) 
f#(max(0, s(x)), max(max(s(y), 0), 0), max(0, max(max(s(z), 0), 0))) 
f#(p(s(max(0, s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) 
f#(f(0, 0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) 
f#(max(0, s(x)), p(s(max(s(y), 0))), max(0, max(max(s(z), 0), 0))) 
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), min(0, _x81)))) 
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(0, max(max(s(z), 0), 0))) 
f#(max(0, s(x)), max(s(y), 0), max(min(0, _x51), max(max(s(z), 0), 0))) 
f#(max(0, s(x)), max(s(y), 0), p(s(max(0, max(max(s(z), 0), 0))))) 
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) 
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) 
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(p(s(s(z))), 0), 0))) 
f#(max(max(0, s(x)), 0), max(s(y), 0), max(0, max(max(s(z), 0), 0))) 
f#(max(0, s(x)), max(s(y), 0), max(0, f(0, max(s(z), 0), 0))) 
f#(max(0, s(x)), f(0, s(y), 0), max(0, max(max(s(z), 0), 0))) 
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(s(z), 0), 0), 0))) 
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(s(_x82), s(_x81)), 0), 0))) 
f#(max(0, s(x)), max(s(y), 0), f(0, 0, max(max(s(z), 0), 0))) 
f#(max(0, s(x)), max(s(y), 0), max(max(0, max(max(s(z), 0), 0)), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), min(_x81, 0)))) 
f#(max(0, s(x)), max(s(y), 0), max(0, max(p(s(max(s(z), 0))), 0))) 
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(0, max(max(s(z), 0), 0))) 
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(min(s(_x82), s(_x81)), 0), 0))) 
f#(max(0, s(x)), max(s(y), 0), max(0, max(f(0, s(z), 0), 0))) 
f#(max(0, s(x)), max(p(s(s(y))), 0), max(0, max(max(s(z), 0), 0))) 
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) 
f#(max(0, s(x)), max(max(0, s(y)), 0), max(0, max(max(s(z), 0), 0))) 
f#(max(0, s(x)), f(s(y), 0, 0), max(0, max(max(s(z), 0), 0))) 
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), min(0, _x91)), 0))) 
f#(max(0, max(0, s(x))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) 
f#(max(0, s(x)), max(0, max(s(y), 0)), max(0, max(max(s(z), 0), 0))) 
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(0, max(s(z), 0)), 0))) 
Thus, the rule f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is replaced by the following rules:
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), min(_x81, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, 0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(0, s(z)), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), min(_x91, 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(f(s(z), 0, 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(0, max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(min(_x51, 0), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), min(0, _x81)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(0, max(max(s(z), 0), 0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(0, max(s(z), 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(min(s(_x82), s(_x81)), 0), 0))) → f#(max(s(x), max(s(y), s(min(_x82, _x81)))), p(min(s(x), max(s(y), s(min(_x82, _x81))))), min(s(x), min(s(y), s(min(_x82, _x81)))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), min(0, _x91)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, max(max(s(z), 0), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), max(0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, 0), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(0)), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), p(s(0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(p(s(s(z))), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(min(0, _x51), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(p(s(max(s(z), 0))), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), max(0, 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(s(z), 0), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(max(s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, p(s(max(max(s(z), 0), 0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(f(0, s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), p(s(0))), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(0, max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(s(_x82), s(_x81)), 0), 0))) → f#(max(s(x), max(s(y), s(max(_x82, _x81)))), p(min(s(x), max(s(y), s(max(_x82, _x81))))), min(s(x), min(s(y), s(max(_x82, _x81)))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Problem 15: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(max(s(x), 0), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(f(0, 0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(min(s(_x62), s(_x61)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x62, _x61)), s(z))), p(min(s(x), max(s(min(_x62, _x61)), s(z)))), min(s(x), min(s(min(_x62, _x61)), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(s(x), max(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(max(_x32, _x31)), s(z))), p(min(s(x), max(s(max(_x32, _x31)), s(z)))), min(s(x), min(s(max(_x32, _x31)), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, min(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), min(0, _x91)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(f(0, 0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), max(0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, 0), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(f(0, s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, f(s(x), 0, 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))f#(max(0, max(s(x), 0)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(p(s(s(y))), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(max(s(s(y)), 0)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(s(x))), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), min(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(min(_x32, _x31)), s(z))), p(min(s(x), max(s(min(_x32, _x31)), s(z)))), min(s(x), min(s(min(_x32, _x31)), s(z))))f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))f#(s(x), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, f(0, s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, p(s(max(max(s(z), 0), 0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(s(_x82), s(_x81)), 0), 0))) → f#(max(s(x), max(s(y), s(max(_x82, _x81)))), p(min(s(x), max(s(y), s(max(_x82, _x81))))), min(s(x), min(s(y), s(max(_x82, _x81)))))
f#(max(0, s(x)), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), min(0, _x61))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, min(_x41, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(f(0, 0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(p(s(s(y))))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))f#(f(0, s(x), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(p(s(s(y))), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(min(0, _x31), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(p(s(0)), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(s(x), max(0, s(y)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(max(s(y), 0))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, min(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), max(0, 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, p(s(s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, 0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(0, s(z)), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(min(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))
f#(max(0, s(x)), max(max(p(s(s(y))), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(f(s(z), 0, 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(max(0, max(s(x), p(s(0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(min(_x51, 0), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(f(0, 0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(p(s(s(x))), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(max(0, s(s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(min(0, _x51), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), p(s(0))), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, max(s(x), 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), min(_x81, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(max(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(p(s(s(y))), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(p(s(0)), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(p(s(0)), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(s(x), p(s(s(y))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, max(s(x), 0)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(0, max(s(z), 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(min(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(min(s(_x82), s(_x81)), 0), 0))) → f#(max(s(x), max(s(y), s(min(_x82, _x81)))), p(min(s(x), max(s(y), s(min(_x82, _x81))))), min(s(x), min(s(y), s(min(_x82, _x81)))))f#(max(0, f(0, 0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, max(max(0, s(x)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, max(s(x), 0), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), p(s(0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(0)), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(p(s(max(s(z), 0))), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, f(max(s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(p(s(s(s(y))))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(max(0, s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(f(0, s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, f(0, s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), min(_x91, 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(min(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))
f#(max(0, max(s(x), max(0, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(max(0, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(max(0, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(0, max(max(s(z), 0), 0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(f(0, 0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(min(0, _x61), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(p(s(s(z))), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(f(0, s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(max(s(_x62), s(_x61)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x62, _x61)), s(z))), p(min(s(x), max(s(max(_x62, _x61)), s(z)))), min(s(x), min(s(max(_x62, _x61)), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))f#(max(0, s(x)), max(s(y), 0), max(0, max(0, max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(f(0, s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(s(x), 0), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(s(x), min(_x61, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(0, max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), min(0, _x81)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, max(max(s(z), 0), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(f(min(_x31, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(min(_x61, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(s(z), 0), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, min(0, _x41), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Rewrite Rules

min(0, y) → 0min(x, 0) → 0
min(s(x), s(y)) → s(min(x, y))max(0, y) → y
max(x, 0) → xmax(s(x), s(y)) → s(max(x, y))
p(s(x)) → xf(s(x), s(y), s(z)) → f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f(0, y, z) → max(y, z)f(x, 0, z) → max(x, z)
f(x, y, 0) → max(x, y)

Original Signature

Termination of terms over the following signature is verified: min, f, 0, max, s, p

Strategy

The left-hand side of the rule f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(max(min(0, _x31), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(z), 0), 0), 0, 0)) 
f#(max(0, p(s(s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(p(s(0)), s(z), 0), 0, 0)) 
f#(max(0, min(s(_x42), s(_x41))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), p(s(max(s(y), max(0, 0)))), f(f(0, s(z), 0), 0, 0)) 
f#(max(max(0, s(x)), 0), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(max(f(0, s(z), 0), 0), 0, 0)) 
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(0, max(0, 0))), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(0, _x61), 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(_x71, 0))) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(0, _x71))) 
f#(max(0, s(x)), max(0, max(s(y), max(0, 0))), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(max(0, s(y)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(max(0, 0), s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), max(0, f(f(0, s(z), 0), 0, 0))) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(min(_x61, 0), s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), p(s(f(f(0, s(z), 0), 0, 0)))) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(0, _x81)), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(min(0, _x61), s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(_x61, 0), 0)) 
f#(max(0, s(x)), max(max(s(y), 0), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(max(0, f(0, s(z), 0)), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(min(_x61, 0), 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, p(s(0)))) 
f#(max(0, s(x)), max(max(s(y), max(0, 0)), 0), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(p(s(s(y))), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(0, s(z)), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), p(s(max(0, 0)))), f(f(0, s(z), 0), 0, 0)) 
f#(p(s(max(0, s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(_x81, 0)), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), p(s(0)), 0)) 
f#(max(0, s(x)), max(s(y), max(0, min(_x71, 0))), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), f(s(y), max(0, 0), 0), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, max(0, s(x))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, s(x), 0), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(max(0, 0), 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(max(0, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), max(0, 0)), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), p(s(0))), 0, 0)) 
f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(p(s(0)), 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(p(s(0)), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(min(0, _x61), 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, p(s(s(z))), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, max(0, 0))) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), max(0, p(s(0)))), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), f(s(y), 0, max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(min(_x31, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), max(f(f(0, s(z), 0), 0, 0), 0)) 
f#(max(0, max(s(_x42), s(_x41))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(0, min(0, _x71))), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(p(s(f(0, s(z), 0))), 0, 0)) 
f#(max(0, s(x)), f(0, s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) 
Thus, the rule f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is replaced by the following rules:
f#(max(0, s(x)), max(s(y), max(0, 0)), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, p(s(0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), max(0, 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(max(0, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(p(s(0)), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, min(_x71, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), max(0, 0)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(min(_x61, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), max(min(0, _x61), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, min(0, _x71))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(p(s(s(y))), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Problem 16: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(max(s(x), 0), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(min(s(_x62), s(_x61)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x62, _x61)), s(z))), p(min(s(x), max(s(min(_x62, _x61)), s(z)))), min(s(x), min(s(min(_x62, _x61)), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(s(x), max(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(max(_x32, _x31)), s(z))), p(min(s(x), max(s(max(_x32, _x31)), s(z)))), min(s(x), min(s(max(_x32, _x31)), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, min(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), min(0, _x91)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(f(0, 0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, 0), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), max(0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(f(0, s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, f(s(x), 0, 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))
f#(max(0, max(s(x), 0)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(p(s(s(y))), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(max(s(s(y)), 0)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(s(x), s(y), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(s(x))), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), min(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(min(_x32, _x31)), s(z))), p(min(s(x), max(s(min(_x32, _x31)), s(z)))), min(s(x), min(s(min(_x32, _x31)), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))
f#(max(0, f(0, s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, p(s(max(max(s(z), 0), 0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(s(_x82), s(_x81)), 0), 0))) → f#(max(s(x), max(s(y), s(max(_x82, _x81)))), p(min(s(x), max(s(y), s(max(_x82, _x81))))), min(s(x), min(s(y), s(max(_x82, _x81)))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), min(0, _x61))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, min(_x41, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(f(0, 0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(p(s(s(y))))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), max(0, 0)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))
f#(f(0, s(x), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(p(s(s(y))), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(min(0, _x31), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(f(0, s(x), 0), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(0, s(y)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(max(s(y), 0))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, min(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), max(0, 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, p(s(s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, 0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(0, s(z)), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, p(s(0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(min(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))
f#(max(0, s(x)), max(max(p(s(s(y))), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(f(s(z), 0, 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(max(0, max(s(x), p(s(0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(min(_x51, 0), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))f#(f(0, 0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(0, max(0, s(x))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(p(s(s(x))), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(min(0, _x61), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(max(0, s(s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(min(0, _x51), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), p(s(0))), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, max(s(x), 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), min(_x81, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(max(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), max(0, 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(p(s(s(y))), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(max(0, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(p(s(0)), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(p(s(0)), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(s(x), p(s(s(y))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, min(_x71, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, max(s(x), 0)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(0, max(s(z), 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(min(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(min(s(_x82), s(_x81)), 0), 0))) → f#(max(s(x), max(s(y), s(min(_x82, _x81)))), p(min(s(x), max(s(y), s(min(_x82, _x81))))), min(s(x), min(s(y), s(min(_x82, _x81)))))f#(max(0, f(0, 0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, max(max(0, s(x)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, max(s(x), 0), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), p(s(0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(0)), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(p(s(max(s(z), 0))), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, f(max(s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, min(0, _x71))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(p(s(s(s(y))))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(max(0, s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(f(0, s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, f(0, s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))f#(s(x), s(y), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), min(_x91, 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(min(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))f#(max(max(0, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), max(0, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(max(0, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(max(0, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(p(s(0)), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(0, max(max(s(z), 0), 0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(min(0, _x61), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(p(s(s(z))), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(f(0, s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(max(s(_x62), s(_x61)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x62, _x61)), s(z))), p(min(s(x), max(s(max(_x62, _x61)), s(z)))), min(s(x), min(s(max(_x62, _x61)), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(0, max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))
f#(max(0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(f(0, s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(s(x), 0), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), min(_x61, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(0, max(s(y), max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, f(0, max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), min(0, _x81)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(min(_x61, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, max(max(s(z), 0), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(f(min(_x31, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(min(_x61, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(s(z), 0), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, min(0, _x41), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Rewrite Rules

min(0, y) → 0min(x, 0) → 0
min(s(x), s(y)) → s(min(x, y))max(0, y) → y
max(x, 0) → xmax(s(x), s(y)) → s(max(x, y))
p(s(x)) → xf(s(x), s(y), s(z)) → f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f(0, y, z) → max(y, z)f(x, 0, z) → max(x, z)
f(x, y, 0) → max(x, y)

Original Signature

Termination of terms over the following signature is verified: f, min, max, 0, s, p

Strategy

The left-hand side of the rule f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), max(0, 0), 0)) 
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), max(0, 0), 0), 0)) 
f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, max(0, 0)), 0)) 
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), max(0, 0), 0))) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), min(_x71, 0))) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), min(0, _x71))) 
f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), max(0, 0), 0)) 
f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), p(s(0)))) 
f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(max(0, 0))), 0)) 
f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(0, 0), 0), 0)) 
f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(p(s(0)), 0), 0)) 
f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, min(0, _x81)), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(0, _x71), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, min(_x81, 0)), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), max(0, 0))) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, p(s(0))), 0)) 
f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), max(0, 0), 0)))) 
f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), max(0, 0), 0)) 
f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), max(0, 0), 0)) 
Thus, the rule f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is replaced by the following rules:
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(0, _x71), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(0, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(p(s(0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), max(0, 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(max(0, 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), max(0, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), max(0, 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Problem 17: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(max(s(x), 0), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(min(s(_x62), s(_x61)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x62, _x61)), s(z))), p(min(s(x), max(s(min(_x62, _x61)), s(z)))), min(s(x), min(s(min(_x62, _x61)), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(s(x), max(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(max(_x32, _x31)), s(z))), p(min(s(x), max(s(max(_x32, _x31)), s(z)))), min(s(x), min(s(max(_x32, _x31)), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, min(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), min(0, _x91)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(f(0, 0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), max(0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, 0), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(f(0, s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, f(s(x), 0, 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), max(0, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))f#(max(0, max(s(x), 0)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(p(s(s(y))), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(max(s(s(y)), 0)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(s(x), s(y), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(s(x))), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), min(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(min(_x32, _x31)), s(z))), p(min(s(x), max(s(min(_x32, _x31)), s(z)))), min(s(x), min(s(min(_x32, _x31)), s(z))))
f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))
f#(p(s(max(0, s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, f(0, s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, p(s(max(max(s(z), 0), 0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(s(_x82), s(_x81)), 0), 0))) → f#(max(s(x), max(s(y), s(max(_x82, _x81)))), p(min(s(x), max(s(y), s(max(_x82, _x81))))), min(s(x), min(s(y), s(max(_x82, _x81)))))f#(max(0, s(x)), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), min(0, _x61))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, min(_x41, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(f(0, 0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(p(s(s(y))))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), max(0, 0)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))
f#(f(0, s(x), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(p(s(s(y))), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(min(0, _x31), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), max(0, 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(max(0, 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(0, s(y)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(max(s(y), 0))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, min(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), max(0, 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, p(s(s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, 0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(0, s(z)), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, p(s(0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(0, _x71), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(min(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))f#(max(0, s(x)), max(max(p(s(s(y))), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(f(s(z), 0, 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))f#(max(0, max(s(x), p(s(0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(min(_x51, 0), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))f#(f(0, 0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(0, max(0, s(x))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(p(s(s(x))), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(min(0, _x61), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(max(0, s(s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(min(0, _x51), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), p(s(0))), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, max(s(x), 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), max(0, 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), min(_x81, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(max(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), max(0, 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(p(s(s(y))), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(0, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(max(0, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(p(s(0)), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(p(s(0)), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(s(x), p(s(s(y))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, min(_x71, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, max(s(x), 0)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(0, max(s(z), 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(min(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(min(s(_x82), s(_x81)), 0), 0))) → f#(max(s(x), max(s(y), s(min(_x82, _x81)))), p(min(s(x), max(s(y), s(min(_x82, _x81))))), min(s(x), min(s(y), s(min(_x82, _x81)))))f#(max(0, f(0, 0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, max(max(0, s(x)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, max(s(x), 0), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(0)), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), p(s(0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(0, s(x)), max(s(y), 0), max(0, max(p(s(max(s(z), 0))), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(max(s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(p(s(s(s(y))))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, min(0, _x71))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(max(0, s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(f(0, s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, f(0, s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), min(_x91, 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(min(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))
f#(max(0, max(s(x), max(0, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(max(0, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(max(0, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(p(s(0)), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(p(s(0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(0, max(max(s(z), 0), 0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(f(0, 0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(min(0, _x61), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(p(s(s(z))), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(f(0, s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(max(s(_x62), s(_x61)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x62, _x61)), s(z))), p(min(s(x), max(s(max(_x62, _x61)), s(z)))), min(s(x), min(s(max(_x62, _x61)), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(0, max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(f(0, s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(x), 0), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, max(s(x), min(_x61, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(0, s(y)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(0, max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), min(0, _x81)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(min(_x61, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, max(max(s(z), 0), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(f(min(_x31, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(min(_x61, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(s(z), 0), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, min(0, _x41), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Rewrite Rules

min(0, y) → 0min(x, 0) → 0
min(s(x), s(y)) → s(min(x, y))max(0, y) → y
max(x, 0) → xmax(s(x), s(y)) → s(max(x, y))
p(s(x)) → xf(s(x), s(y), s(z)) → f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f(0, y, z) → max(y, z)f(x, 0, z) → max(x, z)
f(x, y, 0) → max(x, y)

Original Signature

Termination of terms over the following signature is verified: min, f, 0, max, s, p

Strategy

The left-hand side of the rule f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), max(0, 0))) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, min(0, _x101)), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(min(_x71, 0), 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, max(min(_x71, 0), 0)), 0)) 
f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, min(_x101, 0)), 0), 0)) 
f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(p(s(min(_x71, 0))), 0), 0)) 
f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), p(s(0))), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, min(_x71, 0), 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), max(0, 0)), 0)) 
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), min(_x71, 0))) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), p(s(0)))) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), min(_x81, 0)), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), min(0, _x81)), 0)) 
f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)))) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(max(min(_x71, 0), 0))), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, max(0, 0)), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), min(0, _x71))) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(0, min(_x71, 0)), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), max(min(_x71, 0), 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), max(min(_x71, 0), 0), 0))) 
f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(min(_x71, 0), 0, 0), 0)) 
f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, p(s(0))), 0), 0)) 
Thus, the rule f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is replaced by the following rules:
f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, min(_x101, 0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, p(s(0))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(min(_x71, 0), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), max(min(_x71, 0), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(max(min(_x71, 0), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(0, min(_x71, 0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, max(0, 0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, max(min(_x71, 0), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, min(0, _x101)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), max(min(_x71, 0), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(p(s(min(_x71, 0))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(min(_x71, 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Problem 18: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(max(s(x), 0), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(f(0, 0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(max(min(_x71, 0), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(min(s(_x62), s(_x61)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x62, _x61)), s(z))), p(min(s(x), max(s(min(_x62, _x61)), s(z)))), min(s(x), min(s(min(_x62, _x61)), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(max(_x32, _x31)), s(z))), p(min(s(x), max(s(max(_x32, _x31)), s(z)))), min(s(x), min(s(max(_x32, _x31)), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, min(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), min(0, _x91)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(f(0, 0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), max(0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, 0), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(f(0, s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, f(s(x), 0, 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), max(0, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))f#(max(0, max(s(x), 0)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(p(s(s(y))), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(max(s(s(y)), 0)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(min(_x71, 0), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), max(min(_x71, 0), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(s(x))), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), min(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(min(_x32, _x31)), s(z))), p(min(s(x), max(s(min(_x32, _x31)), s(z)))), min(s(x), min(s(min(_x32, _x31)), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, f(0, s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, p(s(max(max(s(z), 0), 0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(s(_x82), s(_x81)), 0), 0))) → f#(max(s(x), max(s(y), s(max(_x82, _x81)))), p(min(s(x), max(s(y), s(max(_x82, _x81))))), min(s(x), min(s(y), s(max(_x82, _x81)))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), min(0, _x61))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, p(s(0))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, min(_x41, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(f(0, 0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(p(s(s(y))))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), max(0, 0)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))
f#(f(0, s(x), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(p(s(s(y))), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(min(0, _x31), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(min(_x71, 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, min(_x101, 0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), max(0, 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(max(0, 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, max(0, 0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(0, s(y)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(max(s(y), 0))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, min(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), max(0, 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, p(s(s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(p(s(min(_x71, 0))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, 0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(0, s(z)), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, p(s(0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(0, _x71), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(min(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))f#(max(0, s(x)), max(max(p(s(s(y))), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(f(s(z), 0, 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))f#(max(0, max(s(x), p(s(0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(min(_x51, 0), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(f(0, 0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(p(s(s(x))), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(min(0, _x61), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(max(0, s(s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(min(0, _x51), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, min(0, _x101)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), p(s(0))), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, max(s(x), 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), max(0, 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), min(_x81, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(max(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), max(0, 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(p(s(s(y))), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(p(s(0)), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(p(s(0)), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(max(0, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(0, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(s(x), p(s(s(y))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, min(_x71, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, max(s(x), 0)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(0, max(s(z), 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(min(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))f#(max(0, f(0, 0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(min(s(_x82), s(_x81)), 0), 0))) → f#(max(s(x), max(s(y), s(min(_x82, _x81)))), p(min(s(x), max(s(y), s(min(_x82, _x81))))), min(s(x), min(s(y), s(min(_x82, _x81)))))f#(f(0, 0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, max(max(0, s(x)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, max(s(x), 0), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), p(s(0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(0)), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(p(s(max(s(z), 0))), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, f(max(s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, min(0, _x71))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(p(s(s(s(y))))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(max(0, s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(f(0, s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, f(0, s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))
f#(s(x), s(y), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), min(_x91, 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(min(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))f#(max(max(0, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), max(0, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(max(0, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(max(0, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(p(s(0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(p(s(0)), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(0, max(max(s(z), 0), 0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(0, min(_x71, 0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(min(0, _x61), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(p(s(s(z))), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(f(0, s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(max(s(_x62), s(_x61)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x62, _x61)), s(z))), p(min(s(x), max(s(max(_x62, _x61)), s(z)))), min(s(x), min(s(max(_x62, _x61)), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(0, max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), max(min(_x71, 0), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(f(0, s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(x), 0), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), min(_x61, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(0, max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), min(0, _x81)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(min(_x61, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, max(max(s(z), 0), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))f#(f(min(_x31, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(min(_x61, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(s(z), 0), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, max(min(_x71, 0), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, min(0, _x41), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Rewrite Rules

min(0, y) → 0min(x, 0) → 0
min(s(x), s(y)) → s(min(x, y))max(0, y) → y
max(x, 0) → xmax(s(x), s(y)) → s(max(x, y))
p(s(x)) → xf(s(x), s(y), s(z)) → f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f(0, y, z) → max(y, z)f(x, 0, z) → max(x, z)
f(x, y, 0) → max(x, y)

Original Signature

Termination of terms over the following signature is verified: f, min, max, 0, s, p

Strategy

The left-hand side of the rule f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(max(0, p(s(s(x)))), max(max(s(y), 0), 0), max(f(0, s(z), 0), 0)) 
f#(max(max(0, p(s(s(x)))), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), max(min(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), min(_x61, 0))) 
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(min(0, _x61), s(z), 0), 0)) 
f#(f(0, p(s(s(x))), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), max(0, 0))) 
f#(max(0, max(0, p(s(s(x))))), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), max(0, 0)), max(f(0, s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), f(s(y), 0, 0), max(f(0, s(z), 0), 0)) 
f#(max(0, p(p(s(s(s(x)))))), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, p(max(s(s(x)), 0))), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), min(_x51, 0)), max(f(0, s(z), 0), 0)) 
f#(max(0, p(s(p(s(s(x)))))), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), max(0, max(s(y), 0)), max(f(0, s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, max(0, s(z)), 0), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(min(_x61, 0), s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), p(s(max(f(0, s(z), 0), 0)))) 
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, max(s(z), 0), 0), 0)) 
f#(max(0, p(s(s(x)))), f(0, s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), p(s(max(s(y), 0))), max(f(0, s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, min(s(_x72), s(_x71)), 0), 0)) 
f#(max(p(s(0)), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), max(p(s(s(y))), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), max(p(s(f(0, s(z), 0))), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), max(0, max(f(0, s(z), 0), 0))) 
f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(0, f(0, s(z), 0)), 0)) 
f#(max(0, p(s(max(0, s(x))))), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(max(0, 0), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), max(max(0, s(y)), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), p(s(0))), 0)) 
f#(max(0, max(p(s(s(x))), 0)), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(p(s(max(0, p(s(s(x)))))), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), min(_x81, 0)), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, max(s(_x72), s(_x71)), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), f(0, f(0, s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, p(s(s(z))), 0), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), p(s(0)))) 
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), min(0, _x61))) 
f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, p(s(min(s(_x62), s(_x61))))), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(p(s(0)), s(z), 0), 0)) 
f#(max(0, p(s(max(s(_x62), s(_x61))))), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(f(0, s(z), 0), 0), 0)) 
f#(max(0, p(max(0, s(s(x))))), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(min(0, _x31), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), max(0, 0)), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(max(0, 0), s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), max(max(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) 
f#(max(min(_x31, 0), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), min(0, _x81)), 0)) 
f#(max(0, p(s(max(s(x), 0)))), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), min(0, _x51)), max(f(0, s(z), 0), 0)) 
f#(max(0, p(s(s(x)))), max(s(y), p(s(0))), max(f(0, s(z), 0), 0)) 
Thus, the rule f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is replaced by the following rules:
f#(max(0, p(s(s(x)))), f(s(y), 0, 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(min(s(_x62), s(_x61))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(min(_x62, _x61)), max(s(y), s(z))), p(min(s(min(_x62, _x61)), max(s(y), s(z)))), min(s(min(_x62, _x61)), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(0, max(f(0, s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(p(s(s(y))), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(p(s(s(x))), 0)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(max(s(_x62), s(_x61))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(max(_x62, _x61)), max(s(y), s(z))), p(min(s(max(_x62, _x61)), max(s(y), s(z)))), min(s(max(_x62, _x61)), min(s(y), s(z))))
f#(max(max(0, 0), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(min(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, min(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, p(s(s(x)))), max(s(y), min(0, _x51)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), f(0, f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(max(0, s(s(x))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(max(0, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), f(0, s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), min(_x51, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(max(0, s(y)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(p(s(0)), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, max(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), p(s(max(s(y), 0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, p(s(s(x))), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(0, f(0, s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(p(s(s(x)))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), max(0, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(max(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, p(s(s(x)))), max(max(s(y), 0), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(min(_x61, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(f(0, s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(max(s(s(x)), 0))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(p(s(f(0, s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(max(0, s(x))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, p(s(s(x)))), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(p(s(s(s(x)))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(max(s(x), 0)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(min(0, _x61), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, p(s(s(x)))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(0, max(s(y), 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), p(s(0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, p(s(s(x))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), p(s(max(f(0, s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Problem 19: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(max(s(x), 0), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), min(0, _x51)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(max(min(_x71, 0), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(min(s(_x62), s(_x61)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x62, _x61)), s(z))), p(min(s(x), max(s(min(_x62, _x61)), s(z)))), min(s(x), min(s(min(_x62, _x61)), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(s(x), max(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(max(_x32, _x31)), s(z))), p(min(s(x), max(s(max(_x32, _x31)), s(z)))), min(s(x), min(s(max(_x32, _x31)), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, min(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), min(0, _x91)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(f(0, 0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), max(0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, 0), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(max(s(s(x)), 0))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, p(s(s(x)))), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(f(0, s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, f(s(x), 0, 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), max(0, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))
f#(max(0, max(s(x), 0)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(p(s(s(y))), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, p(s(s(x))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(min(s(_x62), s(_x61))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(min(_x62, _x61)), max(s(y), s(z))), p(min(s(min(_x62, _x61)), max(s(y), s(z)))), min(s(min(_x62, _x61)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(max(s(s(y)), 0)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(min(_x71, 0), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), max(min(_x71, 0), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), min(_x51, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(s(x))), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, max(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, s(x)), max(p(s(s(y))), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), max(0, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), min(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(min(_x32, _x31)), s(z))), p(min(s(x), max(s(min(_x32, _x31)), s(z)))), min(s(x), min(s(min(_x32, _x31)), s(z))))f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, f(0, s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, p(s(max(max(s(z), 0), 0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(s(_x82), s(_x81)), 0), 0))) → f#(max(s(x), max(s(y), s(max(_x82, _x81)))), p(min(s(x), max(s(y), s(max(_x82, _x81))))), min(s(x), min(s(y), s(max(_x82, _x81)))))f#(max(0, s(x)), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(0, max(f(0, s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), min(0, _x61))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, p(s(0))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(p(s(s(x))), 0)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, min(_x41, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(min(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(f(0, 0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(p(s(s(y))))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), max(0, 0)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))f#(f(0, s(x), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(max(0, s(y)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(p(s(s(y))), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(max(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(p(s(f(0, s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(min(0, _x31), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, p(s(s(x)))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(min(_x71, 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, min(_x101, 0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(max(0, s(s(x))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(max(0, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), f(0, s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), max(0, 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(max(0, 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, max(0, 0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(0, s(y)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(max(s(y), 0))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, min(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), max(0, 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, p(s(s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), p(s(0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(p(s(min(_x71, 0))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, 0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(0, s(z)), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, p(s(0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(0, _x71), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(min(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))f#(max(0, s(x)), max(max(p(s(s(y))), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(f(s(z), 0, 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, min(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(s(x), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(max(0, max(s(x), p(s(0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(min(_x51, 0), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(0, f(0, s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(f(0, 0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(p(s(s(x))), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(min(0, _x61), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(max(0, s(s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(min(0, _x51), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(p(s(s(s(x)))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, min(0, _x101)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, max(s(x), 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), p(s(0))), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), max(0, 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(max(0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), min(_x81, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), f(s(y), 0, 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(max(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), max(0, 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(p(s(s(y))), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(0, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(max(0, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(p(s(0)), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(p(s(0)), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(s(x), p(s(s(y))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, min(_x71, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, max(s(x), 0)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(p(s(0)), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(0, max(s(z), 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(min(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))
f#(f(0, p(s(s(x))), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(min(s(_x82), s(_x81)), 0), 0))) → f#(max(s(x), max(s(y), s(min(_x82, _x81)))), p(min(s(x), max(s(y), s(min(_x82, _x81))))), min(s(x), min(s(y), s(min(_x82, _x81)))))
f#(max(0, f(0, 0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(f(0, 0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, p(s(p(s(s(x)))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(max(0, s(x)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, max(s(x), 0), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(max(s(y), 0), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(0)), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), p(s(0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(min(_x61, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(p(s(max(s(z), 0))), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(max(0, s(x))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(max(s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(p(s(s(s(y))))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, min(0, _x71))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(max(0, s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(f(0, s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(0, max(s(y), 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, f(0, s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), min(_x91, 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(max(s(_x62), s(_x61))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(max(_x62, _x61)), max(s(y), s(z))), p(min(s(max(_x62, _x61)), max(s(y), s(z)))), min(s(max(_x62, _x61)), min(s(y), s(z))))
f#(min(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))f#(max(max(0, 0), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), max(0, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(max(0, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(max(0, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(p(s(0)), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(p(s(0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(0, max(max(s(z), 0), 0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(0, min(_x71, 0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(min(0, _x61), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(p(s(s(z))), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(f(0, s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(max(s(x), 0)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(f(0, s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(max(s(_x62), s(_x61)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x62, _x61)), s(z))), p(min(s(x), max(s(max(_x62, _x61)), s(z)))), min(s(x), min(s(max(_x62, _x61)), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), max(min(_x71, 0), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(0, max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(f(0, s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(x), 0), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(p(s(s(y))), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(s(x), min(_x61, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), f(0, f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, f(0, max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), min(0, _x81)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(min(_x61, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), p(s(max(s(y), 0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, max(max(s(z), 0), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(f(min(_x31, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(min(_x61, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(s(z), 0), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, max(min(_x71, 0), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, min(0, _x41), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(min(0, _x61), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), p(s(max(f(0, s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Rewrite Rules

min(0, y) → 0min(x, 0) → 0
min(s(x), s(y)) → s(min(x, y))max(0, y) → y
max(x, 0) → xmax(s(x), s(y)) → s(max(x, y))
p(s(x)) → xf(s(x), s(y), s(z)) → f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f(0, y, z) → max(y, z)f(x, 0, z) → max(x, z)
f(x, y, 0) → max(x, y)

Original Signature

Termination of terms over the following signature is verified: min, f, 0, max, s, p

Strategy

The left-hand side of the rule f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(f(0, 0, p(s(s(x)))), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) 
f#(f(0, min(0, _x41), p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), max(0, 0))) 
f#(f(0, 0, max(0, p(s(s(x))))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) 
f#(f(min(0, _x31), 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) 
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) 
f#(f(0, 0, p(p(s(s(s(x)))))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), f(s(y), 0, 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(max(s(s(x)), 0))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) 
f#(f(0, 0, p(s(p(s(s(x)))))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(s(max(s(_x72), s(_x71))))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(max(f(0, 0, p(s(s(x)))), 0), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) 
f#(f(0, 0, p(s(s(x)))), f(0, s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) 
f#(f(0, p(s(0)), p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) 
f#(f(0, min(_x41, 0), p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, max(0, 0), p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(s(max(0, s(x))))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), p(s(0))), 0)) 
f#(f(0, 0, p(s(s(x)))), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, max(p(s(s(x))), 0)), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) 
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) 
f#(f(min(_x31, 0), 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), f(0, max(s(z), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) 
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(f(s(z), 0, 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), p(s(0)))) 
f#(f(0, 0, p(s(min(s(_x72), s(_x71))))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) 
f#(p(s(f(0, 0, p(s(s(x)))))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(p(s(0)), 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(max(0, s(s(x))))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), f(max(s(z), 0), 0, 0)) 
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) 
f#(f(max(0, 0), 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(s(max(s(x), 0)))), max(s(y), 0), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) 
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) 
f#(f(0, 0, p(s(s(x)))), max(s(y), p(s(0))), max(max(s(z), 0), 0)) 
f#(max(0, f(0, 0, p(s(s(x))))), max(s(y), 0), max(max(s(z), 0), 0)) 
Thus, the rule f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is replaced by the following rules:
f#(f(0, 0, p(s(s(x)))), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(p(s(s(x))), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, p(s(0)), p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, max(0, 0), p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, f(0, 0, p(s(s(x))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, min(_x41, 0), p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(max(s(_x72), s(_x71))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x72, _x71)), max(s(y), s(z))), p(min(s(max(_x72, _x71)), max(s(y), s(z)))), min(s(max(_x72, _x71)), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(max(0, s(s(x))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(max(0, 0), 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, min(0, _x41), p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(min(0, _x31), 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(f(0, 0, p(s(s(x)))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(p(s(0)), 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(p(s(s(x)))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(f(0, 0, p(s(s(x)))), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(f(0, 0, p(s(s(x)))), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(max(s(s(x)), 0))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(max(0, s(x))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(p(s(s(s(x)))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(min(_x31, 0), 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(max(s(x), 0)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(min(s(_x72), s(_x71))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x72, _x71)), max(s(y), s(z))), p(min(s(min(_x72, _x71)), max(s(y), s(z)))), min(s(min(_x72, _x71)), min(s(y), s(z))))f#(f(0, 0, max(0, p(s(s(x))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Problem 20: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(max(s(x), 0), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), min(0, _x51)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(max(min(_x71, 0), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(min(s(_x62), s(_x61)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x62, _x61)), s(z))), p(min(s(x), max(s(min(_x62, _x61)), s(z)))), min(s(x), min(s(min(_x62, _x61)), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(max(_x32, _x31)), s(z))), p(min(s(x), max(s(max(_x32, _x31)), s(z)))), min(s(x), min(s(max(_x32, _x31)), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, min(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), min(0, _x91)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(f(0, 0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), max(0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, 0), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(max(s(s(x)), 0))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(max(s(s(x)), 0))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, p(s(s(x)))), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(f(0, s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(f(min(_x31, 0), 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, f(s(x), 0, 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), max(0, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))
f#(max(0, max(s(x), 0)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(p(s(s(y))), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(0, p(s(s(x))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, p(s(s(x))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(min(s(_x62), s(_x61))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(min(_x62, _x61)), max(s(y), s(z))), p(min(s(min(_x62, _x61)), max(s(y), s(z)))), min(s(min(_x62, _x61)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(max(s(s(y)), 0)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, min(_x41, 0), p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(min(_x71, 0), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(max(s(_x72), s(_x71))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x72, _x71)), max(s(y), s(z))), p(min(s(max(_x72, _x71)), max(s(y), s(z)))), min(s(max(_x72, _x71)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), max(min(_x71, 0), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(f(0, 0, p(s(s(x)))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), min(_x51, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(s(x))), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, max(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), max(0, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), min(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(min(_x32, _x31)), s(z))), p(min(s(x), max(s(min(_x32, _x31)), s(z)))), min(s(x), min(s(min(_x32, _x31)), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, f(0, s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, p(s(max(max(s(z), 0), 0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(s(_x82), s(_x81)), 0), 0))) → f#(max(s(x), max(s(y), s(max(_x82, _x81)))), p(min(s(x), max(s(y), s(max(_x82, _x81))))), min(s(x), min(s(y), s(max(_x82, _x81)))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(0, max(f(0, s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), min(0, _x61))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(p(s(s(x))), 0)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, p(s(0))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(p(s(s(x))), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, min(_x41, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(min(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(f(0, 0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(p(s(s(y))))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), max(0, 0)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))f#(f(0, s(x), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(max(0, s(y)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(p(s(s(y))), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, p(s(s(x)))), max(max(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(f(0, 0, p(s(s(x)))), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(p(s(f(0, s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(min(0, _x31), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(f(0, s(x), 0), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, p(s(s(x)))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(min(_x71, 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, min(_x101, 0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(max(0, s(s(x))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(max(0, s(s(x))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(max(0, 0), 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(max(0, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), f(0, s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), max(0, 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(max(0, 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, max(0, 0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(0, s(y)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(max(s(y), 0))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, min(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), max(0, 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, p(s(s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), p(s(0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(p(s(min(_x71, 0))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, 0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(0, s(z)), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, p(s(0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(0, _x71), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(min(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))
f#(max(0, s(x)), max(max(p(s(s(y))), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(f(s(z), 0, 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, f(0, 0, p(s(s(x))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, min(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, s(x)), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(max(p(s(0)), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), p(s(0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, min(0, _x41), p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(min(_x51, 0), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(0, f(0, s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(f(0, 0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(p(s(s(x))), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(min(0, _x61), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(max(0, s(s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(min(0, _x51), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(p(s(s(s(x)))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(p(s(s(s(x)))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, min(0, _x101)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), p(s(0))), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, max(s(x), 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), max(0, 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), min(_x81, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), f(s(y), 0, 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(max(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), max(0, 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(p(s(s(y))), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(p(s(0)), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(p(s(0)), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(max(0, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(0, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(s(x), p(s(s(y))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, min(_x71, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, max(s(x), 0)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(p(s(0)), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(p(s(0)), 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(0, max(s(z), 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, p(s(s(x))), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(min(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))f#(max(0, f(0, 0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(min(s(_x82), s(_x81)), 0), 0))) → f#(max(s(x), max(s(y), s(min(_x82, _x81)))), p(min(s(x), max(s(y), s(min(_x82, _x81))))), min(s(x), min(s(y), s(min(_x82, _x81)))))f#(max(0, p(s(p(s(s(x)))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(f(0, 0, p(s(p(s(s(x)))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(max(0, s(x)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, max(s(x), 0), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(max(s(y), 0), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), p(s(0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(0)), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(min(_x61, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(p(s(max(s(z), 0))), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(max(0, p(s(max(0, s(x))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(max(0, s(x))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(max(s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, min(0, _x71))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(p(s(s(s(y))))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(max(0, s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(f(0, s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(0, max(s(y), 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, f(0, s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))
f#(s(x), s(y), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), min(_x91, 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, p(s(0)), p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(max(s(_x62), s(_x61))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(max(_x62, _x61)), max(s(y), s(z))), p(min(s(max(_x62, _x61)), max(s(y), s(z)))), min(s(max(_x62, _x61)), min(s(y), s(z))))f#(max(max(0, 0), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(min(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))f#(f(0, max(0, 0), p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), max(0, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(max(0, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(max(0, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(p(s(0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(p(s(0)), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(0, max(max(s(z), 0), 0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(0, min(_x71, 0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(min(0, _x61), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(p(s(s(z))), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(f(0, s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(max(0, p(s(max(s(x), 0)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(max(s(x), 0)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(f(0, s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(max(s(_x62), s(_x61)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x62, _x61)), s(z))), p(min(s(x), max(s(max(_x62, _x61)), s(z)))), min(s(x), min(s(max(_x62, _x61)), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(0, max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))
f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), max(min(_x71, 0), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(min(s(_x72), s(_x71))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x72, _x71)), max(s(y), s(z))), p(min(s(min(_x72, _x71)), max(s(y), s(z)))), min(s(min(_x72, _x71)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(f(0, s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(x), 0), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(p(s(s(y))), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), min(_x61, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), f(0, f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))f#(max(0, s(x)), f(0, s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, f(0, max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(min(0, _x31), 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), min(0, _x81)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(min(_x61, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), p(s(max(s(y), 0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, max(max(s(z), 0), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))f#(f(min(_x31, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(min(_x61, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(s(z), 0), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, max(min(_x71, 0), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(min(0, _x61), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, min(0, _x41), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), p(s(max(f(0, s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Rewrite Rules

min(0, y) → 0min(x, 0) → 0
min(s(x), s(y)) → s(min(x, y))max(0, y) → y
max(x, 0) → xmax(s(x), s(y)) → s(max(x, y))
p(s(x)) → xf(s(x), s(y), s(z)) → f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f(0, y, z) → max(y, z)f(x, 0, z) → max(x, z)
f(x, y, 0) → max(x, y)

Original Signature

Termination of terms over the following signature is verified: f, min, max, 0, s, p

Strategy

The left-hand side of the rule f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(f(0, 0, p(s(s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(z), 0), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, max(0, 0))) 
f#(f(0, 0, max(s(x), 0)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(p(s(f(0, s(z), 0))), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(min(_x61, 0), s(z), 0), 0, 0)) 
f#(max(0, f(0, 0, s(x))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(max(f(0, s(z), 0), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), max(0, f(f(0, s(z), 0), 0, 0))) 
f#(f(max(0, 0), 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(min(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(max(0, f(0, s(z), 0)), 0, 0)) 
f#(f(0, min(_x41, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, p(s(0)))) 
f#(p(s(f(0, 0, s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, max(s(_x52), s(_x51))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, min(0, _x71))), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, max(0, 0))), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, p(s(0)))), f(f(0, s(z), 0), 0, 0)) 
f#(f(min(_x31, 0), 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(f(0, 0, s(x)), 0), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(max(s(y), 0), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), p(s(0))), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(p(s(0)), 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, p(s(0)), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(_x61, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, min(_x71, 0))), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), p(s(0)), 0)) 
f#(f(0, 0, s(x)), f(s(y), 0, max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, p(s(s(z))), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(max(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(_x81, 0)), 0, 0)) 
f#(f(0, 0, s(x)), max(0, max(s(y), max(0, 0))), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(max(0, s(y)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(min(0, _x31), 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, max(0, s(z)), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(max(0, 0), s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(min(0, _x61), s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(max(s(y), max(0, 0)), 0), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(_x71, 0))) 
f#(f(0, 0, s(x)), max(s(y), max(min(_x61, 0), 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), p(s(max(s(y), max(0, 0)))), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, max(0, s(x))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(0, _x61), 0)) 
f#(f(0, min(0, _x41), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(0, _x71))) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(p(s(0)), s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), f(0, s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(min(0, _x61), 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), p(s(max(0, 0)))), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, min(s(_x52), s(_x51))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), max(f(f(0, s(z), 0), 0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), max(0, 0)), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(max(0, 0), 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, max(0, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(p(s(s(y))), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(0, _x81)), 0, 0)) 
f#(f(0, 0, s(x)), f(s(y), max(0, 0), 0), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), p(s(f(f(0, s(z), 0), 0, 0)))) 
f#(f(p(s(0)), 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) 
Thus, the rule f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is replaced by the following rules:
f#(f(0, 0, s(x)), max(s(y), max(min(0, _x61), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(max(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, min(0, _x41), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(f(0, 0, s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(min(_x61, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, min(0, _x71))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), f(s(y), max(0, 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(0, s(x))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(min(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), f(0, s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), p(s(max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(f(0, 0, s(x)), 0), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(p(s(0)), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, p(s(0)), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, min(_x71, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, min(s(_x52), s(_x51))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))
f#(f(0, 0, max(s(x), 0)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(max(s(y), 0), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(f(0, 0, s(x)), max(0, max(s(y), max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(max(0, s(y)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(s(_x52), s(_x51))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(max(0, 0), 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(max(s(y), max(0, 0)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(p(s(0)), 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, f(0, 0, s(x))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, min(_x41, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(p(s(s(y))), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), f(s(y), 0, max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(max(0, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, max(0, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(min(_x31, 0), 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(min(0, _x31), 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(f(0, 0, s(x)), max(s(y), max(0, p(s(0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), p(s(max(s(y), max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Problem 21: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(max(s(x), 0), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), min(0, _x51)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(max(0, s(y)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(0, max(s(y), max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(max(s(s(x)), 0))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(max(s(s(x)), 0))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, f(s(x), 0, 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), max(0, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(f(0, 0, p(s(max(s(_x72), s(_x71))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x72, _x71)), max(s(y), s(z))), p(min(s(max(_x72, _x71)), max(s(y), s(z)))), min(s(max(_x72, _x71)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), max(min(_x71, 0), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, p(s(0)), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(p(s(0)), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, min(_x71, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(f(0, 0, p(s(s(x)))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(s(x))), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(max(0, 0), 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(p(s(0)), 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(s(_x82), s(_x81)), 0), 0))) → f#(max(s(x), max(s(y), s(max(_x82, _x81)))), p(min(s(x), max(s(y), s(max(_x82, _x81))))), min(s(x), min(s(y), s(max(_x82, _x81)))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(p(s(s(x))), 0)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(p(s(s(x))), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(f(0, 0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(p(s(s(y))))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), max(0, 0)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(p(s(s(y))), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(f(0, 0, p(s(s(x)))), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, f(0, 0, s(x))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(min(_x71, 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, min(_x101, 0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(f(0, 0, s(x)), f(s(y), max(0, 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(min(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), f(0, s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), max(0, 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(s(x), 0)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(max(s(y), 0), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(max(0, 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, max(0, 0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, min(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(p(s(min(_x71, 0))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(min(0, _x61), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(0, s(z)), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(0, _x71), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(min(_x61, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, f(0, 0, p(s(s(x))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, min(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(min(_x51, 0), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(0, f(0, s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(max(0, s(x)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(min(0, _x61), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(max(0, s(s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(min(0, _x51), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, p(p(s(s(s(x)))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(p(s(s(s(x)))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, min(0, _x101)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), p(s(0))), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, max(s(x), 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), max(0, 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), p(s(max(s(y), max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, min(_x71, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, max(s(x), 0)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(0, max(s(z), 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(min(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(min(s(_x82), s(_x81)), 0), 0))) → f#(max(s(x), max(s(y), s(min(_x82, _x81)))), p(min(s(x), max(s(y), s(min(_x82, _x81))))), min(s(x), min(s(y), s(min(_x82, _x81)))))
f#(f(0, 0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(f(0, max(s(x), 0), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(max(s(y), 0), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), p(s(0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(0)), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(min(_x61, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(max(0, p(s(max(0, s(x))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(max(0, s(x))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, min(0, _x71))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(max(0, s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(max(0, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, max(0, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(0, max(s(y), 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(f(0, s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, min(0, _x41), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(max(s(_x62), s(_x61))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(max(_x62, _x61)), max(s(y), s(z))), p(min(s(max(_x62, _x61)), max(s(y), s(z)))), min(s(max(_x62, _x61)), min(s(y), s(z))))f#(max(max(0, 0), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, max(0, 0), p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(p(s(0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(p(s(0)), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(0, max(max(s(z), 0), 0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(0, min(_x71, 0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(p(s(s(z))), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(f(0, s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(f(0, 0, s(x)), max(max(s(y), max(0, 0)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(max(s(x), 0)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(max(s(x), 0)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(max(s(_x62), s(_x61)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x62, _x61)), s(z))), p(min(s(x), max(s(max(_x62, _x61)), s(z)))), min(s(x), min(s(max(_x62, _x61)), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(0, max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(min(s(_x72), s(_x71))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x72, _x71)), max(s(y), s(z))), p(min(s(min(_x72, _x71)), max(s(y), s(z)))), min(s(min(_x72, _x71)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(f(0, s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), min(_x61, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), f(0, f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(f(0, 0, s(x)), 0), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), min(0, _x81)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(min(_x61, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), p(s(max(s(y), 0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(f(min(_x31, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(min(0, _x61), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(min(0, _x31), 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), p(s(max(f(0, s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(f(0, 0, s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, min(0, _x71))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(s(x), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(max(min(_x71, 0), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(min(s(_x62), s(_x61)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x62, _x61)), s(z))), p(min(s(x), max(s(min(_x62, _x61)), s(z)))), min(s(x), min(s(min(_x62, _x61)), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(max(_x32, _x31)), s(z))), p(min(s(x), max(s(max(_x32, _x31)), s(z)))), min(s(x), min(s(max(_x32, _x31)), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, min(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), min(0, _x91)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(f(0, 0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, 0), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), max(0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(f(0, s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, p(s(s(x)))), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(f(min(_x31, 0), 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))
f#(max(0, max(s(x), 0)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(p(s(s(y))), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, p(s(0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, p(s(s(x))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(0, p(s(s(x))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(min(s(_x62), s(_x61))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(min(_x62, _x61)), max(s(y), s(z))), p(min(s(min(_x62, _x61)), max(s(y), s(z)))), min(s(min(_x62, _x61)), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, min(_x41, 0), p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(max(s(s(y)), 0)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(min(_x71, 0), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), min(_x51, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, max(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, s(x)), max(p(s(s(y))), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), max(0, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), min(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(min(_x32, _x31)), s(z))), p(min(s(x), max(s(min(_x32, _x31)), s(z)))), min(s(x), min(s(min(_x32, _x31)), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, f(0, s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, p(s(max(max(s(z), 0), 0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(0, max(f(0, s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), min(0, _x61))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, p(s(0))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, min(_x41, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(min(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), p(s(max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))f#(f(0, s(x), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, p(s(s(x)))), max(max(0, s(y)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(max(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(f(0, 0, p(s(s(x)))), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(p(s(f(0, s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(min(0, _x31), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(p(s(0)), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, p(s(s(x)))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(max(0, s(s(x))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(max(0, s(s(x))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(max(0, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(max(0, 0), 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(s(_x52), s(_x51))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(max(s(y), 0))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(0, s(y)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(f(0, 0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), max(0, 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), f(s(y), 0, max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, p(s(s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), p(s(0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, 0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, p(s(0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(max(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(p(s(s(y))), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(min(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(f(s(z), 0, 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), p(s(0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, min(0, _x41), p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))f#(f(0, 0, min(s(_x52), s(_x51))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(p(s(s(x))), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(min(0, _x31), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), min(_x81, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), f(s(y), 0, 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(max(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), max(0, 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(p(s(s(y))), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(0, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(max(0, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(p(s(0)), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(p(s(0)), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(0, s(x))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(s(x), p(s(s(y))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(p(s(0)), 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(p(s(0)), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, p(s(s(x))), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, f(0, 0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(p(s(s(x)))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(p(s(s(x)))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(max(0, s(x)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(p(s(max(s(z), 0))), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(max(s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(p(s(s(y))), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(p(s(s(s(y))))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(f(0, s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, f(0, s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), min(_x91, 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(f(0, p(s(0)), p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(min(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))f#(max(0, max(s(x), max(0, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(max(0, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(max(0, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(min(0, _x61), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, min(_x41, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))f#(max(0, s(x)), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(f(0, s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(min(_x31, 0), 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), max(min(_x71, 0), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))f#(max(0, s(x)), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(x), 0), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(p(s(s(y))), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), f(0, s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, f(0, max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(min(0, _x31), 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, max(max(s(z), 0), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(min(_x61, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(s(z), 0), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, max(min(_x71, 0), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, min(0, _x41), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Rewrite Rules

min(0, y) → 0min(x, 0) → 0
min(s(x), s(y)) → s(min(x, y))max(0, y) → y
max(x, 0) → xmax(s(x), s(y)) → s(max(x, y))
p(s(x)) → xf(s(x), s(y), s(z)) → f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f(0, y, z) → max(y, z)f(x, 0, z) → max(x, z)
f(x, y, 0) → max(x, y)

Original Signature

Termination of terms over the following signature is verified: min, f, 0, max, s, p

Strategy

The left-hand side of the rule f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(max(0, p(s(s(x)))), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, max(s(z), 0), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, min(0, _x81))), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, max(0, 0))) 
f#(max(0, max(s(x), 0)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(min(_x61, 0), s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(p(s(f(0, s(z), 0))), 0, 0)) 
f#(max(max(0, s(x)), 0), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(min(0, _x31), s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(max(f(0, s(z), 0), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), max(0, f(f(0, s(z), 0), 0, 0))) 
f#(max(0, s(x)), max(s(y), f(max(0, 0), 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, min(_x81, 0))), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(min(_x31, 0), s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(max(0, f(0, s(z), 0)), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, p(s(0)))) 
f#(max(0, s(x)), max(max(s(y), f(0, 0, 0)), 0), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(0, f(0, 0, 0))), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, max(0, 0))), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(0, max(s(y), f(0, 0, 0))), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, p(s(0)))), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, max(s(_x42), s(_x41))), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(min(_x61, 0), 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), max(f(0, 0, 0), 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(max(s(y), 0), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(p(s(0)), s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(0, s(x)), max(s(y), f(0, p(s(0)), 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), p(s(0))), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, min(_x71, 0), 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), min(_x61, 0), 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), p(s(0)), 0)) 
f#(max(0, s(x)), f(s(y), 0, f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, p(s(s(z))), 0), 0, 0)) 
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(p(s(max(0, s(x)))), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), p(s(max(s(y), f(0, 0, 0)))), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), min(_x81, 0)), 0, 0)) 
f#(max(0, s(x)), max(max(0, s(y)), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, max(0, s(z)), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(max(0, 0), s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(min(0, _x61), s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, min(_x71, 0))) 
f#(max(0, max(0, s(x))), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), min(0, _x61), 0)) 
f#(max(0, s(x)), f(s(y), f(0, 0, 0), 0), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, min(0, _x71))) 
f#(f(0, s(x), 0), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(p(s(0)), s(z), 0), 0, 0)) 
f#(max(0, s(x)), f(0, s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(f(0, 0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), max(f(f(0, s(z), 0), 0, 0), 0)) 
f#(max(0, min(s(_x42), s(_x41))), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), max(0, 0)), 0, 0)) 
f#(max(max(0, 0), s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, max(0, 0), 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(p(s(s(y))), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), min(0, _x81)), 0, 0)) 
f#(max(0, s(x)), max(s(y), p(s(f(0, 0, 0)))), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), p(s(f(f(0, s(z), 0), 0, 0)))) 
f#(max(0, s(x)), max(s(y), f(p(s(0)), 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(min(0, _x61), 0, 0)), f(f(0, s(z), 0), 0, 0)) 
f#(max(0, s(x)), max(s(y), f(0, min(0, _x71), 0)), f(f(0, s(z), 0), 0, 0)) 
Thus, the rule f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is replaced by the following rules:
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), f(0, 0, 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, min(_x81, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), f(0, 0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(f(0, 0, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, min(0, _x81))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, p(s(0)), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, s(x)), max(s(y), f(0, 0, max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(f(0, 0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), f(0, 0, 0)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, min(_x71, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(min(_x61, 0), 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, f(0, 0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(max(0, 0), 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(p(s(0)), 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), f(0, 0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, min(0, _x71), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, max(0, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(max(max(0, s(x)), 0), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, p(s(0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(min(0, _x61), 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Problem 22: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(max(s(x), 0), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), min(0, _x51)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(0, max(s(y), max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(max(0, s(y)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), p(s(f(0, 0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, min(_x71, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(max(s(s(x)), 0))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(max(s(s(x)), 0))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, f(s(x), 0, 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), max(0, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, min(_x81, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(max(s(_x72), s(_x71))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x72, _x71)), max(s(y), s(z))), p(min(s(max(_x72, _x71)), max(s(y), s(z)))), min(s(max(_x72, _x71)), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), max(min(_x71, 0), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(p(s(0)), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, p(s(0)), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, p(s(0)), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(f(0, 0, p(s(s(x)))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, min(_x71, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(s(x))), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(max(0, 0), 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(max(0, 0), 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(p(s(0)), 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(p(s(0)), 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(s(_x82), s(_x81)), 0), 0))) → f#(max(s(x), max(s(y), s(max(_x82, _x81)))), p(min(s(x), max(s(y), s(max(_x82, _x81))))), min(s(x), min(s(y), s(max(_x82, _x81)))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(p(s(s(x))), 0)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(p(s(s(x))), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(f(0, 0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(p(s(s(y))))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), max(0, 0)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(p(s(s(y))), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(f(0, 0, p(s(s(x)))), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, f(0, 0, s(x))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(min(_x71, 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, min(_x101, 0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(f(0, 0, s(x)), f(s(y), max(0, 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(min(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), f(0, s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), max(0, 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(s(x), 0)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(max(s(y), 0), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(max(0, 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, max(0, 0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, min(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(p(s(min(_x71, 0))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(min(0, _x61), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(0, s(z)), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(0, _x71), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), f(0, 0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(min(_x61, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, f(0, 0, p(s(s(x))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, min(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(min(_x51, 0), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(f(0, s(x), 0), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(0, f(0, s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(0, s(x)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(min(_x61, 0), 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(min(0, _x61), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(max(0, s(s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(min(0, _x51), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(f(0, 0, p(p(s(s(s(x)))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(p(s(s(s(x)))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, min(0, _x101)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, max(s(x), 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), p(s(0))), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), max(0, 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(p(s(max(0, s(x)))), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), p(s(max(s(y), max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, min(_x71, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, max(s(x), 0)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(0, max(s(z), 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(min(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(min(s(_x82), s(_x81)), 0), 0))) → f#(max(s(x), max(s(y), s(min(_x82, _x81)))), p(min(s(x), max(s(y), s(min(_x82, _x81))))), min(s(x), min(s(y), s(min(_x82, _x81)))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(f(0, max(s(x), 0), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(max(s(y), 0), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(0)), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), p(s(0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(min(_x61, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(f(0, 0, p(s(max(0, s(x))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(max(0, s(x))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, min(0, _x71))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, max(0, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(max(0, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(max(0, s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, max(0, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(0, max(s(y), 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(min(0, _x61), 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(f(0, s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, min(0, _x41), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(max(s(_x62), s(_x61))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(max(_x62, _x61)), max(s(y), s(z))), p(min(s(max(_x62, _x61)), max(s(y), s(z)))), min(s(max(_x62, _x61)), min(s(y), s(z))))
f#(f(0, max(0, 0), p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(p(s(0)), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(p(s(0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(0, max(max(s(z), 0), 0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(0, min(_x71, 0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(p(s(s(z))), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(f(0, s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(max(s(y), max(0, 0)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(max(s(x), 0)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(max(s(x), 0)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(max(s(_x62), s(_x61)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x62, _x61)), s(z))), p(min(s(x), max(s(max(_x62, _x61)), s(z)))), min(s(x), min(s(max(_x62, _x61)), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(0, max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(min(s(_x72), s(_x71))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x72, _x71)), max(s(y), s(z))), p(min(s(min(_x72, _x71)), max(s(y), s(z)))), min(s(min(_x72, _x71)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(f(0, s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), f(0, 0, 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), min(_x61, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), f(0, f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))
f#(max(f(0, 0, s(x)), 0), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), min(0, _x81)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(min(_x61, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), p(s(max(s(y), 0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))f#(f(min(_x31, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(min(0, _x61), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, min(0, _x71), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(min(0, _x31), 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), p(s(max(f(0, s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(f(0, 0, s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, min(0, _x71))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(s(x), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(max(min(_x71, 0), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(min(s(_x62), s(_x61)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x62, _x61)), s(z))), p(min(s(x), max(s(min(_x62, _x61)), s(z)))), min(s(x), min(s(min(_x62, _x61)), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(max(_x32, _x31)), s(z))), p(min(s(x), max(s(max(_x32, _x31)), s(z)))), min(s(x), min(s(max(_x32, _x31)), s(z))))
f#(max(0, s(x)), max(max(s(y), f(0, 0, 0)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, min(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), min(0, _x91)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(f(0, 0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, 0), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), max(0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(f(0, s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, p(s(s(x)))), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(f(min(_x31, 0), 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))
f#(max(0, max(s(x), 0)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(p(s(s(y))), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, p(s(0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, p(s(0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, p(s(s(x))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(0, p(s(s(x))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(min(s(_x62), s(_x61))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(min(_x62, _x61)), max(s(y), s(z))), p(min(s(min(_x62, _x61)), max(s(y), s(z)))), min(s(min(_x62, _x61)), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, min(_x41, 0), p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(max(s(s(y)), 0)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(min(_x71, 0), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), min(_x51, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, max(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, s(x)), max(p(s(s(y))), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), max(0, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), min(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(min(_x32, _x31)), s(z))), p(min(s(x), max(s(min(_x32, _x31)), s(z)))), min(s(x), min(s(min(_x32, _x31)), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, f(0, s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, p(s(max(max(s(z), 0), 0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), f(0, 0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(0, max(f(0, s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), min(0, _x61))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, p(s(0))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, min(_x41, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(min(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(f(0, 0, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), p(s(max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, min(0, _x81))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))
f#(f(0, s(x), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, p(s(s(x)))), max(max(0, s(y)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(max(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(f(0, 0, p(s(s(x)))), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, f(0, 0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(p(s(f(0, s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(min(0, _x31), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(p(s(0)), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, p(s(s(x)))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(max(0, s(s(x))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(max(0, s(s(x))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(max(0, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(max(0, 0), 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(s(_x52), s(_x51))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(max(s(y), 0))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(0, s(y)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), max(0, 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), f(s(y), 0, max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, p(s(s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), p(s(0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, 0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, p(s(0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(f(0, 0, s(x)), max(max(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(p(s(s(y))), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(min(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(f(s(z), 0, 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), p(s(0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, min(0, _x41), p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))
f#(f(0, 0, min(s(_x52), s(_x51))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(p(s(s(x))), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(min(0, _x31), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), min(_x81, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), f(s(y), 0, 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(max(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), max(0, 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(p(s(s(y))), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(0, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(max(0, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(p(s(0)), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(p(s(0)), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(0, s(x))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(s(x), p(s(s(y))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(p(s(0)), 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(p(s(0)), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, p(s(s(x))), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, f(0, 0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(p(s(s(x)))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(p(s(s(x)))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(max(0, s(x)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(p(s(max(s(z), 0))), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(max(s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(p(s(s(y))), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(p(s(s(y))), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(p(s(s(s(y))))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(f(0, s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, f(0, s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), min(_x91, 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(f(0, p(s(0)), p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(min(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))
f#(max(0, max(s(x), max(0, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(max(0, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(max(0, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(min(0, _x61), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))f#(f(0, min(_x41, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(f(0, s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), max(min(_x71, 0), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(min(_x31, 0), 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(x), 0), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(p(s(s(y))), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), f(0, s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(min(0, _x31), 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, f(0, max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, max(max(s(z), 0), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(min(_x61, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(s(z), 0), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, max(min(_x71, 0), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, min(0, _x41), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Rewrite Rules

min(0, y) → 0min(x, 0) → 0
min(s(x), s(y)) → s(min(x, y))max(0, y) → y
max(x, 0) → xmax(s(x), s(y)) → s(max(x, y))
p(s(x)) → xf(s(x), s(y), s(z)) → f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f(0, y, z) → max(y, z)f(x, 0, z) → max(x, z)
f(x, y, 0) → max(x, y)

Original Signature

Termination of terms over the following signature is verified: f, min, max, 0, s, p

Strategy

The left-hand side of the rule f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, min(0, _x81)), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), max(0, 0))) 
f#(f(0, 0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), max(0, 0), 0)) 
f#(max(0, f(0, 0, s(x))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(max(0, 0), 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, min(_x81, 0)), 0)) 
f#(f(0, 0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), max(0, 0), 0)) 
f#(f(0, min(_x41, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), p(s(0)))) 
f#(p(s(f(0, 0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, max(s(_x52), s(_x51))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, max(0, 0)), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, p(s(0))), 0)) 
f#(f(min(_x31, 0), 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(max(f(0, 0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(p(s(0)), 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), max(0, 0), 0)) 
f#(f(0, p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(min(0, _x31), 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), max(0, 0), 0))) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), min(_x71, 0))) 
f#(f(0, 0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, min(0, _x41), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), min(0, _x71))) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(max(0, 0))), 0)) 
f#(f(0, 0, min(s(_x52), s(_x51))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), max(0, 0), 0)))) 
f#(f(0, 0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), max(0, 0), 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(0, 0), 0), 0)) 
f#(f(0, max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(p(s(0)), 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(0, _x71), 0), 0)) 
Thus, the rule f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is replaced by the following rules:
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), max(0, 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, min(0, _x41), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(f(0, 0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(max(0, 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(f(0, 0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(p(s(0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, min(s(_x52), s(_x51))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))
f#(f(0, 0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), max(0, 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(f(0, 0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), max(0, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(s(_x52), s(_x51))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(max(0, 0), 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(p(s(0)), 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, f(0, 0, s(x))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, min(_x41, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(0, _x71), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(0, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(min(_x31, 0), 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(min(0, _x31), 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Problem 23: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(max(s(x), 0), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), min(0, _x51)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), max(0, 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(max(0, s(y)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(0, max(s(y), max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), p(s(f(0, 0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, min(_x71, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(max(s(s(x)), 0))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(max(s(s(x)), 0))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, f(s(x), 0, 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), max(0, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, min(_x81, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(f(0, 0, p(s(max(s(_x72), s(_x71))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x72, _x71)), max(s(y), s(z))), p(min(s(max(_x72, _x71)), max(s(y), s(z)))), min(s(max(_x72, _x71)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), max(min(_x71, 0), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, p(s(0)), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, p(s(0)), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(p(s(0)), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(p(s(0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, min(_x71, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(f(0, 0, p(s(s(x)))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(s(x))), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(max(0, 0), 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(max(0, 0), 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(max(0, 0), 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(p(s(0)), 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(p(s(0)), 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(p(s(0)), 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(s(_x82), s(_x81)), 0), 0))) → f#(max(s(x), max(s(y), s(max(_x82, _x81)))), p(min(s(x), max(s(y), s(max(_x82, _x81))))), min(s(x), min(s(y), s(max(_x82, _x81)))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(p(s(s(x))), 0)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(p(s(s(x))), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(f(0, 0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(p(s(s(y))))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), max(0, 0)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(p(s(s(y))), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(f(0, 0, p(s(s(x)))), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, f(0, 0, s(x))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, f(0, 0, s(x))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, s(x), 0), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(min(_x71, 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, min(_x101, 0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(f(0, 0, s(x)), f(s(y), max(0, 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(f(0, 0, s(x)), max(min(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), f(0, s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(s(z), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), max(0, 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(s(x), 0)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(max(s(y), 0), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(max(0, 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, max(0, 0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), max(0, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, min(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(p(s(min(_x71, 0))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(min(0, _x61), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(0, s(z)), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, p(s(0)), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), f(0, 0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(0, _x71), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(min(_x61, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, f(0, 0, p(s(s(x))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, min(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(f(0, 0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(min(_x51, 0), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(f(0, s(x), 0), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(0, f(0, s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))
f#(max(0, s(x)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(min(_x61, 0), 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(min(0, _x61), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), min(0, _x51)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(max(0, s(s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(min(0, _x51), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, p(p(s(s(s(x)))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(p(s(s(s(x)))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, min(0, _x101)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), p(s(0))), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, max(s(x), 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), max(0, 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), p(s(max(s(y), max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(p(s(s(z))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(0, s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, min(_x71, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, max(s(x), 0)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), max(0, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(0, max(s(z), 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(min(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(min(s(_x82), s(_x81)), 0), 0))) → f#(max(s(x), max(s(y), s(min(_x82, _x81)))), p(min(s(x), max(s(y), s(min(_x82, _x81))))), min(s(x), min(s(y), s(min(_x82, _x81)))))f#(f(0, 0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(f(0, max(s(x), 0), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(max(s(y), 0), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), p(s(0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(0)), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(min(_x61, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(0, p(s(max(0, s(x))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(max(0, s(x))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, min(0, _x71))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, max(0, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(max(0, s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(max(0, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, max(0, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(0, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(0, max(s(y), 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(min(0, _x61), 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(f(0, s(x), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, min(0, _x41), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, min(0, _x41), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(max(s(_x62), s(_x61))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(max(_x62, _x61)), max(s(y), s(z))), p(min(s(max(_x62, _x61)), max(s(y), s(z)))), min(s(max(_x62, _x61)), min(s(y), s(z))))f#(max(max(0, 0), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, max(0, 0), p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), min(_x51, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(p(s(0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(p(s(0)), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(0, max(max(s(z), 0), 0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(p(s(s(y))), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(0, min(_x71, 0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(p(s(s(z))), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(f(0, s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(f(0, 0, s(x)), max(max(s(y), max(0, 0)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(max(s(x), 0)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(max(s(x), 0)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(max(s(_x62), s(_x61)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x62, _x61)), s(z))), p(min(s(x), max(s(max(_x62, _x61)), s(z)))), min(s(x), min(s(max(_x62, _x61)), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(0, max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(min(s(_x72), s(_x71))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x72, _x71)), max(s(y), s(z))), p(min(s(min(_x72, _x71)), max(s(y), s(z)))), min(s(min(_x72, _x71)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(f(0, s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), f(0, 0, 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), min(_x61, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), f(0, f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(f(0, 0, s(x)), 0), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))f#(max(f(0, 0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), min(0, _x81)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(min(_x61, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), p(s(max(s(y), 0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))f#(f(min(_x31, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), f(0, s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(min(0, _x61), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(0, _x71), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, min(0, _x71), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(min(0, _x31), 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(min(0, _x31), 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), p(s(max(f(0, s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(f(0, 0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(f(0, 0, s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, min(0, _x71))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(s(x), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(max(min(_x71, 0), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(min(s(_x62), s(_x61)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x62, _x61)), s(z))), p(min(s(x), max(s(min(_x62, _x61)), s(z)))), min(s(x), min(s(min(_x62, _x61)), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(max(_x32, _x31)), s(z))), p(min(s(x), max(s(max(_x32, _x31)), s(z)))), min(s(x), min(s(max(_x32, _x31)), s(z))))f#(max(0, s(x)), max(max(s(y), f(0, 0, 0)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, min(s(_x52), s(_x51))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), min(0, _x91)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(f(0, 0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, 0), max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), max(0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(p(s(f(0, s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, p(s(s(x)))), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(f(min(_x31, 0), 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))f#(max(0, max(s(x), 0)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(p(s(s(y))), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, p(s(0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, p(s(0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, p(s(s(x))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(0, p(s(s(x))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, max(0, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(min(s(_x62), s(_x61))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(min(_x62, _x61)), max(s(y), s(z))), p(min(s(min(_x62, _x61)), max(s(y), s(z)))), min(s(min(_x62, _x61)), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), max(0, 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(_x42), s(_x41))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, min(_x41, 0), p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(max(s(s(y)), 0)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), f(s(y), 0, 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(min(_x71, 0), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), min(_x51, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, max(s(_x72), s(_x71)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(0, s(x)), max(p(s(s(y))), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(max(0, s(y)), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), max(0, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), min(s(_x32), s(_x31)), s(z)) → f#(max(s(x), max(s(min(_x32, _x31)), s(z))), p(min(s(x), max(s(min(_x32, _x31)), s(z)))), min(s(x), min(s(min(_x32, _x31)), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, max(0, s(z)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, f(0, s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, p(s(max(max(s(z), 0), 0))))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), f(0, 0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(0, max(f(0, s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), min(0, _x61))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, p(s(0))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, min(_x41, 0), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(min(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(f(0, 0, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(max(0, 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), p(s(max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, min(0, _x81))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(min(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(min(_x52, _x51)))), p(min(s(x), max(s(y), s(min(_x52, _x51))))), min(s(x), min(s(y), s(min(_x52, _x51)))))
f#(f(0, s(x), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(0, _x61), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, p(s(s(x)))), max(max(0, s(y)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(0, max(s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(max(s(_x42), s(_x41)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(f(0, 0, p(s(s(x)))), max(max(s(_x42), s(_x41)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, f(0, 0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(p(s(f(0, s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(max(0, s(z)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(min(0, _x31), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(p(s(0)), s(x)), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, p(s(s(x)))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(s(z), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), min(0, _x61))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(max(0, s(s(x))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(max(0, s(s(x))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(max(0, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(max(0, 0), 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, s(z), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(s(_x52), s(_x51))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))
f#(f(0, 0, max(s(_x52), s(_x51))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(p(s(0)), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(max(s(y), 0))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(0, s(y)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), s(y), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(f(0, 0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), max(0, 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(_x31, 0), s(x)), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(f(0, 0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(s(y), 0, f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), f(s(y), 0, max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), max(0, 0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, p(s(s(y)))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(0, s(x))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(0, _x81)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(p(s(s(y))), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(0, s(z)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(0, max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), p(s(0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(0, 0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(max(f(0, s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, p(s(0)))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(f(0, 0, s(x)), max(max(s(_x42), s(_x41)), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(p(s(s(y))), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(min(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), s(y), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(f(s(z), 0, 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(min(s(_x42), s(_x41)), 0), s(z)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(p(s(max(0, max(s(x), 0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), p(s(0)))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, min(0, _x41), p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, min(s(_x52), s(_x51))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(s(_x22), s(_x21)), s(y), s(z)) → f#(max(s(max(_x22, _x21)), max(s(y), s(z))), p(min(s(max(_x22, _x21)), max(s(y), s(z)))), min(s(max(_x22, _x21)), min(s(y), s(z))))f#(f(0, 0, min(s(_x52), s(_x51))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(min(_x52, _x51)), max(s(y), s(z))), p(min(s(min(_x52, _x51)), max(s(y), s(z)))), min(s(min(_x52, _x51)), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(p(s(max(s(z), 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, max(0, 0))), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(max(0, max(0, s(x))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(p(s(s(x))), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), p(s(max(s(y), 0))), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), s(z)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(min(0, _x31), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(p(s(f(0, s(z), 0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), 0), min(_x81, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), f(s(y), 0, 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), f(s(y), 0, 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(s(x), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(max(s(_x52), s(_x51)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(max(_x52, _x51)), max(s(y), s(z))), p(min(s(max(_x52, _x51)), max(s(y), s(z)))), min(s(max(_x52, _x51)), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), max(0, 0), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(p(s(s(y))), 0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(max(0, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), max(0, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(max(0, 0), 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(p(s(0)), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(p(s(0)), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, max(0, s(x))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(s(x), p(s(s(y))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(p(s(0)), 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(p(s(0)), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, p(s(s(x))), 0), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, f(0, 0, s(x))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(p(s(s(x)))))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(p(s(s(x)))))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(max(0, s(x)), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, min(0, _x81)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, max(p(s(max(s(z), 0))), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(max(s(z), 0), 0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))
f#(f(0, 0, s(x)), max(p(s(s(y))), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(p(s(s(s(y))))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(max(f(0, s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), p(s(max(s(z), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), min(_x51, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(0, f(0, s(z), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(min(_x61, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), p(s(max(max(s(z), 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), max(max(min(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(min(_x62, _x61)))), p(min(s(x), max(s(y), s(min(_x62, _x61))))), min(s(x), min(s(y), s(min(_x62, _x61)))))
f#(s(x), s(y), max(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(max(_x42, _x41)))), p(min(s(x), max(s(y), s(max(_x42, _x41))))), min(s(x), min(s(y), s(max(_x42, _x41)))))f#(max(0, s(x)), max(s(y), 0), max(0, max(max(s(z), min(_x91, 0)), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), p(s(s(x)))), max(s(y), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, p(s(0)), p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(min(s(_x22), s(_x21)), max(s(y), 0), s(z)) → f#(max(s(min(_x22, _x21)), max(s(y), s(z))), p(min(s(min(_x22, _x21)), max(s(y), s(z)))), min(s(min(_x22, _x21)), min(s(y), s(z))))f#(max(max(0, 0), max(s(x), 0)), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), max(0, 0))), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(max(0, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(max(0, 0), 0, s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), max(f(0, p(s(s(z))), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(max(0, s(y)), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(0, s(y)), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(s(z), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, max(s(z), 0), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), min(s(_x42), s(_x41))) → f#(max(s(x), max(s(y), s(min(_x42, _x41)))), p(min(s(x), max(s(y), s(min(_x42, _x41))))), min(s(x), min(s(y), s(min(_x42, _x41)))))f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), min(0, _x51)), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(min(0, _x61), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(s(y), 0), max(0, s(z))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(_x71, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(0, s(z), min(_x81, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), min(_x61, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(max(0, 0), s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, p(s(s(z))), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(max(0, f(0, s(z), 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, min(_x41, 0), s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(s(y), 0), max(max(max(s(_x62), s(_x61)), 0), 0)) → f#(max(s(x), max(s(y), s(max(_x62, _x61)))), p(min(s(x), max(s(y), s(max(_x62, _x61))))), min(s(x), min(s(y), s(max(_x62, _x61)))))
f#(f(0, min(_x41, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(f(0, s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), min(_x61, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(min(_x71, 0), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), 0), max(s(z), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(s(x), max(0, max(s(y), 0)), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(min(_x31, 0), 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), max(min(_x71, 0), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(max(s(_x52), s(_x51)), 0)) → f#(max(s(x), max(s(y), s(max(_x52, _x51)))), p(min(s(x), max(s(y), s(max(_x52, _x51))))), min(s(x), min(s(y), s(max(_x52, _x51)))))f#(f(min(_x31, 0), 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), p(s(max(s(y), 0))), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(f(0, max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), max(max(max(s(z), 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, min(s(_x72), s(_x71)), 0), 0, 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))
f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), max(min(_x71, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(s(x), 0), s(y), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), p(s(0))), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), p(s(0))), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(f(0, 0, p(s(s(x)))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(p(s(s(y))), 0), max(f(0, s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, min(s(_x42), s(_x41))), max(p(s(s(y))), 0), max(max(s(z), 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), p(s(0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), p(s(s(z)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, 0, s(x)), f(0, s(y), max(0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), max(0, max(max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(0, max(s(z), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(min(0, _x31), 0, p(s(s(x)))), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), max(s(z), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(max(s(y), 0), 0), s(z)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(s(z), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(0, max(max(s(z), 0), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), 0), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(max(s(z), min(0, _x71)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(min(_x61, 0), s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), min(_x81, 0)), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), p(s(f(f(0, s(z), 0), 0, 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(0, max(max(max(s(z), 0), 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(s(x), 0)), max(s(y), min(0, _x51)), max(s(z), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, max(min(_x71, 0), 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), 0, min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(0, _x31), s(x)), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, min(0, _x41), s(x)), max(s(y), 0), max(max(s(z), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), max(0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), max(f(s(z), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, s(x)), 0), max(s(y), f(0, 0, 0)), f(f(0, s(z), 0), 0, 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Rewrite Rules

min(0, y) → 0min(x, 0) → 0
min(s(x), s(y)) → s(min(x, y))max(0, y) → y
max(x, 0) → xmax(s(x), s(y)) → s(max(x, y))
p(s(x)) → xf(s(x), s(y), s(z)) → f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f(0, y, z) → max(y, z)f(x, 0, z) → max(x, z)
f(x, y, 0) → max(x, y)

Original Signature

Termination of terms over the following signature is verified: min, f, 0, max, s, p

Strategy

The left-hand side of the rule f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), f(0, 0, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(min(0, _x71), 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), max(0, 0))) 
f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, min(0, _x91)), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(max(0, 0), 0, 0), 0)) 
f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), f(0, 0, 0), 0)) 
f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), p(s(0)))) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, f(0, 0, 0)), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, max(0, 0)), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, p(s(0))), 0)) 
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(f(0, 0, 0), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), f(0, 0, 0), 0)))) 
f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), f(0, 0, 0), 0)) 
f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, p(s(0)), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), f(0, 0, 0), 0))) 
f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, min(_x81, 0), 0), 0)) 
f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), min(_x71, 0))) 
f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), min(0, _x71))) 
f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), f(0, 0, 0), 0)) 
f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(min(_x71, 0), 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), f(0, 0, 0), 0)) 
f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, max(0, 0), 0), 0)) 
f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), f(0, 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, min(0, _x81), 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(f(0, 0, 0))), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(p(s(0)), 0, 0), 0)) 
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, min(_x91, 0)), 0)) 
Thus, the rule f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))) is replaced by the following rules:
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), max(0, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(_x81, 0)), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, min(_x81, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(p(s(0)), s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(f(0, 0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(min(_x61, 0), s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(max(_x42, _x41)), s(z))), p(min(s(x), max(s(max(_x42, _x41)), s(z)))), min(s(x), min(s(max(_x42, _x41)), s(z))))f#(max(0, s(x)), max(s(y), max(0, 0)), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, min(_x91, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), p(s(0))), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), min(0, _x71))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, max(0, s(x))), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(min(0, _x61), s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(min(s(_x42), s(_x41)), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(min(_x42, _x41)), s(z))), p(min(s(x), max(s(min(_x42, _x41)), s(z)))), min(s(x), min(s(min(_x42, _x41)), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(f(0, 0, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), min(_x71, 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), f(0, s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(_x51, 0)), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), p(s(0))), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(p(s(0)), s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, p(s(0)), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(0, max(s(y), 0)), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(min(_x31, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(max(f(0, s(z), 0), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(x), 0)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(max(s(y), 0), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(_x72), s(_x71)), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(max(_x72, _x71)))), p(min(s(x), max(s(y), s(max(_x72, _x71))))), min(s(x), min(s(y), s(max(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, min(0, _x91)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), max(f(f(0, s(z), 0), f(0, 0, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, max(0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(max(0, s(y)), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(f(0, s(x), 0), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), p(s(f(0, 0, 0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(min(0, _x71), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(max(0, f(0, s(z), 0)), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), max(0, f(0, 0, 0)), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(max(0, 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), p(s(max(s(y), 0))), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(p(s(0)), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(s(z), 0), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(max(0, 0), s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, max(0, s(z)), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), p(s(0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), min(0, _x51)), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, p(s(s(x)))), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(min(0, _x31), s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), p(s(f(f(0, s(z), 0), f(0, 0, 0), 0)))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(p(s(s(y))), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, max(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(max(_x42, _x41)), max(s(y), s(z))), p(min(s(max(_x42, _x41)), max(s(y), s(z)))), min(s(max(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), f(s(y), 0, 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, min(s(_x42), s(_x41))), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(min(_x42, _x41)), max(s(y), s(z))), p(min(s(min(_x42, _x41)), max(s(y), s(z)))), min(s(min(_x42, _x41)), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), max(0, 0)), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(max(0, 0), s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), min(0, _x81)), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, max(0, 0), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, min(0, _x81), 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, p(s(s(z))), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), max(0, f(f(0, s(z), 0), f(0, 0, 0), 0))) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(p(s(max(0, s(x)))), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(max(0, s(x)), 0), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(f(0, min(s(_x72), s(_x71)), 0), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(min(_x72, _x71)))), p(min(s(x), max(s(y), s(min(_x72, _x71))))), min(s(x), min(s(y), s(min(_x72, _x71)))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(0, 0, p(s(0))), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f#(max(0, s(x)), max(s(y), 0), f(p(s(f(0, s(z), 0))), f(0, 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))f#(max(0, s(x)), max(s(y), 0), f(f(0, s(z), 0), f(min(_x71, 0), 0, 0), 0)) → f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))

Problem 4: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

min#(s(x), s(y)) → min#(x, y)

Rewrite Rules

min(0, y) → 0min(x, 0) → 0
min(s(x), s(y)) → s(min(x, y))max(0, y) → y
max(x, 0) → xmax(s(x), s(y)) → s(max(x, y))
p(s(x)) → xf(s(x), s(y), s(z)) → f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))
f(0, y, z) → max(y, z)f(x, 0, z) → max(x, z)
f(x, y, 0) → max(x, y)

Original Signature

Termination of terms over the following signature is verified: min, f, 0, max, s, p

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

min#(s(x), s(y)) → min#(x, y)