TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60138 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 (3ms).
 |    | – Problem 4 was processed with processor BackwardsNarrowing (3ms).
 |    |    | – Problem 5 was processed with processor BackwardsNarrowing (8ms).
 |    |    |    | – Problem 6 was processed with processor BackwardsNarrowing (11ms).
 |    |    |    |    | – Problem 7 was processed with processor BackwardsNarrowing (11ms).
 |    |    |    |    |    | – Problem 8 was processed with processor BackwardsNarrowing (10ms).
 |    |    |    |    |    |    | – Problem 9 was processed with processor BackwardsNarrowing (16ms).
 |    |    |    |    |    |    |    | – Problem 10 was processed with processor BackwardsNarrowing (14ms).
 |    |    |    |    |    |    |    |    | – Problem 11 was processed with processor BackwardsNarrowing (15ms).
 |    |    |    |    |    |    |    |    |    | – Problem 12 was processed with processor BackwardsNarrowing (17ms).
 |    |    |    |    |    |    |    |    |    |    | – Problem 13 was processed with processor BackwardsNarrowing (17ms).
 |    |    |    |    |    |    |    |    |    |    |    | – Problem 14 was processed with processor BackwardsNarrowing (60ms).
 |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 15 was processed with processor BackwardsNarrowing (32ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 16 was processed with processor BackwardsNarrowing (63ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 17 was processed with processor BackwardsNarrowing (44ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 18 was processed with processor BackwardsNarrowing (85ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 19 was processed with processor BackwardsNarrowing (31ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 20 was processed with processor BackwardsNarrowing (100ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 21 was processed with processor BackwardsNarrowing (46ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 22 was processed with processor BackwardsNarrowing (51ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 23 was processed with processor BackwardsNarrowing (444ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 24 remains open; application of the following processors failed [BackwardsNarrowing (450ms), BackwardsNarrowing (402ms), BackwardsNarrowing (379ms), BackwardsNarrowing (131ms), BackwardsNarrowing (157ms), BackwardsNarrowing (304ms), BackwardsNarrowing (352ms), BackwardsNarrowing (327ms), BackwardsNarrowing (283ms), BackwardsNarrowing (548ms), BackwardsNarrowing (412ms), BackwardsNarrowing (674ms), BackwardsNarrowing (765ms), BackwardsNarrowing (707ms), BackwardsNarrowing (371ms), BackwardsNarrowing (269ms), BackwardsNarrowing (397ms), BackwardsNarrowing (835ms), BackwardsNarrowing (1019ms), BackwardsNarrowing (735ms), BackwardsNarrowing (942ms), BackwardsNarrowing (1162ms), BackwardsNarrowing (895ms), BackwardsNarrowing (788ms), BackwardsNarrowing (1030ms), BackwardsNarrowing (982ms), BackwardsNarrowing (370ms), BackwardsNarrowing (1013ms), BackwardsNarrowing (1077ms), BackwardsNarrowing (309ms), BackwardsNarrowing (330ms), BackwardsNarrowing (1173ms), BackwardsNarrowing (1474ms), BackwardsNarrowing (1296ms), BackwardsNarrowing (494ms), BackwardsNarrowing (1633ms), BackwardsNarrowing (726ms), BackwardsNarrowing (1333ms), BackwardsNarrowing (818ms), BackwardsNarrowing (1582ms), BackwardsNarrowing (859ms), BackwardsNarrowing (2024ms), BackwardsNarrowing (2482ms), BackwardsNarrowing (3303ms), BackwardsNarrowing (3168ms), BackwardsNarrowing (4520ms)].

The following open problems remain:

Open Dependency Pair Problem 3

Dependency Pairs

f#(0, s(0), X) → f#(X, +(X, X), X)

Rewrite Rules

+(X, 0) → X+(X, s(Y)) → s(+(X, Y))
f(0, s(0), X) → f(X, +(X, X), X)g(X, Y) → X
g(X, Y) → Y

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, +

Problem 1: DependencyGraph

Dependency Pair Problem

Dependency Pairs

f#(0, s(0), X) → +#(X, X)f#(0, s(0), X) → f#(X, +(X, X), X)
+#(X, s(Y)) → +#(X, Y)

Rewrite Rules

+(X, 0) → X+(X, s(Y)) → s(+(X, Y))
f(0, s(0), X) → f(X, +(X, X), X)g(X, Y) → X
g(X, Y) → Y

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, +

Strategy

The following SCCs where found

f#(0, s(0), X) → f#(X, +(X, X), X)
+#(X, s(Y)) → +#(X, Y)

Problem 2: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

+#(X, s(Y)) → +#(X, Y)

Rewrite Rules

+(X, 0) → X+(X, s(Y)) → s(+(X, Y))
f(0, s(0), X) → f(X, +(X, X), X)g(X, Y) → X
g(X, Y) → Y

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, +

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

+#(X, s(Y)) → +#(X, Y)

Problem 3: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(0, s(0), X) → f#(X, +(X, X), X)

Rewrite Rules

+(X, 0) → X+(X, s(Y)) → s(+(X, Y))
f(0, s(0), X) → f(X, +(X, X), X)g(X, Y) → X
g(X, Y) → Y

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, +

Strategy

The left-hand side of the rule f#(0, s(0), X) → f#(X, +(X, X), X) 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#(0, s(g(_x42, 0)), X) 
f#(0, g(_x32, s(0)), X) 
f#(0, s(g(0, _x41)), X) 
f#(g(_x22, 0), s(0), X) 
f#(g(0, _x21), s(0), X) 
f#(0, s(+(0, 0)), X) 
f#(+(0, 0), s(0), X) 
f#(0, g(s(0), _x31), X) 
f#(0, +(s(0), 0), X) 
Thus, the rule f#(0, s(0), X) → f#(X, +(X, X), X) is replaced by the following rules:
f#(g(_x22, 0), s(0), X) → f#(X, +(X, X), X)f#(0, s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(0, s(+(0, 0)), X) → f#(X, +(X, X), X)f#(+(0, 0), s(0), X) → f#(X, +(X, X), X)
f#(0, g(s(0), _x31), X) → f#(X, +(X, X), X)f#(0, g(_x32, s(0)), X) → f#(X, +(X, X), X)
f#(0, s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(0, +(s(0), 0), X) → f#(X, +(X, X), X)
f#(g(0, _x21), s(0), X) → f#(X, +(X, X), X)

Problem 4: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(g(_x22, 0), s(0), X) → f#(X, +(X, X), X)f#(0, s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(0, s(+(0, 0)), X) → f#(X, +(X, X), X)f#(+(0, 0), s(0), X) → f#(X, +(X, X), X)
f#(0, g(s(0), _x31), X) → f#(X, +(X, X), X)f#(0, g(_x32, s(0)), X) → f#(X, +(X, X), X)
f#(0, s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(0, +(s(0), 0), X) → f#(X, +(X, X), X)
f#(g(0, _x21), s(0), X) → f#(X, +(X, X), X)

Rewrite Rules

+(X, 0) → X+(X, s(Y)) → s(+(X, Y))
f(0, s(0), X) → f(X, +(X, X), X)g(X, Y) → X
g(X, Y) → Y

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, +

Strategy

The left-hand side of the rule f#(g(_x22, 0), s(0), X) → f#(X, +(X, X), X) 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#(+(g(_x22, 0), 0), s(0), X) 
f#(g(_x22, 0), +(s(0), 0), X) 
f#(g(_x22, 0), s(g(_x42, 0)), X) 
f#(g(_x22, 0), g(_x32, s(0)), X) 
f#(g(_x22, g(_x52, 0)), s(0), X) 
f#(g(_x22, +(0, 0)), s(0), X) 
f#(g(_x22, g(0, _x51)), s(0), X) 
f#(g(_x22, 0), s(g(0, _x41)), X) 
f#(g(_x22, 0), g(s(0), _x31), X) 
f#(g(_x22, 0), s(+(0, 0)), X) 
f#(g(g(_x22, 0), _x31), s(0), X) 
f#(g(_x32, g(_x22, 0)), s(0), X) 
Thus, the rule f#(g(_x22, 0), s(0), X) → f#(X, +(X, X), X) is replaced by the following rules:
f#(g(_x22, 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(0)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(0), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(0, 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(0), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(0), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(0), X) → f#(X, +(X, X), X)

Problem 5: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(g(_x22, 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(0)), X) → f#(X, +(X, X), X)
f#(0, s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(0), X) → f#(X, +(X, X), X)
f#(+(0, 0), s(0), X) → f#(X, +(X, X), X)f#(0, s(+(0, 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(0, 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x42, 0)), X) → f#(X, +(X, X), X)
f#(0, +(s(0), 0), X) → f#(X, +(X, X), X)f#(0, s(g(_x42, 0)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(0), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(0), X) → f#(X, +(X, X), X)f#(0, g(s(0), _x31), X) → f#(X, +(X, X), X)
f#(0, g(_x32, s(0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(0), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(0), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(0), X) → f#(X, +(X, X), X)f#(g(0, _x21), s(0), X) → f#(X, +(X, X), X)

Rewrite Rules

+(X, 0) → X+(X, s(Y)) → s(+(X, Y))
f(0, s(0), X) → f(X, +(X, X), X)g(X, Y) → X
g(X, Y) → Y

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, +

Strategy

The left-hand side of the rule f#(g(_x22, 0), s(g(0, _x41)), X) → f#(X, +(X, X), X) 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#(g(_x22, g(0, _x51)), s(g(0, _x41)), X) 
f#(g(_x32, g(_x22, 0)), s(g(0, _x41)), X) 
f#(g(_x22, 0), s(g(_x52, g(0, _x41))), X) 
f#(g(_x22, 0), g(_x32, s(g(0, _x41))), X) 
f#(g(_x22, 0), s(g(g(_x62, 0), _x41)), X) 
f#(g(_x22, 0), s(g(g(0, _x41), _x51)), X) 
f#(g(_x22, 0), g(s(g(0, _x41)), _x31), X) 
f#(+(g(_x22, 0), 0), s(g(0, _x41)), X) 
f#(g(_x22, 0), s(g(g(0, _x61), _x41)), X) 
f#(g(_x22, 0), s(g(+(0, 0), _x41)), X) 
f#(g(g(_x22, 0), _x31), s(g(0, _x41)), X) 
f#(g(_x22, 0), s(+(g(0, _x41), 0)), X) 
f#(g(_x22, g(_x52, 0)), s(g(0, _x41)), X) 
f#(g(_x22, 0), +(s(g(0, _x41)), 0), X) 
f#(g(_x22, +(0, 0)), s(g(0, _x41)), X) 
Thus, the rule f#(g(_x22, 0), s(g(0, _x41)), X) → f#(X, +(X, X), X) is replaced by the following rules:
f#(g(_x22, 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(0, _x41)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(0, _x41)), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(0, 0), _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x62, 0), _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(0, _x61), _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(0, _x41), 0)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(0, _x41)), X) → f#(X, +(X, X), X)

Problem 6: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(g(_x22, 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(0), X) → f#(X, +(X, X), X)
f#(+(0, 0), s(0), X) → f#(X, +(X, X), X)f#(0, s(+(0, 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(0, _x41))), X) → f#(X, +(X, X), X)f#(0, +(s(0), 0), X) → f#(X, +(X, X), X)
f#(0, s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(0, _x41)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(0, _x41), 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(0), 0), X) → f#(X, +(X, X), X)
f#(0, g(_x32, s(0)), X) → f#(X, +(X, X), X)f#(0, g(s(0), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(0, s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(0, 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(0, _x41)), 0), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(0, 0), _x41)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x62, 0), _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(0, _x61), _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(0), _x31), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(0), X) → f#(X, +(X, X), X)f#(g(0, _x21), s(0), X) → f#(X, +(X, X), X)

Rewrite Rules

+(X, 0) → X+(X, s(Y)) → s(+(X, Y))
f(0, s(0), X) → f(X, +(X, X), X)g(X, Y) → X
g(X, Y) → Y

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, +

Strategy

The left-hand side of the rule f#(g(_x22, 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X) 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#(g(_x22, 0), s(g(g(g(0, _x41), _x51), _x61)), X) 
f#(g(_x22, 0), s(g(g(g(0, _x81), _x41), _x51)), X) 
f#(g(_x22, g(0, _x51)), s(g(g(0, _x41), _x51)), X) 
f#(g(_x22, 0), +(s(g(g(0, _x41), _x51)), 0), X) 
f#(g(g(_x22, 0), _x31), s(g(g(0, _x41), _x51)), X) 
f#(g(_x22, 0), s(g(+(g(0, _x41), 0), _x51)), X) 
f#(g(_x22, 0), g(s(g(g(0, _x41), _x51)), _x31), X) 
f#(g(_x22, 0), s(+(g(g(0, _x41), _x51), 0)), X) 
f#(g(_x22, 0), s(g(g(+(0, 0), _x41), _x51)), X) 
f#(g(_x22, 0), s(g(g(g(0, _x41), _x71), _x51)), X) 
f#(g(_x22, 0), g(_x32, s(g(g(0, _x41), _x51))), X) 
f#(g(_x22, g(_x52, 0)), s(g(g(0, _x41), _x51)), X) 
f#(g(_x22, 0), s(g(_x62, g(g(0, _x41), _x51))), X) 
f#(g(_x22, +(0, 0)), s(g(g(0, _x41), _x51)), X) 
f#(g(_x22, 0), s(g(g(g(_x82, 0), _x41), _x51)), X) 
f#(g(_x22, 0), s(g(g(_x72, g(0, _x41)), _x51)), X) 
f#(g(_x32, g(_x22, 0)), s(g(g(0, _x41), _x51)), X) 
f#(+(g(_x22, 0), 0), s(g(g(0, _x41), _x51)), X) 
Thus, the rule f#(g(_x22, 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X) is replaced by the following rules:
f#(g(g(_x22, 0), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)

Problem 7: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(g(g(_x22, 0), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(0), X) → f#(X, +(X, X), X)
f#(0, s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(0), 0), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x42, 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(0, 0), _x41)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(0, _x61), _x41)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(0), X) → f#(X, +(X, X), X)f#(g(0, _x21), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(0)), X) → f#(X, +(X, X), X)f#(0, s(+(0, 0)), X) → f#(X, +(X, X), X)
f#(+(0, 0), s(0), X) → f#(X, +(X, X), X)f#(0, +(s(0), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(0, _x41)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(0, _x41), 0)), X) → f#(X, +(X, X), X)f#(0, g(s(0), _x31), X) → f#(X, +(X, X), X)
f#(0, g(_x32, s(0)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(0, s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(0, 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(0, _x41)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x62, 0), _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(0), _x31), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(0), X) → f#(X, +(X, X), X)

Rewrite Rules

+(X, 0) → X+(X, s(Y)) → s(+(X, Y))
f(0, s(0), X) → f(X, +(X, X), X)g(X, Y) → X
g(X, Y) → Y

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, +

Strategy

The left-hand side of the rule f#(g(g(_x22, 0), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X) 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#(g(g(_x22, 0), _x31), s(g(g(_x72, g(0, _x41)), _x51)), X) 
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(0, _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(0, _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(+(g(g(0, _x41), _x51), 0)), X) 
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(0, _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x81), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(+(g(0, _x41), 0), _x51)), X) 
f#(g(g(_x22, 0), _x31), g(s(g(g(0, _x41), _x51)), _x31), X) 
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(0, _x41), _x51))), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, 0), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x51), _x61)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(0, _x41), _x51)), X) 
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(0, _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), +(s(g(g(0, _x41), _x51)), 0), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x71), _x51)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(0, _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(0, _x41), _x51))), X) 
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(0, _x41), _x51)), X) 
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(0, _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(+(0, 0), _x41), _x51)), X) 
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(0, _x41), _x51)), X) 
Thus, the rule f#(g(g(_x22, 0), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X) is replaced by the following rules:
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)

Problem 8: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(g(g(_x22, 0), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(0), X) → f#(X, +(X, X), X)
f#(0, s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(0), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(0, 0), _x41)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(0, _x61), _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(0), X) → f#(X, +(X, X), X)f#(g(0, _x21), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(0)), X) → f#(X, +(X, X), X)f#(0, s(+(0, 0)), X) → f#(X, +(X, X), X)
f#(+(0, 0), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(0, +(s(0), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(0, _x41)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(0, _x41), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(0, g(_x32, s(0)), X) → f#(X, +(X, X), X)f#(0, g(s(0), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(0, s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(0, 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(0, _x41)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x62, 0), _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(0), _x31), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)

Rewrite Rules

+(X, 0) → X+(X, s(Y)) → s(+(X, Y))
f(0, s(0), X) → f(X, +(X, X), X)g(X, Y) → X
g(X, Y) → Y

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, +

Strategy

The left-hand side of the rule f#(g(g(_x22, 0), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X) 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#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x71), _x51)), X) 
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(0, 0), _x41), _x51)), X) 
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(0, 0), _x41), _x51)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(0, 0), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), +(s(g(g(+(0, 0), _x41), _x51)), 0), X) 
f#(g(g(_x22, 0), _x31), s(+(g(g(+(0, 0), _x41), _x51), 0)), X) 
f#(g(g(_x22, 0), _x31), s(g(+(g(+(0, 0), _x41), 0), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(_x102, 0)), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x92, 0), 0), _x41), _x51)), X) 
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(0, 0), _x41), _x51))), X) 
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(0, 0), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x51), _x61)), X) 
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(0, 0), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(0, 0), _x41), _x51))), X) 
f#(g(g(_x22, 0), _x31), g(s(g(g(+(0, 0), _x41), _x51)), _x31), X) 
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(+(+(0, 0), 0), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(+(0, +(0, 0)), _x41), _x51)), X) 
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) 
Thus, the rule f#(g(g(_x22, 0), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X) is replaced by the following rules:
f#(g(g(_x22, 0), _x31), +(s(g(g(+(0, 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(+(0, 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(+(0, 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x92, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(+(0, 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(+(0, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)

Problem 9: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(0, s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(+(0, 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(0), 0), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x42, 0)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(0, 0), _x41)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x92, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(+(0, 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(0, _x61), _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(0, _x21), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(+(0, 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(0)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(0, 0), s(0), X) → f#(X, +(X, X), X)f#(0, s(+(0, 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(0, _x41))), X) → f#(X, +(X, X), X)f#(0, +(s(0), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(0, _x41)), _x31), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(0, _x41), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(0, g(s(0), _x31), X) → f#(X, +(X, X), X)
f#(0, g(_x32, s(0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(0, s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(0, 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(0, _x41)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(+(0, 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x62, 0), _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(+(0, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(0), _x31), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(0), X) → f#(X, +(X, X), X)

Rewrite Rules

+(X, 0) → X+(X, s(Y)) → s(+(X, Y))
f(0, s(0), X) → f(X, +(X, X), X)g(X, Y) → X
g(X, Y) → Y

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, +

Strategy

The left-hand side of the rule f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X) 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#(g(g(_x22, +(0, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(g(+(0, 0), _x81), _x41)), _x51)), X) 
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x101), _x81), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x102, +(0, 0)), _x81), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x81), 0), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(_x122, 0)), _x81), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), g(s(g(g(g(+(0, 0), _x81), _x41), _x51)), _x31), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) 
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(g(+(0, 0), _x81), _x41), _x51))), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(_x112, 0), 0), _x81), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), +(s(g(g(g(+(0, 0), _x81), _x41), _x51)), 0), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(+(+(0, 0), 0), _x81), _x41), _x51)), X) 
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(+(g(g(+(0, 0), _x81), _x41), 0), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x91), _x41), _x51)), X) 
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) 
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(0, _x121)), _x81), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(+(g(g(g(+(0, 0), _x81), _x41), _x51), 0)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x51), _x61)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x71), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(_x92, g(+(0, 0), _x81)), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, +(0, 0)), _x81), _x41), _x51)), X) 
Thus, the rule f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X) is replaced by the following rules:
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(_x112, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(0, _x121)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(g(+(0, 0), _x81), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(g(+(0, 0), _x81), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(g(+(0, 0), _x81), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(g(+(0, 0), _x81), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(g(+(0, 0), _x81), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x81), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(+(0, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x92, g(+(0, 0), _x81)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(_x122, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x102, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x101), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)

Problem 10: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(g(_x22, 0), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(0, s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(g(+(0, 0), _x81), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(+(0, 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(0), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(g(+(0, 0), _x81), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(0, 0), _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(+(0, 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(0, _x121)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(0, 0), s(0), X) → f#(X, +(X, X), X)f#(0, s(+(0, 0)), X) → f#(X, +(X, X), X)
f#(0, +(s(0), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(0, g(_x32, s(0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(0, s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(+(0, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(+(0, 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x102, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x101), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(_x112, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(0), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(g(+(0, 0), _x81), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x42, 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(_x122, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x92, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(+(0, 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(0, _x61), _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(0, _x21), s(0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(0)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(0, _x41)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(g(+(0, 0), _x81), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(g(+(0, 0), _x81), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(0, _x41), 0)), X) → f#(X, +(X, X), X)
f#(0, g(s(0), _x31), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(0, 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x81), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(0, _x41)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x92, g(+(0, 0), _x81)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x62, 0), _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(+(0, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(0), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(0), X) → f#(X, +(X, X), X)

Rewrite Rules

+(X, 0) → X+(X, s(Y)) → s(+(X, Y))
f(0, s(0), X) → f(X, +(X, X), X)g(X, Y) → X
g(X, Y) → Y

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, +

Strategy

The left-hand side of the rule f#(g(_x22, 0), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X) 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#(g(_x22, 0), g(s(g(_x52, g(0, _x41))), _x31), X) 
f#(g(_x22, 0), +(s(g(_x52, g(0, _x41))), 0), X) 
f#(g(_x22, 0), s(+(g(_x52, g(0, _x41)), 0)), X) 
f#(g(_x22, g(_x52, 0)), s(g(_x52, g(0, _x41))), X) 
f#(g(_x22, 0), s(g(_x52, g(_x82, g(0, _x41)))), X) 
f#(g(_x22, +(0, 0)), s(g(_x52, g(0, _x41))), X) 
f#(g(_x22, g(0, _x51)), s(g(_x52, g(0, _x41))), X) 
f#(g(_x22, 0), s(g(_x52, g(+(0, 0), _x41))), X) 
f#(g(_x22, 0), s(g(_x52, g(g(_x92, 0), _x41))), X) 
f#(g(_x22, 0), s(g(g(_x52, g(0, _x41)), _x61)), X) 
f#(g(g(_x22, 0), _x31), s(g(_x52, g(0, _x41))), X) 
f#(+(g(_x22, 0), 0), s(g(_x52, g(0, _x41))), X) 
f#(g(_x22, 0), s(g(_x52, g(g(0, _x41), _x81))), X) 
f#(g(_x22, 0), g(_x32, s(g(_x52, g(0, _x41)))), X) 
f#(g(_x22, 0), s(g(_x62, g(_x52, g(0, _x41)))), X) 
f#(g(_x22, 0), s(g(_x52, +(g(0, _x41), 0))), X) 
f#(g(_x22, 0), s(g(_x52, g(g(0, _x91), _x41))), X) 
f#(g(_x32, g(_x22, 0)), s(g(_x52, g(0, _x41))), X) 
Thus, the rule f#(g(_x22, 0), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X) is replaced by the following rules:
f#(g(_x22, g(0, _x51)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(g(0, _x91), _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(g(_x92, 0), _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(g(0, _x41), _x81))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(_x52, g(0, _x41)), 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(_x82, g(0, _x41)))), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(_x52, g(0, _x41))), 0), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x52, g(0, _x41)), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, +(g(0, _x41), 0))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(+(0, 0), _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(_x52, g(0, _x41))), _x31), X) → f#(X, +(X, X), X)

Problem 11: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(g(_x22, 0), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(0, s(g(_x42, 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(g(+(0, 0), _x81), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(+(0, 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(0), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(g(+(0, 0), _x81), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(g(_x92, 0), _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(0, 0), _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(_x52, g(0, _x41))), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(+(0, 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(0, _x121)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(0, s(+(0, 0)), X) → f#(X, +(X, X), X)f#(+(0, 0), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(g(0, _x91), _x41))), X) → f#(X, +(X, X), X)f#(0, +(s(0), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(_x52, g(0, _x41)), 0)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x52, g(0, _x41)), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(0, g(_x32, s(0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(0, s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(+(0, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(+(0, 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x102, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x101), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(_x112, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(_x82, g(0, _x41)))), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(g(+(0, 0), _x81), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(_x52, g(0, _x41))), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(_x122, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x92, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(+(0, 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(0, _x61), _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(0, _x21), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(0)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(g(0, _x41), _x81))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(0, _x41)), _x31), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, +(g(0, _x41), 0))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(g(+(0, 0), _x81), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(g(+(0, 0), _x81), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(0, _x41), 0)), X) → f#(X, +(X, X), X)
f#(0, g(s(0), _x31), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(+(0, 0), _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x81), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(0, 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(0, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(0, _x41)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x92, g(+(0, 0), _x81)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x62, 0), _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(+(0, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(0), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(0), X) → f#(X, +(X, X), X)

Rewrite Rules

+(X, 0) → X+(X, s(Y)) → s(+(X, Y))
f(0, s(0), X) → f(X, +(X, X), X)g(X, Y) → X
g(X, Y) → Y

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, +

Strategy

The left-hand side of the rule f#(g(_x22, 0), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X) 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#(g(g(_x22, 0), _x31), s(g(g(_x72, g(0, _x41)), _x51)), X) 
f#(g(_x22, g(0, _x51)), s(g(g(_x72, g(0, _x41)), _x51)), X) 
f#(g(_x22, 0), g(s(g(g(_x72, g(0, _x41)), _x51)), _x31), X) 
f#(g(_x22, 0), s(g(g(g(_x72, g(0, _x41)), _x81), _x51)), X) 
f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x111), _x41)), _x51)), X) 
f#(g(_x22, +(0, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) 
f#(g(_x22, 0), s(g(g(_x72, +(g(0, _x41), 0)), _x51)), X) 
f#(g(_x22, 0), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) 
f#(g(_x22, 0), s(g(_x62, g(g(_x72, g(0, _x41)), _x51))), X) 
f#(g(_x22, 0), g(_x32, s(g(g(_x72, g(0, _x41)), _x51))), X) 
f#(g(_x22, 0), s(+(g(g(_x72, g(0, _x41)), _x51), 0)), X) 
f#(g(_x22, 0), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) 
f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x41), _x101)), _x51)), X) 
f#(+(g(_x22, 0), 0), s(g(g(_x72, g(0, _x41)), _x51)), X) 
f#(g(_x22, 0), +(s(g(g(_x72, g(0, _x41)), _x51)), 0), X) 
f#(g(_x22, 0), s(g(+(g(_x72, g(0, _x41)), 0), _x51)), X) 
f#(g(_x22, 0), s(g(g(_x82, g(_x72, g(0, _x41))), _x51)), X) 
f#(g(_x22, 0), s(g(g(_x72, g(g(_x112, 0), _x41)), _x51)), X) 
f#(g(_x32, g(_x22, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) 
f#(g(_x22, g(_x52, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) 
f#(g(_x22, 0), s(g(g(_x72, g(_x102, g(0, _x41))), _x51)), X) 
Thus, the rule f#(g(_x22, 0), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X) is replaced by the following rules:
f#(g(_x22, 0), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x111), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x62, g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x41), _x101)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(_x72, g(0, _x41)), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x82, g(_x72, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(g(_x72, g(0, _x41)), 0), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(_x72, g(0, _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(0, _x41)), _x81), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(_x102, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, +(g(0, _x41), 0)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(g(_x112, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(g(_x72, g(0, _x41)), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)

Problem 12: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(0, s(g(_x42, 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(g(+(0, 0), _x81), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(_x72, g(0, _x41)), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(_x72, g(0, _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(+(0, 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(0), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(g(+(0, 0), _x81), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x111), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(g(_x92, 0), _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(g(_x72, g(0, _x41)), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(0, 0), _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(0, _x41)), _x81), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(_x52, g(0, _x41))), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(+(0, 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(0, _x121)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(g(0, _x91), _x41))), X) → f#(X, +(X, X), X)
f#(+(0, 0), s(0), X) → f#(X, +(X, X), X)f#(0, s(+(0, 0)), X) → f#(X, +(X, X), X)
f#(0, +(s(0), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(_x52, g(0, _x41)), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x52, g(0, _x41)), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x62, g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(0, g(_x32, s(0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(g(_x112, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, +(g(0, _x41), 0)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(0, s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(+(0, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(+(0, 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x102, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x101), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(_x112, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(_x82, g(0, _x41)))), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(_x102, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(g(+(0, 0), _x81), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(_x52, g(0, _x41))), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x82, g(_x72, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x92, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(_x122, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(+(0, 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(0, _x61), _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(0, _x21), s(0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(0)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(g(0, _x41), _x81))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x41), _x101)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(0, _x41)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, +(g(0, _x41), 0))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(g(+(0, 0), _x81), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(g(+(0, 0), _x81), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(0, _x41), 0)), X) → f#(X, +(X, X), X)
f#(0, g(s(0), _x31), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(+(0, 0), _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(g(_x72, g(0, _x41)), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(0, 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x81), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(0, _x41)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x92, g(+(0, 0), _x81)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x62, 0), _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(+(0, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(0), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(0), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)

Rewrite Rules

+(X, 0) → X+(X, s(Y)) → s(+(X, Y))
f(0, s(0), X) → f(X, +(X, X), X)g(X, Y) → X
g(X, Y) → Y

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, +

Strategy

The left-hand side of the rule f#(g(_x22, 0), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X) 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#(g(_x22, 0), s(g(g(_x92, g(g(_x72, g(0, _x41)), _x51)), _x61)), X) 
f#(g(_x22, 0), s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), X) 
f#(g(_x22, 0), s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), X) 
f#(g(_x22, 0), s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), X) 
f#(g(_x22, 0), s(g(g(g(_x102, g(_x72, g(0, _x41))), _x51), _x61)), X) 
f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x81)), X) 
f#(g(_x22, 0), s(g(g(g(_x72, g(_x122, g(0, _x41))), _x51), _x61)), X) 
f#(g(_x32, g(_x22, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) 
f#(g(_x22, 0), s(g(g(g(_x72, g(g(_x132, 0), _x41)), _x51), _x61)), X) 
f#(g(_x22, 0), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) 
f#(+(g(_x22, 0), 0), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) 
f#(g(_x22, +(0, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) 
f#(g(_x22, 0), +(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), X) 
f#(g(_x22, 0), s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), X) 
f#(g(_x22, g(_x52, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) 
f#(g(_x22, 0), s(g(_x82, g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) 
f#(g(_x22, 0), s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), X) 
f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x131), _x41)), _x51), _x61)), X) 
f#(g(_x22, g(0, _x51)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) 
f#(g(_x22, 0), g(_x32, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) 
f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x91), _x61)), X) 
f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x101), _x51), _x61)), X) 
f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x41), _x121)), _x51), _x61)), X) 
Thus, the rule f#(g(_x22, 0), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X) is replaced by the following rules:
f#(g(_x22, 0), s(g(_x82, g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x41), _x121)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x81)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(g(_x132, 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x131), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x101), _x51), _x61)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x102, g(_x72, g(0, _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x91), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x92, g(g(_x72, g(0, _x41)), _x51)), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(_x122, g(0, _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), X) → f#(X, +(X, X), X)

Problem 13: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(0, s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(_x72, g(0, _x41)), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(g(+(0, 0), _x81), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(g(_x72, g(0, _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(+(0, 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(0), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(g(+(0, 0), _x81), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x82, g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x111), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(g(_x92, 0), _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(g(_x72, g(0, _x41)), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(0, 0), _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(0, _x41)), _x81), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x102, g(_x72, g(0, _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x92, g(g(_x72, g(0, _x41)), _x51)), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(_x52, g(0, _x41))), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(+(0, 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(0, _x121)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(g(0, _x91), _x41))), X) → f#(X, +(X, X), X)
f#(+(0, 0), s(0), X) → f#(X, +(X, X), X)f#(0, s(+(0, 0)), X) → f#(X, +(X, X), X)
f#(0, +(s(0), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(_x52, g(0, _x41)), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x101), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x52, g(0, _x41)), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x91), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x62, g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(0, g(_x32, s(0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(g(_x112, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, +(g(0, _x41), 0)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(0, s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(+(0, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(+(0, 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x102, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x101), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(_x122, g(0, _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(_x112, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(_x82, g(0, _x41)))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(_x102, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(g(+(0, 0), _x81), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x42, 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(_x52, g(0, _x41))), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x131), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x82, g(_x72, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(_x122, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x92, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(+(0, 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(0, _x61), _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), X) → f#(X, +(X, X), X)
f#(g(0, _x21), s(0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(0)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(g(0, _x41), _x81))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x41), _x101)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(g(_x132, 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(0, _x41)), _x31), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, +(g(0, _x41), 0))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(g(+(0, 0), _x81), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(g(+(0, 0), _x81), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(0, _x41), 0)), X) → f#(X, +(X, X), X)f#(0, g(s(0), _x31), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(+(0, 0), _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(g(_x72, g(0, _x41)), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x41), _x121)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x81), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(0, 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x81)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(0, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(0, _x41)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x92, g(+(0, 0), _x81)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x62, 0), _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(+(0, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(0), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)

Rewrite Rules

+(X, 0) → X+(X, s(Y)) → s(+(X, Y))
f(0, s(0), X) → f(X, +(X, X), X)g(X, Y) → X
g(X, Y) → Y

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, +

Strategy

The left-hand side of the rule f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X) 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#(g(g(_x22, 0), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) 
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) 
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) 
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) 
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) 
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) 
Thus, the rule f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X) is replaced by the following rules:
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)

Problem 14: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(0, s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(g(+(0, 0), _x81), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(0), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x111), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(g(_x72, g(0, _x41)), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(0, 0), _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(0, _x41)), _x81), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(_x52, g(0, _x41))), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(+(0, 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(0, s(+(0, 0)), X) → f#(X, +(X, X), X)f#(+(0, 0), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(g(0, _x91), _x41))), X) → f#(X, +(X, X), X)f#(0, +(s(0), 0), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(_x52, g(0, _x41)), 0)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x101), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x52, g(0, _x41)), _x61)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(g(_x112, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(+(0, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(+(0, 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x102, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x101), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(_x112, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(_x82, g(0, _x41)))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(g(+(0, 0), _x81), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(_x52, g(0, _x41))), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x131), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x82, g(_x72, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(+(0, 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(0, _x61), _x41)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x41), _x101)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(g(_x132, 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(0, _x41)), _x31), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, +(g(0, _x41), 0))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(+(0, 0), _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x81), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x81)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(0, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x92, g(+(0, 0), _x81)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(_x72, g(0, _x41)), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(_x72, g(0, _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(+(0, 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(g(+(0, 0), _x81), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x82, g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(g(_x92, 0), _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x102, g(_x72, g(0, _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x92, g(g(_x72, g(0, _x41)), _x51)), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(0, _x121)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x91), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(0, g(_x32, s(0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, +(g(0, _x41), 0)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(0, s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(_x122, g(0, _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(_x102, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x92, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(_x122, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), X) → f#(X, +(X, X), X)f#(g(0, _x21), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(0)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(g(0, _x41), _x81))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(g(+(0, 0), _x81), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(g(+(0, 0), _x81), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(0, _x41), 0)), X) → f#(X, +(X, X), X)f#(0, g(s(0), _x31), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(g(_x72, g(0, _x41)), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x41), _x121)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(0, 0)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(0, _x41)), 0), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x62, 0), _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(+(0, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(0), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)

Rewrite Rules

+(X, 0) → X+(X, s(Y)) → s(+(X, Y))
f(0, s(0), X) → f(X, +(X, X), X)g(X, Y) → X
g(X, Y) → Y

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, +

Strategy

The left-hand side of the rule f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X) 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#(g(+(+(g(_x22, 0), 0), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) 
f#(g(+(g(_x22, g(_x82, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) 
f#(+(g(+(g(_x22, 0), 0), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(+(g(_x22, 0), g(0, _x71)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(+(g(_x22, 0), 0), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) 
f#(g(+(g(_x22, +(0, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(g(+(g(_x22, 0), 0), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) 
f#(g(_x42, g(+(g(_x22, 0), 0), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) 
f#(g(+(g(g(_x22, 0), _x61), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(+(g(_x22, 0), 0), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(+(g(_x62, g(_x22, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(+(g(_x22, 0), 0), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) 
f#(g(+(g(_x22, 0), 0), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) 
f#(g(+(g(_x22, 0), g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(+(g(_x22, g(0, _x81)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(g(_x52, +(g(_x22, 0), 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) 
f#(g(+(g(_x22, 0), +(0, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
Thus, the rule f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X) is replaced by the following rules:
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(0, _x81)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, 0), _x61), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x42, g(+(g(_x22, 0), 0), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(+(g(_x22, 0), 0), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x62, g(_x22, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, +(0, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(+(g(_x22, 0), 0), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), g(0, _x71)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, 0), 0), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x82, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, 0), 0), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), +(0, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, +(g(_x22, 0), 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)

Problem 15: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(g(+(g(_x22, 0), 0), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(0, s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(g(+(0, 0), _x81), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(0), 0), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x111), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(g(_x72, g(0, _x41)), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(0, 0), _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(0, _x41)), _x81), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x52, +(g(_x22, 0), 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(_x52, g(0, _x41))), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(+(0, 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, 0), _x61), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(0, s(+(0, 0)), X) → f#(X, +(X, X), X)f#(+(0, 0), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(g(0, _x91), _x41))), X) → f#(X, +(X, X), X)f#(0, +(s(0), 0), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(_x52, g(0, _x41)), 0)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x101), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x52, g(0, _x41)), _x61)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, +(0, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(g(_x112, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x62, g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(+(0, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(+(0, 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x102, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, 0), 0), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x101), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(_x112, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(_x82, g(0, _x41)))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(g(+(0, 0), _x81), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x131), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(_x52, g(0, _x41))), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x82, g(_x72, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x82, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(+(0, 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(0, _x61), _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x41), _x101)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(g(_x132, 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(+(g(_x22, 0), 0), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(0, _x41)), _x31), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, +(g(0, _x41), 0))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(+(g(_x22, 0), 0), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(+(0, 0), _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), g(0, _x71)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x81), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x81)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x92, g(+(0, 0), _x81)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(_x72, g(0, _x41)), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(_x72, g(0, _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(+(0, 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(g(+(0, 0), _x81), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x82, g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(g(_x92, 0), _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x102, g(_x72, g(0, _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x92, g(g(_x72, g(0, _x41)), _x51)), _x61)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(0, _x81)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(0, _x121)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x91), _x61)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x62, g(_x22, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(0, g(_x32, s(0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, +(g(0, _x41), 0)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(0, s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(_x122, g(0, _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(0), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(_x102, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x42, 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, 0), 0), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(_x122, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x92, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), +(0, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(0, _x21), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(0)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(g(0, _x41), _x81))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(g(+(0, 0), _x81), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(+(g(_x22, 0), 0), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(g(+(0, 0), _x81), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(0, _x41), 0)), X) → f#(X, +(X, X), X)
f#(0, g(s(0), _x31), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(g(_x72, g(0, _x41)), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x41), _x121)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(0, 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(0, _x41)), 0), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x62, 0), _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(+(0, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(0), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(0), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)

Rewrite Rules

+(X, 0) → X+(X, s(Y)) → s(+(X, Y))
f(0, s(0), X) → f(X, +(X, X), X)g(X, Y) → X
g(X, Y) → Y

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, +

Strategy

The left-hand side of the rule f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X) 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#(+(g(g(_x22, g(_x72, 0)), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) 
f#(g(g(g(_x22, g(_x72, 0)), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) 
f#(g(g(_x22, +(g(_x72, 0), 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, g(_x102, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(g(g(_x22, g(_x72, 0)), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) 
f#(g(g(_x22, g(g(_x72, 0), _x81)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) 
f#(g(g(_x22, g(_x82, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, +(0, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) 
f#(g(g(_x22, g(_x72, g(0, _x101))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) 
f#(g(_x42, g(g(_x22, g(_x72, 0)), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) 
Thus, the rule f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X) is replaced by the following rules:
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(_x72, 0), 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, g(0, _x101))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, g(_x102, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, g(_x72, 0)), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x82, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(g(_x72, 0), _x81)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, g(_x72, 0)), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, g(_x72, 0)), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, +(0, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, g(_x72, 0)), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)

Problem 16: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(0, s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(g(+(0, 0), _x81), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(0), 0), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x111), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(g(_x72, g(0, _x41)), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(0, 0), _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(0, _x41)), _x81), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, +(0, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x52, +(g(_x22, 0), 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(_x52, g(0, _x41))), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(+(0, 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, 0), _x61), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(0, s(+(0, 0)), X) → f#(X, +(X, X), X)f#(+(0, 0), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(g(0, _x91), _x41))), X) → f#(X, +(X, X), X)f#(0, +(s(0), 0), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(_x52, g(0, _x41)), 0)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x101), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x52, g(0, _x41)), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, +(0, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(g(_x112, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(+(0, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, g(_x72, 0)), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(+(0, 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x102, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, 0), 0), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x101), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(_x112, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(_x82, g(0, _x41)))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x82, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(g(+(0, 0), _x81), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(_x52, g(0, _x41))), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x131), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x82, g(_x72, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x82, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(+(0, 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(0, _x61), _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x41), _x101)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(g(_x132, 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x42, g(+(g(_x22, 0), 0), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(0, _x41)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, +(g(0, _x41), 0))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(+(g(_x22, 0), 0), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(+(0, 0), _x41))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), g(0, _x71)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(g(_x72, 0), _x81)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x81), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x81)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x92, g(+(0, 0), _x81)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, g(_x72, 0)), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(_x72, g(0, _x41)), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(_x72, g(0, _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(+(0, 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(g(+(0, 0), _x81), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x82, g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(g(_x92, 0), _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x102, g(_x72, g(0, _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x92, g(g(_x72, g(0, _x41)), _x51)), _x61)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(0, _x81)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(0, _x121)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(_x72, 0), 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x91), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x62, g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x62, g(_x22, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(0, g(_x32, s(0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, g(_x102, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, +(g(0, _x41), 0)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, g(_x72, 0)), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(0, s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(_x122, g(0, _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(0), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(_x102, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, 0), 0), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x92, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(_x122, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, g(_x72, 0)), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), +(0, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), X) → f#(X, +(X, X), X)
f#(g(0, _x21), s(0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(0)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(g(0, _x41), _x81))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, g(0, _x101))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, 0), 0), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(g(+(0, 0), _x81), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(g(+(0, 0), _x81), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(0, _x41), 0)), X) → f#(X, +(X, X), X)
f#(0, g(s(0), _x31), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(g(_x72, g(0, _x41)), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x41), _x121)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(0, 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(0, _x41)), 0), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x62, 0), _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(+(0, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(0), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)

Rewrite Rules

+(X, 0) → X+(X, s(Y)) → s(+(X, Y))
f(0, s(0), X) → f(X, +(X, X), X)g(X, Y) → X
g(X, Y) → Y

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, +

Strategy

The left-hand side of the rule f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X) 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#(g(g(_x22, g(_x72, g(_x102, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x22, g(g(_x72, 0), _x81)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x71), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(_x112, g(0, _x101))), _x41), _x51)), X) 
f#(g(g(g(_x22, g(_x72, 0)), _x51), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(_x62, g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), g(0, _x101)), 0), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(+(g(+(g(0, _x91), g(0, _x101)), _x41), 0), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(0, _x101), _x111)), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), +(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), 0), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), _x61)), X) 
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), 0), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(+(g(g(_x22, g(_x72, 0)), _x31), 0), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x81), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(_x102, g(0, _x91)), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x91), _x101), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(g(_x22, g(_x72, 0)), _x31), _x41), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x22, +(g(_x72, 0), 0)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) 
f#(g(g(_x22, g(_x72, g(0, _x101))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x82, +(g(0, _x91), g(0, _x101))), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(+(0, 0), _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(_x112, 0), _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x22, g(_x82, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(+(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), 0)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x111), _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(+(0, 0), _x101)), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), g(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), _x31), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(_x122, 0), _x101)), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, +(0, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(_x72, g(+(g(0, _x91), g(0, _x101)), _x41)), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), +(g(0, _x101), 0)), _x41), _x51)), X) 
f#(g(_x42, g(g(_x22, g(_x72, 0)), _x31)), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(0, _x121), _x101)), _x41), _x51)), X) 
Thus, the rule f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X) is replaced by the following rules:
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(+(0, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(_x62, g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x82, +(g(0, _x91), g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x111), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), g(0, _x101)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(+(g(+(g(0, _x91), g(0, _x101)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(+(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(_x122, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, g(_x72, 0)), _x31)), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(0, _x121), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, +(0, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(+(0, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(_x72, 0), 0)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, g(0, _x101))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, g(_x72, 0)), _x31), 0), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(_x112, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(_x112, g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), +(g(0, _x101), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(g(_x72, 0), _x81)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x91), _x101), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), 0), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(0, _x101), _x111)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, g(_x72, 0)), _x51), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(_x72, g(+(g(0, _x91), g(0, _x101)), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(_x102, g(0, _x91)), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, g(_x102, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, g(_x72, 0)), _x31), _x41), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x82, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), +(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), 0), X) → f#(X, +(X, X), X)

Problem 17: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(g(+(g(_x22, 0), 0), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(0, s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(g(+(0, 0), _x81), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(0), 0), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(_x112, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x111), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(g(_x72, g(0, _x41)), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(0, 0), _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(0, _x41)), _x81), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, +(0, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), +(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x52, +(g(_x22, 0), 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(_x52, g(0, _x41))), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(+(0, 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, 0), _x61), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(0, s(+(0, 0)), X) → f#(X, +(X, X), X)f#(+(0, 0), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(g(0, _x91), _x41))), X) → f#(X, +(X, X), X)f#(0, +(s(0), 0), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(_x52, g(0, _x41)), 0)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x101), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x52, g(0, _x41)), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, +(0, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(g(_x112, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(+(0, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, g(_x72, 0)), _x31), 0), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(+(0, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, g(_x72, 0)), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(+(0, 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x102, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, 0), 0), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x101), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(_x112, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(+(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(_x82, g(0, _x41)))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x82, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, g(0, _x101))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(g(+(0, 0), _x81), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), +(g(0, _x101), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(_x52, g(0, _x41))), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x131), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x82, g(_x72, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x82, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, g(_x72, 0)), _x51), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(+(0, 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(_x102, g(0, _x91)), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(0, _x61), _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x82, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x111), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x41), _x101)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(g(_x132, 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x42, g(+(g(_x22, 0), 0), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(0, _x41)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, +(g(0, _x41), 0))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(+(g(_x22, 0), 0), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(+(0, 0), _x41))), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, g(_x72, 0)), _x31)), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), g(0, _x71)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(g(_x72, 0), _x81)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x81), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x81)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x92, g(+(0, 0), _x81)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, g(_x102, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, g(_x72, 0)), _x31), _x41), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, g(_x72, 0)), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(_x72, g(0, _x41)), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(_x72, g(0, _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(+(0, 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(g(+(0, 0), _x81), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x82, g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(g(_x92, 0), _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), 0), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x102, g(_x72, g(0, _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x92, g(g(_x72, g(0, _x41)), _x51)), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(0, _x81)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(_x62, g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(0, _x121)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x82, +(g(0, _x91), g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(_x72, 0), 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(_x122, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x91), _x61)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x62, g(_x22, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(0, g(_x32, s(0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, g(_x102, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, +(g(0, _x41), 0)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, g(_x72, 0)), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(_x72, 0), 0)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(_x112, g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(0, s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(g(_x72, 0), _x81)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(_x122, g(0, _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), g(0, _x101)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(_x102, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(0, _x121), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x42, 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, 0), 0), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(_x122, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x92, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(_x72, g(+(g(0, _x91), g(0, _x101)), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, g(_x72, 0)), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), +(0, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(0, _x21), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(+(0, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(0)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(g(0, _x41), _x81))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(+(g(+(g(0, _x91), g(0, _x101)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, g(0, _x101))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(g(+(0, 0), _x81), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(+(g(_x22, 0), 0), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(g(+(0, 0), _x81), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(0, _x41), 0)), X) → f#(X, +(X, X), X)
f#(0, g(s(0), _x31), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(g(_x72, g(0, _x41)), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, +(0, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x41), _x121)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(0, 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x91), _x101), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(0, _x41)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(0, _x101), _x111)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x62, 0), _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(+(0, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(0), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(0), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)

Rewrite Rules

+(X, 0) → X+(X, s(Y)) → s(+(X, Y))
f(0, s(0), X) → f(X, +(X, X), X)g(X, Y) → X
g(X, Y) → Y

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, +

Strategy

The left-hand side of the rule f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X) 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#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(+(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), 0)), X) 
f#(g(g(_x52, g(_x22, g(_x72, g(0, _x121)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(g(_x52, g(_x22, g(_x72, 0))), _x61), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), g(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), _x31), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(_x62, g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) 
f#(g(g(_x52, g(_x82, g(_x22, g(_x72, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), g(_x32, s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(+(g(+(g(0, _x91), g(0, _x101)), _x41), 0), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(g(0, _x101), _x111)), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(g(_x112, 0), _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(g(0, _x111), _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(_x112, g(0, _x101))), _x41), _x51)), X) 
f#(g(+(g(_x52, g(_x22, g(_x72, 0))), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(g(_x122, 0), _x101)), _x41), _x51)), X) 
f#(g(g(_x62, g(_x52, g(_x22, g(_x72, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(_x82, +(g(0, _x91), g(0, _x101))), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(_x72, g(+(g(0, _x91), g(0, _x101)), _x41)), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(+(0, 0), _x101)), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, +(g(_x72, 0), 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), +(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), 0), X) 
f#(g(g(_x52, +(g(_x22, g(_x72, 0)), 0)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(_x102, g(0, _x91)), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(+(g(0, _x91), g(0, _x101)), 0), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x81), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x72, g(_x122, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, g(g(_x72, 0), _x101))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(_x42, g(g(_x52, g(_x22, g(_x72, 0))), _x31)), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(g(0, _x91), _x101), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x102, g(_x72, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(g(_x52, g(_x22, g(_x72, 0))), _x31), _x41), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(+(g(0, _x91), 0), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(+(0, 0), _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x52, g(g(_x22, g(_x72, 0)), _x81)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x72, +(0, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), _x61)), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(g(0, _x121), _x101)), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x71), _x51)), X) 
f#(+(g(g(_x52, g(_x22, g(_x72, 0))), _x31), 0), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), +(g(0, _x101), 0)), _x41), _x51)), X) 
Thus, the rule f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X) is replaced by the following rules:
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(_x72, g(+(g(0, _x91), g(0, _x101)), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(+(0, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(_x112, g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(_x102, g(0, _x91)), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x52, g(_x22, g(_x72, 0))), _x31)), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(+(g(0, _x91), g(0, _x101)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, g(_x122, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x62, g(_x52, g(_x22, g(_x72, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), +(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(+(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x52, g(_x22, g(_x72, 0))), _x31), _x41), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), g(_x32, s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(_x82, +(g(0, _x91), g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x52, g(_x22, g(_x72, 0))), _x31), 0), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x82, g(_x22, g(_x72, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, +(g(_x22, g(_x72, 0)), 0)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x52, g(_x22, g(_x72, 0))), _x61), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(g(_x22, g(_x72, 0)), _x81)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(g(_x112, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(g(_x122, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(+(0, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(g(0, _x91), _x101), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(g(0, _x111), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x102, g(_x72, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(+(g(0, _x91), 0), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x52, g(_x22, g(_x72, 0))), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(+(g(+(g(0, _x91), g(0, _x101)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, +(g(_x72, 0), 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(_x62, g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(g(_x72, 0), _x101))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), g(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), +(g(0, _x101), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, +(0, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(g(0, _x101), _x111)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(g(0, _x121), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, g(0, _x121)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)

Problem 18: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(g(+(g(_x22, 0), 0), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(0, s(g(_x42, 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(g(+(0, 0), _x81), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(0), 0), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x82, g(_x22, g(_x72, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(g(_x122, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(_x112, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x111), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x102, g(_x72, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(g(_x72, g(0, _x41)), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(0, 0), _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(0, _x41)), _x81), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, +(g(_x72, 0), 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, +(0, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(g(0, _x121), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), +(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x52, +(g(_x22, 0), 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(_x52, g(0, _x41))), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(+(0, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(+(0, 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, 0), _x61), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(0, s(+(0, 0)), X) → f#(X, +(X, X), X)
f#(+(0, 0), s(0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(g(0, _x91), _x41))), X) → f#(X, +(X, X), X)
f#(0, +(s(0), 0), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(_x52, g(0, _x41)), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x101), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x52, g(0, _x41)), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x62, g(_x52, g(_x22, g(_x72, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, +(0, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(g(_x112, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x52, g(_x22, g(_x72, 0))), _x61), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(+(0, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, g(_x72, 0)), _x31), 0), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(+(0, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, g(_x72, 0)), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(+(0, 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x102, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, 0), 0), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x101), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(g(0, _x101), _x111)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(_x72, g(+(g(0, _x91), g(0, _x101)), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(_x112, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(+(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x52, g(_x22, g(_x72, 0))), _x31)), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(_x82, g(0, _x41)))), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, g(_x122, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x82, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, g(0, _x101))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(g(+(0, 0), _x81), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), +(g(0, _x101), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(_x52, g(0, _x41))), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x131), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x82, g(_x72, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x82, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, g(_x72, 0)), _x51), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(+(0, 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(_x102, g(0, _x91)), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(0, _x61), _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x82, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(_x112, g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x111), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x41), _x101)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(g(_x132, 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x42, g(+(g(_x22, 0), 0), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(0, _x41)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, +(g(0, _x41), 0))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(+(g(_x22, 0), 0), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(_x82, +(g(0, _x91), g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(+(0, 0), _x41))), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, g(_x72, 0)), _x31)), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(g(0, _x91), _x101), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), g(0, _x71)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(g(_x72, 0), _x81)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x81), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x81)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(+(g(0, _x91), 0), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x92, g(+(0, 0), _x81)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(_x62, g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, g(_x102, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, g(_x72, 0)), _x31), _x41), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, +(0, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, g(0, _x121)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, g(_x72, 0)), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(_x72, g(0, _x41)), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(_x72, g(0, _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(+(0, 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x52, g(_x22, g(_x72, 0))), _x31), 0), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(g(+(0, 0), _x81), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x82, g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(+(0, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(g(_x92, 0), _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), 0), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x102, g(_x72, g(0, _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), g(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x92, g(g(_x72, g(0, _x41)), _x51)), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(0, _x81)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(_x62, g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x82, +(g(0, _x91), g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(0, _x121)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(_x122, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(_x72, 0), 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x91), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x62, g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), +(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(+(g(_x62, g(_x22, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(+(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x52, g(_x22, g(_x72, 0))), _x31), _x41), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(0, g(_x32, s(0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, g(_x102, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, +(g(0, _x41), 0)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, +(g(_x22, g(_x72, 0)), 0)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, g(_x72, 0)), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(g(_x22, g(_x72, 0)), _x81)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(g(_x112, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(_x72, 0), 0)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(_x112, g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(0, s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(g(_x72, 0), _x81)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(_x122, g(0, _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), g(0, _x101)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(_x102, g(0, _x91)), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(+(g(0, _x91), g(0, _x101)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(_x102, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(0, _x121), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x42, 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(g(0, _x111), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, 0), 0), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x52, g(_x22, g(_x72, 0))), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x92, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(_x122, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(+(g(+(g(0, _x91), g(0, _x101)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(_x72, g(+(g(0, _x91), g(0, _x101)), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(g(_x72, 0), _x101))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, g(_x72, 0)), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), +(0, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), X) → f#(X, +(X, X), X)
f#(g(0, _x21), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(+(0, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(0)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(+(g(+(g(0, _x91), g(0, _x101)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(g(0, _x41), _x81))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, g(0, _x101))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, 0), 0), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(g(+(0, 0), _x81), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(g(+(0, 0), _x81), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(0, _x41), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), g(_x32, s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)f#(0, g(s(0), _x31), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(g(_x72, g(0, _x41)), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, +(0, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x41), _x121)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(0, 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x91), _x101), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(0, _x41)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(0, _x101), _x111)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x62, 0), _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(+(0, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(0), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), +(g(0, _x101), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(0), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)

Rewrite Rules

+(X, 0) → X+(X, s(Y)) → s(+(X, Y))
f(0, s(0), X) → f(X, +(X, X), X)g(X, Y) → X
g(X, Y) → Y

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, +

Strategy

The left-hand side of the rule f#(g(_x22, 0), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X) 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#(g(_x22, 0), g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), _x81), X) 
f#(g(_x22, 0), g(s(g(_x102, g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31), X) 
f#(g(_x22, 0), g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x101)), _x31), X) 
f#(g(_x22, 0), g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x111), _x61)), _x31), X) 
f#(g(_x22, 0), g(s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), _x31), X) 
f#(g(_x22, 0), g(s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), _x31), X) 
f#(g(g(_x22, 0), _x31), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) 
f#(g(_x22, 0), g(s(g(g(_x112, g(g(_x72, g(0, _x41)), _x51)), _x61)), _x31), X) 
f#(g(_x22, +(0, 0)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) 
f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) 
f#(g(_x22, 0), g(s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), _x31), X) 
f#(g(_x22, 0), g(s(g(g(g(_x72, g(g(0, _x41), _x141)), _x51), _x61)), _x31), X) 
f#(g(_x22, 0), g(s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), _x31), X) 
f#(g(_x22, 0), g(s(g(g(g(_x72, g(g(0, _x151), _x41)), _x51), _x61)), _x31), X) 
f#(g(_x22, 0), g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x91), _x31), X) 
f#(g(_x22, 0), g(s(g(g(g(_x72, g(g(_x152, 0), _x41)), _x51), _x61)), _x31), X) 
f#(g(_x22, 0), g(+(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), _x31), X) 
f#(g(_x22, 0), g(s(g(g(g(_x122, g(_x72, g(0, _x41))), _x51), _x61)), _x31), X) 
f#(g(_x22, 0), +(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), 0), X) 
f#(g(_x22, g(0, _x51)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) 
f#(g(_x32, g(_x22, 0)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) 
f#(g(_x22, 0), g(s(g(g(g(g(_x72, g(0, _x41)), _x121), _x51), _x61)), _x31), X) 
f#(g(_x22, 0), g(g(_x92, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31), X) 
f#(g(_x22, 0), g(s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), _x31), X) 
f#(g(_x22, g(_x52, 0)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) 
f#(g(_x22, 0), g(s(g(g(g(_x72, g(_x142, g(0, _x41))), _x51), _x61)), _x31), X) 
f#(+(g(_x22, 0), 0), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) 
Thus, the rule f#(g(_x22, 0), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X) is replaced by the following rules:
f#(g(_x22, 0), g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), _x81), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(_x102, g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, g(g(_x152, 0), _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x111), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(_x112, g(g(_x72, g(0, _x41)), _x51)), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x91), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(+(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, g(_x142, g(0, _x41))), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(_x72, g(g(0, _x41), _x141)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, g(g(0, _x151), _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(_x122, g(_x72, g(0, _x41))), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(g(_x92, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), 0), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(g(_x72, g(0, _x41)), _x121), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x101)), _x31), X) → f#(X, +(X, X), X)

Problem 19: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(0, s(g(_x42, 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(g(+(0, 0), _x81), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(0), 0), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x82, g(_x22, g(_x72, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(g(_x122, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(_x112, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x111), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x102, g(_x72, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(g(_x72, g(0, _x41)), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(0, 0), _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(0, _x41)), _x81), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, +(g(_x72, 0), 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, +(0, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(g(0, _x121), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), +(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x52, +(g(_x22, 0), 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(_x52, g(0, _x41))), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(+(0, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(+(0, 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, g(g(_x152, 0), _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, 0), _x61), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(0, s(+(0, 0)), X) → f#(X, +(X, X), X)f#(+(0, 0), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(g(0, _x91), _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x111), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(0, +(s(0), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(_x52, g(0, _x41)), 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x101), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x52, g(0, _x41)), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x62, g(_x52, g(_x22, g(_x72, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(+(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, +(0, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(g(_x112, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, g(g(0, _x151), _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(g(_x52, g(_x22, g(_x72, 0))), _x61), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(+(0, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, g(_x72, 0)), _x31), 0), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x62, g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(+(0, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, g(_x72, 0)), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(+(0, 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x102, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(+(g(_x22, 0), 0), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x101), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(g(0, _x101), _x111)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(_x72, g(+(g(0, _x91), g(0, _x101)), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(_x112, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(+(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x52, g(_x22, g(_x72, 0))), _x31)), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(_x82, g(0, _x41)))), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, g(_x122, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x82, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, g(0, _x101))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(g(+(0, 0), _x81), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), +(g(0, _x101), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(g(_x92, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(_x52, g(0, _x41))), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x131), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x82, g(_x72, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x82, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, g(_x72, 0)), _x51), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(+(0, 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(_x102, g(0, _x91)), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(0, _x61), _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x101)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x82, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(_x112, g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x111), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x41), _x101)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(g(_x132, 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x42, g(+(g(_x22, 0), 0), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(0, _x41)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, +(g(0, _x41), 0))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(+(g(_x22, 0), 0), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(_x82, +(g(0, _x91), g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(+(0, 0), _x41))), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, g(_x72, 0)), _x31)), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(g(0, _x91), _x101), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), g(0, _x71)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(g(_x72, 0), _x81)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x81), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x81)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(+(g(0, _x91), 0), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x92, g(+(0, 0), _x81)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(_x62, g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, g(_x102, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, g(_x72, 0)), _x31), _x41), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, +(0, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, g(_x72, 0)), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, g(0, _x121)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(_x102, g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(_x72, g(0, _x41)), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(_x72, g(0, _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(+(0, 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x52, g(_x22, g(_x72, 0))), _x31), 0), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(g(+(0, 0), _x81), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x82, g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(+(0, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(g(_x92, 0), _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), 0), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x102, g(_x72, g(0, _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(g(_x72, g(0, _x41)), _x121), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), g(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x92, g(g(_x72, g(0, _x41)), _x51)), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(0, _x81)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(_x62, g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(0, _x121)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x82, +(g(0, _x91), g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(_x72, 0), 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(_x122, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(_x112, g(g(_x72, g(0, _x41)), _x51)), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x62, g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x91), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), +(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x62, g(_x22, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x52, g(_x22, g(_x72, 0))), _x31), _x41), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(+(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(0, g(_x32, s(0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, g(_x102, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, +(g(_x22, g(_x72, 0)), 0)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, +(g(0, _x41), 0)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, g(_x72, 0)), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(g(_x22, g(_x72, 0)), _x81)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(g(_x112, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(_x72, 0), 0)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(_x112, g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(0, s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(g(_x72, 0), _x81)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(_x122, g(0, _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), _x81), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(0), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), g(0, _x101)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(_x102, g(0, _x91)), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(+(g(0, _x91), g(0, _x101)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x91), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, g(_x142, g(0, _x41))), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(_x102, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(_x122, g(_x72, g(0, _x41))), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(0, _x121), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(g(0, _x111), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, 0), 0), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x52, g(_x22, g(_x72, 0))), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(0), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(+(g(+(g(0, _x91), g(0, _x101)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(_x122, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x92, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(_x72, g(+(g(0, _x91), g(0, _x101)), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(g(_x72, 0), _x101))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, g(_x72, 0)), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), +(0, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(0, _x21), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(+(0, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(0)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(g(0, _x41), _x81))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(+(g(+(g(0, _x91), g(0, _x101)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, g(0, _x101))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(g(+(0, 0), _x81), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(+(g(_x22, 0), 0), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(g(+(0, 0), _x81), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(0, _x41), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), g(_x32, s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)f#(0, g(s(0), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, g(g(0, _x41), _x141)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(g(_x72, g(0, _x41)), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, +(0, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x41), _x121)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(0, 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x91), _x101), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(0, _x41)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(0, _x101), _x111)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x62, 0), _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(+(0, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(0), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), +(g(0, _x101), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(0), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)

Rewrite Rules

+(X, 0) → X+(X, s(Y)) → s(+(X, Y))
f(0, s(0), X) → f(X, +(X, X), X)g(X, Y) → X
g(X, Y) → Y

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, +

Strategy

The left-hand side of the rule f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X) 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#(g(_x22, 0), +(g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), 0), X) 
f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(g(_x182, 0), _x41)), _x51), _x61)), _x31)), X) 
f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), _x31)), X) 
f#(g(_x32, g(_x22, 0)), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) 
f#(g(g(_x22, 0), _x31), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) 
f#(g(_x22, 0), g(_x82, g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), _x111)), X) 
f#(g(_x22, 0), g(_x82, g(s(g(_x132, g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31)), X) 
f#(g(_x22, 0), g(_x82, g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x121), _x31)), X) 
f#(g(_x22, +(0, 0)), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) 
f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), _x31)), X) 
f#(g(_x22, g(_x52, 0)), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) 
f#(+(g(_x22, 0), 0), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) 
f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(g(0, _x181), _x41)), _x51), _x61)), _x31)), X) 
f#(g(_x22, 0), g(_x82, +(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), 0)), X) 
f#(g(_x22, 0), g(_x82, g(s(g(g(g(g(_x72, g(0, _x41)), _x151), _x51), _x61)), _x31)), X) 
f#(g(_x22, 0), g(_x82, g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x141), _x61)), _x31)), X) 
f#(g(_x22, 0), g(_x82, g(+(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), _x31)), X) 
f#(g(_x22, 0), g(_x82, g(s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), _x31)), X) 
f#(g(_x22, 0), g(g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), _x91), X) 
f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(g(0, _x41), _x171)), _x51), _x61)), _x31)), X) 
f#(g(_x22, 0), g(_x92, g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31))), X) 
f#(g(_x22, 0), g(_x82, g(s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), _x31)), X) 
f#(g(_x22, g(0, _x51)), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) 
f#(g(_x22, 0), g(_x82, g(s(g(g(_x142, g(g(_x72, g(0, _x41)), _x51)), _x61)), _x31)), X) 
f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x152, g(_x72, g(0, _x41))), _x51), _x61)), _x31)), X) 
f#(g(_x22, 0), g(_x82, g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x131)), _x31)), X) 
f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(_x172, g(0, _x41))), _x51), _x61)), _x31)), X) 
f#(g(_x22, 0), g(_x82, g(s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), _x31)), X) 
f#(g(_x22, 0), g(_x82, g(g(_x122, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31)), X) 
f#(g(_x22, 0), g(_x82, g(_x112, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31))), X) 
Thus, the rule f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X) is replaced by the following rules:
f#(g(_x22, 0), g(_x82, g(s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x152, g(_x72, g(0, _x41))), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(_x142, g(g(_x72, g(0, _x41)), _x51)), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), _x31)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(_x172, g(0, _x41))), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(g(_x72, g(0, _x41)), _x151), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x121), _x31)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(+(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), _x31)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, +(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), _x91), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x131)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x141), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), _x111)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(_x132, g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(_x112, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(g(_x122, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), 0), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(g(0, _x41), _x171)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(g(0, _x181), _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(g(_x182, 0), _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x92, g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31))), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)

Problem 20: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(g(+(g(_x22, 0), 0), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(0, s(g(_x42, 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x121), _x31)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x111), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x102, g(_x72, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, +(g(_x72, 0), 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(_x52, g(0, _x41))), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(+(0, 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(_x72, g(g(_x152, 0), _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, 0), _x61), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x111), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(_x52, g(0, _x41)), 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x52, g(0, _x41)), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x62, g(_x52, g(_x22, g(_x72, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, +(0, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, g(g(0, _x151), _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, g(_x72, 0)), _x31), 0), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x62, g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(+(0, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, g(_x72, 0)), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(+(0, 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x102, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(+(g(_x22, 0), 0), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x152, g(_x72, g(0, _x41))), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(_x112, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(+(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x52, g(_x22, g(_x72, 0))), _x31)), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(_x82, g(0, _x41)))), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, g(_x122, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x141), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x82, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(g(+(0, 0), _x81), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), +(g(0, _x101), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(g(_x92, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, g(_x72, 0)), _x51), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(0, _x61), _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(_x102, g(0, _x91)), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(_x112, g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(_x42, g(+(g(_x22, 0), 0), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(0, _x41)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(_x82, +(g(0, _x91), g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(+(0, 0), _x41))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), g(0, _x71)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x81)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x92, g(+(0, 0), _x81)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(_x62, g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, g(_x102, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, g(_x72, 0)), _x31), _x41), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, +(0, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, g(0, _x121)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, g(_x72, 0)), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(_x102, g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(g(_x72, g(0, _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x52, g(_x22, g(_x72, 0))), _x31), 0), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(g(+(0, 0), _x81), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x82, g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(g(_x92, 0), _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(g(_x122, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x102, g(_x72, g(0, _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(g(0, _x41), _x171)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(g(_x72, g(0, _x41)), _x121), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), g(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(0, _x81)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(_x62, g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(0, _x121)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(_x122, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(_x112, g(g(_x72, g(0, _x41)), _x51)), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x62, g(_x22, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x52, g(_x22, g(_x72, 0))), _x31), _x41), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, +(g(0, _x41), 0)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, g(_x72, 0)), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(g(_x22, g(_x72, 0)), _x81)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(g(_x112, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(_x72, 0), 0)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(_x112, g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(g(_x72, 0), _x81)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), _x81), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x91), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, g(_x142, g(0, _x41))), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(_x102, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(+(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), _x31)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(_x72, g(+(g(0, _x91), g(0, _x101)), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(g(_x72, 0), _x101))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), +(0, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(+(g(+(g(0, _x91), g(0, _x101)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, g(0, _x101))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, 0), 0), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(0, _x41), 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, g(g(0, _x41), _x141)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(g(_x72, g(0, _x41)), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, +(0, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(0, 0)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(0, _x101), _x111)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(+(0, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), +(g(0, _x101), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(g(+(0, 0), _x81), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(0), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x82, g(_x22, g(_x72, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(g(_x122, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(_x112, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(_x132, g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(g(_x72, g(0, _x41)), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(0, 0), _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(0, _x41)), _x81), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, +(0, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(g(0, _x121), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, +(g(_x22, 0), 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), +(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(+(0, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(g(0, _x91), _x41))), X) → f#(X, +(X, X), X)f#(+(0, 0), s(0), X) → f#(X, +(X, X), X)
f#(0, s(+(0, 0)), X) → f#(X, +(X, X), X)f#(0, +(s(0), 0), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x101), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(+(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(g(_x112, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x52, g(_x22, g(_x72, 0))), _x61), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(+(0, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x101), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(g(0, _x101), _x111)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(_x72, g(+(g(0, _x91), g(0, _x101)), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, +(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, g(0, _x101))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x131), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(_x52, g(0, _x41))), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x82, g(_x72, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x82, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(g(0, _x181), _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(+(0, 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x101)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x82, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x111), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(g(_x132, 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x41), _x101)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, +(g(0, _x41), 0))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(g(g(_x72, g(0, _x41)), _x151), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(+(+(g(_x22, 0), 0), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, g(_x72, 0)), _x31)), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(g(0, _x91), _x101), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(g(_x72, 0), _x81)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(_x112, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x81), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(0, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(+(g(0, _x91), 0), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(_x72, g(0, _x41)), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(+(0, 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(+(0, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), _x111)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), 0), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(g(_x182, 0), _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x92, g(g(_x72, g(0, _x41)), _x51)), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x82, +(g(0, _x91), g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(_x72, 0), 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x91), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), +(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(_x172, g(0, _x41))), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(+(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(0, g(_x32, s(0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, g(_x102, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, +(g(_x22, g(_x72, 0)), 0)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), _x91), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(0, s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x92, g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31))), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(_x122, g(0, _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), g(0, _x101)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(_x102, g(0, _x91)), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(+(g(0, _x91), g(0, _x101)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(_x122, g(_x72, g(0, _x41))), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(0, _x121), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x131)), _x31)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(g(0, _x111), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, 0), 0), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x52, g(_x22, g(_x72, 0))), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x92, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(_x122, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(+(g(+(g(0, _x91), g(0, _x101)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, g(_x72, 0)), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), X) → f#(X, +(X, X), X)
f#(g(0, _x21), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(+(0, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(_x142, g(g(_x72, g(0, _x41)), _x51)), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(g(0, _x41), _x81))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(g(+(0, 0), _x81), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(g(+(0, 0), _x81), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), g(_x32, s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(0, g(s(0), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x41), _x121)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x91), _x101), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(0, _x41)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x62, 0), _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(0), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)

Rewrite Rules

+(X, 0) → X+(X, s(Y)) → s(+(X, Y))
f(0, s(0), X) → f(X, +(X, X), X)g(X, Y) → X
g(X, Y) → Y

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, +

Strategy

The left-hand side of the rule f#(0, s(g(_x42, 0)), X) → f#(X, +(X, X), X) 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#(0, s(g(_x52, g(_x42, 0))), X) 
f#(0, s(+(g(_x42, 0), 0)), X) 
f#(0, g(_x32, s(g(_x42, 0))), X) 
f#(+(0, 0), s(g(_x42, 0)), X) 
f#(g(_x22, 0), s(g(_x42, 0)), X) 
f#(0, s(g(_x42, g(_x72, 0))), X) 
f#(g(0, _x21), s(g(_x42, 0)), X) 
f#(0, s(g(_x42, +(0, 0))), X) 
f#(0, +(s(g(_x42, 0)), 0), X) 
f#(0, s(g(_x42, g(0, _x71))), X) 
f#(0, g(s(g(_x42, 0)), _x31), X) 
f#(0, s(g(g(_x42, 0), _x51)), X) 
Thus, the rule f#(0, s(g(_x42, 0)), X) → f#(X, +(X, X), X) is replaced by the following rules:
f#(0, +(s(g(_x42, 0)), 0), X) → f#(X, +(X, X), X)f#(g(0, _x21), s(g(_x42, 0)), X) → f#(X, +(X, X), X)
f#(0, s(g(g(_x42, 0), _x51)), X) → f#(X, +(X, X), X)f#(0, g(_x32, s(g(_x42, 0))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(0, s(g(_x42, g(_x72, 0))), X) → f#(X, +(X, X), X)
f#(+(0, 0), s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(0, s(g(_x42, g(0, _x71))), X) → f#(X, +(X, X), X)
f#(0, s(g(_x42, +(0, 0))), X) → f#(X, +(X, X), X)f#(0, s(g(_x52, g(_x42, 0))), X) → f#(X, +(X, X), X)
f#(0, g(s(g(_x42, 0)), _x31), X) → f#(X, +(X, X), X)f#(0, s(+(g(_x42, 0), 0)), X) → f#(X, +(X, X), X)

Problem 21: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(g(+(g(_x22, 0), 0), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x121), _x31)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x111), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x102, g(_x72, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, +(g(_x72, 0), 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(_x52, g(0, _x41))), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(+(0, 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, g(g(_x152, 0), _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, 0), _x61), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x111), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(_x52, g(0, _x41)), 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), _x31)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x52, g(0, _x41)), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x62, g(_x52, g(_x22, g(_x72, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, +(0, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(_x72, g(g(0, _x151), _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, g(_x72, 0)), _x31), 0), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(+(0, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, g(_x72, 0)), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(+(0, 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x102, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, 0), 0), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x152, g(_x72, g(0, _x41))), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(_x112, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x52, g(_x22, g(_x72, 0))), _x31)), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(+(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(_x82, g(0, _x41)))), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, g(_x122, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(0, s(+(g(_x42, 0), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x141), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x82, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(g(+(0, 0), _x81), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), +(g(0, _x101), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(g(_x92, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, g(_x72, 0)), _x51), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(0, _x61), _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(_x102, g(0, _x91)), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(_x112, g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(_x42, g(+(g(_x22, 0), 0), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(0, _x41)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(_x82, +(g(0, _x91), g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(+(0, 0), _x41))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), g(0, _x71)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x81)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x92, g(+(0, 0), _x81)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(_x62, g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, g(_x102, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, g(_x72, 0)), _x31), _x41), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(0, 0), s(g(_x42, 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, +(0, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, g(0, _x121)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, g(_x72, 0)), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(_x102, g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(_x72, g(0, _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x52, g(_x22, g(_x72, 0))), _x31), 0), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(0, s(g(_x42, g(_x72, 0))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(g(+(0, 0), _x81), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x82, g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(g(_x92, 0), _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(g(_x122, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(g(0, _x41), _x171)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x102, g(_x72, g(0, _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(g(_x72, g(0, _x41)), _x121), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), g(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(0, _x81)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(_x62, g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(0, _x121)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(_x122, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(_x112, g(g(_x72, g(0, _x41)), _x51)), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x62, g(_x22, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x52, g(_x22, g(_x72, 0))), _x31), _x41), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, +(g(0, _x41), 0)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, g(_x72, 0)), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(g(_x22, g(_x72, 0)), _x81)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(g(_x112, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(_x72, 0), 0)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(_x112, g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(g(_x72, 0), _x81)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), _x81), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(0), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x91), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, g(_x142, g(0, _x41))), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(_x102, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(+(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), _x31)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(_x72, g(+(g(0, _x91), g(0, _x101)), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(g(_x72, 0), _x101))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), +(0, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(+(g(+(g(0, _x91), g(0, _x101)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, g(0, _x101))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, 0), 0), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(0, _x41), 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, g(g(0, _x41), _x141)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(g(_x72, g(0, _x41)), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, +(0, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(0, _x21), s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(0, 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(0, _x101), _x111)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(+(0, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), +(g(0, _x101), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(g(+(0, 0), _x81), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(0), 0), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x82, g(_x22, g(_x72, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(g(_x122, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(_x112, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(0, g(_x32, s(g(_x42, 0))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(_x132, g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(g(_x72, g(0, _x41)), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(0, 0), _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(0, _x41)), _x81), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, +(0, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(g(0, _x121), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, +(g(_x22, 0), 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), +(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(+(0, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(g(0, _x91), _x41))), X) → f#(X, +(X, X), X)f#(+(0, 0), s(0), X) → f#(X, +(X, X), X)
f#(0, s(+(0, 0)), X) → f#(X, +(X, X), X)f#(0, +(s(0), 0), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x101), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(+(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(g(_x112, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x52, g(_x22, g(_x72, 0))), _x61), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)
f#(0, s(g(_x52, g(_x42, 0))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(0, +(s(g(_x42, 0)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(+(0, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x101), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(g(0, _x101), _x111)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(_x72, g(+(g(0, _x91), g(0, _x101)), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, +(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, g(0, _x101))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(0, s(g(_x42, g(0, _x71))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x131), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(_x52, g(0, _x41))), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x82, g(_x72, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x82, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(g(0, _x181), _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(+(0, 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x101)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x82, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x111), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(g(_x132, 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x41), _x101)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, +(g(0, _x41), 0))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(g(_x72, g(0, _x41)), _x151), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(+(+(g(_x22, 0), 0), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, g(_x72, 0)), _x31)), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(g(0, _x91), _x101), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(g(_x72, 0), _x81)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(_x112, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x81), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(+(g(0, _x91), 0), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(_x72, g(0, _x41)), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(+(0, 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(+(0, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), _x111)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), 0), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(g(_x182, 0), _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x92, g(g(_x72, g(0, _x41)), _x51)), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x82, +(g(0, _x91), g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(_x72, 0), 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x91), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x62, g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), +(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(_x172, g(0, _x41))), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(+(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(0, g(_x32, s(0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, g(_x102, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, +(g(_x22, g(_x72, 0)), 0)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), _x91), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(0, s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x92, g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31))), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(_x122, g(0, _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), g(0, _x101)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(_x102, g(0, _x91)), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(+(g(0, _x91), g(0, _x101)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x122, g(_x72, g(0, _x41))), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(0, _x121), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x131)), _x31)), X) → f#(X, +(X, X), X)
f#(0, s(g(g(_x42, 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(g(0, _x111), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, 0), 0), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(0, s(g(_x42, +(0, 0))), X) → f#(X, +(X, X), X)f#(g(+(g(_x52, g(_x22, g(_x72, 0))), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(+(g(+(g(0, _x91), g(0, _x101)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(_x122, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x92, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, g(_x72, 0)), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), X) → f#(X, +(X, X), X)f#(g(0, _x21), s(0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(+(0, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(_x142, g(g(_x72, g(0, _x41)), _x51)), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(g(0, _x41), _x81))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(g(+(0, 0), _x81), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(g(+(0, 0), _x81), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), g(_x32, s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)f#(0, g(s(0), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x41), _x121)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x91), _x101), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(0, _x41)), 0), X) → f#(X, +(X, X), X)f#(0, g(s(g(_x42, 0)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x62, 0), _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(0), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)

Rewrite Rules

+(X, 0) → X+(X, s(Y)) → s(+(X, Y))
f(0, s(0), X) → f(X, +(X, X), X)g(X, Y) → X
g(X, Y) → Y

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, +

Strategy

The left-hand side of the rule f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X) 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#(g(g(_x22, 0), _x31), s(g(g(g(_x82, g(+(0, 0), _x111)), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x82, +(0, 0)), _x91), _x41), _x51)), X) 
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(g(_x122, 0), 0)), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(g(_x82, +(0, 0)), _x41)), _x51)), X) 
f#(g(g(_x22, 0), _x31), g(s(g(g(g(_x82, +(0, 0)), _x41), _x51)), _x31), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(g(0, _x121), 0)), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, +(0, 0))), _x41), _x51)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, g(_x132, 0))), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(g(_x82, +(0, 0)), _x41), _x51))), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, g(_x112, +(0, 0))), _x41), _x51)), X) 
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x82, +(0, 0)), _x41), _x71), _x51)), X) 
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x82, +(0, 0)), 0), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), +(s(g(g(g(_x82, +(0, 0)), _x41), _x51)), 0), X) 
f#(g(g(_x22, 0), _x31), s(+(g(g(g(_x82, +(0, 0)), _x41), _x51), 0)), X) 
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(+(g(g(_x82, +(0, 0)), _x41), 0), _x51)), X) 
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, g(0, _x131))), _x41), _x51)), X) 
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) 
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x82, +(0, 0)), _x41), _x51), _x61)), X) 
f#(g(g(_x22, 0), _x31), s(g(g(g(_x92, g(_x82, +(0, 0))), _x41), _x51)), X) 
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(g(_x82, +(0, 0)), _x41), _x51))), X) 
Thus, the rule f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X) is replaced by the following rules:
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, g(+(0, 0), _x111)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(g(0, _x121), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(g(_x82, +(0, 0)), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(g(_x82, +(0, 0)), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(g(_x82, +(0, 0)), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x82, +(0, 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x82, +(0, 0)), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(g(_x122, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, +(0, 0))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(g(_x82, +(0, 0)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, g(_x132, 0))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(g(_x82, +(0, 0)), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x82, +(0, 0)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, g(_x112, +(0, 0))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(g(_x82, +(0, 0)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x92, g(_x82, +(0, 0))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(g(_x82, +(0, 0)), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x82, +(0, 0)), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, g(0, _x131))), _x41), _x51)), X) → f#(X, +(X, X), X)

Problem 22: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(g(+(g(_x22, 0), 0), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x121), _x31)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x111), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x102, g(_x72, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, +(g(_x72, 0), 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(_x52, g(0, _x41))), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(+(0, 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, g(g(_x152, 0), _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, 0), _x61), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x111), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(_x52, g(0, _x41)), 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), _x31)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x52, g(0, _x41)), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(g(_x82, +(0, 0)), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x62, g(_x52, g(_x22, g(_x72, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, +(0, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(_x72, g(g(0, _x151), _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, +(0, 0))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, g(_x72, 0)), _x31), 0), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x62, g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x82, +(0, 0)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(+(0, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, g(_x72, 0)), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(+(0, 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x102, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, 0), 0), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x152, g(_x72, g(0, _x41))), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(_x112, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(+(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x52, g(_x22, g(_x72, 0))), _x31)), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(_x82, g(0, _x41)))), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, g(_x122, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(0, s(+(g(_x42, 0), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x141), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x82, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(g(+(0, 0), _x81), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), +(g(0, _x101), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(g(_x92, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, g(_x72, 0)), _x51), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(0, _x61), _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(_x102, g(0, _x91)), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, g(+(0, 0), _x111)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(_x112, g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(_x42, g(+(g(_x22, 0), 0), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(0, _x41)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(_x82, +(g(0, _x91), g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(+(0, 0), _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), g(0, _x71)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x81)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x92, g(+(0, 0), _x81)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(_x62, g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, g(_x102, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, g(_x72, 0)), _x31), _x41), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(0, 0), s(g(_x42, 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, +(0, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, g(_x72, 0)), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, g(0, _x121)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(_x102, g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(_x72, g(0, _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(0, s(g(_x42, g(_x72, 0))), X) → f#(X, +(X, X), X)f#(+(g(g(_x52, g(_x22, g(_x72, 0))), _x31), 0), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(g(+(0, 0), _x81), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x82, g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(g(_x92, 0), _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(g(_x122, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, g(_x112, +(0, 0))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x102, g(_x72, g(0, _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(g(0, _x41), _x171)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(g(_x72, g(0, _x41)), _x121), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x82, +(0, 0)), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), g(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(0, _x81)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(_x62, g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(0, _x121)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(_x122, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(_x112, g(g(_x72, g(0, _x41)), _x51)), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x62, g(_x22, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x52, g(_x22, g(_x72, 0))), _x31), _x41), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, +(g(0, _x41), 0)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, g(_x72, 0)), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(g(_x22, g(_x72, 0)), _x81)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(g(_x112, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(_x72, 0), 0)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(_x112, g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(g(_x72, 0), _x81)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, g(0, _x131))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), _x81), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(g(0, _x121), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x91), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, g(_x142, g(0, _x41))), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(_x102, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x82, +(0, 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(+(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(_x72, g(+(g(0, _x91), g(0, _x101)), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(g(_x72, 0), _x101))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), +(0, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(+(g(+(g(0, _x91), g(0, _x101)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, g(0, _x101))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(+(g(_x22, 0), 0), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(0, _x41), 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(_x72, g(g(0, _x41), _x141)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(g(_x72, g(0, _x41)), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(g(_x82, +(0, 0)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, +(0, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(0, _x21), s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(0, 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(0, _x101), _x111)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(+(0, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), +(g(0, _x101), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(g(_x82, +(0, 0)), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(g(+(0, 0), _x81), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(0), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x82, +(0, 0)), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x82, g(_x22, g(_x72, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(g(_x122, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(g(_x122, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(_x112, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(0, g(_x32, s(g(_x42, 0))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(_x132, g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(g(_x72, g(0, _x41)), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(0, 0), _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(0, _x41)), _x81), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, +(0, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(g(0, _x121), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, +(g(_x22, 0), 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), +(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(+(0, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(g(0, _x91), _x41))), X) → f#(X, +(X, X), X)f#(+(0, 0), s(0), X) → f#(X, +(X, X), X)
f#(0, s(+(0, 0)), X) → f#(X, +(X, X), X)f#(0, +(s(0), 0), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x101), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(+(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(g(_x112, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x52, g(_x22, g(_x72, 0))), _x61), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)f#(0, s(g(_x52, g(_x42, 0))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, g(_x132, 0))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(0, +(s(g(_x42, 0)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(+(0, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(g(_x82, +(0, 0)), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x101), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(g(0, _x101), _x111)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(_x72, g(+(g(0, _x91), g(0, _x101)), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, +(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, g(0, _x101))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(0, s(g(_x42, g(0, _x71))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x131), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(_x52, g(0, _x41))), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x82, g(_x72, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x82, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(g(0, _x181), _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(+(0, 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x101)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x82, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x111), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(g(_x132, 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x41), _x101)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, +(g(0, _x41), 0))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(g(_x72, g(0, _x41)), _x151), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(+(+(g(_x22, 0), 0), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, g(_x72, 0)), _x31)), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(g(0, _x91), _x101), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(g(_x72, 0), _x81)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(_x112, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x81), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(+(g(0, _x91), 0), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(_x72, g(0, _x41)), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(+(0, 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(+(0, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), _x111)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(g(_x82, +(0, 0)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), 0), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(g(_x182, 0), _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x92, g(g(_x72, g(0, _x41)), _x51)), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x82, +(g(0, _x91), g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(_x72, 0), 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x91), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), +(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(_x172, g(0, _x41))), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(+(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(0, g(_x32, s(0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, g(_x102, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, +(g(_x22, g(_x72, 0)), 0)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), _x91), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(0, s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x92, g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31))), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(_x122, g(0, _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), g(0, _x101)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(_x102, g(0, _x91)), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(+(g(0, _x91), g(0, _x101)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(g(_x82, +(0, 0)), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(_x122, g(_x72, g(0, _x41))), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(0, _x121), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x131)), _x31)), X) → f#(X, +(X, X), X)f#(0, s(g(g(_x42, 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x42, 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(g(0, _x111), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, 0), 0), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x92, g(_x82, +(0, 0))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(0, s(g(_x42, +(0, 0))), X) → f#(X, +(X, X), X)f#(g(+(g(_x52, g(_x22, g(_x72, 0))), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x92, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(_x122, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(+(g(+(g(0, _x91), g(0, _x101)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, g(_x72, 0)), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), X) → f#(X, +(X, X), X)f#(g(0, _x21), s(0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(+(0, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(_x142, g(g(_x72, g(0, _x41)), _x51)), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(g(0, _x41), _x81))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(g(+(0, 0), _x81), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(g(+(0, 0), _x81), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), g(_x32, s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)f#(0, g(s(0), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x41), _x121)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x91), _x101), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(0, _x41)), 0), X) → f#(X, +(X, X), X)f#(0, g(s(g(_x42, 0)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(g(_x82, +(0, 0)), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x62, 0), _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(0), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)

Rewrite Rules

+(X, 0) → X+(X, s(Y)) → s(+(X, Y))
f(0, s(0), X) → f(X, +(X, X), X)g(X, Y) → X
g(X, Y) → Y

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, +

Strategy

The left-hand side of the rule f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X) 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#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x71), _x51)), X) 
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(g(_x102, +(0, 0)), _x81), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(+(g(g(+(0, 0), _x81), _x41), 0), _x51)), X) 
f#(+(g(g(_x22, g(_x72, 0)), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, g(_x122, 0)), _x81), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x92, g(+(0, 0), _x81)), _x41), _x51)), X) 
f#(g(g(_x22, g(g(_x72, 0), _x81)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(+(0, 0), _x81), 0), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(+(0, 0), 0), _x81), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(_x72, g(g(+(0, 0), _x81), _x41)), _x51)), X) 
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, +(0, 0)), _x81), _x41), _x51)), X) 
f#(g(g(_x22, g(_x82, g(_x72, 0))), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(_x112, 0), 0), _x81), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, +(0, 0))), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) 
f#(g(_x42, g(g(_x22, g(_x72, 0)), _x31)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(g(+(0, 0), _x101), _x81), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, g(_x102, 0))), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) 
f#(g(g(g(_x22, g(_x72, 0)), _x51), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x51), _x61)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), g(s(g(g(g(+(0, 0), _x81), _x41), _x51)), _x31), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) 
f#(g(g(_x22, g(_x72, g(0, _x101))), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) 
f#(g(g(g(_x22, g(_x72, 0)), _x31), _x41), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, g(0, _x121)), _x81), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(g(+(0, 0), _x81), _x91), _x41), _x51)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(+(g(g(g(+(0, 0), _x81), _x41), _x51), 0)), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), +(s(g(g(g(+(0, 0), _x81), _x41), _x51)), 0), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(_x62, g(g(g(+(0, 0), _x81), _x41), _x51))), X) 
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) 
f#(g(g(_x22, +(g(_x72, 0), 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) 
Thus, the rule f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X) is replaced by the following rules:
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x92, g(+(0, 0), _x81)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, g(0, _x121)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, g(_x122, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, +(0, 0))), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(+(g(g(+(0, 0), _x81), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(g(+(0, 0), _x101), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, g(_x72, 0)), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), +(s(g(g(g(+(0, 0), _x81), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(_x62, g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, g(_x72, 0)), _x31)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, g(_x102, 0))), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(+(g(g(g(+(0, 0), _x81), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(g(+(0, 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(+(0, 0), _x81), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, g(_x72, 0)), _x31), _x41), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, g(0, _x101))), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(_x72, g(g(+(0, 0), _x81), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(s(g(g(g(+(0, 0), _x81), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(+(0, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(_x72, 0), 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(g(_x102, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(g(_x72, 0), _x81)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(_x112, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, g(_x72, 0)), _x51), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x82, g(_x72, 0))), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)

Problem 23: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

f#(+(g(+(g(_x22, g(_x72, +(0, 0))), g(0, _x81)), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), _x51), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), g(_x32, s(g(+(g(g(+(0, 0), _x81), _x41), 0), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), s(g(g(_x72, g(g(+(0, 0), _x81), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x72, g(+(g(_x82, g(+(+(0, 0), 0), _x151)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, 0), _x61), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(0, _x111), _x141), _x151), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(+(g(0, _x151), 0), +(0, 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(_x52, g(0, _x41)), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), +(0, 0)), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, g(_x102, 0))), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x52, g(0, _x41)), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(+(0, g(_x142, 0)), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x121), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(_x82, +(+(0, +(0, 0)), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, +(0, 0))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, g(_x72, 0)), _x31), 0), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(g(_x132, +(g(_x82, +(+(0, 0), 0)), 0)), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, +(g(_x72, 0), 0)), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(+(g(g(0, _x111), _x141), 0), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(g(s(g(g(g(g(_x72, g(0, _x41)), _x171), _x51), _x61)), _x121), _x31)), X) → f#(X, +(X, X), X)f#(g(+(+(g(_x22, g(_x72, 0)), 0), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(g(+(0, 0), _x131), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x112, g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(+(g(_x142, 0), 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(+(0, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(g(0, _x101), _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x102, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x102, g(_x82, +(+(0, 0), +(0, 0)))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), s(g(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(g(g(_x82, +(+(0, 0), 0)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, 0), 0), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(g(0, _x111), _x231), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, g(0, _x101))), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x72, g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x111)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), g(s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x152, g(_x72, g(0, _x41))), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(+(g(_x82, +(+(0, +(0, 0)), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(_x132, +(g(g(0, _x111), _x141), g(_x152, 0))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, g(_x122, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), g(_x32, s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(g(0, _x101), _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, g(_x162, +(+(0, 0), 0))), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(_x82, g(0, _x41)))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, +(g(_x72, 0), 0)), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x131), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(_x82, +(+(0, 0), +(0, 0))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, +(g(_x22, g(_x72, 0)), 0)), _x31), s(g(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x141), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(g(+(0, 0), _x81), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), g(+(0, 0), _x141))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(+(g(0, _x71), 0), 0)), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, +(g(0, _x71), 0)), 0), _x31), s(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, g(_x102, 0))), 0), _x31), s(g(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, +(g(0, _x71), 0))), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(+(0, 0), 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(+(0, +(0, 0)), +(0, 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, g(0, _x101))), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), g(_x52, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(_x142, g(0, _x111)), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, g(_x122, 0))), 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x51), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(+(g(0, _x71), 0), _x81)), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(g(_x92, g(_x82, +(+(0, 0), 0))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(+(g(_x22, g(_x72, 0)), 0), _x31)), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(+(g(_x22, 0), 0), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x82, g(_x22, g(_x72, 0))), 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x172, g(_x152, 0)), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, g(+(+(0, 0), +(0, 0)), _x121)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, g(0, _x61)), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, g(0, _x71)), _x31), 0), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x211)), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), g(_x32, s(g(g(g(+(g(_x142, 0), 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(_x82, +(+(0, 0), g(_x132, 0))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, +(g(_x72, 0), 0)), _x61), 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x62, g(_x22, g(_x72, 0))), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(g(_x82, +(+(g(_x132, 0), 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), g(_x32, s(g(g(g(g(+(0, 0), _x81), _x41), _x111), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(g(0, _x101), _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(_x72, 0), 0)), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x121), _x31), _x111)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(+(g(_x22, g(_x72, 0)), 0), _x31)), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(g(_x82, +(+(g(_x132, 0), 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, g(_x102, 0))), 0), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, g(_x72, 0)), _x31), _x41), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), 0), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(+(0, 0), s(g(_x42, 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(g(0, _x181), 0), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, g(0, _x121)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(_x152, 0), _x111), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), g(_x92, 0)), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(+(g(0, _x111), 0), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(+(g(_x132, g(_x162, 0)), 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x82, +(g(0, _x71), g(0, _x101)))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(+(g(_x152, 0), 0), +(0, 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, +(g(_x22, g(_x72, 0)), 0)), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(g(_x192, 0), 0), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x102, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x82, g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(g(_x92, 0), _x41))), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), g(g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), _x61), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), 0), s(g(g(g(_x92, g(+(0, 0), _x81)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), g(s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(+(0, g(_x122, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(+(g(_x132, 0), +(0, 0)), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), +(0, 0)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(+(0, 0), _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(+(g(_x22, g(_x72, 0)), 0), _x31)), s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x82, +(g(0, _x71), 0))), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x82, +(+(g(_x132, 0), 0), 0)), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, +(g(_x72, 0), 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x101), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(0, _x121)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x82, g(_x72, 0))), 0), _x31), s(g(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), +(g(_x152, g(0, _x181)), 0)), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(g(g(_x22, g(_x72, 0)), _x61), _x81), 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, g(0, _x71)), _x31), _x41), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(g(_x102, 0), _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(_x62, g(_x22, g(_x72, 0))), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, +(g(0, _x41), 0)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, g(_x72, 0)), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(g(_x22, g(_x72, 0)), _x81)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(+(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(g(_x152, g(_x82, +(+(0, 0), 0))), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(+(0, +(0, 0)), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), g(_x182, 0))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, +(0, 0))), g(_x82, 0)), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, +(g(_x72, 0), 0)), _x61), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(0, _x111), +(0, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31)), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x52, +(g(_x22, g(_x72, 0)), 0)), _x31), s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(_x102, g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(g(0, _x71), _x91), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(+(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), 0), _x51), 0)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, +(g(_x72, 0), 0)), 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31)), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x92, g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41))), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(+(g(_x22, g(_x72, 0)), 0), _x31)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, g(0, _x171)))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x42, g(_x22, g(0, _x91))), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), g(s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(_x102, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(g(0, _x171), 0), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(g(_x62, 0), _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(_x62, g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), 0), s(g(g(g(g(+(0, 0), _x81), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x131)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(+(0, 0), _x101))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), +(0, 0)), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x62, g(_x22, g(_x72, 0))), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), _x91), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x161), _x61)), _x121), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x102, g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(_x72, g(+(g(0, _x91), g(0, _x101)), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(g(+(0, 0), _x181), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), g(s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(g(_x72, 0), _x81)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, +(g(0, _x71), 0)), _x51), _x31), s(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(_x172, 0), _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(_x112, g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x121), _x31))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), +(0, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(+(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), 0), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x52, g(+(g(_x22, g(_x72, 0)), 0), _x31)), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), +(0, +(0, 0)))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(_x102, g(g(+(g(0, _x111), 0), _x81), _x91)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), g(_x72, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(_x112, g(0, _x101)))), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), g(0, _x71)), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, g(_x122, +(+(0, 0), 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, +(g(_x42, g(_x22, 0)), 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(g(_x72, 0), _x111)), _x61), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(_x102, g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), g(s(g(0, _x41)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(g(+(0, 0), _x131), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(g(_x82, +(+(0, 0), 0)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), 0), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), g(s(g(g(g(+(0, 0), _x81), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, g(0, _x101))), _x31), g(_x32, s(g(g(g(g(+(0, 0), _x81), _x41), _x111), _x51))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(_x72, g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(0, _x41), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x72, g(+(g(_x82, +(g(_x162, +(0, 0)), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, +(g(0, _x71), 0)), _x31), 0), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(_x62, g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, +(g(_x22, g(_x72, 0)), 0)), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, +(0, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(g(s(g(g(g(_x72, g(_x192, g(0, _x41))), _x51), _x61)), _x121), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), g(_x32, s(g(g(g(g(+(0, 0), _x81), _x41), _x111), _x51))), X) → f#(X, +(X, X), X)f#(g(0, _x21), s(g(_x42, 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(0, 0)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x131), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), 0), s(g(g(g(g(+(0, 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(+(g(0, _x71), 0), _x81)), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(0, _x101), _x111)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, g(0, _x101))), 0), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(+(g(_x22, g(_x72, +(0, 0))), 0), 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(+(g(_x82, g(+(+(0, 0), 0), _x121)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), g(_x32, s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(+(g(g(_x132, 0), _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(_x102, g(g(g(+(0, 0), _x81), _x41), _x51)))), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), s(g(g(g(+(0, g(_x122, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, +(g(0, _x71), 0)), _x31), 0), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), g(_x32, s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x42, g(+(g(_x22, g(_x72, 0)), 0), _x31)), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(_x92, g(+(0, 0), _x81)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x82, +(0, 0)), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, g(0, _x101))), 0), _x31), s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(0, _x111), _x161), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(0, g(_x32, s(g(_x42, 0))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), +(0, 0))), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(_x132, g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(+(g(0, _x111), 0), _x81), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), s(g(g(g(+(0, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(0, 0), _x41)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, +(g(_x72, 0), 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(+(g(_x22, g(_x72, 0)), 0), _x31), _x51), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, +(0, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(_x92, g(0, _x71)), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(+(+(0, 0), +(0, 0)), 0)), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(0, s(+(0, 0)), X) → f#(X, +(X, X), X)
f#(+(0, 0), s(0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x52, g(g(0, _x91), _x41))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), g(_x32, s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(g(_x152, g(0, _x181)), _x191)), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), +(s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, +(0, g(0, _x141)))), 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x42, g(_x22, 0)), g(_x52, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), +(0, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), g(0, _x71)), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, g(_x152, 0)), +(0, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), +(g(_x152, 0), 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(_x172, 0), _x111), _x141), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), g(s(g(g(g(+(0, 0), _x81), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(g(_x52, g(_x22, g(_x72, 0))), _x61), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(0, s(g(_x52, g(_x42, 0))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), g(0, _x71)), _x31), s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x92, +(g(_x82, +(+(0, 0), 0)), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(+(g(_x132, g(0, _x161)), 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(+(g(0, _x71), 0), g(0, _x101))), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(+(g(_x82, +(+(0, 0), 0)), 0), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, +(g(0, _x181), 0))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x82, g(_x72, 0))), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(g(0, _x101), _x111)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), g(_x32, s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(+(g(_x112, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(+(g(_x182, g(g(0, _x111), _x141)), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(g(_x102, 0), _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(g(_x82, +(+(g(_x132, 0), 0), 0)), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x42, g(+(g(_x22, g(_x72, 0)), 0), _x31)), s(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(+(g(_x82, +(+(0, 0), g(0, _x141))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, g(_x72, 0)), 0), _x51), _x31), s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, g(_x132, 0))), _x61), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(g(_x122, +(0, 0)), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(0, _x71))), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), +(0, 0)), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(0, s(g(_x42, g(0, _x71))), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x72, +(g(_x132, 0), 0))), 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x131), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x82, g(_x72, g(0, _x41))), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(+(0, 0), +(0, 0)), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(+(0, 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), +(g(0, _x101), 0))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x101)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(g(_x72, 0), _x81)), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(+(g(_x42, g(_x22, 0)), 0), s(g(g(0, _x61), _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), g(s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, g(+(+(g(_x132, 0), 0), 0), _x111)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(0, _x111), 0), _x131), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(+(g(_x22, g(_x72, 0)), 0), _x61), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(+(g(g(0, _x111), _x141), 0), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), g(0, _x71)), _x31), s(g(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x41), _x101)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), +(+(0, 0), 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, +(0, 0)), +(0, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x62, g(_x22, g(_x72, 0))), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(g(0, _x191), 0), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(+(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61), _x91)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(g(_x72, g(0, _x41)), _x151), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, +(g(0, _x71), g(0, _x101)))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(_x82, g(+(+(0, 0), 0), _x111)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), +(0, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x72, +(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), 0)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(_x182, 0))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), g(_x162, 0)), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(_x162, g(g(0, _x171), _x111)), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(g(g(+(0, 0), _x151), _x81), _x41), _x111), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(_x132, +(g(g(g(0, _x171), _x111), _x141), g(_x152, 0))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(_x162, g(0, _x111)), _x141), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(0, _x111), _x161), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x81), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x132, g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81))), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(+(g(g(g(+(0, 0), _x81), _x41), _x111), 0), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(+(g(0, _x91), 0), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(_x132, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, +(g(_x72, +(0, 0)), 0)), 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, g(s(g(g(g(+(0, 0), _x81), _x41), _x51)), _x91)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x82, +(g(0, _x71), g(0, _x101)))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(g(0, _x121), _x101))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(+(g(g(_x132, 0), _x141), 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), +(s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(g(0, _x71), _x91), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)f#(+(g(_x42, g(_x22, 0)), +(0, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), +(s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), s(g(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(g(g(+(0, 0), _x81), _x141), _x41), _x111), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(g(0, _x71), _x91), 0)), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(+(0, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), _x111)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x72, g(+(+(g(_x82, +(+(0, 0), 0)), 0), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, g(_x72, 0)), 0), _x31), _x41), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(g(_x82, +(+(g(_x132, 0), 0), 0)), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(+(g(_x22, g(_x72, 0)), 0), _x31), _x41), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(g(_x182, 0), _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(+(g(0, _x111), 0), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x92, g(g(_x72, g(0, _x41)), _x51)), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(g(s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), _x121), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, g(0, _x71)), _x51), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(+(0, g(0, _x121)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), +(0, 0)), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), g(0, _x111)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(0, g(_x32, s(0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, +(g(0, _x71), 0)), 0), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, +(g(_x22, g(_x72, 0)), 0)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(g(_x152, g(0, _x181)), _x161)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), _x91), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(0, s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(+(g(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x61), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x62, g(_x32, s(g(g(g(g(+(0, 0), _x81), _x41), _x111), _x51)))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(g(_x72, 0), _x81)), 0), _x31), s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), _x61), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, +(g(0, _x71), g(0, _x101))), 0), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, g(0, _x101))), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(_x82, +(+(g(0, _x131), 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, 0)), g(0, _x81)), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(+(g(_x152, 0), 0), _x161)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(+(0, g(_x162, 0)), +(0, 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(g(_x162, 0), 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(_x102, g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), g(_x152, 0)), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), g(0, _x101)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(g(0, _x101), _x111))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(g(s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), _x121), _x31)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(g(_x82, +(+(g(_x132, 0), 0), 0)), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(+(+(g(_x82, +(+(0, 0), 0)), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(g(_x82, +(+(g(_x132, 0), 0), 0)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(g(_x82, +(+(0, 0), g(_x132, 0))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), s(g(g(g(+(0, g(0, _x121)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, +(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), 0)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, g(0, _x101))), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), +(0, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(+(g(_x82, g(_x122, +(+(0, 0), 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x102, +(g(0, _x111), 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(_x102, 0))), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), g(_x32, g(s(g(g(g(+(0, 0), _x81), _x41), _x51)), _x91)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(g(0, _x171), _x111), _x161), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), 0), _x41), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x62, g(_x22, g(_x72, 0))), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(g(0, _x111), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(_x72, g(g(+(0, 0), _x81), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), s(g(g(g(g(_x102, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x92, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(+(g(g(g(0, _x171), _x111), _x141), 0), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), s(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, +(g(0, _x71), 0)), _x31), 0), s(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(+(g(_x22, g(_x72, 0)), 0), _x31), _x41), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, +(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), 0)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(+(0, g(0, _x151)), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(g(s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), _x121), _x31)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(_x122, g(+(0, 0), _x81)), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(_x82, +(+(g(_x132, 0), 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, +(g(_x22, g(_x72, 0)), 0)), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(g(+(0, 0), _x81), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x52, +(g(_x22, g(_x72, 0)), 0)), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), g(_x72, 0)), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(_x92, g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(g(_x152, 0), _x161)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(0, g(s(0), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(+(g(0, _x71), g(0, _x101)), _x81)), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(+(0, 0), 0), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(+(0, 0), _x71), 0)), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), g(0, _x71)), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x91), _x101), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(+(0, 0), +(0, 0))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(0, g(s(g(_x42, 0)), _x31), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), s(g(g(g(+(0, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, +(g(_x22, g(_x72, 0)), 0)), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(+(g(g(g(g(+(0, 0), _x81), _x41), _x111), _x51), 0))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(+(g(0, _x71), g(0, _x101)), _x81)), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, +(g(0, _x71), 0)), _x51), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, g(_x102, 0))), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), g(_x192, 0))), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(g(0, _x71), _x81)), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x62, 0), _x41)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), g(_x72, 0)), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(_x62, g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(0), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), +(+(g(_x152, 0), 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(_x92, g(0, _x71)), g(0, _x101))), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(g(s(g(g(_x162, g(g(_x72, g(0, _x41)), _x51)), _x61)), _x121), _x31)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(_x192, g(0, _x181)))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(+(0, 0), 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(_x132, +(g(0, _x111), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x82, g(_x72, 0))), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x42, g(_x22, 0)), 0), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), +(g(0, _x101), 0))), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), +(s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(_x212, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(g(0, _x121), _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), +(0, g(0, _x161)))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, g(_x72, 0)), _x31), 0), g(_x32, s(g(g(g(g(+(0, 0), _x81), _x41), _x111), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), g(_x32, s(g(g(g(+(0, g(_x152, 0)), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(_x72, g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(+(0, 0), _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), +(s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), 0), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(g(0, _x61), _x41)), X) → f#(X, +(X, X), X)f#(+(g(_x52, g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31)), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(0), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(g(0, _x121), _x101))), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(+(g(0, _x71), g(0, _x101)), 0)), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(+(0, 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(+(g(0, _x71), 0), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x72, g(g(_x152, 0), _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(0, _x151)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, +(g(_x72, 0), 0)), 0), _x31), s(g(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x111), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(g(_x122, 0), _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(g(_x72, 0), _x81)), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), _x31)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(_x72, g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), g(s(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(g(_x82, +(0, 0)), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, +(g(0, _x71), 0)), _x31)), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(_x92, g(0, _x71)), 0)), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(_x172, 0), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(_x62, g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x121), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, +(g(0, _x71), 0))), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(0, 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, +(g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81), 0)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x62, g(_x22, g(_x72, 0))), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(g(_x72, 0), _x81)), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x72, 0)), g(_x82, 0)), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x42, g(_x22, 0)), 0), _x31), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, g(0, _x101))), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(+(0, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, g(_x112, +(+(g(_x132, 0), 0), 0))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(+(0, +(0, 0)), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x52, g(_x22, g(_x72, 0))), _x31)), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(+(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(_x62, +(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(g(_x142, 0), 0), +(0, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(g(_x92, 0), _x71)), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(0, s(+(g(_x42, 0), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), s(g(g(g(g(_x102, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(+(0, 0), 0), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(+(g(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, +(s(g(g(g(+(0, 0), _x81), _x41), _x51)), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, g(_x92, s(g(g(g(g(+(0, 0), _x81), _x41), _x111), _x51)))), X) → f#(X, +(X, X), X)f#(+(g(_x42, g(_x22, 0)), 0), g(s(g(0, _x41)), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x162, g(_x152, 0))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(+(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(+(g(_x22, g(_x72, 0)), 0), 0), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, +(g(0, _x71), 0)), 0), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x101), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), +(0, 0)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x101), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), +(0, 0)), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), 0), s(g(+(g(g(+(0, 0), _x81), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), _x41), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(g(0, _x141), 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(g(_x122, 0), _x101))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(+(g(_x82, +(g(_x132, +(0, 0)), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), +(0, 0)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(_x112, g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(+(g(_x22, g(_x72, 0)), 0), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(+(g(0, _x111), g(_x122, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(0, _x41)), _x31), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), +(s(g(0, _x41)), 0), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(_x152, g(g(0, _x111), _x141)), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, g(_x212, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181))))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x82, +(+(g(_x132, 0), 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(_x82, +(g(0, _x91), g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(+(0, 0), _x71)), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x82, g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x121), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(_x92, g(0, _x71)), g(0, _x101))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(+(0, 0), g(0, _x131))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x92, g(+(0, 0), _x81)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(+(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x111), _x51), _x61)), X) → f#(X, +(X, X), X)f#(+(+(g(_x42, g(_x22, 0)), 0), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(+(g(g(g(+(0, 0), _x81), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, g(_x72, 0)), _x51), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, +(0, 0))), _x31), g(_x32, s(g(g(g(g(+(0, 0), _x81), _x41), _x111), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), 0), s(g(g(g(g(+(0, 0), _x81), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(g(+(0, 0), _x81), _x121), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(+(+(0, 0), 0), +(0, 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(g(g(+(0, 0), _x81), _x41), _x111), _x121), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(+(g(_x22, g(_x72, 0)), 0), _x31)), s(g(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x41), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), g(_x32, s(g(g(g(+(0, g(0, _x151)), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), s(+(g(g(g(+(0, 0), _x81), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, g(_x112, +(0, 0))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(g(_x82, +(+(+(0, 0), 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), 0), s(g(g(g(+(+(0, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(+(g(0, _x71), 0), _x81)), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(0), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(_x72, g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, g(_x102, 0))), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(g(_x72, g(0, _x41)), _x121), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(+(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(g(_x262, 0), _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(+(+(g(0, _x111), 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, +(g(g(_x22, g(_x72, 0)), _x61), 0)), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(+(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), 0), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(_x62, g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(_x132, +(g(g(0, _x111), _x141), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), +(s(g(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, g(0, _x121)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(_x112, g(0, _x101)))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, +(0, +(0, 0)))), 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, +(g(0, _x71), g(0, _x101))), 0), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), s(g(g(g(g(+(0, 0), _x81), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(+(g(0, _x71), g(0, _x101)), 0)), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(+(g(_x142, g(_x132, 0)), 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(g(_x122, 0), _x101))), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(g(g(_x82, +(+(0, 0), 0)), _x151), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(g(_x112, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(_x72, 0), 0)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), g(_x32, s(g(g(g(g(_x132, +(0, 0)), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), s(g(+(g(g(+(0, 0), _x81), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), g(_x122, 0)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, g(_x72, 0)), 0), _x51), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(g(0, _x141), 0), +(0, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, +(g(0, _x71), 0)), _x31)), s(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, +(0, 0))), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, g(0, _x131))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(+(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(_x72, 0), 0)), _x31), g(_x32, s(g(g(g(g(+(0, 0), _x81), _x41), _x111), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(+(g(0, _x71), 0), 0)), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x82, g(_x72, 0))), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x42, g(_x22, 0)), 0), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(_x72, g(g(_x82, +(+(0, 0), 0)), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, g(_x72, 0)), 0), _x31), _x41), s(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), g(_x32, s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(g(_x192, 0), _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(+(g(0, _x111), 0), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(+(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), g(s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), +(0, 0))), _x31), s(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(g(_x132, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x121)), _x31)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), g(0, _x71)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, +(0, 0)), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, +(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, g(_x172, +(+(0, 0), 0))), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(0, _x111), _x161), _x141), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(g(_x82, +(+(0, 0), +(0, 0))), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x62, g(_x22, g(_x72, 0))), 0), _x31), s(g(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x82, g(_x72, 0))), 0), _x31), s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(_x92, g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41)), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(g(_x82, +(+(g(_x132, 0), 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(g(+(0, 0), _x131), +(0, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), +(g(0, _x101), 0))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(+(g(+(g(0, _x91), g(0, _x101)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(+(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), 0), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), g(s(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), g(_x32, s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, g(0, _x101))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(+(0, 0), _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), g(_x152, +(0, 0)))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, g(_x192, 0)), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), s(g(_x62, g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, g(0, _x181)), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(g(0, _x111), _x141), _x181), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(+(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x101), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x102, g(_x82, +(+(0, 0), 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(_x112, g(g(+(0, 0), _x81), _x41)), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), g(_x142, 0)), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(+(g(_x82, +(+(g(0, _x141), 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), s(g(g(g(+(g(_x112, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(g(g(+(0, 0), _x81), _x41), _x131), _x111), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x192, g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x51), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(+(g(_x82, +(+(0, 0), 0)), 0), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(+(0, 0), _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(g(0, _x171), _x181), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(g(+(0, 0), _x171), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), s(g(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), g(_x82, g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x121), _x31)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(0, _x111), g(0, _x151)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(+(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(+(0, 0), _x71), g(0, _x101))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x82, g(_x72, 0))), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(+(g(g(_x22, g(_x72, 0)), _x61), 0), 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(g(s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), _x121), _x31)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(_x122, g(g(g(+(0, 0), _x81), _x41), _x111)), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(g(_x122, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), 0), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, +(g(_x72, 0), 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(+(g(0, _x131), 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(g(_x72, 0), _x81)), 0), _x31), s(g(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(_x112, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(+(g(_x72, g(0, _x41)), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x82, g(_x72, 0))), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x102, g(_x72, 0))), 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), 0), s(g(g(g(g(_x102, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(0, _x71)), 0), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(+(g(_x22, g(_x72, 0)), 0), 0), _x31), s(g(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), g(0, _x91)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), +(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(_x112, g(0, _x101)))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), g(0, _x111)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(+(g(_x22, g(_x72, 0)), 0), _x61), 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(_x62, g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(g(_x82, +(+(0, 0), +(0, 0))), _x111), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(0, +(s(0), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(_x102, 0))), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x101), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(_x82, +(g(_x122, +(0, 0)), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), g(_x72, 0)), _x31), s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(g(0, _x191), _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(+(+(0, 0), 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(+(g(_x22, g(_x72, 0)), 0), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), g(0, _x161)), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(0, g(_x132, 0))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(+(0, 0), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(g(_x102, 0), _x71), g(0, _x101))), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x162, g(_x152, 0))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), g(_x32, s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0), _x51))), X) → f#(X, +(X, X), X)
f#(+(g(_x22, +(0, 0)), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(+(g(0, _x171), 0), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(_x102, g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(g(_x82, +(+(0, 0), g(0, _x131))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), 0), s(g(g(g(+(0, g(0, _x121)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(g(_x142, 0), 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), g(_x32, s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(_x82, +(+(+(0, 0), 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x101), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(g(_x82, +(+(0, 0), +(0, 0))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(g(_x22, g(_x72, +(0, 0))), _x81), 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(_x72, g(+(g(0, _x91), g(0, _x101)), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x151), _x111), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x171), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, g(_x192, 0)), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), +(0, 0)), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(_x152, g(g(0, _x111), _x141)), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), 0)), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), g(_x172, 0))), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), g(_x82, g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x121), _x31)), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), s(g(g(g(+(0, g(_x122, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(g(_x82, +(+(0, 0), 0)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), g(_x32, s(g(g(g(g(+(0, 0), _x131), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x101), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x72, g(g(_x122, +(g(_x82, +(+(0, 0), 0)), 0)), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(+(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), 0), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(+(0, 0), _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), 0), s(g(g(+(g(+(0, 0), _x81), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x82, g(_x72, 0))), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, g(0, _x101))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x72, +(0, 0))), +(0, 0)), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, +(g(0, _x131), 0))), 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), g(_x112, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), +(0, 0)), _x31), s(g(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(+(g(+(g(0, _x111), 0), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(_x52, g(0, _x41))), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(g(_x82, +(+(g(_x132, 0), 0), 0)), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(g(_x82, +(+(0, 0), 0)), _x141), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), g(_x32, s(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x82, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(g(_x102, +(g(_x82, +(+(0, 0), +(0, 0))), 0)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), g(_x142, +(0, 0)))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(_x82, +(+(0, 0), g(0, _x131))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x101), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x82, g(_x22, g(_x72, +(0, 0)))), 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(+(g(g(_x22, g(_x72, 0)), _x81), 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(0, 0)), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x42, g(g(_x22, 0), _x71)), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(g(0, _x241), _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x42, g(_x22, 0)), 0), s(g(+(0, 0), _x41)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x131), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, +(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), 0)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), +(0, 0)), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(g(_x82, +(+(g(_x132, 0), 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), g(_x82, 0))), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), g(_x32, s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(g(0, _x101), _x111))), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(g(+(g(0, _x161), 0), _x81), _x41), _x111), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), +(s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(+(0, 0), _x71), g(0, _x101))), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(_x82, +(+(0, g(0, _x141)), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), s(g(+(g(g(+(0, 0), _x81), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(g(0, _x71), _x91), g(0, _x101))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), +(s(g(g(g(+(0, 0), _x81), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(+(0, 0), 0), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x131), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(+(+(0, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), g(0, _x141)), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x82, g(_x72, 0))), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(+(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x121), 0), _x31)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, +(g(0, _x71), 0)), _x31)), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x82, g(_x72, 0))), 0), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(g(+(0, 0), _x81), _x41), _x51), _x101))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(_x72, g(0, _x41)), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(g(_x72, 0), _x111)), _x61), 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x62, +(g(_x22, g(_x72, +(0, 0))), 0)), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(+(0, 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(g(_x82, +(+(0, +(0, 0)), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(+(g(0, _x71), g(0, _x101)), _x81)), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, g(0, _x101))), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), g(+(0, 0), _x151))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(g(+(g(_x162, 0), 0), _x81), _x41), _x111), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(+(0, 0), _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, g(_x72, 0)), _x31), 0), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(_x122, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41))), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(_x222, g(g(0, _x111), _x141)), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(_x82, g(_x112, +(+(0, 0), 0))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x92, g(+(0, 0), _x81)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, g(_x152, 0)), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(_x72, g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(_x72, 0), 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(+(g(_x102, g(_x82, +(+(0, 0), 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(+(g(0, _x71), 0), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(_x102, g(g(g(g(+(0, 0), _x81), _x41), _x111), _x51)))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), +(0, 0)), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(g(_x72, 0), _x81)), 0), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x112, g(_x72, 0))), _x61), 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x121), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x82, g(_x72, 0))), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x92, g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, +(g(0, _x71), g(0, _x101))), 0), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(g(_x172, 0), 0), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, g(_x72, 0)), 0), _x31), _x41), s(g(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, g(_x102, 0))), _x31), g(_x32, s(g(g(g(g(+(0, 0), _x81), _x41), _x111), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), g(s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), g(_x72, 0)), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(g(_x72, +(0, 0)), _x101)), 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, g(0, _x191)), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), +(s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(_x102, g(0, _x91)), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, +(g(0, _x71), 0)), _x31), _x41), s(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(+(g(0, _x91), g(0, _x101)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(_x72, g(+(0, 0), _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), g(0, _x191))), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(+(+(g(_x132, 0), 0), 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x42, g(_x72, g(_x22, 0))), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(+(g(_x42, g(_x22, g(_x92, 0))), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, +(g(0, _x71), g(0, _x101)))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(g(_x72, 0), _x81)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(+(0, 0), _x81), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(_x42, 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(g(s(g(g(g(_x172, g(_x72, g(0, _x41))), _x51), _x61)), _x121), _x31)), X) → f#(X, +(X, X), X)f#(g(+(g(_x52, g(_x22, g(_x72, 0))), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x82, g(g(_x22, g(_x72, 0)), _x61)), 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), g(0, _x61)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(g(_x72, 0), _x81)), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, g(_x72, 0)), 0), _x51), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(+(g(0, _x111), +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(+(g(g(g(_x72, g(0, _x41)), _x51), _x61), 0)), X) → f#(X, +(X, X), X)f#(g(0, _x21), s(0), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(0, _x111), 0), _x81), _x121), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, g(_x132, +(+(0, 0), +(0, 0)))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(g(_x132, +(0, 0)), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(+(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), 0), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x121), _x131), _x31)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x101), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(g(+(0, 0), _x81), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), 0), s(g(g(g(+(0, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(g(_x72, 0), _x81)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(g(_x102, 0), _x71), g(0, _x101))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, g(_x72, 0)), _x51), _x31), g(_x32, s(g(g(g(g(+(0, 0), _x81), _x41), _x111), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), +(0, 0))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x91), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(g(0, _x41), _x121)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, g(_x72, 0)), 0), _x51), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(+(g(_x132, 0), 0), g(_x132, 0))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), s(g(g(g(+(g(_x112, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(g(_x82, +(0, 0)), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), +(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), s(0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, +(0, 0)), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x91), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, +(g(0, _x71), 0)), _x31), _x41), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(+(0, 0), _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(g(_x202, 0), _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), g(s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x162, +(g(_x152, 0), 0))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), +(s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(g(_x182, 0), 0), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, g(+(+(0, 0), 0), _x171)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(+(g(0, _x141), 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(+(g(_x22, g(_x72, 0)), 0), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(+(g(_x82, +(+(0, g(0, _x151)), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x131), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, +(g(0, _x71), 0))), _x31), s(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), +(s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), s(g(g(g(+(+(0, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, +(0, 0))), _x61), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, g(_x72, 0)), _x31), _x41), g(_x32, s(g(g(g(g(+(0, 0), _x81), _x41), _x111), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), g(_x32, s(g(g(g(_x122, g(+(0, 0), _x81)), _x41), _x51))), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), 0), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(_x162, g(0, _x111)), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), +(s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x62, g(_x52, g(_x22, g(_x72, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x51), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(g(_x202, 0), _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, g(_x72, 0)), 0), _x51), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(_x92, g(0, _x71)), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(g(_x172, +(0, 0)), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(+(g(0, _x71), 0), _x81)), _x31), s(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), g(0, _x61)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), g(_x32, s(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x82, +(0, 0)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(+(g(g(+(0, 0), _x81), _x41), 0), _x51))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(_x62, g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), _x41), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(+(g(_x82, +(+(+(0, 0), 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x42, g(_x22, 0)), 0), g(_x32, s(g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(_x112, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, g(0, _x101))), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), g(_x32, s(g(_x102, g(g(g(+(0, 0), _x81), _x41), _x51)))), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, g(_x122, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, +(g(0, _x71), g(0, _x101)))), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(+(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), g(0, _x121)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), g(_x32, s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(g(_x72, 0), _x81)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(_x62, g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), g(s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), +(g(0, _x101), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(g(_x82, +(+(0, 0), 0)), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(g(_x92, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, g(_x72, 0)), _x51), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(+(g(g(0, _x111), _x141), 0), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x32, g(_x22, 0)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), g(_x62, 0)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(_x102, g(0, _x91)), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(0, _x61), _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(_x62, g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51))), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, 0), _x31), 0), s(g(g(g(_x82, +(+(g(_x132, 0), 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), _x41), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(_x62, g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, g(+(0, 0), _x111)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(+(0, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(g(0, _x101), _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(+(0, 0), g(_x132, 0))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(g(g(_x142, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x121), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(_x132, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), g(_x32, s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), g(0, _x71)), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), 0), s(g(_x62, g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(+(0, 0), _x41))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(0, _x111), 0), _x101), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), g(_x72, 0)), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(0, _x51)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x81)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, g(_x102, 0))), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(g(_x142, +(g(_x82, +(+(0, 0), 0)), 0)), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, g(0, _x151)), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, +(g(g(_x22, g(_x72, 0)), _x61), 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(0, _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, g(_x102, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(_x72, +(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(g(_x122, 0), _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, +(0, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, g(_x172, 0)))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x232, g(_x152, g(0, _x181))))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, g(_x72, 0)), _x31), _x41), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(+(g(_x72, g(0, _x41)), 0), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), 0), s(+(g(g(g(+(0, 0), _x81), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, g(0, _x151)), +(0, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), +(g(0, _x151), 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(+(g(g(_x72, g(0, _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(_x82, +(+(0, g(_x142, 0)), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(+(g(_x82, +(+(0, g(_x152, 0)), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(0, s(g(_x42, g(_x72, 0))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(g(+(0, 0), _x81), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, g(0, _x101))), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(g(_x72, 0), _x81)), _x31), g(_x32, s(g(g(g(g(+(0, 0), _x81), _x41), _x111), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(+(0, 0), _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(+(g(_x22, g(_x72, 0)), 0), _x31)), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, g(0, _x181)), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, g(0, _x101))), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), +(g(0, _x101), 0))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(g(0, _x41), _x171)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x102, g(_x72, g(0, _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(g(0, _x181), _x211))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, +(g(0, _x71), 0)), _x31), _x41), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), g(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, +(g(0, _x71), 0)), _x31)), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(g(g(+(0, 0), _x81), _x41), _x111), _x51), _x101))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(_x112, g(g(_x72, g(0, _x41)), _x51)), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(g(0, _x111), _x191), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(g(_x132, +(0, 0)), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(_x62, g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), +(g(_x32, s(g(g(g(g(+(0, 0), _x81), _x41), _x111), _x51))), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(g(g(_x152, +(0, 0)), _x81), _x41), _x111), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(g(_x72, 0), _x81)), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, 0)), +(0, 0)), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(+(g(0, _x111), 0), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), +(s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(g(0, _x121), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x42, g(_x22, 0)), 0), s(+(g(0, _x41), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(0), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(+(+(0, 0), 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), g(_x32, s(g(g(g(+(+(0, 0), 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), s(g(g(+(g(+(0, 0), _x81), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), +(0, 0))), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x91), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(+(g(0, _x71), g(0, _x101)), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(g(s(g(g(g(_x72, g(g(0, _x41), _x191)), _x51), _x61)), _x121), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x82, +(0, 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x51), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(+(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), _x31)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(+(g(0, _x111), 0), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x42, g(_x22, 0)), _x51), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(0, _x111), _x141), _x151), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), s(g(g(g(g(+(0, 0), _x81), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), +(0, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, +(+(0, 0), 0))), 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(0, _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, +(g(0, _x71), 0)), _x51), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x92, g(_x82, +(+(0, 0), 0))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(_x152, g(g(0, _x111), _x141)), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, g(_x72, 0)), 0), _x31), _x41), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(+(g(0, _x71), g(0, _x101)), _x81)), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(+(0, 0), _x111), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(g(_x102, 0), _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), 0), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(g(_x72, 0), _x101))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x72, +(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), 0)), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), +(s(g(g(g(+(0, 0), _x81), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(+(g(_x82, +(+(0, 0), 0)), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), +(s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0)), 0), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(+(0, 0), _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), g(_x32, s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, g(_x72, 0)), 0), _x31), _x41), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(+(0, g(_x152, 0)), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), +(s(g(g(g(+(0, 0), _x81), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(_x72, g(g(0, _x41), _x141)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(+(g(_x82, +(+(0, 0), +(0, 0))), 0), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(g(_x72, g(0, _x41)), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(+(g(0, _x111), 0), _x141), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, +(g(_x72, 0), 0)), 0), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(_x232, g(0, _x111)), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(g(_x82, +(0, 0)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(+(g(g(g(+(0, 0), _x81), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x162, g(_x152, g(0, _x181)))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x142, g(_x82, +(+(0, 0), 0))), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(+(g(_x42, g(_x22, 0)), 0), s(g(g(_x62, 0), _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x101), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(+(0, 0), _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(+(g(_x82, +(+(0, 0), +(0, 0))), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(+(0, 0), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, +(g(_x22, g(_x72, 0)), 0)), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(g(_x102, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(+(g(_x22, g(_x72, 0)), 0), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x82, g(0, _x71))), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), g(_x112, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(g(_x82, +(0, 0)), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x82, +(g(0, _x71), g(0, _x101)))), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(+(g(_x82, +(g(+(0, 0), _x131), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(+(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x102, g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41))), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(+(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), 0), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), 0), s(g(g(g(+(0, g(_x122, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(g(0, _x111), _x141), _x221), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(_x72, g(0, _x41)), _x81), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), +(0, 0))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, +(g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x121), _x31), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, g(_x102, 0))), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), _x41), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(g(0, _x121), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x42, g(_x22, 0)), 0), +(s(g(0, _x41)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(_x132, g(g(+(0, 0), _x81), _x41)), _x111), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), g(0, _x181))), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(+(g(_x22, g(_x72, 0)), 0), _x51), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(+(g(_x122, g(0, _x111)), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x191), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x92, g(_x22, g(_x72, 0))), _x61), 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(_x72, g(g(_x112, 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x92, g(_x82, g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x121), _x31))), X) → f#(X, +(X, X), X)
f#(0, +(s(g(_x42, 0)), 0), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x51), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), +(s(g(g(g(_x82, +(0, 0)), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(+(+(g(_x22, g(_x72, 0)), 0), 0), _x31), s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x62, g(_x22, g(_x72, 0))), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(g(0, _x221), _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(0, _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), +(s(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, g(_x72, 0)), _x31)), g(_x32, s(g(g(g(g(+(0, 0), _x81), _x41), _x111), _x51))), X) → f#(X, +(X, X), X)f#(g(g(+(g(_x22, g(_x72, 0)), 0), _x51), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, g(_x122, +(+(0, 0), +(0, 0)))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(g(_x72, 0), _x101)), 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, +(g(0, _x71), 0)), 0), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(+(g(0, _x71), 0), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(+(g(_x132, 0), g(0, _x141)), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x82, +(g(0, _x71), g(0, _x101)))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(_x162, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81))), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(+(0, 0), _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, g(_x72, 0)), 0), _x31), _x41), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(+(0, 0), _x101))), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x131), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, +(0, g(_x142, 0)))), 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), +(g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), 0), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(+(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x82, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(+(g(g(g(+(0, 0), _x81), _x41), _x51), 0))), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, +(g(0, _x71), g(0, _x101)))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, g(_x92, s(g(g(g(+(0, 0), _x81), _x41), _x51)))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x101), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), g(0, _x71)), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(g(0, _x111), _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x72, g(_x112, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41))), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(g(_x132, 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), g(s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(g(_x82, g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x121), _x31)), _x91), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, g(_x72, 0)), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(+(+(g(_x22, 0), 0), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(+(g(0, _x71), g(0, _x101)), 0)), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(g(_x82, +(+(0, 0), 0)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, g(_x72, 0)), _x31)), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(g(0, _x91), _x101), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(_x102, g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), s(g(g(g(g(+(0, 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(_x112, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(+(0, 0), _x81), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(0, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(+(g(+(g(0, _x111), 0), _x81), 0), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x82, g(_x72, 0))), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(0, _x91), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(_x62, g(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(g(s(g(g(g(_x72, +(g(0, _x41), 0)), _x51), _x61)), _x121), _x31)), X) → f#(X, +(X, X), X)f#(g(+(g(_x82, g(g(_x22, g(_x72, 0)), _x61)), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x72, g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x121), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), +(g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), 0), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), g(_x32, s(g(g(g(g(+(0, 0), _x81), _x41), _x111), _x51))), X) → f#(X, +(X, X), X)
f#(+(g(_x52, g(_x42, g(_x22, 0))), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, g(_x102, 0))), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(g(0, _x101), _x71), g(0, _x101))), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(g(0, _x101), _x111))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x72, g(+(g(_x82, +(g(+(0, 0), _x161), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31)), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, g(_x72, 0)), _x31)), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, g(_x72, 0)), 0), _x51), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(_x132, +(g(g(0, _x111), _x141), +(g(_x152, 0), 0))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(+(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), s(+(g(g(g(+(0, 0), _x81), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(_x92, g(0, _x71)), 0)), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(g(_x102, 0), _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(+(0, 0), _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(g(_x82, +(0, 0)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(+(g(0, _x91), 0), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(_x82, +(g(+(0, 0), _x121), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(g(+(0, 0), _x81), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, +(0, 0)), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(+(+(g(_x22, g(_x72, 0)), 0), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(g(s(g(g(g(_x72, g(g(0, _x201), _x41)), _x51), _x61)), _x121), _x31)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, g(+(+(0, 0), +(0, 0)), _x131)), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(0, _x111), _x141), _x151), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), g(_x62, 0)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), s(g(g(g(g(+(0, 0), _x101), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(_x62, g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(+(g(g(+(0, 0), _x81), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(g(_x52, g(0, _x41))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(+(g(g(+(0, 0), _x81), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), +(s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(+(g(0, _x71), 0), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x161)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(+(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(_x22, g(_x52, 0)), g(_x82, g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x121), _x31)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, g(_x132, 0))), _x61), 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x32, +(g(_x22, 0), 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x82, +(+(g(_x132, 0), 0), 0)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), g(0, _x51)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), 0), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), g(0, _x71)), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(+(0, 0), _x111), _x141), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, g(0, _x131))), _x61), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(_x62, g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(g(_x82, +(g(_x122, +(0, 0)), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, g(_x182, 0)), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(_x72, 0), 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(_x82, +(+(g(_x132, 0), 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(_x72, g(_x122, g(0, _x41))), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(0, _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(+(g(+(0, 0), _x81), 0), _x41), _x111), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(g(_x82, +(+(g(_x132, 0), 0), 0)), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(+(g(g(0, _x131), _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(g(_x102, 0), _x71), 0)), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x131)), _x31)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), _x41), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(_x102, g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, g(_x102, 0))), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x92, g(_x82, +(0, 0))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), s(g(g(g(g(+(0, 0), _x101), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), g(_x32, s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51))), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), g(_x32, s(g(0, _x41))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(g(_x122, +(g(_x132, 0), 0)), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(+(0, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(g(_x82, +(+(0, 0), 0)), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), +(0, 0)), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, g(g(0, _x41), _x81))), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x82, +(+(0, 0), 0)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(_x102, 0))), _x31), s(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), g(0, _x71)), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(g(g(_x22, g(_x72, 0)), _x61), _x81), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(g(+(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), _x121), _x31)), X) → f#(X, +(X, X), X)f#(+(g(_x22, g(_x62, 0)), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(g(0, _x261), _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), g(_x32, s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(+(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(g(+(0, g(_x172, 0)), _x81), _x41), _x111), _x51))), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x102, g(_x72, +(0, 0)))), 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), +(s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), g(_x142, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(+(g(g(0, _x111), _x141), 0), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, +(g(_x72, 0), 0)), 0), _x31), s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(_x72, g(g(+(g(0, _x111), 0), _x81), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(+(0, g(0, _x141)), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(_x72, g(g(_x82, +(+(0, 0), 0)), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x112, g(_x82, +(+(0, 0), +(0, 0)))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(g(0, _x41)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), g(_x32, s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(+(g(0, _x111), 0), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(_x102, 0))), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), s(g(g(g(_x92, g(+(0, 0), _x81)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), g(_x72, 0)), _x31), s(g(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, g(_x72, 0)), _x51), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(g(0, _x121), _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(g(0, _x201), _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(_x42, g(_x22, 0)), g(0, _x51)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(+(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), g(0, _x81))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(_x152, g(g(g(0, _x171), _x111), _x141)), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(g(_x142, +(0, 0)), +(0, 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), s(g(g(g(+(+(0, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), g(_x32, s(+(g(g(g(+(0, 0), _x81), _x41), _x51), 0))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(g(_x82, +(g(+(0, 0), _x121), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x62, g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51)))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(g(0, _x111), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(_x72, g(g(0, _x111), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, +(g(0, _x71), 0)), _x51), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x102, g(_x72, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), g(_x82, g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x121), _x31)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, +(g(_x72, 0), 0))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(g(+(+(0, 0), 0), _x81), _x41), _x111), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), g(_x112, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(g(_x72, 0), _x81)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(_x52, g(0, _x41))), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, +(s(g(g(g(g(+(0, 0), _x81), _x41), _x111), _x51)), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(g(0, _x71), _x91), 0)), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(+(g(_x22, g(_x72, 0)), 0), _x61), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), 0), +(s(g(g(g(+(0, 0), _x81), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51))), X) → f#(X, +(X, X), X)f#(+(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), +(s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, +(0, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(+(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(_x72, g(g(0, _x151), _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), g(s(g(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x121), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, +(0, 0)))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), g(_x32, s(g(g(g(g(+(0, 0), _x81), _x121), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, +(g(_x72, 0), 0)), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(+(0, 0), 0), +(0, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(g(_x72, g(0, _x41)), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(+(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0), _x51), 0)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, g(_x72, 0)), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(+(g(+(0, 0), _x81), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), g(_x32, s(g(g(+(g(+(0, 0), _x81), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, +(g(_x72, 0), 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(+(0, 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(+(0, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, +(g(0, _x71), 0)), _x31), 0), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(_x152, g(g(0, _x111), _x141)), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), +(g(_x152, g(0, _x181)), 0))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, g(_x72, 0)), _x51), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(g(_x82, +(+(g(_x132, 0), 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(+(g(_x82, +(+(0, 0), g(_x142, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(+(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), g(0, _x171))), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(g(s(g(g(g(_x72, g(g(_x202, 0), _x41)), _x51), _x61)), _x121), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(g(+(g(_x132, 0), 0), _x121), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(g(_x152, 0), _x171), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(+(g(g(_x72, g(0, _x41)), _x51), 0), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x82, +(+(g(_x132, 0), 0), 0)), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(g(+(0, 0), _x101), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), g(s(g(g(g(+(0, 0), _x81), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(_x72, g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, g(0, _x71)), _x31)), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x82, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(g(_x82, +(+(0, g(0, _x141)), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(_x182, g(0, _x171)), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(g(+(0, 0), _x141), +(0, 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(_x62, g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, g(_x72, 0)), _x31), _x41), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), g(_x72, 0)), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x51), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), 0), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, 0), _x31)), s(g(g(g(_x82, +(+(g(_x132, 0), 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, g(_x182, 0))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, g(+(+(0, 0), 0), _x111)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(g(s(g(g(g(g(_x72, g(0, _x41)), _x51), _x61), _x151)), _x121), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x141), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, +(g(0, _x71), 0)), _x31), _x41), s(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(g(_x112, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, +(0, 0))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x72, g(+(g(_x132, g(_x82, +(+(0, 0), 0))), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x62, g(_x22, g(_x72, 0))), 0), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(0, _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, +(0, 0))), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(g(_x92, +(g(_x82, +(+(0, 0), +(0, 0))), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x82, +(+(g(_x132, 0), 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), g(s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x92, g(_x22, g(_x72, 0))), _x61), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, g(0, _x101))), 0), _x31), s(g(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, +(g(0, _x71), 0))), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(g(0, _x101), _x71), g(0, _x101))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), g(0, _x71)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), 0), s(g(g(g(+(g(_x112, 0), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(0, _x111), _x161), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(+(g(0, _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(g(_x222, 0), _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(+(g(_x22, g(_x72, 0)), 0), _x31)), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x82, +(g(0, _x91), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(g(0, _x101), _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(+(g(+(0, 0), _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(_x62, g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x72, g(+(g(g(_x82, +(+(0, 0), 0)), _x131), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, g(0, _x191)), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, g(_x72, 0)), 0), _x31), _x41), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(+(g(_x22, g(_x72, 0)), 0), _x31)), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(_x102, g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(_x92, g(+(g(0, _x111), 0), _x81)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x131), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, g(+(+(0, 0), 0), _x161)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(+(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), 0), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), g(s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(0, _x111), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(g(_x152, 0), _x161)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x121), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x52, g(_x22, g(_x72, 0))), _x31), 0), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(_x62, g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(g(0, _x71), _x91), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(g(+(0, 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x82, g(_x72, 0))), _x31), g(_x32, s(g(g(g(g(+(0, 0), _x81), _x41), _x111), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(g(_x122, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x31)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), +(0, 0)), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), 0), g(s(g(g(g(+(0, 0), _x81), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), +(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), 0), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), s(g(_x62, g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x82, +(0, 0)), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(0, _x81)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), +(0, 0)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), +(0, 0)), _x31), s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(_x122, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(0, 0)), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(+(0, 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x62, g(_x22, 0)), 0), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(g(0, _x101), _x111))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x52, g(_x22, g(_x72, 0))), _x31), _x41), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31)), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(0, g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(g(+(g(0, _x111), 0), _x81), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(_x72, g(g(+(0, 0), _x81), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(_x112, g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, +(g(_x22, g(_x72, 0)), 0)), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(+(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), 0), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(g(0, _x91), _x71)), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(+(g(g(0, _x111), _x141), 0), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), s(g(g(g(_x92, g(+(0, 0), _x81)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), _x81), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(g(_x82, g(_x112, +(+(0, 0), 0))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x82, +(g(0, _x71), 0))), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, +(g(0, _x181), 0)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(s(g(g(g(_x72, g(_x142, g(0, _x41))), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(g(g(_x22, g(_x72, 0)), _x91), _x61), 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), g(_x32, g(_x92, s(g(g(g(+(0, 0), _x81), _x41), _x51)))), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), 0), s(g(g(g(g(+(0, 0), _x101), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(+(g(g(+(g(0, _x111), 0), _x81), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(g(0, _x181), _x191))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(_x252, g(0, _x181))))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(g(0, _x181), _x251)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x82, +(g(0, _x71), 0))), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), g(s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(+(+(g(g(0, _x111), _x141), 0), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(_x62, g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(+(g(g(+(0, 0), _x81), _x41), 0), _x111), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(g(g(0, _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(+(g(_x22, 0), 0), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(_x92, g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x101), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(g(_x82, +(+(0, g(_x142, 0)), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, g(+(+(0, 0), 0), _x121)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, g(0, _x121))), 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(+(0, 0), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(+(g(+(g(g(0, _x111), _x141), 0), _x81), 0), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), +(g(0, _x101), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(g(+(0, 0), _x121), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), +(s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x82, +(g(0, _x71), 0))), _x31), s(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(+(g(g(+(0, 0), _x81), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(g(_x132, +(0, 0)), +(0, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), g(0, _x71)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x42, g(_x22, +(0, 0))), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(_x62, g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(s(0), 0), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x82, g(_x22, g(_x72, 0)))), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), 0), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(g(_x122, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), g(0, _x151)), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), g(_x62, g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51)))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(g(_x92, +(g(_x82, +(+(0, 0), 0)), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(_x162, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81))), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(0, _x91), g(_x102, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), +(s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(+(0, g(0, _x161)), +(0, 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(+(g(+(g(_x82, +(+(0, 0), +(g(0, _x161), 0))), 0), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(+(g(_x42, +(g(_x22, 0), 0)), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), g(s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(0, 0), _x101), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), g(_x32, s(g(g(g(+(g(0, _x141), 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x52, +(g(_x22, 0), 0)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(+(g(0, _x91), g(+(0, 0), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x112, g(_x72, 0))), _x61), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), s(g(g(g(+(0, g(0, _x121)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), g(_x32, +(s(g(g(g(+(0, 0), _x81), _x41), _x51)), 0)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(+(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(g(_x32, s(g(g(g(g(+(0, 0), _x81), _x41), _x111), _x51))), _x61), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(+(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), 0), _x31), X) → f#(X, +(X, X), X)
f#(g(_x42, g(g(_x22, g(_x72, 0)), _x31)), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(g(g(_x72, g(0, _x41)), _x51), _x61))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), +(s(g(g(+(g(0, _x91), 0), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(g(_x82, +(+(g(0, _x131), 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(+(0, 0), _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), 0), s(g(g(_x72, g(g(+(0, 0), _x81), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x32, s(g(g(0, _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(_x72, g(+(g(0, _x91), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(+(g(_x132, 0), 0), g(0, _x131))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), g(_x32, s(g(g(_x112, g(g(+(0, 0), _x81), _x41)), _x51))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(0, _x111), _x141), _x151), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(_x62, g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)f#(+(g(_x22, 0), 0), g(_x82, g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), g(_x32, s(g(g(g(+(0, +(0, 0)), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, +(0, 0))), _x61), 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(+(g(_x22, 0), 0), s(+(g(0, _x41), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), s(g(g(+(g(+(0, 0), _x81), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, g(s(g(g(g(g(+(0, 0), _x81), _x41), _x111), _x51)), _x91)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(g(+(0, +(0, 0)), _x81), _x41), _x111), _x51))), X) → f#(X, +(X, X), X)f#(g(+(g(_x62, g(_x22, g(_x72, 0))), 0), _x31), s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), +(s(g(g(g(+(0, 0), _x81), _x41), _x51)), 0), X) → f#(X, +(X, X), X)f#(g(g(+(g(_x22, g(_x72, 0)), 0), _x51), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(+(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), 0), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, g(_x102, 0))), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, +(0, 0)), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x132, g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81))), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), g(_x32, s(g(g(+(g(0, _x91), 0), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(+(g(0, _x91), 0), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, g(_x102, 0))), 0), _x31), s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(+(g(_x22, g(_x72, 0)), 0), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, +(g(0, _x71), g(0, _x101))), 0), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, +(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x31), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), g(0, _x141))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81), _x161)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(g(0, _x201), _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(+(0, 0), _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(+(0, 0), _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x141), _x121), _x31)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, g(_x202, 0)), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(g(0, _x71), _x91), g(0, _x101))), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(+(g(g(g(_x82, +(+(g(_x132, 0), 0), 0)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(+(0, 0), _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(g(_x102, 0), _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), g(0, _x71)), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), g(0, _x111)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(0, _x51)), s(0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(g(0, _x181), _x41)), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, +(0, 0))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(0, _x41)), X) → f#(X, +(X, X), X)f#(g(+(g(g(_x22, g(_x72, 0)), _x61), 0), _x31), g(_x32, s(g(g(g(g(+(0, 0), _x81), _x41), _x51), _x101))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(g(0, _x171), _x111), _x141), _x151), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(_x72, g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(_x162, g(0, _x111)), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(+(g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81), 0), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(_x92, g(0, _x71)), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(+(g(g(0, _x111), _x141), g(_x152, 0)), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(+(g(g(_x82, +(+(0, 0), 0)), _x101), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x92, g(_x82, +(+(g(_x132, 0), 0), 0))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, +(0, 0)), g(_x82, g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x121), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), g(_x182, 0))), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x52, +(g(0, _x41), 0))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(g(_x142, g(+(0, 0), _x81)), _x41), _x111), _x51))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(_x72, g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x121)), _x51), 0)), X) → f#(X, +(X, X), X)f#(+(+(g(_x22, 0), 0), 0), s(g(0, _x41)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(+(g(g(_x82, +(+(0, 0), 0)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(_x42, g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31)), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(g(_x242, 0), _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x51), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(g(g(_x22, g(_x72, 0)), _x91), _x61), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(g(0, _x71), _x91), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(g(_x72, 0), _x81)), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(_x72, g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, +(0, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(_x102, g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(g(_x82, g(+(+(0, 0), 0), _x111)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(+(g(0, _x71), 0), g(0, _x101))), _x31), s(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), s(g(g(_x72, g(g(+(0, 0), _x81), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(+(g(g(0, _x111), _x121), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(0, _x91), g(0, _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x71), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(g(_x152, g(0, _x181)), _x231))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(+(g(_x132, +(0, 0)), 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(_x72, g(+(g(_x82, g(_x152, +(+(0, 0), 0))), 0), _x41)), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(+(g(g(0, _x171), _x111), 0), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(+(g(_x132, 0), 0), +(0, 0))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, g(_x102, 0))), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(+(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x131), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(_x32, s(g(g(g(g(+(0, g(0, _x171)), _x81), _x41), _x111), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), g(s(g(g(g(+(0, 0), _x81), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), 0), _x71), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(+(0, +(0, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x22, 0), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(_x192, g(0, _x111)), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(+(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x101), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(_x112, g(0, _x101)))), _x31), s(+(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(+(+(g(g(_x22, g(_x72, 0)), _x61), 0), 0), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, +(0, 0)), 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(g(_x82, +(g(0, _x91), g(0, _x101))), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(_x162, g(0, _x111)), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(g(0, _x101), _x71), 0)), _x31), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(+(+(g(_x22, g(_x72, 0)), 0), 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(_x122, g(g(_x192, g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181))))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), s(g(g(g(g(_x72, g(0, _x41)), _x51), _x91), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), s(g(_x62, g(_x52, g(0, _x41)))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(+(g(_x102, g(0, _x91)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(s(g(g(g(_x72, g(_x172, g(0, _x41))), _x51), _x61)), _x31)), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(_x62, g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, 0)), _x61), g(_x72, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(_x22, g(_x52, 0)), s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, g(_x72, g(_x102, 0))), _x31), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(_x92, g(0, _x71)), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), +(0, 0))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), +(0, 0))), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, g(_x72, 0)), 0), _x51), _x31), s(g(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), +(0, 0)), _x31), s(g(g(g(+(g(0, _x111), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, +(0, 0))), 0), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(+(g(g(_x62, +(g(_x22, g(_x72, 0)), 0)), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(+(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(+(g(0, _x111), g(0, _x121)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, +(g(0, _x181), 0))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(+(g(_x82, +(+(g(_x142, 0), 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, g(+(0, 0), _x121))), 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), g(s(g(g(g(_x82, +(0, 0)), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, g(_x72, g(0, _x131))), _x61), 0), _x31), g(_x32, s(g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x52, +(g(_x22, g(_x72, 0)), 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), _x41), s(g(g(+(g(_x82, +(+(0, 0), 0)), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), g(_x32, s(g(g(g(g(+(g(0, _x111), 0), _x81), _x91), _x41), _x51))), X) → f#(X, +(X, X), X)
f#(g(_x32, g(_x22, 0)), s(g(g(_x72, g(0, _x41)), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(s(g(g(g(_x122, g(_x72, g(0, _x41))), _x51), _x61)), _x31), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(_x72, 0)), _x31), s(g(g(+(g(0, _x91), g(g(0, _x121), _x101)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, g(_x72, 0)), 0), _x31), _x41), s(g(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), g(_x72, 0)), _x31), s(g(g(g(g(_x122, g(g(_x172, +(g(g(0, _x111), _x141), g(_x152, g(0, _x181)))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(0, s(g(g(_x42, 0), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(+(g(0, _x91), 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, 0), 0), _x31), 0), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)f#(0, s(g(_x42, +(0, 0))), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(g(_x182, +(0, 0)), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, g(_x112, +(+(0, 0), 0))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(+(0, g(_x122, 0)), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x52, g(_x22, g(_x72, 0))), _x31), s(g(+(g(+(g(0, _x91), g(0, _x101)), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, g(_x122, +(0, 0)))), 0), _x31), 0), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, g(_x72, 0)), _x31), _x41), s(g(g(+(g(0, _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(+(g(g(g(+(g(g(g(0, _x171), _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), 0), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(+(g(g(g(+(g(g(0, _x111), _x141), +(g(_x152, 0), 0)), _x81), _x91), _x41), 0), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(_x62, g(g(g(+(0, 0), _x81), _x41), _x51))), X) → f#(X, +(X, X), X)f#(g(g(_x22, g(0, _x71)), _x31), s(g(g(g(_x92, g(_x82, +(+(0, 0), 0))), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x32, s(0)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), g(_x82, g(s(g(g(_x142, g(g(_x72, g(0, _x41)), _x51)), _x61)), _x31)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), 0)), +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, 0), _x31), s(g(g(+(g(g(_x112, 0), _x91), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), _x41), s(g(g(g(_x72, g(+(g(_x82, +(+(0, 0), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(_x22, 0), +(g(_x82, g(g(s(g(g(g(_x72, g(0, _x41)), _x51), _x61)), _x121), _x31)), 0), X) → f#(X, +(X, X), X)
f#(g(_x22, 0), g(_x82, g(g(s(g(_x152, g(g(g(_x72, g(0, _x41)), _x51), _x61))), _x121), _x31)), X) → f#(X, +(X, X), X)f#(g(g(g(_x22, 0), _x31), _x41), s(g(g(g(_x82, +(+(0, 0), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), s(g(g(g(g(+(g(g(g(_x172, 0), _x111), _x141), g(_x152, g(0, _x181))), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, g(_x22, 0)), _x31), s(g(g(g(+(0, 0), _x81), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), g(s(g(g(g(g(+(g(g(0, _x111), _x141), g(_x152, 0)), _x81), _x91), _x41), _x51)), _x31), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, g(_x72, 0)), 0), _x31), 0), s(g(g(g(g(+(0, 0), _x81), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), g(_x72, 0)), _x31), s(g(g(g(g(_x122, g(+(g(g(0, _x111), _x141), g(_x152, g(0, _x181))), _x81)), _x91), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, +(g(0, _x71), g(0, _x101))), _x31), s(g(g(g(_x72, g(+(g(_x82, +(+(0, g(0, _x201)), 0)), 0), _x41)), _x51), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, g(_x72, 0)), 0), _x31), +(s(g(g(g(g(+(g(g(0, _x111), _x141), 0), _x81), _x91), _x41), _x51)), 0), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(g(g(_x82, +(0, 0)), _x41), _x51)), X) → f#(X, +(X, X), X)f#(g(g(_x22, +(g(0, _x71), 0)), _x31), s(g(g(+(g(_x82, +(+(0, 0), +(0, g(_x162, 0)))), 0), _x41), _x51)), X) → f#(X, +(X, X), X)
f#(g(g(_x22, 0), _x31), s(g(g(g(_x82, +(+(g(_x132, 0), g(_x142, 0)), 0)), _x41), _x51)), X) → f#(X, +(X, X), X)

Rewrite Rules

+(X, 0) → X+(X, s(Y)) → s(+(X, Y))
f(0, s(0), X) → f(X, +(X, X), X)g(X, Y) → X
g(X, Y) → Y

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, +

Strategy

The left-hand side of the rule f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X) 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#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), g(0, _x81))), X) 
f#(g(+(g(_x22, 0), g(_x72, 0)), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(g(_x62, +(g(g(+(g(0, _x91), 0), _x41), _x51), 0))), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), +(0, 0))), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51), 0)), X) 
f#(g(g(+(g(_x22, 0), 0), _x51), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(0, _x91), g(_x122, 0)), _x41), _x51), 0)), X) 
f#(g(+(g(_x22, 0), 0), _x31), +(s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), 0), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(0, _x91), g(0, _x121)), _x41), _x51), 0)), X) 
f#(g(+(g(_x22, 0), g(0, _x71)), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(+(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0), 0)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(g(0, _x91), _x111), 0), _x41), _x51), 0)), X) 
f#(+(g(+(g(_x22, 0), 0), _x31), 0), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51), 0)), X) 
f#(g(+(+(g(_x22, 0), 0), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) 
f#(g(+(g(_x22, +(0, 0)), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(g(0, _x121), _x91), 0), _x41), _x51), 0)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51), 0)), X) 
f#(g(+(g(g(_x22, 0), _x61), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(g(+(g(0, _x91), 0), _x101), _x41), _x51), 0)), X) 
f#(g(+(g(_x22, g(0, _x81)), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(g(_x102, +(g(0, _x91), 0)), _x41), _x51), 0)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51), 0)), X) 
f#(g(+(g(_x22, 0), 0), _x31), g(_x32, s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0))), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(_x72, g(g(+(g(0, _x91), 0), _x41), _x51)), 0)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(g(+(g(0, _x91), 0), _x41), _x81), _x51), 0)), X) 
f#(g(+(g(_x22, 0), +(0, 0)), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(_x82, g(+(g(0, _x91), 0), _x41)), _x51), 0)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(g(_x122, 0), _x91), 0), _x41), _x51), 0)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(g(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0), _x61)), X) 
f#(g(+(g(_x22, 0), 0), _x31), +(g(g(+(g(0, _x91), 0), _x41), _x51), s(0)), X) 
f#(g(+(g(_x22, 0), 0), _x31), g(s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), _x31), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x71), 0)), X) 
f#(g(g(_x52, +(g(_x22, 0), 0)), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), g(_x82, 0))), X) 
f#(g(+(g(_x62, g(_x22, 0)), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) 
f#(g(g(+(g(_x22, 0), 0), _x31), _x41), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) 
f#(g(_x42, g(+(g(_x22, 0), 0), _x31)), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) 
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(_x112, g(0, _x91)), 0), _x41), _x51), 0)), X) 
f#(g(+(g(_x22, g(_x82, 0)), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) 
Thus, the rule f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X) is replaced by the following rules:
f#(g(+(g(_x22, 0), 0), _x31), s(g(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0), _x61)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(g(+(g(0, _x91), 0), _x41), _x81), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(g(_x22, 0), _x61), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(_x42, g(+(g(_x22, 0), 0), _x31)), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(_x82, 0)), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(+(g(+(g(+(g(0, _x91), 0), _x41), 0), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(+(g(_x22, 0), 0), _x31), _x41), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(+(g(_x72, g(g(+(g(0, _x91), 0), _x41), _x51)), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(g(0, _x91), _x111), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(+(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0), 0)), X) → f#(X, +(X, X), X)
f#(+(g(+(g(_x22, 0), 0), _x31), 0), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(+(0, 0), _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(g(0, _x121), _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, +(0, 0)), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(g(_x102, +(g(0, _x91), 0)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), g(s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), _x31), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(0, _x91), g(_x122, 0)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), +(s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), 0), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), +(0, 0))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), +(0, 0)), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, g(0, _x81)), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), g(0, _x81))), X) → f#(X, +(X, X), X)
f#(g(+(+(g(_x22, 0), 0), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), +(g(g(+(g(0, _x91), 0), _x41), _x51), s(0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(g(+(g(0, _x91), 0), _x41), _x51), _x71), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(_x82, g(+(g(0, _x91), 0), _x41)), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), g(_x72, 0)), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x62, g(_x22, 0)), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(g(+(g(0, _x91), 0), _x101), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), g(0, _x71)), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(0, _x91), g(0, _x121)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(g(+(g(_x22, 0), 0), _x51), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(g(_x62, +(g(g(+(g(0, _x91), 0), _x41), _x51), 0))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(g(_x122, 0), _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), g(_x32, s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0))), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(_x112, g(0, _x91)), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(0, _x91), +(0, 0)), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(+(g(0, _x91), 0), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)
f#(g(g(_x52, +(g(_x22, 0), 0)), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), 0)), X) → f#(X, +(X, X), X)f#(g(+(g(_x22, 0), 0), _x31), s(+(g(g(+(g(0, _x91), 0), _x41), _x51), g(_x82, 0))), X) → f#(X, +(X, X), X)