TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60000 ms.

The following DP Processors were used


Problem 1 was processed with processor DependencyGraph (99ms).
 | – Problem 2 was processed with processor SubtermCriterion (1ms).
 | – Problem 3 was processed with processor ForwardNarrowing (2ms).
 |    | – Problem 7 was processed with processor ForwardNarrowing (2ms).
 |    |    | – Problem 8 was processed with processor ForwardNarrowing (2ms).
 |    |    |    | – Problem 9 was processed with processor ForwardNarrowing (8ms).
 |    |    |    |    | – Problem 10 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    | – Problem 11 was processed with processor ForwardNarrowing (8ms).
 |    |    |    |    |    |    | – Problem 12 was processed with processor ForwardNarrowing (7ms).
 |    |    |    |    |    |    |    | – Problem 13 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    | – Problem 14 was processed with processor ForwardNarrowing (11ms).
 |    |    |    |    |    |    |    |    |    | – Problem 15 was processed with processor ForwardNarrowing (12ms).
 |    |    |    |    |    |    |    |    |    |    | – Problem 16 was processed with processor ForwardNarrowing (12ms).
 |    |    |    |    |    |    |    |    |    |    |    | – Problem 17 was processed with processor ForwardNarrowing (8ms).
 |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 18 was processed with processor ForwardNarrowing (7ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 19 was processed with processor ForwardNarrowing (9ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 20 was processed with processor ForwardNarrowing (11ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 21 was processed with processor ForwardNarrowing (53ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 22 was processed with processor ForwardNarrowing (13ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 23 was processed with processor ForwardNarrowing (12ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 24 was processed with processor ForwardNarrowing (13ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 25 was processed with processor ForwardNarrowing (19ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 26 was processed with processor ForwardNarrowing (257ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 27 remains open; application of the following processors failed [ForwardNarrowing (237ms), ForwardNarrowing (230ms), ForwardNarrowing (257ms), ForwardNarrowing (334ms), ForwardNarrowing (100ms), ForwardNarrowing (304ms), ForwardNarrowing (211ms), ForwardNarrowing (380ms), ForwardNarrowing (239ms), ForwardNarrowing (236ms), ForwardNarrowing (138ms), ForwardNarrowing (270ms), ForwardNarrowing (456ms), ForwardNarrowing (235ms), ForwardNarrowing (399ms), ForwardNarrowing (386ms), ForwardNarrowing (340ms), ForwardNarrowing (639ms), ForwardNarrowing (514ms), ForwardNarrowing (563ms), ForwardNarrowing (574ms), ForwardNarrowing (229ms), ForwardNarrowing (239ms), ForwardNarrowing (546ms), ForwardNarrowing (635ms), ForwardNarrowing (515ms), ForwardNarrowing (526ms), ForwardNarrowing (640ms), ForwardNarrowing (751ms), ForwardNarrowing (533ms), ForwardNarrowing (476ms), ForwardNarrowing (740ms), ForwardNarrowing (615ms), ForwardNarrowing (436ms), ForwardNarrowing (277ms), ForwardNarrowing (569ms), ForwardNarrowing (824ms), ForwardNarrowing (417ms), ForwardNarrowing (645ms), ForwardNarrowing (695ms), ForwardNarrowing (272ms), ForwardNarrowing (918ms), ForwardNarrowing (828ms), ForwardNarrowing (timeout)].
 | – Problem 4 was processed with processor SubtermCriterion (0ms).
 | – Problem 5 was processed with processor SubtermCriterion (1ms).
 |    | – Problem 6 was processed with processor PolynomialLinearRange4iUR (28ms).

The following open problems remain:

Open Dependency Pair Problem 3

Dependency Pairs

top#(mark(X)) → top#(proper(X))top#(ok(X)) → top#(active(X))

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, ok, mark, proper, top

Problem 1: DependencyGraph

Dependency Pair Problem

Dependency Pairs

active#(f(X1, X2, X3)) → f#(X1, active(X2), X3)proper#(f(X1, X2, X3)) → f#(proper(X1), proper(X2), proper(X3))
top#(mark(X)) → top#(proper(X))top#(ok(X)) → top#(active(X))
f#(X1, mark(X2), X3) → f#(X1, X2, X3)active#(f(b, X, c)) → f#(X, c, X)
top#(ok(X)) → active#(X)proper#(f(X1, X2, X3)) → proper#(X3)
active#(f(X1, X2, X3)) → active#(X2)proper#(f(X1, X2, X3)) → proper#(X1)
top#(mark(X)) → proper#(X)proper#(f(X1, X2, X3)) → proper#(X2)
f#(ok(X1), ok(X2), ok(X3)) → f#(X1, X2, X3)

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, mark, ok, proper, top

Strategy

The following SCCs where found

active#(f(X1, X2, X3)) → active#(X2)
f#(X1, mark(X2), X3) → f#(X1, X2, X3)f#(ok(X1), ok(X2), ok(X3)) → f#(X1, X2, X3)
proper#(f(X1, X2, X3)) → proper#(X3)proper#(f(X1, X2, X3)) → proper#(X1)
proper#(f(X1, X2, X3)) → proper#(X2)
top#(mark(X)) → top#(proper(X))top#(ok(X)) → top#(active(X))

Problem 2: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

proper#(f(X1, X2, X3)) → proper#(X3)proper#(f(X1, X2, X3)) → proper#(X1)
proper#(f(X1, X2, X3)) → proper#(X2)

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, mark, ok, proper, top

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

proper#(f(X1, X2, X3)) → proper#(X3)proper#(f(X1, X2, X3)) → proper#(X1)
proper#(f(X1, X2, X3)) → proper#(X2)

Problem 3: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(mark(X)) → top#(proper(X))top#(ok(X)) → top#(active(X))

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, mark, ok, proper, top

Strategy

The right-hand side of the rule top#(mark(X)) → top#(proper(X)) is 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
top#(ok(b)) 
top#(f(proper(_x21), proper(_x22), proper(_x23))) 
top#(ok(c)) 
Thus, the rule top#(mark(X)) → top#(proper(X)) is replaced by the following rules:
top#(mark(c)) → top#(ok(c))top#(mark(f(_x21, _x22, _x23))) → top#(f(proper(_x21), proper(_x22), proper(_x23)))
top#(mark(b)) → top#(ok(b))

Problem 7: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(mark(c)) → top#(ok(c))top#(ok(X)) → top#(active(X))
top#(mark(f(_x21, _x22, _x23))) → top#(f(proper(_x21), proper(_x22), proper(_x23)))top#(mark(b)) → top#(ok(b))

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, ok, mark, proper, top

Strategy

The right-hand side of the rule top#(ok(X)) → top#(active(X)) is 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
top#(mark(b)) 
top#(f(_x21, active(_x22), _x23)) 
top#(mark(f(_x21, c, _x21))) 
Thus, the rule top#(ok(X)) → top#(active(X)) is replaced by the following rules:
top#(ok(c)) → top#(mark(b))top#(ok(f(_x21, _x22, _x23))) → top#(f(_x21, active(_x22), _x23))
top#(ok(f(b, _x21, c))) → top#(mark(f(_x21, c, _x21)))

Problem 8: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(mark(c)) → top#(ok(c))top#(ok(c)) → top#(mark(b))
top#(ok(f(_x21, _x22, _x23))) → top#(f(_x21, active(_x22), _x23))top#(mark(f(_x21, _x22, _x23))) → top#(f(proper(_x21), proper(_x22), proper(_x23)))
top#(mark(b)) → top#(ok(b))top#(ok(f(b, _x21, c))) → top#(mark(f(_x21, c, _x21)))

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, mark, ok, proper, top

Strategy

The right-hand side of the rule top#(ok(f(_x21, _x22, _x23))) → top#(f(_x21, active(_x22), _x23)) is 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
top#(f(_x21, mark(b), _x23)) 
top#(f(_x21, mark(f(_x51, c, _x51)), _x23)) 
top#(f(_x21, f(_x51, active(_x52), _x53), _x23)) 
Thus, the rule top#(ok(f(_x21, _x22, _x23))) → top#(f(_x21, active(_x22), _x23)) is replaced by the following rules:
top#(ok(f(_x21, f(b, _x51, c), _x23))) → top#(f(_x21, mark(f(_x51, c, _x51)), _x23))top#(ok(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(_x21, f(_x51, active(_x52), _x53), _x23))
top#(ok(f(_x21, c, _x23))) → top#(f(_x21, mark(b), _x23))

Problem 9: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(mark(c)) → top#(ok(c))top#(ok(c)) → top#(mark(b))
top#(ok(f(_x21, f(b, _x51, c), _x23))) → top#(f(_x21, mark(f(_x51, c, _x51)), _x23))top#(mark(f(_x21, _x22, _x23))) → top#(f(proper(_x21), proper(_x22), proper(_x23)))
top#(ok(f(b, _x21, c))) → top#(mark(f(_x21, c, _x21)))top#(mark(b)) → top#(ok(b))
top#(ok(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(_x21, f(_x51, active(_x52), _x53), _x23))top#(ok(f(_x21, c, _x23))) → top#(f(_x21, mark(b), _x23))

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, ok, mark, proper, top

Strategy

The right-hand side of the rule top#(mark(f(_x21, _x22, _x23))) → top#(f(proper(_x21), proper(_x22), proper(_x23))) is 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
top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), proper(_x23))) 
top#(f(ok(b), proper(_x22), proper(_x23))) 
top#(f(proper(_x21), ok(c), proper(_x23))) 
top#(f(proper(_x21), proper(_x22), ok(c))) 
top#(f(proper(_x21), proper(_x22), ok(b))) 
top#(f(proper(_x21), ok(b), proper(_x23))) 
top#(f(proper(_x21), proper(_x22), f(proper(_x61), proper(_x62), proper(_x63)))) 
top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x23))) 
top#(f(ok(c), proper(_x22), proper(_x23))) 
Thus, the rule top#(mark(f(_x21, _x22, _x23))) → top#(f(proper(_x21), proper(_x22), proper(_x23))) is replaced by the following rules:
top#(mark(f(_x21, c, _x23))) → top#(f(proper(_x21), ok(c), proper(_x23)))top#(mark(f(_x21, _x22, b))) → top#(f(proper(_x21), proper(_x22), ok(b)))
top#(mark(f(_x21, _x22, c))) → top#(f(proper(_x21), proper(_x22), ok(c)))top#(mark(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x23)))
top#(mark(f(c, _x22, _x23))) → top#(f(ok(c), proper(_x22), proper(_x23)))top#(mark(f(b, _x22, _x23))) → top#(f(ok(b), proper(_x22), proper(_x23)))
top#(mark(f(_x21, b, _x23))) → top#(f(proper(_x21), ok(b), proper(_x23)))top#(mark(f(f(_x41, _x42, _x43), _x22, _x23))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), proper(_x23)))
top#(mark(f(_x21, _x22, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), proper(_x22), f(proper(_x61), proper(_x62), proper(_x63))))

Problem 10: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(mark(f(_x21, c, _x23))) → top#(f(proper(_x21), ok(c), proper(_x23)))top#(mark(f(_x21, _x22, b))) → top#(f(proper(_x21), proper(_x22), ok(b)))
top#(mark(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x23)))top#(mark(f(b, _x22, _x23))) → top#(f(ok(b), proper(_x22), proper(_x23)))
top#(mark(f(_x21, b, _x23))) → top#(f(proper(_x21), ok(b), proper(_x23)))top#(ok(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(_x21, f(_x51, active(_x52), _x53), _x23))
top#(ok(f(b, _x21, c))) → top#(mark(f(_x21, c, _x21)))top#(mark(c)) → top#(ok(c))
top#(ok(f(_x21, f(b, _x51, c), _x23))) → top#(f(_x21, mark(f(_x51, c, _x51)), _x23))top#(ok(c)) → top#(mark(b))
top#(mark(f(_x21, _x22, c))) → top#(f(proper(_x21), proper(_x22), ok(c)))top#(mark(f(c, _x22, _x23))) → top#(f(ok(c), proper(_x22), proper(_x23)))
top#(mark(f(f(_x41, _x42, _x43), _x22, _x23))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), proper(_x23)))top#(mark(b)) → top#(ok(b))
top#(ok(f(_x21, c, _x23))) → top#(f(_x21, mark(b), _x23))top#(mark(f(_x21, _x22, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), proper(_x22), f(proper(_x61), proper(_x62), proper(_x63))))

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, mark, ok, proper, top

Strategy

The right-hand side of the rule top#(mark(f(_x21, c, _x23))) → top#(f(proper(_x21), ok(c), proper(_x23))) is 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
top#(f(ok(c), ok(c), proper(_x23))) 
top#(f(proper(_x21), ok(c), ok(b))) 
top#(f(proper(_x21), ok(c), ok(c))) 
top#(f(proper(_x21), ok(c), f(proper(_x61), proper(_x62), proper(_x63)))) 
top#(f(ok(b), ok(c), proper(_x23))) 
top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), proper(_x23))) 
Thus, the rule top#(mark(f(_x21, c, _x23))) → top#(f(proper(_x21), ok(c), proper(_x23))) is replaced by the following rules:
top#(mark(f(_x21, c, c))) → top#(f(proper(_x21), ok(c), ok(c)))top#(mark(f(f(_x41, _x42, _x43), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(c, c, _x23))) → top#(f(ok(c), ok(c), proper(_x23)))top#(mark(f(_x21, c, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))
top#(mark(f(b, c, _x23))) → top#(f(ok(b), ok(c), proper(_x23)))top#(mark(f(_x21, c, b))) → top#(f(proper(_x21), ok(c), ok(b)))

Problem 11: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(mark(f(f(_x41, _x42, _x43), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(_x21, _x22, b))) → top#(f(proper(_x21), proper(_x22), ok(b)))
top#(mark(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x23)))top#(mark(f(_x21, c, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))
top#(mark(f(b, _x22, _x23))) → top#(f(ok(b), proper(_x22), proper(_x23)))top#(mark(f(_x21, b, _x23))) → top#(f(proper(_x21), ok(b), proper(_x23)))
top#(ok(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(_x21, f(_x51, active(_x52), _x53), _x23))top#(ok(f(b, _x21, c))) → top#(mark(f(_x21, c, _x21)))
top#(mark(f(_x21, c, c))) → top#(f(proper(_x21), ok(c), ok(c)))top#(mark(c)) → top#(ok(c))
top#(ok(f(_x21, f(b, _x51, c), _x23))) → top#(f(_x21, mark(f(_x51, c, _x51)), _x23))top#(ok(c)) → top#(mark(b))
top#(mark(f(_x21, _x22, c))) → top#(f(proper(_x21), proper(_x22), ok(c)))top#(mark(f(c, c, _x23))) → top#(f(ok(c), ok(c), proper(_x23)))
top#(mark(f(c, _x22, _x23))) → top#(f(ok(c), proper(_x22), proper(_x23)))top#(mark(f(b, c, _x23))) → top#(f(ok(b), ok(c), proper(_x23)))
top#(mark(f(f(_x41, _x42, _x43), _x22, _x23))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), proper(_x23)))top#(mark(b)) → top#(ok(b))
top#(mark(f(_x21, c, b))) → top#(f(proper(_x21), ok(c), ok(b)))top#(ok(f(_x21, c, _x23))) → top#(f(_x21, mark(b), _x23))
top#(mark(f(_x21, _x22, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), proper(_x22), f(proper(_x61), proper(_x62), proper(_x63))))

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, ok, mark, proper, top

Strategy

The right-hand side of the rule top#(mark(f(f(_x41, _x42, _x43), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), proper(_x23))) is 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
top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), proper(_x23))) 
top#(f(f(proper(_x41), ok(c), proper(_x43)), ok(c), proper(_x23))) 
top#(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x42), proper(_x43)), ok(c), proper(_x23))) 
top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), proper(_x23))) 
top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), proper(_x23))) 
top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), proper(_x23))) 
top#(f(f(proper(_x41), f(proper(_x71), proper(_x72), proper(_x73)), proper(_x43)), ok(c), proper(_x23))) 
top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), proper(_x23))) 
top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), ok(c))) 
top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), f(proper(_x61), proper(_x62), proper(_x63)))) 
top#(f(f(proper(_x41), proper(_x42), f(proper(_x81), proper(_x82), proper(_x83))), ok(c), proper(_x23))) 
top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), ok(b))) 
Thus, the rule top#(mark(f(f(_x41, _x42, _x43), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), proper(_x23))) is replaced by the following rules:
top#(mark(f(f(c, _x42, _x43), c, _x23))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(_x41, _x42, _x43), c, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), ok(b)))
top#(mark(f(f(_x41, _x42, c), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), proper(_x23)))top#(mark(f(f(_x41, _x42, _x43), c, c))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, f(_x81, _x82, _x83)), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x81), proper(_x82), proper(_x83))), ok(c), proper(_x23)))top#(mark(f(f(_x41, _x42, _x43), c, f(_x61, _x62, _x63)))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))
top#(mark(f(f(_x41, f(_x71, _x72, _x73), _x43), c, _x23))) → top#(f(f(proper(_x41), f(proper(_x71), proper(_x72), proper(_x73)), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(_x41, b, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(f(f(_x61, _x62, _x63), _x42, _x43), c, _x23))) → top#(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x42), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(b, _x42, _x43), c, _x23))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(f(_x41, _x42, b), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), proper(_x23)))top#(mark(f(f(_x41, c, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(c), proper(_x43)), ok(c), proper(_x23)))

Problem 12: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(mark(f(f(_x41, _x42, _x43), c, c))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, _x22, b))) → top#(f(proper(_x21), proper(_x22), ok(b)))
top#(mark(f(_x21, c, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))top#(mark(f(f(_x41, _x42, b), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), proper(_x23)))
top#(mark(f(_x21, b, _x23))) → top#(f(proper(_x21), ok(b), proper(_x23)))top#(ok(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(_x21, f(_x51, active(_x52), _x53), _x23))
top#(mark(f(_x21, c, c))) → top#(f(proper(_x21), ok(c), ok(c)))top#(mark(f(c, c, _x23))) → top#(f(ok(c), ok(c), proper(_x23)))
top#(mark(f(_x21, c, b))) → top#(f(proper(_x21), ok(c), ok(b)))top#(mark(f(_x21, _x22, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), proper(_x22), f(proper(_x61), proper(_x62), proper(_x63))))
top#(mark(f(f(_x41, _x42, c), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), proper(_x23)))top#(mark(f(f(_x41, _x42, f(_x81, _x82, _x83)), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x81), proper(_x82), proper(_x83))), ok(c), proper(_x23)))
top#(mark(f(f(_x41, f(_x71, _x72, _x73), _x43), c, _x23))) → top#(f(f(proper(_x41), f(proper(_x71), proper(_x72), proper(_x73)), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(f(_x61, _x62, _x63), _x42, _x43), c, _x23))) → top#(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x42), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x23)))top#(mark(f(b, _x22, _x23))) → top#(f(ok(b), proper(_x22), proper(_x23)))
top#(ok(f(b, _x21, c))) → top#(mark(f(_x21, c, _x21)))top#(mark(f(f(_x41, c, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(c), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(f(c, _x42, _x43), c, _x23))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), proper(_x23)))top#(mark(c)) → top#(ok(c))
top#(mark(f(f(_x41, _x42, _x43), c, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), ok(b)))top#(mark(f(f(_x41, _x42, _x43), c, f(_x61, _x62, _x63)))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))
top#(ok(c)) → top#(mark(b))top#(ok(f(_x21, f(b, _x51, c), _x23))) → top#(f(_x21, mark(f(_x51, c, _x51)), _x23))
top#(mark(f(_x21, _x22, c))) → top#(f(proper(_x21), proper(_x22), ok(c)))top#(mark(f(f(_x41, b, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(c, _x22, _x23))) → top#(f(ok(c), proper(_x22), proper(_x23)))top#(mark(f(b, c, _x23))) → top#(f(ok(b), ok(c), proper(_x23)))
top#(mark(f(f(b, _x42, _x43), c, _x23))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(_x41, _x42, _x43), _x22, _x23))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), proper(_x23)))
top#(mark(b)) → top#(ok(b))top#(ok(f(_x21, c, _x23))) → top#(f(_x21, mark(b), _x23))

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, mark, ok, proper, top

Strategy

The right-hand side of the rule top#(mark(f(f(_x41, _x42, _x43), c, c))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), ok(c))) is 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
top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), ok(c))) 
top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), proper(_x43)), ok(c), ok(c))) 
top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x43)), ok(c), ok(c))) 
top#(f(f(proper(_x41), proper(_x42), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c))) 
top#(f(f(proper(_x41), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), ok(c))) 
top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), ok(c))) 
top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), ok(c))) 
Thus, the rule top#(mark(f(f(_x41, _x42, _x43), c, c))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), ok(c))) is replaced by the following rules:
top#(mark(f(f(_x41, _x42, b), c, c))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), ok(c)))top#(mark(f(f(b, _x42, _x43), c, c))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, f(_x61, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), _x42, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, _x43), c, c))) → top#(f(f(proper(_x41), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, b, _x43), c, c))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, c), c, c))) → top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), ok(c)))top#(mark(f(f(c, _x42, _x43), c, c))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, f(_x51, _x52, _x53), _x43), c, c))) → top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x43)), ok(c), ok(c)))

Problem 13: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(mark(f(_x21, _x22, b))) → top#(f(proper(_x21), proper(_x22), ok(b)))top#(mark(f(f(_x41, c, _x43), c, c))) → top#(f(f(proper(_x41), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(_x21, c, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))top#(mark(f(f(_x41, _x42, b), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), proper(_x23)))
top#(mark(f(_x21, b, _x23))) → top#(f(proper(_x21), ok(b), proper(_x23)))top#(ok(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(_x21, f(_x51, active(_x52), _x53), _x23))
top#(mark(f(f(_x41, _x42, c), c, c))) → top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), ok(c)))top#(mark(f(_x21, c, c))) → top#(f(proper(_x21), ok(c), ok(c)))
top#(mark(f(f(b, _x42, _x43), c, c))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), ok(c)))top#(mark(f(c, c, _x23))) → top#(f(ok(c), ok(c), proper(_x23)))
top#(mark(f(f(_x41, b, _x43), c, c))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, c, b))) → top#(f(proper(_x21), ok(c), ok(b)))
top#(mark(f(f(_x41, f(_x51, _x52, _x53), _x43), c, c))) → top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, _x22, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), proper(_x22), f(proper(_x61), proper(_x62), proper(_x63))))
top#(mark(f(f(_x41, _x42, c), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), proper(_x23)))top#(mark(f(f(_x41, _x42, f(_x81, _x82, _x83)), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x81), proper(_x82), proper(_x83))), ok(c), proper(_x23)))
top#(mark(f(f(_x41, _x42, f(_x61, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), _x42, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, f(_x71, _x72, _x73), _x43), c, _x23))) → top#(f(f(proper(_x41), f(proper(_x71), proper(_x72), proper(_x73)), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(f(_x61, _x62, _x63), _x42, _x43), c, _x23))) → top#(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x42), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x23)))top#(mark(f(b, _x22, _x23))) → top#(f(ok(b), proper(_x22), proper(_x23)))
top#(ok(f(b, _x21, c))) → top#(mark(f(_x21, c, _x21)))top#(mark(f(f(_x41, c, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(c), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(f(c, _x42, _x43), c, _x23))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(_x41, _x42, _x43), c, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), ok(b)))
top#(mark(c)) → top#(ok(c))top#(mark(f(f(_x41, _x42, _x43), c, f(_x61, _x62, _x63)))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))
top#(mark(f(f(_x41, _x42, b), c, c))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), ok(c)))top#(ok(f(_x21, f(b, _x51, c), _x23))) → top#(f(_x21, mark(f(_x51, c, _x51)), _x23))
top#(ok(c)) → top#(mark(b))top#(mark(f(f(_x41, b, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(_x21, _x22, c))) → top#(f(proper(_x21), proper(_x22), ok(c)))top#(mark(f(c, _x22, _x23))) → top#(f(ok(c), proper(_x22), proper(_x23)))
top#(mark(f(f(b, _x42, _x43), c, _x23))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(b, c, _x23))) → top#(f(ok(b), ok(c), proper(_x23)))
top#(mark(f(f(_x41, _x42, _x43), _x22, _x23))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), proper(_x23)))top#(mark(b)) → top#(ok(b))
top#(mark(f(f(c, _x42, _x43), c, c))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), ok(c)))top#(ok(f(_x21, c, _x23))) → top#(f(_x21, mark(b), _x23))

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, ok, mark, proper, top

Strategy

The right-hand side of the rule top#(mark(f(_x21, _x22, b))) → top#(f(proper(_x21), proper(_x22), ok(b))) is 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
top#(f(ok(c), proper(_x22), ok(b))) 
top#(f(proper(_x21), ok(b), ok(b))) 
top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), ok(b))) 
top#(f(proper(_x21), ok(c), ok(b))) 
top#(f(ok(b), proper(_x22), ok(b))) 
top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), ok(b))) 
Thus, the rule top#(mark(f(_x21, _x22, b))) → top#(f(proper(_x21), proper(_x22), ok(b))) is replaced by the following rules:
top#(mark(f(_x21, f(_x51, _x52, _x53), b))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), ok(b)))top#(mark(f(f(_x41, _x42, _x43), _x22, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), ok(b)))
top#(mark(f(_x21, b, b))) → top#(f(proper(_x21), ok(b), ok(b)))top#(mark(f(c, _x22, b))) → top#(f(ok(c), proper(_x22), ok(b)))
top#(mark(f(_x21, c, b))) → top#(f(proper(_x21), ok(c), ok(b)))top#(mark(f(b, _x22, b))) → top#(f(ok(b), proper(_x22), ok(b)))

Problem 14: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(mark(f(f(_x41, c, _x43), c, c))) → top#(f(f(proper(_x41), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, c, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))
top#(mark(f(f(_x41, _x42, b), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), proper(_x23)))top#(mark(f(_x21, b, _x23))) → top#(f(proper(_x21), ok(b), proper(_x23)))
top#(ok(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(_x21, f(_x51, active(_x52), _x53), _x23))top#(mark(f(f(_x41, _x42, c), c, c))) → top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), ok(c)))
top#(mark(f(_x21, c, c))) → top#(f(proper(_x21), ok(c), ok(c)))top#(mark(f(f(b, _x42, _x43), c, c))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), ok(c)))
top#(mark(f(c, c, _x23))) → top#(f(ok(c), ok(c), proper(_x23)))top#(mark(f(f(_x41, b, _x43), c, c))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, f(_x51, _x52, _x53), _x43), c, c))) → top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, c, b))) → top#(f(proper(_x21), ok(c), ok(b)))
top#(mark(f(b, _x22, b))) → top#(f(ok(b), proper(_x22), ok(b)))top#(mark(f(_x21, _x22, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), proper(_x22), f(proper(_x61), proper(_x62), proper(_x63))))
top#(mark(f(f(_x41, _x42, c), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), proper(_x23)))top#(mark(f(f(_x41, _x42, f(_x81, _x82, _x83)), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x81), proper(_x82), proper(_x83))), ok(c), proper(_x23)))
top#(mark(f(f(_x41, _x42, f(_x61, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), _x42, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, f(_x71, _x72, _x73), _x43), c, _x23))) → top#(f(f(proper(_x41), f(proper(_x71), proper(_x72), proper(_x73)), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(f(_x61, _x62, _x63), _x42, _x43), c, _x23))) → top#(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x42), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x23)))top#(mark(f(b, _x22, _x23))) → top#(f(ok(b), proper(_x22), proper(_x23)))
top#(mark(f(c, _x22, b))) → top#(f(ok(c), proper(_x22), ok(b)))top#(ok(f(b, _x21, c))) → top#(mark(f(_x21, c, _x21)))
top#(mark(f(f(_x41, c, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(c), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(c, _x42, _x43), c, _x23))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), proper(_x23)))
top#(mark(c)) → top#(ok(c))top#(mark(f(f(_x41, _x42, _x43), c, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), ok(b)))
top#(mark(f(f(_x41, _x42, b), c, c))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), ok(c)))top#(mark(f(f(_x41, _x42, _x43), c, f(_x61, _x62, _x63)))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))
top#(ok(c)) → top#(mark(b))top#(ok(f(_x21, f(b, _x51, c), _x23))) → top#(f(_x21, mark(f(_x51, c, _x51)), _x23))
top#(mark(f(_x21, _x22, c))) → top#(f(proper(_x21), proper(_x22), ok(c)))top#(mark(f(f(_x41, b, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(c, _x22, _x23))) → top#(f(ok(c), proper(_x22), proper(_x23)))top#(mark(f(_x21, f(_x51, _x52, _x53), b))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), ok(b)))
top#(mark(f(b, c, _x23))) → top#(f(ok(b), ok(c), proper(_x23)))top#(mark(f(f(b, _x42, _x43), c, _x23))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(f(_x41, _x42, _x43), _x22, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), ok(b)))top#(mark(f(f(_x41, _x42, _x43), _x22, _x23))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), proper(_x23)))
top#(mark(f(_x21, b, b))) → top#(f(proper(_x21), ok(b), ok(b)))top#(mark(b)) → top#(ok(b))
top#(mark(f(f(c, _x42, _x43), c, c))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), ok(c)))top#(ok(f(_x21, c, _x23))) → top#(f(_x21, mark(b), _x23))

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, mark, ok, proper, top

Strategy

The right-hand side of the rule top#(mark(f(f(_x41, c, _x43), c, c))) → top#(f(f(proper(_x41), ok(c), proper(_x43)), ok(c), ok(c))) is 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
top#(f(f(ok(b), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(proper(_x41), ok(c), ok(c)), ok(c), ok(c))) 
top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(proper(_x41), ok(c), ok(b)), ok(c), ok(c))) 
top#(f(f(ok(c), ok(c), proper(_x43)), ok(c), ok(c))) 
Thus, the rule top#(mark(f(f(_x41, c, _x43), c, c))) → top#(f(f(proper(_x41), ok(c), proper(_x43)), ok(c), ok(c))) is replaced by the following rules:
top#(mark(f(f(f(_x51, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(c, c, _x43), c, c))) → top#(f(f(ok(c), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, b), c, c))) → top#(f(f(proper(_x41), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, c), c, c))) → top#(f(f(proper(_x41), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(b, c, _x43), c, c))) → top#(f(f(ok(b), ok(c), proper(_x43)), ok(c), ok(c)))

Problem 15: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(mark(f(f(f(_x51, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, c), c, c))) → top#(f(f(proper(_x41), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, c), c, c))) → top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), ok(c)))top#(mark(f(f(b, _x42, _x43), c, c))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(b, _x22, b))) → top#(f(ok(b), proper(_x22), ok(b)))
top#(mark(f(f(b, c, _x43), c, c))) → top#(f(f(ok(b), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, _x42, f(_x81, _x82, _x83)), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x81), proper(_x82), proper(_x83))), ok(c), proper(_x23)))
top#(mark(f(f(_x41, f(_x71, _x72, _x73), _x43), c, _x23))) → top#(f(f(proper(_x41), f(proper(_x71), proper(_x72), proper(_x73)), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(f(_x61, _x62, _x63), _x42, _x43), c, _x23))) → top#(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x42), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(b, _x22, _x23))) → top#(f(ok(b), proper(_x22), proper(_x23)))top#(ok(f(b, _x21, c))) → top#(mark(f(_x21, c, _x21)))
top#(mark(f(f(c, _x42, _x43), c, _x23))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(_x41, _x42, _x43), c, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), ok(b)))
top#(mark(f(f(_x41, _x42, b), c, c))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), ok(c)))top#(mark(f(f(_x41, _x42, _x43), c, f(_x61, _x62, _x63)))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))
top#(ok(f(_x21, f(b, _x51, c), _x23))) → top#(f(_x21, mark(f(_x51, c, _x51)), _x23))top#(mark(f(f(_x41, b, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(c, _x22, _x23))) → top#(f(ok(c), proper(_x22), proper(_x23)))top#(mark(f(f(_x41, _x42, _x43), _x22, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), ok(b)))
top#(mark(f(_x21, b, b))) → top#(f(proper(_x21), ok(b), ok(b)))top#(mark(f(f(c, _x42, _x43), c, c))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), ok(c)))
top#(ok(f(_x21, c, _x23))) → top#(f(_x21, mark(b), _x23))top#(mark(f(f(c, c, _x43), c, c))) → top#(f(f(ok(c), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(_x21, c, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))top#(mark(f(f(_x41, _x42, b), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), proper(_x23)))
top#(mark(f(_x21, b, _x23))) → top#(f(proper(_x21), ok(b), proper(_x23)))top#(ok(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(_x21, f(_x51, active(_x52), _x53), _x23))
top#(mark(f(_x21, c, c))) → top#(f(proper(_x21), ok(c), ok(c)))top#(mark(f(c, c, _x23))) → top#(f(ok(c), ok(c), proper(_x23)))
top#(mark(f(f(_x41, b, _x43), c, c))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, b), c, c))) → top#(f(f(proper(_x41), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(_x21, c, b))) → top#(f(proper(_x21), ok(c), ok(b)))top#(mark(f(f(_x41, f(_x51, _x52, _x53), _x43), c, c))) → top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x43)), ok(c), ok(c)))
top#(mark(f(_x21, _x22, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), proper(_x22), f(proper(_x61), proper(_x62), proper(_x63))))top#(mark(f(f(_x41, _x42, c), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), proper(_x23)))
top#(mark(f(f(_x41, _x42, f(_x61, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), _x42, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), proper(_x43)), ok(c), ok(c)))
top#(mark(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x23)))top#(mark(f(c, _x22, b))) → top#(f(ok(c), proper(_x22), ok(b)))
top#(mark(f(f(_x41, c, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(c), proper(_x43)), ok(c), proper(_x23)))top#(mark(c)) → top#(ok(c))
top#(ok(c)) → top#(mark(b))top#(mark(f(_x21, _x22, c))) → top#(f(proper(_x21), proper(_x22), ok(c)))
top#(mark(f(_x21, f(_x51, _x52, _x53), b))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), ok(b)))top#(mark(f(f(b, _x42, _x43), c, _x23))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(b, c, _x23))) → top#(f(ok(b), ok(c), proper(_x23)))top#(mark(f(f(_x41, _x42, _x43), _x22, _x23))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), proper(_x23)))
top#(mark(b)) → top#(ok(b))

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, ok, mark, proper, top

Strategy

The right-hand side of the rule top#(mark(f(f(f(_x51, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c))) is 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
top#(f(f(f(ok(b), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(ok(c), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), ok(b), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), ok(c), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), proper(_x52), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), proper(_x52), ok(b)), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(c)), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), proper(_x52), ok(c)), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(b)), ok(c), ok(c))) 
Thus, the rule top#(mark(f(f(f(_x51, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c))) is replaced by the following rules:
top#(mark(f(f(f(f(_x61, _x62, _x63), _x52, _x53), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(ok(b), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, _x53), c, c), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, b, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), ok(b), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, c), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), ok(c)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(c, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(ok(c), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, b), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), ok(b)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), c, b), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, c, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), ok(c), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))

Problem 16: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(mark(f(f(_x41, c, c), c, c))) → top#(f(f(proper(_x41), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(_x41, _x42, c), c, c))) → top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), ok(c)))
top#(mark(f(f(b, _x42, _x43), c, c))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(c, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(ok(c), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(b, _x22, b))) → top#(f(ok(b), proper(_x22), ok(b)))top#(mark(f(f(b, c, _x43), c, c))) → top#(f(f(ok(b), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, f(_x81, _x82, _x83)), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x81), proper(_x82), proper(_x83))), ok(c), proper(_x23)))top#(mark(f(f(_x41, f(_x71, _x72, _x73), _x43), c, _x23))) → top#(f(f(proper(_x41), f(proper(_x71), proper(_x72), proper(_x73)), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(f(f(_x61, _x62, _x63), _x42, _x43), c, _x23))) → top#(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x42), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(b, _x22, _x23))) → top#(f(ok(b), proper(_x22), proper(_x23)))
top#(ok(f(b, _x21, c))) → top#(mark(f(_x21, c, _x21)))top#(mark(f(f(c, _x42, _x43), c, _x23))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(f(_x41, _x42, _x43), c, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), ok(b)))top#(mark(f(f(_x41, _x42, _x43), c, f(_x61, _x62, _x63)))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))
top#(mark(f(f(_x41, _x42, b), c, c))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), ok(c)))top#(ok(f(_x21, f(b, _x51, c), _x23))) → top#(f(_x21, mark(f(_x51, c, _x51)), _x23))
top#(mark(f(f(_x41, b, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(c, _x22, _x23))) → top#(f(ok(c), proper(_x22), proper(_x23)))
top#(mark(f(f(_x41, _x42, _x43), _x22, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), ok(b)))top#(mark(f(_x21, b, b))) → top#(f(proper(_x21), ok(b), ok(b)))
top#(mark(f(f(f(_x51, b, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), ok(b), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(c, _x42, _x43), c, c))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), ok(c)))
top#(ok(f(_x21, c, _x23))) → top#(f(_x21, mark(b), _x23))top#(mark(f(f(f(_x51, _x52, _x53), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(b, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(ok(b), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(c, c, _x43), c, c))) → top#(f(f(ok(c), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(_x21, c, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))top#(mark(f(f(_x41, _x42, b), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), proper(_x23)))
top#(mark(f(_x21, b, _x23))) → top#(f(proper(_x21), ok(b), proper(_x23)))top#(ok(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(_x21, f(_x51, active(_x52), _x53), _x23))
top#(mark(f(_x21, c, c))) → top#(f(proper(_x21), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(c, c, _x23))) → top#(f(ok(c), ok(c), proper(_x23)))top#(mark(f(f(_x41, b, _x43), c, c))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, b), c, c))) → top#(f(f(proper(_x41), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), c, c), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, _x53), c, b), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(_x21, c, b))) → top#(f(proper(_x21), ok(c), ok(b)))
top#(mark(f(f(_x41, f(_x51, _x52, _x53), _x43), c, c))) → top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, _x22, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), proper(_x22), f(proper(_x61), proper(_x62), proper(_x63))))
top#(mark(f(f(_x41, _x42, c), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), proper(_x23)))top#(mark(f(f(f(f(_x61, _x62, _x63), _x52, _x53), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, f(_x61, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), _x42, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), proper(_x43)), ok(c), ok(c)))
top#(mark(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x23)))top#(mark(f(c, _x22, b))) → top#(f(ok(c), proper(_x22), ok(b)))
top#(mark(f(f(f(_x51, _x52, b), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), ok(b)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, c), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), ok(c)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(c), proper(_x43)), ok(c), proper(_x23)))top#(mark(c)) → top#(ok(c))
top#(ok(c)) → top#(mark(b))top#(mark(f(_x21, _x22, c))) → top#(f(proper(_x21), proper(_x22), ok(c)))
top#(mark(f(_x21, f(_x51, _x52, _x53), b))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), ok(b)))top#(mark(f(b, c, _x23))) → top#(f(ok(b), ok(c), proper(_x23)))
top#(mark(f(f(b, _x42, _x43), c, _x23))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(_x41, _x42, _x43), _x22, _x23))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), proper(_x23)))
top#(mark(b)) → top#(ok(b))top#(mark(f(f(f(_x51, c, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), ok(c), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, mark, ok, proper, top

Strategy

The right-hand side of the rule top#(mark(f(f(_x41, c, c), c, c))) → top#(f(f(proper(_x41), ok(c), ok(c)), ok(c), ok(c))) is 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
top#(f(f(ok(c), ok(c), ok(c)), ok(c), ok(c))) 
top#(f(f(ok(b), ok(c), ok(c)), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(c)), ok(c), ok(c))) 
Thus, the rule top#(mark(f(f(_x41, c, c), c, c))) → top#(f(f(proper(_x41), ok(c), ok(c)), ok(c), ok(c))) is replaced by the following rules:
top#(mark(f(f(c, c, c), c, c))) → top#(f(f(ok(c), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), c, c), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(b, c, c), c, c))) → top#(f(f(ok(b), ok(c), ok(c)), ok(c), ok(c)))

Problem 17: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(mark(f(f(_x41, _x42, c), c, c))) → top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), ok(c)))top#(mark(f(f(c, c, c), c, c))) → top#(f(f(ok(c), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(b, _x42, _x43), c, c))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(b, c, c), c, c))) → top#(f(f(ok(b), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(c, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(ok(c), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(b, _x22, b))) → top#(f(ok(b), proper(_x22), ok(b)))
top#(mark(f(f(b, c, _x43), c, c))) → top#(f(f(ok(b), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, _x42, f(_x81, _x82, _x83)), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x81), proper(_x82), proper(_x83))), ok(c), proper(_x23)))
top#(mark(f(f(_x41, f(_x71, _x72, _x73), _x43), c, _x23))) → top#(f(f(proper(_x41), f(proper(_x71), proper(_x72), proper(_x73)), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(f(_x61, _x62, _x63), _x42, _x43), c, _x23))) → top#(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x42), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(b, _x22, _x23))) → top#(f(ok(b), proper(_x22), proper(_x23)))top#(ok(f(b, _x21, c))) → top#(mark(f(_x21, c, _x21)))
top#(mark(f(f(c, _x42, _x43), c, _x23))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(_x41, _x42, _x43), c, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), ok(b)))
top#(mark(f(f(_x41, _x42, b), c, c))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), ok(c)))top#(mark(f(f(_x41, _x42, _x43), c, f(_x61, _x62, _x63)))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))
top#(ok(f(_x21, f(b, _x51, c), _x23))) → top#(f(_x21, mark(f(_x51, c, _x51)), _x23))top#(mark(f(f(_x41, b, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(c, _x22, _x23))) → top#(f(ok(c), proper(_x22), proper(_x23)))top#(mark(f(f(_x41, _x42, _x43), _x22, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), ok(b)))
top#(mark(f(f(f(_x51, b, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), ok(b), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, b, b))) → top#(f(proper(_x21), ok(b), ok(b)))
top#(mark(f(f(c, _x42, _x43), c, c))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), ok(c)))top#(ok(f(_x21, c, _x23))) → top#(f(_x21, mark(b), _x23))
top#(mark(f(f(f(_x51, _x52, _x53), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(b, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(ok(b), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(c, c, _x43), c, c))) → top#(f(f(ok(c), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, c, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))
top#(mark(f(f(_x41, _x42, b), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), proper(_x23)))top#(mark(f(_x21, b, _x23))) → top#(f(proper(_x21), ok(b), proper(_x23)))
top#(ok(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(_x21, f(_x51, active(_x52), _x53), _x23))top#(mark(f(_x21, c, c))) → top#(f(proper(_x21), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(c, c, _x23))) → top#(f(ok(c), ok(c), proper(_x23)))
top#(mark(f(f(_x41, b, _x43), c, c))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, b), c, c))) → top#(f(f(proper(_x41), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, _x53), c, c), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), c, b), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(_x21, c, b))) → top#(f(proper(_x21), ok(c), ok(b)))top#(mark(f(f(_x41, f(_x51, _x52, _x53), _x43), c, c))) → top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x43)), ok(c), ok(c)))
top#(mark(f(_x21, _x22, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), proper(_x22), f(proper(_x61), proper(_x62), proper(_x63))))top#(mark(f(f(_x41, _x42, c), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), proper(_x23)))
top#(mark(f(f(f(f(_x61, _x62, _x63), _x52, _x53), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, _x42, f(_x61, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, _x53), _x42, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x23)))
top#(mark(f(f(f(_x51, _x52, c), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), ok(c)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, b), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), ok(b)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(c, _x22, b))) → top#(f(ok(c), proper(_x22), ok(b)))top#(mark(f(f(_x41, c, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(c), proper(_x43)), ok(c), proper(_x23)))
top#(mark(c)) → top#(ok(c))top#(ok(c)) → top#(mark(b))
top#(mark(f(_x21, _x22, c))) → top#(f(proper(_x21), proper(_x22), ok(c)))top#(mark(f(_x21, f(_x51, _x52, _x53), b))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), ok(b)))
top#(mark(f(f(b, _x42, _x43), c, _x23))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(b, c, _x23))) → top#(f(ok(b), ok(c), proper(_x23)))
top#(mark(f(f(_x41, _x42, _x43), _x22, _x23))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), proper(_x23)))top#(mark(b)) → top#(ok(b))
top#(mark(f(f(f(_x51, c, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), ok(c), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, ok, mark, proper, top

Strategy

The right-hand side of the rule top#(mark(f(f(_x41, _x42, c), c, c))) → top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), ok(c))) is 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
top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), ok(c)), ok(c), ok(c))) 
top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), ok(c)), ok(c), ok(c))) 
top#(f(f(ok(b), proper(_x42), ok(c)), ok(c), ok(c))) 
top#(f(f(proper(_x41), ok(b), ok(c)), ok(c), ok(c))) 
top#(f(f(proper(_x41), ok(c), ok(c)), ok(c), ok(c))) 
top#(f(f(ok(c), proper(_x42), ok(c)), ok(c), ok(c))) 
Thus, the rule top#(mark(f(f(_x41, _x42, c), c, c))) → top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), ok(c))) is replaced by the following rules:
top#(mark(f(f(f(_x51, _x52, _x53), _x42, c), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), ok(c)), ok(c), ok(c)))top#(mark(f(f(b, _x42, c), c, c))) → top#(f(f(ok(b), proper(_x42), ok(c)), ok(c), ok(c)))
top#(mark(f(f(_x41, b, c), c, c))) → top#(f(f(proper(_x41), ok(b), ok(c)), ok(c), ok(c)))top#(mark(f(f(_x41, f(_x51, _x52, _x53), c), c, c))) → top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), ok(c)), ok(c), ok(c)))
top#(mark(f(f(c, _x42, c), c, c))) → top#(f(f(ok(c), proper(_x42), ok(c)), ok(c), ok(c)))top#(mark(f(f(_x41, c, c), c, c))) → top#(f(f(proper(_x41), ok(c), ok(c)), ok(c), ok(c)))

Problem 18: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(mark(f(f(_x41, c, c), c, c))) → top#(f(f(proper(_x41), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(c, c, c), c, c))) → top#(f(f(ok(c), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(b, _x42, _x43), c, c))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(b, c, c), c, c))) → top#(f(f(ok(b), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(c, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(ok(c), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(b, _x22, b))) → top#(f(ok(b), proper(_x22), ok(b)))
top#(mark(f(f(b, c, _x43), c, c))) → top#(f(f(ok(b), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, _x42, f(_x81, _x82, _x83)), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x81), proper(_x82), proper(_x83))), ok(c), proper(_x23)))
top#(mark(f(f(_x41, f(_x71, _x72, _x73), _x43), c, _x23))) → top#(f(f(proper(_x41), f(proper(_x71), proper(_x72), proper(_x73)), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(f(_x61, _x62, _x63), _x42, _x43), c, _x23))) → top#(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x42), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(b, _x22, _x23))) → top#(f(ok(b), proper(_x22), proper(_x23)))top#(ok(f(b, _x21, c))) → top#(mark(f(_x21, c, _x21)))
top#(mark(f(f(c, _x42, _x43), c, _x23))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(_x41, _x42, _x43), c, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), ok(b)))
top#(mark(f(f(_x41, _x42, _x43), c, f(_x61, _x62, _x63)))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))top#(mark(f(f(_x41, _x42, b), c, c))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), ok(c)))
top#(ok(f(_x21, f(b, _x51, c), _x23))) → top#(f(_x21, mark(f(_x51, c, _x51)), _x23))top#(mark(f(f(_x41, b, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(c, _x22, _x23))) → top#(f(ok(c), proper(_x22), proper(_x23)))top#(mark(f(f(_x41, _x42, _x43), _x22, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), ok(b)))
top#(mark(f(f(c, _x42, c), c, c))) → top#(f(f(ok(c), proper(_x42), ok(c)), ok(c), ok(c)))top#(mark(f(_x21, b, b))) → top#(f(proper(_x21), ok(b), ok(b)))
top#(mark(f(f(f(_x51, b, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), ok(b), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(c, _x42, _x43), c, c))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), ok(c)))
top#(ok(f(_x21, c, _x23))) → top#(f(_x21, mark(b), _x23))top#(mark(f(f(f(_x51, _x52, _x53), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(b, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(ok(b), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(c, c, _x43), c, c))) → top#(f(f(ok(c), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(_x21, c, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))top#(mark(f(f(_x41, _x42, b), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), proper(_x23)))
top#(mark(f(_x21, b, _x23))) → top#(f(proper(_x21), ok(b), proper(_x23)))top#(ok(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(_x21, f(_x51, active(_x52), _x53), _x23))
top#(mark(f(_x21, c, c))) → top#(f(proper(_x21), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), _x42, c), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(b, _x42, c), c, c))) → top#(f(f(ok(b), proper(_x42), ok(c)), ok(c), ok(c)))
top#(mark(f(f(_x41, f(_x51, _x52, _x53), c), c, c))) → top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), ok(c)), ok(c), ok(c)))top#(mark(f(c, c, _x23))) → top#(f(ok(c), ok(c), proper(_x23)))
top#(mark(f(f(_x41, b, _x43), c, c))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, b), c, c))) → top#(f(f(proper(_x41), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, _x53), c, c), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), c, b), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(_x21, c, b))) → top#(f(proper(_x21), ok(c), ok(b)))top#(mark(f(f(_x41, f(_x51, _x52, _x53), _x43), c, c))) → top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x43)), ok(c), ok(c)))
top#(mark(f(_x21, _x22, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), proper(_x22), f(proper(_x61), proper(_x62), proper(_x63))))top#(mark(f(f(_x41, _x42, c), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), proper(_x23)))
top#(mark(f(f(f(f(_x61, _x62, _x63), _x52, _x53), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, _x42, f(_x61, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, _x53), _x42, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, b, c), c, c))) → top#(f(f(proper(_x41), ok(b), ok(c)), ok(c), ok(c)))
top#(mark(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x23)))top#(mark(f(c, _x22, b))) → top#(f(ok(c), proper(_x22), ok(b)))
top#(mark(f(f(f(_x51, _x52, b), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), ok(b)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, c), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), ok(c)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(c), proper(_x43)), ok(c), proper(_x23)))top#(mark(c)) → top#(ok(c))
top#(ok(c)) → top#(mark(b))top#(mark(f(_x21, _x22, c))) → top#(f(proper(_x21), proper(_x22), ok(c)))
top#(mark(f(_x21, f(_x51, _x52, _x53), b))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), ok(b)))top#(mark(f(b, c, _x23))) → top#(f(ok(b), ok(c), proper(_x23)))
top#(mark(f(f(b, _x42, _x43), c, _x23))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(_x41, _x42, _x43), _x22, _x23))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), proper(_x23)))
top#(mark(b)) → top#(ok(b))top#(mark(f(f(f(_x51, c, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), ok(c), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, mark, ok, proper, top

Strategy

The right-hand side of the rule top#(mark(f(f(_x41, c, c), c, c))) → top#(f(f(proper(_x41), ok(c), ok(c)), ok(c), ok(c))) is 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
top#(f(f(ok(c), ok(c), ok(c)), ok(c), ok(c))) 
top#(f(f(ok(b), ok(c), ok(c)), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(c)), ok(c), ok(c))) 
Thus, the rule top#(mark(f(f(_x41, c, c), c, c))) → top#(f(f(proper(_x41), ok(c), ok(c)), ok(c), ok(c))) is replaced by the following rules:
top#(mark(f(f(c, c, c), c, c))) → top#(f(f(ok(c), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), c, c), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(b, c, c), c, c))) → top#(f(f(ok(b), ok(c), ok(c)), ok(c), ok(c)))

Problem 19: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(mark(f(f(c, c, c), c, c))) → top#(f(f(ok(c), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(b, _x42, _x43), c, c))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(b, c, c), c, c))) → top#(f(f(ok(b), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(c, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(ok(c), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(b, _x22, b))) → top#(f(ok(b), proper(_x22), ok(b)))top#(mark(f(f(b, c, _x43), c, c))) → top#(f(f(ok(b), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, f(_x81, _x82, _x83)), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x81), proper(_x82), proper(_x83))), ok(c), proper(_x23)))top#(mark(f(f(_x41, f(_x71, _x72, _x73), _x43), c, _x23))) → top#(f(f(proper(_x41), f(proper(_x71), proper(_x72), proper(_x73)), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(f(f(_x61, _x62, _x63), _x42, _x43), c, _x23))) → top#(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x42), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(b, _x22, _x23))) → top#(f(ok(b), proper(_x22), proper(_x23)))
top#(ok(f(b, _x21, c))) → top#(mark(f(_x21, c, _x21)))top#(mark(f(f(c, _x42, _x43), c, _x23))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(f(_x41, _x42, _x43), c, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), ok(b)))top#(mark(f(f(_x41, _x42, b), c, c))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, _x43), c, f(_x61, _x62, _x63)))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))top#(ok(f(_x21, f(b, _x51, c), _x23))) → top#(f(_x21, mark(f(_x51, c, _x51)), _x23))
top#(mark(f(f(_x41, b, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(c, _x22, _x23))) → top#(f(ok(c), proper(_x22), proper(_x23)))
top#(mark(f(f(c, _x42, c), c, c))) → top#(f(f(ok(c), proper(_x42), ok(c)), ok(c), ok(c)))top#(mark(f(f(_x41, _x42, _x43), _x22, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), ok(b)))
top#(mark(f(f(f(_x51, b, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), ok(b), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, b, b))) → top#(f(proper(_x21), ok(b), ok(b)))
top#(mark(f(f(c, _x42, _x43), c, c))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), ok(c)))top#(ok(f(_x21, c, _x23))) → top#(f(_x21, mark(b), _x23))
top#(mark(f(f(f(_x51, _x52, _x53), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(b, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(ok(b), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(c, c, _x43), c, c))) → top#(f(f(ok(c), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, c, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))
top#(mark(f(f(_x41, _x42, b), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), proper(_x23)))top#(mark(f(_x21, b, _x23))) → top#(f(proper(_x21), ok(b), proper(_x23)))
top#(ok(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(_x21, f(_x51, active(_x52), _x53), _x23))top#(mark(f(_x21, c, c))) → top#(f(proper(_x21), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, _x53), _x42, c), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(b, _x42, c), c, c))) → top#(f(f(ok(b), proper(_x42), ok(c)), ok(c), ok(c)))top#(mark(f(f(_x41, f(_x51, _x52, _x53), c), c, c))) → top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), ok(c)), ok(c), ok(c)))
top#(mark(f(c, c, _x23))) → top#(f(ok(c), ok(c), proper(_x23)))top#(mark(f(f(_x41, b, _x43), c, c))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, b), c, c))) → top#(f(f(proper(_x41), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), c, c), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, _x53), c, b), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(_x21, c, b))) → top#(f(proper(_x21), ok(c), ok(b)))
top#(mark(f(f(_x41, f(_x51, _x52, _x53), _x43), c, c))) → top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, _x22, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), proper(_x22), f(proper(_x61), proper(_x62), proper(_x63))))
top#(mark(f(f(_x41, _x42, c), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), proper(_x23)))top#(mark(f(f(f(f(_x61, _x62, _x63), _x52, _x53), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, f(_x61, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(_x41, b, c), c, c))) → top#(f(f(proper(_x41), ok(b), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, _x53), _x42, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x23)))
top#(mark(f(f(f(_x51, _x52, c), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), ok(c)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, b), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), ok(b)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(c, _x22, b))) → top#(f(ok(c), proper(_x22), ok(b)))top#(mark(f(f(_x41, c, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(c), proper(_x43)), ok(c), proper(_x23)))
top#(mark(c)) → top#(ok(c))top#(ok(c)) → top#(mark(b))
top#(mark(f(_x21, _x22, c))) → top#(f(proper(_x21), proper(_x22), ok(c)))top#(mark(f(_x21, f(_x51, _x52, _x53), b))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), ok(b)))
top#(mark(f(f(b, _x42, _x43), c, _x23))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(b, c, _x23))) → top#(f(ok(b), ok(c), proper(_x23)))
top#(mark(f(f(_x41, _x42, _x43), _x22, _x23))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), proper(_x23)))top#(mark(b)) → top#(ok(b))
top#(mark(f(f(f(_x51, c, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), ok(c), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, ok, mark, proper, top

Strategy

The right-hand side of the rule top#(mark(f(f(c, c, c), c, c))) → top#(f(f(ok(c), ok(c), ok(c)), ok(c), ok(c))) is 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
top#(f(ok(f(c, c, c)), ok(c), ok(c))) 
Thus, the rule top#(mark(f(f(c, c, c), c, c))) → top#(f(f(ok(c), ok(c), ok(c)), ok(c), ok(c))) is replaced by the following rules:
top#(mark(f(f(c, c, c), c, c))) → top#(f(ok(f(c, c, c)), ok(c), ok(c)))

Problem 20: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(mark(f(f(b, _x42, _x43), c, c))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(b, c, c), c, c))) → top#(f(f(ok(b), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(c, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(ok(c), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(b, _x22, b))) → top#(f(ok(b), proper(_x22), ok(b)))
top#(mark(f(f(b, c, _x43), c, c))) → top#(f(f(ok(b), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, _x42, f(_x81, _x82, _x83)), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x81), proper(_x82), proper(_x83))), ok(c), proper(_x23)))
top#(mark(f(f(_x41, f(_x71, _x72, _x73), _x43), c, _x23))) → top#(f(f(proper(_x41), f(proper(_x71), proper(_x72), proper(_x73)), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(f(_x61, _x62, _x63), _x42, _x43), c, _x23))) → top#(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x42), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(b, _x22, _x23))) → top#(f(ok(b), proper(_x22), proper(_x23)))top#(ok(f(b, _x21, c))) → top#(mark(f(_x21, c, _x21)))
top#(mark(f(f(c, _x42, _x43), c, _x23))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(_x41, _x42, _x43), c, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), ok(b)))
top#(mark(f(f(_x41, _x42, _x43), c, f(_x61, _x62, _x63)))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))top#(mark(f(f(_x41, _x42, b), c, c))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), ok(c)))
top#(ok(f(_x21, f(b, _x51, c), _x23))) → top#(f(_x21, mark(f(_x51, c, _x51)), _x23))top#(mark(f(f(_x41, b, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(c, _x22, _x23))) → top#(f(ok(c), proper(_x22), proper(_x23)))top#(mark(f(f(_x41, _x42, _x43), _x22, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), ok(b)))
top#(mark(f(f(c, _x42, c), c, c))) → top#(f(f(ok(c), proper(_x42), ok(c)), ok(c), ok(c)))top#(mark(f(_x21, b, b))) → top#(f(proper(_x21), ok(b), ok(b)))
top#(mark(f(f(f(_x51, b, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), ok(b), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(c, _x42, _x43), c, c))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(c, c, c), c, c))) → top#(f(ok(f(c, c, c)), ok(c), ok(c)))top#(ok(f(_x21, c, _x23))) → top#(f(_x21, mark(b), _x23))
top#(mark(f(f(f(_x51, _x52, _x53), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(b, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(ok(b), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(c, c, _x43), c, c))) → top#(f(f(ok(c), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, c, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))
top#(mark(f(f(_x41, _x42, b), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), proper(_x23)))top#(mark(f(_x21, b, _x23))) → top#(f(proper(_x21), ok(b), proper(_x23)))
top#(ok(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(_x21, f(_x51, active(_x52), _x53), _x23))top#(mark(f(_x21, c, c))) → top#(f(proper(_x21), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, _x53), _x42, c), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(b, _x42, c), c, c))) → top#(f(f(ok(b), proper(_x42), ok(c)), ok(c), ok(c)))top#(mark(f(f(_x41, f(_x51, _x52, _x53), c), c, c))) → top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), ok(c)), ok(c), ok(c)))
top#(mark(f(c, c, _x23))) → top#(f(ok(c), ok(c), proper(_x23)))top#(mark(f(f(_x41, b, _x43), c, c))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, b), c, c))) → top#(f(f(proper(_x41), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), c, c), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, _x53), c, b), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(_x21, c, b))) → top#(f(proper(_x21), ok(c), ok(b)))
top#(mark(f(f(_x41, f(_x51, _x52, _x53), _x43), c, c))) → top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, _x22, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), proper(_x22), f(proper(_x61), proper(_x62), proper(_x63))))
top#(mark(f(f(_x41, _x42, c), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), proper(_x23)))top#(mark(f(f(f(f(_x61, _x62, _x63), _x52, _x53), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, f(_x61, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), _x42, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, b, c), c, c))) → top#(f(f(proper(_x41), ok(b), ok(c)), ok(c), ok(c)))top#(mark(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x23)))
top#(mark(f(c, _x22, b))) → top#(f(ok(c), proper(_x22), ok(b)))top#(mark(f(f(f(_x51, _x52, b), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), ok(b)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, c), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), ok(c)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(c), proper(_x43)), ok(c), proper(_x23)))
top#(mark(c)) → top#(ok(c))top#(ok(c)) → top#(mark(b))
top#(mark(f(_x21, _x22, c))) → top#(f(proper(_x21), proper(_x22), ok(c)))top#(mark(f(_x21, f(_x51, _x52, _x53), b))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), ok(b)))
top#(mark(f(b, c, _x23))) → top#(f(ok(b), ok(c), proper(_x23)))top#(mark(f(f(b, _x42, _x43), c, _x23))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(f(_x41, _x42, _x43), _x22, _x23))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), proper(_x23)))top#(mark(b)) → top#(ok(b))
top#(mark(f(f(f(_x51, c, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), ok(c), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, mark, ok, proper, top

Strategy

The right-hand side of the rule top#(mark(f(f(b, _x42, _x43), c, c))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), ok(c))) is 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
top#(f(f(ok(b), proper(_x42), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c))) 
top#(f(f(ok(b), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x43)), ok(c), ok(c))) 
top#(f(f(ok(b), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(ok(b), proper(_x42), ok(b)), ok(c), ok(c))) 
top#(f(f(ok(b), proper(_x42), ok(c)), ok(c), ok(c))) 
top#(f(f(ok(b), ok(b), proper(_x43)), ok(c), ok(c))) 
Thus, the rule top#(mark(f(f(b, _x42, _x43), c, c))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), ok(c))) is replaced by the following rules:
top#(mark(f(f(b, _x42, b), c, c))) → top#(f(f(ok(b), proper(_x42), ok(b)), ok(c), ok(c)))top#(mark(f(f(b, _x42, c), c, c))) → top#(f(f(ok(b), proper(_x42), ok(c)), ok(c), ok(c)))
top#(mark(f(f(b, f(_x51, _x52, _x53), _x43), c, c))) → top#(f(f(ok(b), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(b, _x42, f(_x61, _x62, _x63)), c, c))) → top#(f(f(ok(b), proper(_x42), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(b, c, _x43), c, c))) → top#(f(f(ok(b), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(b, b, _x43), c, c))) → top#(f(f(ok(b), ok(b), proper(_x43)), ok(c), ok(c)))

Problem 21: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(mark(f(f(_x41, c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(b, c, c), c, c))) → top#(f(f(ok(b), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(c, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(ok(c), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(b, _x22, b))) → top#(f(ok(b), proper(_x22), ok(b)))top#(mark(f(f(b, c, _x43), c, c))) → top#(f(f(ok(b), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(b, _x42, b), c, c))) → top#(f(f(ok(b), proper(_x42), ok(b)), ok(c), ok(c)))top#(mark(f(f(_x41, _x42, f(_x81, _x82, _x83)), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x81), proper(_x82), proper(_x83))), ok(c), proper(_x23)))
top#(mark(f(f(_x41, f(_x71, _x72, _x73), _x43), c, _x23))) → top#(f(f(proper(_x41), f(proper(_x71), proper(_x72), proper(_x73)), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(f(_x61, _x62, _x63), _x42, _x43), c, _x23))) → top#(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x42), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(b, _x22, _x23))) → top#(f(ok(b), proper(_x22), proper(_x23)))top#(mark(f(f(b, _x42, f(_x61, _x62, _x63)), c, c))) → top#(f(f(ok(b), proper(_x42), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(ok(f(b, _x21, c))) → top#(mark(f(_x21, c, _x21)))top#(mark(f(f(c, _x42, _x43), c, _x23))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(f(_x41, _x42, _x43), c, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), ok(b)))top#(mark(f(f(_x41, _x42, b), c, c))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, _x43), c, f(_x61, _x62, _x63)))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))top#(ok(f(_x21, f(b, _x51, c), _x23))) → top#(f(_x21, mark(f(_x51, c, _x51)), _x23))
top#(mark(f(f(_x41, b, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(c, _x22, _x23))) → top#(f(ok(c), proper(_x22), proper(_x23)))
top#(mark(f(f(c, _x42, c), c, c))) → top#(f(f(ok(c), proper(_x42), ok(c)), ok(c), ok(c)))top#(mark(f(f(_x41, _x42, _x43), _x22, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), ok(b)))
top#(mark(f(f(f(_x51, b, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), ok(b), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, b, b))) → top#(f(proper(_x21), ok(b), ok(b)))
top#(mark(f(f(c, _x42, _x43), c, c))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(c, c, c), c, c))) → top#(f(ok(f(c, c, c)), ok(c), ok(c)))
top#(ok(f(_x21, c, _x23))) → top#(f(_x21, mark(b), _x23))top#(mark(f(f(f(_x51, _x52, _x53), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(b, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(ok(b), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(c, c, _x43), c, c))) → top#(f(f(ok(c), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(_x21, c, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))top#(mark(f(f(_x41, _x42, b), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), proper(_x23)))
top#(mark(f(_x21, b, _x23))) → top#(f(proper(_x21), ok(b), proper(_x23)))top#(ok(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(_x21, f(_x51, active(_x52), _x53), _x23))
top#(mark(f(_x21, c, c))) → top#(f(proper(_x21), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), _x42, c), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(b, _x42, c), c, c))) → top#(f(f(ok(b), proper(_x42), ok(c)), ok(c), ok(c)))
top#(mark(f(f(_x41, f(_x51, _x52, _x53), c), c, c))) → top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), ok(c)), ok(c), ok(c)))top#(mark(f(c, c, _x23))) → top#(f(ok(c), ok(c), proper(_x23)))
top#(mark(f(f(_x41, b, _x43), c, c))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, b), c, c))) → top#(f(f(proper(_x41), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, _x53), c, c), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), c, b), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(_x21, c, b))) → top#(f(proper(_x21), ok(c), ok(b)))top#(mark(f(f(_x41, f(_x51, _x52, _x53), _x43), c, c))) → top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x43)), ok(c), ok(c)))
top#(mark(f(_x21, _x22, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), proper(_x22), f(proper(_x61), proper(_x62), proper(_x63))))top#(mark(f(f(_x41, _x42, c), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), proper(_x23)))
top#(mark(f(f(f(f(_x61, _x62, _x63), _x52, _x53), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, _x42, f(_x61, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(_x41, b, c), c, c))) → top#(f(f(proper(_x41), ok(b), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), _x42, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), proper(_x43)), ok(c), ok(c)))
top#(mark(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x23)))top#(mark(f(f(b, f(_x51, _x52, _x53), _x43), c, c))) → top#(f(f(ok(b), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, c), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), ok(c)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, b), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), ok(b)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(c, _x22, b))) → top#(f(ok(c), proper(_x22), ok(b)))top#(mark(f(f(_x41, c, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(c), proper(_x43)), ok(c), proper(_x23)))
top#(mark(c)) → top#(ok(c))top#(ok(c)) → top#(mark(b))
top#(mark(f(_x21, _x22, c))) → top#(f(proper(_x21), proper(_x22), ok(c)))top#(mark(f(_x21, f(_x51, _x52, _x53), b))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), ok(b)))
top#(mark(f(f(b, _x42, _x43), c, _x23))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(b, c, _x23))) → top#(f(ok(b), ok(c), proper(_x23)))
top#(mark(f(f(_x41, _x42, _x43), _x22, _x23))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), proper(_x23)))top#(mark(b)) → top#(ok(b))
top#(mark(f(f(b, b, _x43), c, c))) → top#(f(f(ok(b), ok(b), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, c, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), ok(c), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, ok, mark, proper, top

Strategy

The right-hand side of the rule top#(mark(f(f(_x41, c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c))) is 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
top#(f(f(proper(_x41), ok(c), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), proper(_x63))), ok(c), ok(c))) 
top#(f(f(proper(_x41), ok(c), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63))), ok(c), ok(c))) 
top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(c), proper(_x63))), ok(c), ok(c))) 
top#(f(f(proper(_x41), ok(c), f(ok(c), proper(_x62), proper(_x63))), ok(c), ok(c))) 
top#(f(f(ok(c), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c))) 
top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(b), proper(_x63))), ok(c), ok(c))) 
top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), ok(c))), ok(c), ok(c))) 
top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), f(proper(_x101), proper(_x102), proper(_x103)))), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c))) 
top#(f(f(proper(_x41), ok(c), f(ok(b), proper(_x62), proper(_x63))), ok(c), ok(c))) 
top#(f(f(ok(b), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c))) 
top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), ok(b))), ok(c), ok(c))) 
Thus, the rule top#(mark(f(f(_x41, c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c))) is replaced by the following rules:
top#(mark(f(f(_x41, c, f(_x61, _x62, c)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), ok(c))), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(c, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(ok(c), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(_x41, c, f(_x61, _x62, b)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), ok(b))), ok(c), ok(c)))top#(mark(f(f(b, c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(c, c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(ok(c), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, _x62, f(_x101, _x102, _x103))), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), f(proper(_x101), proper(_x102), proper(_x103)))), ok(c), ok(c)))
top#(mark(f(f(_x41, c, f(_x61, b, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(b), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(f(_x81, _x82, _x83), _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(_x41, c, f(_x61, c, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(c), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(b, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(ok(b), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(_x41, c, f(_x61, f(_x91, _x92, _x93), _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))

Problem 22: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(mark(f(f(_x41, c, f(_x61, c, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(c), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(b, c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(_x41, c, f(_x61, _x62, f(_x101, _x102, _x103))), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), f(proper(_x101), proper(_x102), proper(_x103)))), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(b, c, c), c, c))) → top#(f(f(ok(b), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(c, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(ok(c), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(b, _x22, b))) → top#(f(ok(b), proper(_x22), ok(b)))top#(mark(f(f(b, c, _x43), c, c))) → top#(f(f(ok(b), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(b, _x42, b), c, c))) → top#(f(f(ok(b), proper(_x42), ok(b)), ok(c), ok(c)))top#(mark(f(f(_x41, _x42, f(_x81, _x82, _x83)), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x81), proper(_x82), proper(_x83))), ok(c), proper(_x23)))
top#(mark(f(f(_x41, c, f(_x61, _x62, b)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), ok(b))), ok(c), ok(c)))top#(mark(f(f(_x41, f(_x71, _x72, _x73), _x43), c, _x23))) → top#(f(f(proper(_x41), f(proper(_x71), proper(_x72), proper(_x73)), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(f(f(_x61, _x62, _x63), _x42, _x43), c, _x23))) → top#(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x42), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(b, _x22, _x23))) → top#(f(ok(b), proper(_x22), proper(_x23)))
top#(mark(f(f(b, _x42, f(_x61, _x62, _x63)), c, c))) → top#(f(f(ok(b), proper(_x42), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(ok(f(b, _x21, c))) → top#(mark(f(_x21, c, _x21)))
top#(mark(f(f(_x41, c, f(f(_x81, _x82, _x83), _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(c, _x42, _x43), c, _x23))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(f(_x41, _x42, _x43), c, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), ok(b)))top#(mark(f(f(_x41, _x42, _x43), c, f(_x61, _x62, _x63)))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))
top#(mark(f(f(_x41, _x42, b), c, c))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), ok(c)))top#(ok(f(_x21, f(b, _x51, c), _x23))) → top#(f(_x21, mark(f(_x51, c, _x51)), _x23))
top#(mark(f(f(_x41, b, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(c, _x22, _x23))) → top#(f(ok(c), proper(_x22), proper(_x23)))
top#(mark(f(f(c, _x42, c), c, c))) → top#(f(f(ok(c), proper(_x42), ok(c)), ok(c), ok(c)))top#(mark(f(f(_x41, _x42, _x43), _x22, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), ok(b)))
top#(mark(f(f(_x41, c, f(_x61, b, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(b), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, b, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), ok(b), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(_x21, b, b))) → top#(f(proper(_x21), ok(b), ok(b)))top#(mark(f(f(c, _x42, _x43), c, c))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(c, c, c), c, c))) → top#(f(ok(f(c, c, c)), ok(c), ok(c)))top#(ok(f(_x21, c, _x23))) → top#(f(_x21, mark(b), _x23))
top#(mark(f(f(f(_x51, _x52, _x53), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(c, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(ok(c), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(_x41, c, f(_x61, _x62, c)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), ok(c))), ok(c), ok(c)))top#(mark(f(f(f(b, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(ok(b), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(c, c, _x43), c, c))) → top#(f(f(ok(c), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, c, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))
top#(mark(f(f(_x41, _x42, b), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), proper(_x23)))top#(mark(f(_x21, b, _x23))) → top#(f(proper(_x21), ok(b), proper(_x23)))
top#(ok(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(_x21, f(_x51, active(_x52), _x53), _x23))top#(mark(f(_x21, c, c))) → top#(f(proper(_x21), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, _x53), _x42, c), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(b, _x42, c), c, c))) → top#(f(f(ok(b), proper(_x42), ok(c)), ok(c), ok(c)))top#(mark(f(f(_x41, f(_x51, _x52, _x53), c), c, c))) → top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), ok(c)), ok(c), ok(c)))
top#(mark(f(c, c, _x23))) → top#(f(ok(c), ok(c), proper(_x23)))top#(mark(f(f(_x41, b, _x43), c, c))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, b), c, c))) → top#(f(f(proper(_x41), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), c, c), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(_x41, f(_x51, _x52, _x53), _x43), c, c))) → top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, c, b))) → top#(f(proper(_x21), ok(c), ok(b)))
top#(mark(f(f(f(_x51, _x52, _x53), c, b), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(_x21, _x22, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), proper(_x22), f(proper(_x61), proper(_x62), proper(_x63))))
top#(mark(f(f(_x41, c, f(b, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(ok(b), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, f(_x91, _x92, _x93), _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, c), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), proper(_x23)))top#(mark(f(f(f(f(_x61, _x62, _x63), _x52, _x53), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, f(_x61, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), _x42, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, b, c), c, c))) → top#(f(f(proper(_x41), ok(b), ok(c)), ok(c), ok(c)))top#(mark(f(f(b, f(_x51, _x52, _x53), _x43), c, c))) → top#(f(f(ok(b), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x43)), ok(c), ok(c)))
top#(mark(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x23)))top#(mark(f(c, _x22, b))) → top#(f(ok(c), proper(_x22), ok(b)))
top#(mark(f(f(f(_x51, _x52, b), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), ok(b)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, c), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), ok(c)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(c), proper(_x43)), ok(c), proper(_x23)))top#(mark(c)) → top#(ok(c))
top#(ok(c)) → top#(mark(b))top#(mark(f(f(c, c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(ok(c), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(_x21, _x22, c))) → top#(f(proper(_x21), proper(_x22), ok(c)))top#(mark(f(_x21, f(_x51, _x52, _x53), b))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), ok(b)))
top#(mark(f(b, c, _x23))) → top#(f(ok(b), ok(c), proper(_x23)))top#(mark(f(f(b, _x42, _x43), c, _x23))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(f(_x41, _x42, _x43), _x22, _x23))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), proper(_x23)))top#(mark(b)) → top#(ok(b))
top#(mark(f(f(b, b, _x43), c, c))) → top#(f(f(ok(b), ok(b), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, c, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), ok(c), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, mark, ok, proper, top

Strategy

The right-hand side of the rule top#(mark(f(f(_x41, c, f(_x61, c, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(c), proper(_x63))), ok(c), ok(c))) is 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
top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), f(proper(_x61), ok(c), proper(_x63))), ok(c), ok(c))) 
top#(f(f(proper(_x41), ok(c), f(ok(b), ok(c), proper(_x63))), ok(c), ok(c))) 
top#(f(f(ok(b), ok(c), f(proper(_x61), ok(c), proper(_x63))), ok(c), ok(c))) 
top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(c), f(proper(_x101), proper(_x102), proper(_x103)))), ok(c), ok(c))) 
top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(c), ok(c))), ok(c), ok(c))) 
top#(f(f(proper(_x41), ok(c), f(ok(c), ok(c), proper(_x63))), ok(c), ok(c))) 
top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(c), ok(b))), ok(c), ok(c))) 
top#(f(f(ok(c), ok(c), f(proper(_x61), ok(c), proper(_x63))), ok(c), ok(c))) 
top#(f(f(proper(_x41), ok(c), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(c), proper(_x63))), ok(c), ok(c))) 
Thus, the rule top#(mark(f(f(_x41, c, f(_x61, c, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(c), proper(_x63))), ok(c), ok(c))) is replaced by the following rules:
top#(mark(f(f(c, c, f(_x61, c, _x63)), c, c))) → top#(f(f(ok(c), ok(c), f(proper(_x61), ok(c), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(b, c, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(ok(b), ok(c), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(b, c, f(_x61, c, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), ok(c), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, c, c)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(c), ok(c))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, _x53), c, f(_x61, c, _x63)), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), f(proper(_x61), ok(c), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(f(_x81, _x82, _x83), c, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(c), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(_x41, c, f(c, c, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(ok(c), ok(c), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, c, f(_x101, _x102, _x103))), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(c), f(proper(_x101), proper(_x102), proper(_x103)))), ok(c), ok(c)))
top#(mark(f(f(_x41, c, f(_x61, c, b)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(c), ok(b))), ok(c), ok(c)))

Problem 23: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(mark(f(f(b, c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, _x62, f(_x101, _x102, _x103))), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), f(proper(_x101), proper(_x102), proper(_x103)))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(b, c, c), c, c))) → top#(f(f(ok(b), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(c, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(ok(c), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(b, _x22, b))) → top#(f(ok(b), proper(_x22), ok(b)))
top#(mark(f(f(b, c, _x43), c, c))) → top#(f(f(ok(b), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(b, _x42, b), c, c))) → top#(f(f(ok(b), proper(_x42), ok(b)), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, f(_x81, _x82, _x83)), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x81), proper(_x82), proper(_x83))), ok(c), proper(_x23)))top#(mark(f(f(_x41, c, f(_x61, _x62, b)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), ok(b))), ok(c), ok(c)))
top#(mark(f(f(_x41, f(_x71, _x72, _x73), _x43), c, _x23))) → top#(f(f(proper(_x41), f(proper(_x71), proper(_x72), proper(_x73)), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(f(_x51, _x52, _x53), c, f(_x61, c, _x63)), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), f(proper(_x61), ok(c), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x61, _x62, _x63), _x42, _x43), c, _x23))) → top#(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x42), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(b, _x22, _x23))) → top#(f(ok(b), proper(_x22), proper(_x23)))
top#(mark(f(f(b, _x42, f(_x61, _x62, _x63)), c, c))) → top#(f(f(ok(b), proper(_x42), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(f(_x81, _x82, _x83), _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(ok(f(b, _x21, c))) → top#(mark(f(_x21, c, _x21)))top#(mark(f(f(c, _x42, _x43), c, _x23))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(f(_x41, _x42, _x43), c, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), ok(b)))top#(mark(f(f(_x41, _x42, b), c, c))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, _x43), c, f(_x61, _x62, _x63)))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))top#(mark(f(f(_x41, c, f(b, c, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(ok(b), ok(c), proper(_x63))), ok(c), ok(c)))
top#(ok(f(_x21, f(b, _x51, c), _x23))) → top#(f(_x21, mark(f(_x51, c, _x51)), _x23))top#(mark(f(f(_x41, b, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(c, _x22, _x23))) → top#(f(ok(c), proper(_x22), proper(_x23)))top#(mark(f(f(c, _x42, c), c, c))) → top#(f(f(ok(c), proper(_x42), ok(c)), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, _x43), _x22, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), ok(b)))top#(mark(f(f(_x41, c, f(_x61, b, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(b), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, b, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), ok(b), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, b, b))) → top#(f(proper(_x21), ok(b), ok(b)))
top#(mark(f(f(c, _x42, _x43), c, c))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(c, c, c), c, c))) → top#(f(ok(f(c, c, c)), ok(c), ok(c)))
top#(ok(f(_x21, c, _x23))) → top#(f(_x21, mark(b), _x23))top#(mark(f(f(f(_x51, _x52, _x53), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(_x41, c, f(c, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(ok(c), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, _x62, c)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), ok(c))), ok(c), ok(c)))
top#(mark(f(f(f(b, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(ok(b), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, c, c)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(c), ok(c))), ok(c), ok(c)))
top#(mark(f(f(c, c, _x43), c, c))) → top#(f(f(ok(c), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(f(_x81, _x82, _x83), c, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(c), proper(_x63))), ok(c), ok(c)))
top#(mark(f(_x21, c, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))top#(mark(f(f(_x41, _x42, b), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), proper(_x23)))
top#(mark(f(_x21, b, _x23))) → top#(f(proper(_x21), ok(b), proper(_x23)))top#(ok(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(_x21, f(_x51, active(_x52), _x53), _x23))
top#(mark(f(_x21, c, c))) → top#(f(proper(_x21), ok(c), ok(c)))top#(mark(f(f(c, c, f(_x61, c, _x63)), c, c))) → top#(f(f(ok(c), ok(c), f(proper(_x61), ok(c), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(b, c, f(_x61, c, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), ok(c), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), _x42, c), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(b, _x42, c), c, c))) → top#(f(f(ok(b), proper(_x42), ok(c)), ok(c), ok(c)))
top#(mark(f(c, c, _x23))) → top#(f(ok(c), ok(c), proper(_x23)))top#(mark(f(f(_x41, f(_x51, _x52, _x53), c), c, c))) → top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), ok(c)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, b), c, c))) → top#(f(f(proper(_x41), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(_x41, b, _x43), c, c))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, _x53), c, c), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), c, b), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(_x21, c, b))) → top#(f(proper(_x21), ok(c), ok(b)))top#(mark(f(f(_x41, f(_x51, _x52, _x53), _x43), c, c))) → top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, f(_x61, f(_x91, _x92, _x93), _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(b, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(ok(b), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(_x21, _x22, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), proper(_x22), f(proper(_x61), proper(_x62), proper(_x63))))top#(mark(f(f(_x41, _x42, c), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), proper(_x23)))
top#(mark(f(f(f(f(_x61, _x62, _x63), _x52, _x53), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, _x42, f(_x61, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(_x41, b, c), c, c))) → top#(f(f(proper(_x41), ok(b), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), _x42, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), proper(_x43)), ok(c), ok(c)))
top#(mark(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x23)))top#(mark(f(f(b, f(_x51, _x52, _x53), _x43), c, c))) → top#(f(f(ok(b), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, f(c, c, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(ok(c), ok(c), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, c), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), ok(c)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, b), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), ok(b)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(c, _x22, b))) → top#(f(ok(c), proper(_x22), ok(b)))
top#(mark(f(f(_x41, c, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(c), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(_x41, c, f(_x61, c, f(_x101, _x102, _x103))), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(c), f(proper(_x101), proper(_x102), proper(_x103)))), ok(c), ok(c)))
top#(mark(c)) → top#(ok(c))top#(ok(c)) → top#(mark(b))
top#(mark(f(f(c, c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(ok(c), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(_x21, _x22, c))) → top#(f(proper(_x21), proper(_x22), ok(c)))
top#(mark(f(_x21, f(_x51, _x52, _x53), b))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), ok(b)))top#(mark(f(f(b, _x42, _x43), c, _x23))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(b, c, _x23))) → top#(f(ok(b), ok(c), proper(_x23)))top#(mark(f(f(_x41, _x42, _x43), _x22, _x23))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), proper(_x23)))
top#(mark(b)) → top#(ok(b))top#(mark(f(f(b, b, _x43), c, c))) → top#(f(f(ok(b), ok(b), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, c, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), ok(c), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, c, b)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(c), ok(b))), ok(c), ok(c)))

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, ok, mark, proper, top

Strategy

The right-hand side of the rule top#(mark(f(f(b, c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c))) is 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
top#(f(f(ok(b), ok(c), f(proper(_x61), proper(_x62), ok(c))), ok(c), ok(c))) 
top#(f(f(ok(b), ok(c), f(proper(_x61), ok(c), proper(_x63))), ok(c), ok(c))) 
top#(f(f(ok(b), ok(c), f(proper(_x61), ok(b), proper(_x63))), ok(c), ok(c))) 
top#(f(f(ok(b), ok(c), f(proper(_x61), proper(_x62), f(proper(_x101), proper(_x102), proper(_x103)))), ok(c), ok(c))) 
top#(f(f(ok(b), ok(c), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63))), ok(c), ok(c))) 
top#(f(f(ok(b), ok(c), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), proper(_x63))), ok(c), ok(c))) 
top#(f(f(ok(b), ok(c), f(ok(b), proper(_x62), proper(_x63))), ok(c), ok(c))) 
top#(f(f(ok(b), ok(c), f(proper(_x61), proper(_x62), ok(b))), ok(c), ok(c))) 
top#(f(f(ok(b), ok(c), f(ok(c), proper(_x62), proper(_x63))), ok(c), ok(c))) 
Thus, the rule top#(mark(f(f(b, c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c))) is replaced by the following rules:
top#(mark(f(f(b, c, f(f(_x81, _x82, _x83), _x62, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(b, c, f(_x61, c, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), ok(c), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(b, c, f(_x61, b, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), ok(b), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(b, c, f(_x61, f(_x91, _x92, _x93), _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(b, c, f(_x61, _x62, f(_x101, _x102, _x103))), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), proper(_x62), f(proper(_x101), proper(_x102), proper(_x103)))), ok(c), ok(c)))top#(mark(f(f(b, c, f(_x61, _x62, c)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), proper(_x62), ok(c))), ok(c), ok(c)))
top#(mark(f(f(b, c, f(b, _x62, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(ok(b), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(b, c, f(c, _x62, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(ok(c), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(b, c, f(_x61, _x62, b)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), proper(_x62), ok(b))), ok(c), ok(c)))

Problem 24: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(mark(f(f(b, c, f(b, _x62, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(ok(b), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, _x62, f(_x101, _x102, _x103))), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), f(proper(_x101), proper(_x102), proper(_x103)))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(b, c, c), c, c))) → top#(f(f(ok(b), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(c, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(ok(c), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(b, _x22, b))) → top#(f(ok(b), proper(_x22), ok(b)))
top#(mark(f(f(b, c, _x43), c, c))) → top#(f(f(ok(b), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(b, _x42, b), c, c))) → top#(f(f(ok(b), proper(_x42), ok(b)), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, f(_x81, _x82, _x83)), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x81), proper(_x82), proper(_x83))), ok(c), proper(_x23)))top#(mark(f(f(_x41, c, f(_x61, _x62, b)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), ok(b))), ok(c), ok(c)))
top#(mark(f(f(_x41, f(_x71, _x72, _x73), _x43), c, _x23))) → top#(f(f(proper(_x41), f(proper(_x71), proper(_x72), proper(_x73)), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(f(_x51, _x52, _x53), c, f(_x61, c, _x63)), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), f(proper(_x61), ok(c), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x61, _x62, _x63), _x42, _x43), c, _x23))) → top#(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x42), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(b, _x22, _x23))) → top#(f(ok(b), proper(_x22), proper(_x23)))
top#(mark(f(f(b, _x42, f(_x61, _x62, _x63)), c, c))) → top#(f(f(ok(b), proper(_x42), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(ok(f(b, _x21, c))) → top#(mark(f(_x21, c, _x21)))
top#(mark(f(f(_x41, c, f(f(_x81, _x82, _x83), _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(c, _x42, _x43), c, _x23))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(f(_x41, _x42, _x43), c, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), ok(b)))top#(mark(f(f(_x41, c, f(b, c, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(ok(b), ok(c), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, _x43), c, f(_x61, _x62, _x63)))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))top#(mark(f(f(_x41, _x42, b), c, c))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), ok(c)))
top#(ok(f(_x21, f(b, _x51, c), _x23))) → top#(f(_x21, mark(f(_x51, c, _x51)), _x23))top#(mark(f(f(b, c, f(_x61, _x62, f(_x101, _x102, _x103))), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), proper(_x62), f(proper(_x101), proper(_x102), proper(_x103)))), ok(c), ok(c)))
top#(mark(f(f(b, c, f(_x61, _x62, c)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), proper(_x62), ok(c))), ok(c), ok(c)))top#(mark(f(f(_x41, b, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(c, _x22, _x23))) → top#(f(ok(c), proper(_x22), proper(_x23)))top#(mark(f(f(c, _x42, c), c, c))) → top#(f(f(ok(c), proper(_x42), ok(c)), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, _x43), _x22, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), ok(b)))top#(mark(f(f(_x41, c, f(_x61, b, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(b), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, b, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), ok(b), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, b, b))) → top#(f(proper(_x21), ok(b), ok(b)))
top#(mark(f(f(c, _x42, _x43), c, c))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(c, c, c), c, c))) → top#(f(ok(f(c, c, c)), ok(c), ok(c)))
top#(ok(f(_x21, c, _x23))) → top#(f(_x21, mark(b), _x23))top#(mark(f(f(f(_x51, _x52, _x53), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(_x41, c, f(c, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(ok(c), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, _x62, c)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), ok(c))), ok(c), ok(c)))
top#(mark(f(f(b, c, f(_x61, b, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), ok(b), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(b, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(ok(b), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(b, c, f(_x61, f(_x91, _x92, _x93), _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, c, c)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(c), ok(c))), ok(c), ok(c)))
top#(mark(f(f(c, c, _x43), c, c))) → top#(f(f(ok(c), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(f(_x81, _x82, _x83), c, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(c), proper(_x63))), ok(c), ok(c)))
top#(mark(f(_x21, c, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))top#(mark(f(f(_x41, _x42, b), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), proper(_x23)))
top#(mark(f(_x21, b, _x23))) → top#(f(proper(_x21), ok(b), proper(_x23)))top#(ok(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(_x21, f(_x51, active(_x52), _x53), _x23))
top#(mark(f(_x21, c, c))) → top#(f(proper(_x21), ok(c), ok(c)))top#(mark(f(f(c, c, f(_x61, c, _x63)), c, c))) → top#(f(f(ok(c), ok(c), f(proper(_x61), ok(c), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), _x42, c), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), ok(c)), ok(c), ok(c)))
top#(mark(f(f(b, c, f(_x61, c, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), ok(c), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(b, c, f(f(_x81, _x82, _x83), _x62, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(b, _x42, c), c, c))) → top#(f(f(ok(b), proper(_x42), ok(c)), ok(c), ok(c)))top#(mark(f(f(_x41, f(_x51, _x52, _x53), c), c, c))) → top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), ok(c)), ok(c), ok(c)))
top#(mark(f(c, c, _x23))) → top#(f(ok(c), ok(c), proper(_x23)))top#(mark(f(f(_x41, b, _x43), c, c))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, b), c, c))) → top#(f(f(proper(_x41), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), c, c), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(_x41, f(_x51, _x52, _x53), _x43), c, c))) → top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, c, b))) → top#(f(proper(_x21), ok(c), ok(b)))
top#(mark(f(f(f(_x51, _x52, _x53), c, b), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(b, c, f(c, _x62, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(ok(c), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(_x21, _x22, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), proper(_x22), f(proper(_x61), proper(_x62), proper(_x63))))top#(mark(f(f(_x41, c, f(b, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(ok(b), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(_x41, c, f(_x61, f(_x91, _x92, _x93), _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(_x41, _x42, c), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), proper(_x23)))
top#(mark(f(f(f(f(_x61, _x62, _x63), _x52, _x53), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, _x42, f(_x61, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, _x53), _x42, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, b, c), c, c))) → top#(f(f(proper(_x41), ok(b), ok(c)), ok(c), ok(c)))
top#(mark(f(f(b, f(_x51, _x52, _x53), _x43), c, c))) → top#(f(f(ok(b), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x23)))
top#(mark(f(f(_x41, c, f(c, c, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(ok(c), ok(c), proper(_x63))), ok(c), ok(c)))top#(mark(f(c, _x22, b))) → top#(f(ok(c), proper(_x22), ok(b)))
top#(mark(f(f(f(_x51, _x52, b), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), ok(b)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, c), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), ok(c)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(c), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(_x41, c, f(_x61, c, f(_x101, _x102, _x103))), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(c), f(proper(_x101), proper(_x102), proper(_x103)))), ok(c), ok(c)))
top#(mark(f(f(b, c, f(_x61, _x62, b)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), proper(_x62), ok(b))), ok(c), ok(c)))top#(mark(c)) → top#(ok(c))
top#(ok(c)) → top#(mark(b))top#(mark(f(f(c, c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(ok(c), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(_x21, _x22, c))) → top#(f(proper(_x21), proper(_x22), ok(c)))top#(mark(f(_x21, f(_x51, _x52, _x53), b))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), ok(b)))
top#(mark(f(b, c, _x23))) → top#(f(ok(b), ok(c), proper(_x23)))top#(mark(f(f(b, _x42, _x43), c, _x23))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(f(_x41, _x42, _x43), _x22, _x23))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), proper(_x23)))top#(mark(b)) → top#(ok(b))
top#(mark(f(f(b, b, _x43), c, c))) → top#(f(f(ok(b), ok(b), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, c, b)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(c), ok(b))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, c, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), ok(c), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, mark, ok, proper, top

Strategy

The right-hand side of the rule top#(mark(f(f(b, c, f(b, _x62, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(ok(b), proper(_x62), proper(_x63))), ok(c), ok(c))) is 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
top#(f(f(ok(b), ok(c), f(ok(b), proper(_x62), f(proper(_x101), proper(_x102), proper(_x103)))), ok(c), ok(c))) 
top#(f(f(ok(b), ok(c), f(ok(b), ok(b), proper(_x63))), ok(c), ok(c))) 
top#(f(f(ok(b), ok(c), f(ok(b), proper(_x62), ok(c))), ok(c), ok(c))) 
top#(f(f(ok(b), ok(c), f(ok(b), ok(c), proper(_x63))), ok(c), ok(c))) 
top#(f(f(ok(b), ok(c), f(ok(b), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63))), ok(c), ok(c))) 
top#(f(f(ok(b), ok(c), f(ok(b), proper(_x62), ok(b))), ok(c), ok(c))) 
Thus, the rule top#(mark(f(f(b, c, f(b, _x62, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(ok(b), proper(_x62), proper(_x63))), ok(c), ok(c))) is replaced by the following rules:
top#(mark(f(f(b, c, f(b, c, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(ok(b), ok(c), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(b, c, f(b, _x62, b)), c, c))) → top#(f(f(ok(b), ok(c), f(ok(b), proper(_x62), ok(b))), ok(c), ok(c)))
top#(mark(f(f(b, c, f(b, _x62, f(_x101, _x102, _x103))), c, c))) → top#(f(f(ok(b), ok(c), f(ok(b), proper(_x62), f(proper(_x101), proper(_x102), proper(_x103)))), ok(c), ok(c)))top#(mark(f(f(b, c, f(b, f(_x91, _x92, _x93), _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(ok(b), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(b, c, f(b, _x62, c)), c, c))) → top#(f(f(ok(b), ok(c), f(ok(b), proper(_x62), ok(c))), ok(c), ok(c)))top#(mark(f(f(b, c, f(b, b, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(ok(b), ok(b), proper(_x63))), ok(c), ok(c)))

Problem 25: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(b, c, c), c, c))) → top#(f(f(ok(b), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(b, c, _x43), c, c))) → top#(f(f(ok(b), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), c, f(_x61, c, _x63)), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), f(proper(_x61), ok(c), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x61, _x62, _x63), _x42, _x43), c, _x23))) → top#(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x42), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(b, _x22, _x23))) → top#(f(ok(b), proper(_x22), proper(_x23)))
top#(mark(f(f(b, _x42, f(_x61, _x62, _x63)), c, c))) → top#(f(f(ok(b), proper(_x42), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(b, c, f(b, _x62, c)), c, c))) → top#(f(f(ok(b), ok(c), f(ok(b), proper(_x62), ok(c))), ok(c), ok(c)))
top#(ok(f(b, _x21, c))) → top#(mark(f(_x21, c, _x21)))top#(mark(f(f(_x41, c, f(f(_x81, _x82, _x83), _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(c, _x42, _x43), c, _x23))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(_x41, _x42, _x43), c, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), ok(b)))
top#(mark(f(f(_x41, _x42, _x43), c, f(_x61, _x62, _x63)))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))top#(ok(f(_x21, f(b, _x51, c), _x23))) → top#(f(_x21, mark(f(_x51, c, _x51)), _x23))
top#(mark(f(f(b, c, f(_x61, _x62, c)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), proper(_x62), ok(c))), ok(c), ok(c)))top#(mark(f(c, _x22, _x23))) → top#(f(ok(c), proper(_x22), proper(_x23)))
top#(mark(f(f(_x41, _x42, _x43), _x22, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), ok(b)))top#(mark(f(_x21, b, b))) → top#(f(proper(_x21), ok(b), ok(b)))
top#(mark(f(f(c, _x42, _x43), c, c))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(c, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(ok(c), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(b, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(ok(b), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, c, c)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(c), ok(c))), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, b), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), proper(_x23)))top#(ok(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(_x21, f(_x51, active(_x52), _x53), _x23))
top#(mark(f(f(c, c, f(_x61, c, _x63)), c, c))) → top#(f(f(ok(c), ok(c), f(proper(_x61), ok(c), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, _x53), _x42, c), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), ok(c)), ok(c), ok(c)))top#(mark(f(f(b, c, f(_x61, c, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), ok(c), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(b, c, f(f(_x81, _x82, _x83), _x62, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), c, b), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, c), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), proper(_x23)))top#(mark(f(f(_x41, _x42, f(_x61, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(c, _x22, b))) → top#(f(ok(c), proper(_x22), ok(b)))top#(mark(f(f(f(_x51, _x52, c), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), ok(c)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(c), proper(_x43)), ok(c), proper(_x23)))top#(mark(c)) → top#(ok(c))
top#(mark(f(f(_x41, _x42, _x43), _x22, _x23))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), proper(_x23)))top#(mark(b)) → top#(ok(b))
top#(mark(f(f(b, b, _x43), c, c))) → top#(f(f(ok(b), ok(b), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, c, b)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(c), ok(b))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, c, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), ok(c), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(b, c, f(b, c, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(ok(b), ok(c), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(b, c, f(b, f(_x91, _x92, _x93), _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(ok(b), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, _x62, f(_x101, _x102, _x103))), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), f(proper(_x101), proper(_x102), proper(_x103)))), ok(c), ok(c)))
top#(mark(f(f(f(c, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(ok(c), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(b, _x22, b))) → top#(f(ok(b), proper(_x22), ok(b)))
top#(mark(f(f(b, _x42, b), c, c))) → top#(f(f(ok(b), proper(_x42), ok(b)), ok(c), ok(c)))top#(mark(f(f(_x41, _x42, f(_x81, _x82, _x83)), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x81), proper(_x82), proper(_x83))), ok(c), proper(_x23)))
top#(mark(f(f(_x41, c, f(_x61, _x62, b)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), ok(b))), ok(c), ok(c)))top#(mark(f(f(_x41, f(_x71, _x72, _x73), _x43), c, _x23))) → top#(f(f(proper(_x41), f(proper(_x71), proper(_x72), proper(_x73)), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(f(b, c, f(b, b, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(ok(b), ok(b), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(_x41, _x42, b), c, c))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, f(b, c, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(ok(b), ok(c), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(b, c, f(_x61, _x62, f(_x101, _x102, _x103))), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), proper(_x62), f(proper(_x101), proper(_x102), proper(_x103)))), ok(c), ok(c)))
top#(mark(f(f(_x41, b, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(c, _x42, c), c, c))) → top#(f(f(ok(c), proper(_x42), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, b, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), ok(b), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, b, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(b), proper(_x63))), ok(c), ok(c)))
top#(ok(f(_x21, c, _x23))) → top#(f(_x21, mark(b), _x23))top#(mark(f(f(c, c, c), c, c))) → top#(f(ok(f(c, c, c)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, _x53), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, _x62, c)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), ok(c))), ok(c), ok(c)))
top#(mark(f(f(b, c, f(_x61, b, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), ok(b), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(b, c, f(_x61, f(_x91, _x92, _x93), _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(c, c, _x43), c, c))) → top#(f(f(ok(c), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, c, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))
top#(mark(f(f(_x41, c, f(f(_x81, _x82, _x83), c, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(c), proper(_x63))), ok(c), ok(c)))top#(mark(f(_x21, b, _x23))) → top#(f(proper(_x21), ok(b), proper(_x23)))
top#(mark(f(_x21, c, c))) → top#(f(proper(_x21), ok(c), ok(c)))top#(mark(f(f(b, _x42, c), c, c))) → top#(f(f(ok(b), proper(_x42), ok(c)), ok(c), ok(c)))
top#(mark(f(c, c, _x23))) → top#(f(ok(c), ok(c), proper(_x23)))top#(mark(f(f(_x41, f(_x51, _x52, _x53), c), c, c))) → top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), ok(c)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, b), c, c))) → top#(f(f(proper(_x41), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(_x41, b, _x43), c, c))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, _x53), c, c), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(b, c, f(c, _x62, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(ok(c), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(_x21, c, b))) → top#(f(proper(_x21), ok(c), ok(b)))top#(mark(f(f(_x41, f(_x51, _x52, _x53), _x43), c, c))) → top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, f(_x61, f(_x91, _x92, _x93), _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(b, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(ok(b), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(_x21, _x22, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), proper(_x22), f(proper(_x61), proper(_x62), proper(_x63))))top#(mark(f(f(f(f(_x61, _x62, _x63), _x52, _x53), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(b, c, f(b, _x62, f(_x101, _x102, _x103))), c, c))) → top#(f(f(ok(b), ok(c), f(ok(b), proper(_x62), f(proper(_x101), proper(_x102), proper(_x103)))), ok(c), ok(c)))top#(mark(f(f(_x41, b, c), c, c))) → top#(f(f(proper(_x41), ok(b), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, _x53), _x42, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x23)))
top#(mark(f(f(b, f(_x51, _x52, _x53), _x43), c, c))) → top#(f(f(ok(b), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(c, c, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(ok(c), ok(c), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, b), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), ok(b)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, c, f(_x101, _x102, _x103))), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(c), f(proper(_x101), proper(_x102), proper(_x103)))), ok(c), ok(c)))
top#(mark(f(f(b, c, f(_x61, _x62, b)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), proper(_x62), ok(b))), ok(c), ok(c)))top#(ok(c)) → top#(mark(b))
top#(mark(f(f(b, c, f(b, _x62, b)), c, c))) → top#(f(f(ok(b), ok(c), f(ok(b), proper(_x62), ok(b))), ok(c), ok(c)))top#(mark(f(f(c, c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(ok(c), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(_x21, _x22, c))) → top#(f(proper(_x21), proper(_x22), ok(c)))top#(mark(f(_x21, f(_x51, _x52, _x53), b))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), ok(b)))
top#(mark(f(b, c, _x23))) → top#(f(ok(b), ok(c), proper(_x23)))top#(mark(f(f(b, _x42, _x43), c, _x23))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), proper(_x23)))

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, ok, mark, proper, top

Strategy

The right-hand side of the rule top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c))) is 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
top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), f(ok(b), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), f(proper(_x61), ok(c), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), ok(c)), ok(c), ok(c))) 
top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), f(proper(_x101), proper(_x102), proper(_x103))), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), f(proper(_x61), ok(b), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), ok(b)), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), ok(c)), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(b)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), f(ok(c), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), ok(b)), ok(c), ok(c))) 
top#(f(f(f(ok(b), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(ok(c), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c))) 
Thus, the rule top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c))) is replaced by the following rules:
top#(mark(f(f(f(f(_x61, _x62, _x63), f(_x61, _x62, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), _x62, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), c), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), ok(c)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(c, _x62, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(ok(c), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(b, _x62, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(ok(b), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, c, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), ok(c), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), b), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), ok(b)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(_x61, _x62, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(ok(b), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, f(_x101, _x102, _x103)), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), f(proper(_x101), proper(_x102), proper(_x103))), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, b, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), ok(b), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), _x53), c, c), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, b), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(b)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), _x53), c, b), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), _x53), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(c, f(_x61, _x62, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(ok(c), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))

Problem 26: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, f(_x101, _x102, _x103), _x73)), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), proper(_x73))), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, b, b), _x62, c), f(b, _x72, f(_x111, b, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), ok(b), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, f(_x111, _x112, _x113), b), _x62, c), f(b, _x72, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), f(proper(_x111), proper(_x112), proper(_x113)), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, b, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), ok(b), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(f(_x131, _x132, _x133), c, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), c), c, b), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), ok(c)), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(f(_x61, _x62, _x63), f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(c, _x82, b), f(_x91, _x92, _x93), c), f(b, _x72, f(_x111, c, c))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), f(proper(_x91), proper(_x92), proper(_x93)), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, c), _x63), _x53), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), ok(c)), proper(_x63)), proper(_x53)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x121, _x122, _x123)), f(_x91, _x92, _x93), c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x121), proper(_x122), proper(_x123))), f(proper(_x91), proper(_x92), proper(_x93)), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, _x72, b)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), ok(b))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x121, _x122, f(_x161, _x162, _x163))), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x121), proper(_x122), f(proper(_x161), proper(_x162), proper(_x163)))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(c, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(ok(c), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, f(c, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(ok(c), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, _x113))), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, c, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, b, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, _x72, f(f(_x131, _x132, _x133), c, c))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), f(_x71, _x72, _x73)), c, c), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, c, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), ok(c), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(b, f(_x91, _x92, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(ok(b), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, f(f(_x111, _x112, _x113), _x102, _x103), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(f(proper(_x111), proper(_x112), proper(_x113)), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(ok(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(_x21, f(_x51, active(_x52), _x53), _x23))top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), f(_x91, _x92, _x93), c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), f(proper(_x91), proper(_x92), proper(_x93)), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(f(_x61, _x62, _x63), f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, b, c))), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), b, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, _x53), _x42, c), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(b, _x62, c), f(b, _x72, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(ok(b), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(f(_x101, _x102, _x103), _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(f(proper(_x101), proper(_x102), proper(_x103)), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, b), _x62, c), f(b, _x72, f(_x111, c, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, c, _x83), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), ok(c), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, _x72, c)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), ok(c))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, _x93), f(_x101, _x102, _x103)), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), f(proper(_x101), proper(_x102), proper(_x103))), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, _x113))), c, c), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(f(_x61, _x62, _x63), f(_x61, _x62, _x63), f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(c, f(f(b, _x82, _x83), b, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(c), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(b, f(_x91, _x92, c), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(ok(b), f(proper(_x91), proper(_x92), ok(c)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, f(_x121, _x122, c)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(proper(_x121), proper(_x122), ok(c))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, _x43), _x22, _x23))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), proper(_x23)))top#(mark(f(f(f(_x51, f(b, _x62, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(ok(b), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(c, f(_x111, _x112, _x113), b), _x62, c), f(b, _x72, f(_x111, c, c))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), f(proper(_x111), proper(_x112), proper(_x113)), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(c, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, c, c))), c, _x43), c, c))) → top#(f(f(f(ok(c), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, c, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), ok(c), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(b, _x82, _x83), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(f(_x111, _x112, _x113), _x92, _x93), _x63), b), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(f(proper(_x111), proper(_x112), proper(_x113)), proper(_x92), proper(_x93)), proper(_x63)), ok(b)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(b, c, f(b, f(_x91, _x92, _x93), _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(ok(b), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, f(_x151, _x152, f(_x191, _x192, _x193))))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), proper(_x152), f(proper(_x191), proper(_x192), proper(_x193)))))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(b, _x22, b))) → top#(f(ok(b), proper(_x22), ok(b)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, c), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(c)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), _x62, c), f(b, f(_x101, _x102, _x103), _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, _x93), c), f(b, _x72, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(f(_x61, _x62, _x63), f(f(_x81, c, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(f(proper(_x81), ok(c), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), f(_x71, b, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x71), ok(b), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(_x71, b, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(proper(_x71), ok(b), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(c, f(_x61, _x62, _x63), _x53), c, b), c, c))) → top#(f(f(f(ok(c), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(b, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(b), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(f(_x111, c, _x113), _x92, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(f(proper(_x111), ok(c), proper(_x113)), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(b, c, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(ok(b), ok(c), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(f(_x111, _x112, c), _x92, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(f(proper(_x111), proper(_x112), ok(c)), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, f(f(_x111, _x112, _x113), _x92, _x93), _x63), c), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(f(proper(_x111), proper(_x112), proper(_x113)), proper(_x92), proper(_x93)), proper(_x63)), ok(c)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, _x132, _x133), c, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, f(_x121, _x122, _x123)), _x62, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, c, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, c), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(c)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, b), c, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), ok(c), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, c), f(_x101, _x102, _x103)), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), ok(c)), f(proper(_x101), proper(_x102), proper(_x103))), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(c, c, c), c, c))) → top#(f(ok(f(c, c, c)), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, _x62, c)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), ok(c))), ok(c), ok(c)))
top#(mark(f(f(b, c, f(_x61, b, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), ok(b), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x121, _x122, _x123)), _x62, c), f(b, b, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), ok(b), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), _x62, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(c, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(c), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(b, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(ok(b), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(b, _x62, c), f(b, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(ok(b), proper(_x62), ok(c)), f(ok(b), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(f(_x101, _x102, _x103), _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(f(proper(_x101), proper(_x102), proper(_x103)), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(c, c, b), _x62, c), f(b, _x72, f(_x111, c, c))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, b))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(b)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, b, c), f(b, f(_x101, _x102, _x103), _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(c, f(f(_x81, _x82, _x83), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(c), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(b, c, f(c, _x62, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(ok(c), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(_x41, f(_x51, _x52, _x53), _x43), c, c))) → top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(f(_x111, f(_x141, _x142, _x143), _x113), _x92, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(f(proper(_x111), f(proper(_x141), proper(_x142), proper(_x143)), proper(_x113)), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, b, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, _x53), _x42, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), proper(_x42), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, f(_x51, _x52, _x53), _x23))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x23)))
top#(mark(f(f(b, f(_x51, _x52, _x53), _x43), c, c))) → top#(f(f(ok(b), f(proper(_x51), proper(_x52), proper(_x53)), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(c, f(f(b, _x82, _x83), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(c), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, f(_x61, c, f(_x101, _x102, _x103))), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(c), f(proper(_x101), proper(_x102), proper(_x103)))), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(c, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(c), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(_x111, f(_x141, _x142, _x143), _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), f(proper(_x141), proper(_x142), proper(_x143)), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, f(_x91, f(_x121, _x122, _x123), c), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), f(proper(_x121), proper(_x122), proper(_x123)), ok(c)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(_x81, _x82, _x83), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(f(_x61, _x62, _x63), f(f(b, _x82, _x83), b, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, c, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), ok(c), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(_x21, f(_x51, _x52, _x53), b))) → top#(f(proper(_x21), f(proper(_x51), proper(_x52), proper(_x53)), ok(b)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, f(_x151, c, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), ok(c), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, b, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), ok(b), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(c, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(c), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, f(_x91, _x92, _x93), _x83), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, f(_x111, _x112, _x113), b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), f(proper(_x111), proper(_x112), proper(_x113)), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(_x61, _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(c, b, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(ok(c), ok(b), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(c, f(_x61, _x62, c), f(b, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(ok(c), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, _x72, f(_x111, b, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(_x111, c, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x61, _x62, _x63), _x42, _x43), c, _x23))) → top#(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x42), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(f(_x51, f(_x61, f(f(_x111, _x112, _x113), b, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(f(proper(_x111), proper(_x112), proper(_x113)), ok(b), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, c, f(f(_x131, b, _x133), _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), ok(c), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, f(_x101, _x102, c), _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), ok(c)), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, c, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(f(_x61, _x62, _x63), f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, c, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), ok(c), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, c), _x63), _x53), c, c), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), ok(c)), proper(_x63)), proper(_x53)), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(b, _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(ok(b), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, _x43), _x22, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), proper(_x22), ok(b)))top#(mark(f(f(f(_x51, f(f(_x81, c, f(_x121, b, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(proper(_x121), ok(b), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, f(b, _x102, _x103), _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), f(ok(b), proper(_x102), proper(_x103)), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, c, b), _x62, c), f(b, _x72, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, c), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(f(_x141, _x142, _x143), _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(f(proper(_x141), proper(_x142), proper(_x143)), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, f(_x131, _x132, _x133)), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), f(proper(_x131), proper(_x132), proper(_x133))), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(_x61, f(_x91, _x92, c), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(ok(b), f(proper(_x61), f(proper(_x91), proper(_x92), ok(c)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, f(_x151, _x152, _x153)))), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, b, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), ok(b), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(f(_x111, _x112, _x113), _x92, _x93), _x63), _x53), c, b), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(f(proper(_x111), proper(_x112), proper(_x113)), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(b, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(b), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, c, f(_x111, c, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), ok(c), f(proper(_x111), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, f(_x171, _x172, _x173)), _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), f(proper(_x171), proper(_x172), proper(_x173))), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, c, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), ok(c), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(f(_x61, _x62, _x63), f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, c), _x63), c), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), ok(c)), proper(_x63)), ok(c)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(c, f(_x61, _x62, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(ok(c), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, b), _x62, c), f(b, _x72, f(_x111, _x112, f(_x151, _x152, _x153)))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, c, f(_x111, c, c))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), ok(c), f(proper(_x111), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), f(_x91, _x92, c), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), f(proper(_x91), proper(_x92), ok(c)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(c, _x22, b))) → top#(f(ok(c), proper(_x22), ok(b)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, c, c))), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), ok(c)))), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, _x93), b), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), ok(b)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, c, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(c), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(b, _x62, _x63), f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(ok(b), proper(_x62), proper(_x63)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, b, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(b, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(b), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, c, _x113))), c, c), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), proper(_x113)))), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(c, _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(ok(c), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, b))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(b)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, _x72, _x73)), c, b), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), proper(_x73))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, f(f(_x111, _x112, _x113), _x92, _x93), c), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(f(proper(_x111), proper(_x112), proper(_x113)), proper(_x92), proper(_x93)), ok(c)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(c, _x92, c), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(ok(c), proper(_x92), ok(c)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(_x61, _x62, _x63), f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(ok(b), f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, c, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, _x82, b), b, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), ok(b)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, f(f(_x121, _x122, _x123), _x102, _x103), _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), f(f(proper(_x121), proper(_x122), proper(_x123)), proper(_x102), proper(_x103)), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, b, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, _x72, f(c, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(c), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), _x62, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(b, _x62, _x63), _x53), c, b), c, c))) → top#(f(f(f(proper(_x51), f(ok(b), proper(_x62), proper(_x63)), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, b))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(b)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, c), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, f(c, _x102, _x103), _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), f(ok(c), proper(_x102), proper(_x103)), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x101, _x102, _x103)), b, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x101), proper(_x102), proper(_x103))), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(_x21, c, c))) → top#(f(proper(_x21), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, b, _x83), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(b), proper(_x83)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, b, _x43), c, c))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(c, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(c), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(f(_x111, _x112, _x113), c, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(f(proper(_x111), proper(_x112), proper(_x113)), ok(c), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), b, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), ok(b), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(_x81, b, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), ok(b), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), b, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), ok(b), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, b, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), ok(b), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, b, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), ok(b), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(b, c, f(b, _x62, b)), c, c))) → top#(f(f(ok(b), ok(c), f(ok(b), proper(_x62), ok(b))), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, b), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(b)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(_x21, _x22, c))) → top#(f(proper(_x21), proper(_x22), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, _x83), b, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x121, b, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x121), ok(b), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, f(_x101, f(_x111, _x112, _x113), _x103), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), f(proper(_x111), proper(_x112), proper(_x113)), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, f(_x101, _x102, _x103), f(_x111, f(_x121, _x122, _x123), _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), f(proper(_x121), proper(_x122), proper(_x123)), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, _x72, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), c, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), ok(c), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, f(_x101, _x102, _x103), f(_x111, b, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), ok(b), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, c))), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, f(_x101, _x102, _x103), b)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), ok(b))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, f(_x101, _x102, _x103), c)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), ok(c))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), c, f(_x61, c, _x63)), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), f(proper(_x61), ok(c), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, _x83), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), proper(_x83)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, f(_x111, _x112, _x113), _x83), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), f(proper(_x111), proper(_x112), proper(_x113)), proper(_x83)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, f(f(_x81, _x82, _x83), _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), f(_x91, _x92, _x93), c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), f(proper(_x91), proper(_x92), proper(_x93)), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, _x93), c), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), ok(c)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, f(_x141, _x142, _x143), c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), f(proper(_x141), proper(_x142), proper(_x143)), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, _x113))), c, c), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(b, _x62, c), f(b, f(_x101, _x102, _x103), _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(ok(b), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, b, c), f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), ok(b), ok(c)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(ok(b), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, c), c), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), ok(c)), ok(c)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), f(_x141, _x142, _x143), f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), f(proper(_x141), proper(_x142), proper(_x143)), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(f(_x61, _x62, _x63), f(_x61, _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(c, f(_x61, _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(c), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(b, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(b), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, c), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(c)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, f(f(_x111, b, _x113), _x92, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(f(proper(_x111), ok(b), proper(_x113)), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, c), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), ok(c)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, c), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, c), _x63), f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), ok(c)), proper(_x63)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, c, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, _x72, f(b, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(b), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), _x62, c), f(b, b, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), ok(c)), f(ok(b), ok(b), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, c, f(_x111, b, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), ok(c), f(proper(_x111), ok(b), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, c, b), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), ok(b)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(_x41, c, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(c), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(f(f(_x51, f(f(c, _x82, b), f(_x91, _x92, _x93), c), f(b, _x72, f(_x111, c, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), f(proper(_x91), proper(_x92), proper(_x93)), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), f(_x91, _x92, _x93), c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), f(proper(_x91), proper(_x92), proper(_x93)), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, c), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, c, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, f(_x101, _x102, c), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), ok(c)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, c, b), f(_x91, _x92, _x93), c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), ok(b)), f(proper(_x91), proper(_x92), proper(_x93)), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, b, _x83), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), ok(b), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, _x113))), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, c, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), ok(c), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(_x71, _x72, b)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(proper(_x71), proper(_x72), ok(b))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, f(f(_x111, _x112, _x113), _x92, _x93), f(_x101, _x102, _x103)), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(f(proper(_x111), proper(_x112), proper(_x113)), proper(_x92), proper(_x93)), f(proper(_x101), proper(_x102), proper(_x103))), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, c, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), ok(c), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, _x72, f(_x111, _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(_x61, f(f(_x111, _x112, _x113), _x92, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(ok(b), f(proper(_x61), f(f(proper(_x111), proper(_x112), proper(_x113)), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(c, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(c), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, c))), c, c), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, _x62, f(_x101, _x102, _x103))), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), f(proper(_x101), proper(_x102), proper(_x103)))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, c, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(b, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(b), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(c, _x52, _x53), c, _x43), c, c))) → top#(f(f(f(ok(c), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, c, f(_x121, _x122, _x123)), _x62, c), f(b, c, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), ok(c), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(f(_x61, _x62, _x63), f(_x61, _x62, c), f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x61), proper(_x62), ok(c)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, f(_x121, _x122, f(_x161, _x162, _x163))), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(proper(_x121), proper(_x122), f(proper(_x161), proper(_x162), proper(_x163)))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, f(_x101, _x102, f(_x141, _x142, _x143)), _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), f(proper(_x141), proper(_x142), proper(_x143))), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, b, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(b), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(f(_x61, _x62, _x63), f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, c))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), b), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), ok(b)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, b, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), ok(b), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, b, f(_x111, b, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), ok(b), f(proper(_x111), ok(b), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, c, c))), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), ok(c)))), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, b, _x83), b, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), ok(b), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, _x82, f(_x101, _x102, _x103)), b, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), f(proper(_x101), proper(_x102), proper(_x103))), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, _x93), c), f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), ok(c)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, f(_x101, _x102, _x103), f(_x111, c, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, f(b, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(ok(b), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, b, f(f(_x131, b, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), ok(b), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x101, _x102, _x103)), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x101), proper(_x102), proper(_x103))), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, c, b), _x62, c), f(b, _x72, f(_x111, f(_x141, _x142, _x143), _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), f(proper(_x141), proper(_x142), proper(_x143)), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, _x93), _x63), f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(_x81, c, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, _x72, _x73)), c, c), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), proper(_x73))), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(b, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(ok(b), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(c, _x62, c), f(b, f(_x101, _x102, _x103), _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(ok(c), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(c, b, b), _x62, c), f(b, _x72, f(_x111, c, c))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), ok(b), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(f(_x61, _x62, _x63), f(_x61, _x62, c), f(b, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, f(_x91, _x92, _x93), _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, f(f(_x111, _x112, _x113), _x92, c), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(f(proper(_x111), proper(_x112), proper(_x113)), proper(_x92), ok(c)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(f(_x61, _x62, _x63), f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, f(_x101, _x102, _x103), f(_x111, c, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(b, _x42, _x43), c, _x23))) → top#(f(f(ok(b), proper(_x42), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(f(_x51, f(f(b, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, c, c))), c, c), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), ok(c)))), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, _x83), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(_x71, _x72, _x73)), c, b), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(b, c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, f(_x111, _x112, _x113), b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), f(proper(_x111), proper(_x112), proper(_x113)), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), f(_x91, _x92, _x93), c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), f(proper(_x91), proper(_x92), proper(_x93)), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(c, _x62, _x63), f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(ok(c), proper(_x62), proper(_x63)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x121, _x122, _x123)), _x62, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(b, _x22, _x23))) → top#(f(ok(b), proper(_x22), proper(_x23)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), c, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), ok(c), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(b, _x42, f(_x61, _x62, _x63)), c, c))) → top#(f(f(ok(b), proper(_x42), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, c, b), _x62, c), f(b, _x72, f(_x111, b, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, _x93), c), f(b, f(_x101, _x102, _x103), _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, b, c))), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), ok(c)))), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(c, _x42, _x43), c, _x23))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(f(f(_x51, f(c, f(f(_x111, _x112, _x113), _x92, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(ok(c), f(f(proper(_x111), proper(_x112), proper(_x113)), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(c, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, b, c))), c, _x43), c, c))) → top#(f(f(f(ok(c), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(f(_x61, _x62, _x63), f(_x61, _x62, c), f(b, f(_x101, _x102, _x103), _x73)), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, c, b))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), ok(b)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(b, c, f(f(_x81, _x82, _x83), _x62, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(c, f(_x61, _x62, c), f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(ok(c), f(proper(_x61), proper(_x62), ok(c)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), b), c, b), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), ok(b)), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(c, f(_x61, _x62, c), f(b, _x72, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(ok(c), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, b), _x62, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), _x62, c), f(b, _x72, f(_x111, _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(c, b, _x133), _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(ok(c), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, b), b, c), f(b, _x72, f(_x111, b, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(c, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(c), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, c, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), ok(c), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, f(_x101, _x102, _x103), f(f(_x121, _x122, _x123), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(f(proper(_x121), proper(_x122), proper(_x123)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(f(_x61, _x62, _x63), f(_x61, _x62, _x63), _x53), c, b), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(_x71, _x72, _x73)), c, c), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(_x61, _x62, c), f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(ok(b), f(proper(_x61), proper(_x62), ok(c)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), f(_x91, _x92, _x93), c), f(b, _x72, f(_x111, b, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), f(proper(_x91), proper(_x92), proper(_x93)), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(_x111, _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(f(_x61, _x62, _x63), f(f(_x81, c, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(f(proper(_x81), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, _x82, c), b, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), ok(c)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(f(_x61, _x62, _x63), f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(c, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(c), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, f(_x101, c, _x103), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), ok(c), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), _x62, c), f(b, c, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), ok(c)), f(ok(b), ok(c), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, c, c), f(b, f(_x101, _x102, _x103), _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), ok(c), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(b, _x92, c), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(ok(b), proper(_x92), ok(c)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, _x62, b)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), proper(_x62), ok(b))), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(f(_x91, _x92, _x93), _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(f(proper(_x91), proper(_x92), proper(_x93)), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(f(b, _x112, _x113), _x92, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(f(ok(b), proper(_x112), proper(_x113)), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(f(_x61, _x62, _x63), f(f(_x81, _x82, _x83), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, b, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(b), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), f(_x71, _x72, _x73)), c, b), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, f(_x101, _x102, _x103)), f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), f(proper(_x101), proper(_x102), proper(_x103))), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(b, c, f(b, b, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(ok(b), ok(b), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(_x71, _x72, c)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(proper(_x71), proper(_x72), ok(c))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), _x62, c), f(b, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), ok(c)), f(ok(b), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, f(_x101, _x102, _x103)), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), f(proper(_x101), proper(_x102), proper(_x103))), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(_x81, _x82, b), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, _x93), c), f(b, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), ok(c)), f(ok(b), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(_x61, f(_x91, _x92, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(ok(b), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(c, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(c), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, c, b), _x62, c), f(b, c, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), ok(c), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), f(_x71, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x71), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(f(_x101, _x102, _x103), _x82, b), _x62, c), f(b, _x72, f(_x111, c, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(f(proper(_x101), proper(_x102), proper(_x103)), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, b, f(_x111, c, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), ok(b), f(proper(_x111), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(f(_x61, _x62, _x63), f(f(b, _x82, _x83), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, _x53), c, c), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(c, f(f(_x81, c, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(ok(c), f(f(proper(_x81), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x121, _x122, b)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x121), proper(_x122), ok(b))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, _x83), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, c, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), ok(c), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, _x72, f(c, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(c), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, f(c, c, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(ok(c), ok(c), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), f(_x71, _x72, b)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x71), proper(_x72), ok(b))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, _x132, b), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), ok(b)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, b))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(b)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(c, f(_x91, _x92, c), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(ok(c), f(proper(_x91), proper(_x92), ok(c)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(c, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(ok(c), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), _x53), c, c), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, c, c))), c, c), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), ok(c)))), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, _x82, b), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), ok(b)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(b, c, _x23))) → top#(f(ok(b), ok(c), proper(_x23)))
top#(mark(f(f(f(_x51, f(f(f(_x101, _x102, _x103), _x82, _x83), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(f(proper(_x101), proper(_x102), proper(_x103)), proper(_x82), proper(_x83)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(f(_x131, _x132, _x133), c, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(_x81, c, b), _x62, c), f(b, _x72, f(_x111, c, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(f(_x131, _x132, _x133), b, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), ok(b), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, f(_x101, _x102, _x103), f(_x111, b, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), ok(b), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), c), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), ok(c)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, f(_x101, _x102, b), _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), ok(b)), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, _x43), c, b))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), ok(b)))top#(mark(f(f(_x41, _x42, _x43), c, f(_x61, _x62, _x63)))) → top#(f(f(proper(_x41), proper(_x42), proper(_x43)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))
top#(ok(f(_x21, f(b, _x51, c), _x23))) → top#(f(_x21, mark(f(_x51, c, _x51)), _x23))top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, f(_x141, _x142, _x143), _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), f(proper(_x141), proper(_x142), proper(_x143)), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(_x91, b, c), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), ok(b), ok(c)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, f(_x121, _x122, _x123)), _x62, c), f(b, b, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), ok(b), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, c, f(_x111, c, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), ok(c), f(proper(_x111), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(c, _x42, _x43), c, c))) → top#(f(f(ok(c), proper(_x42), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), c, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, c), _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), ok(c)), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, c, f(f(_x141, _x142, _x143), _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(f(proper(_x141), proper(_x142), proper(_x143)), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, _x72, f(c, c, c))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(c), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, b, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), ok(b), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, _x42, b), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), proper(_x23)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, _x72, f(_x111, _x112, c))), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, f(_x171, _x172, _x173)), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), f(proper(_x171), proper(_x172), proper(_x173))), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, f(_x141, _x142, _x143), _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), f(proper(_x141), proper(_x142), proper(_x143)), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, b), _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), ok(b)), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(c, _x62, _x63), _x53), c, b), c, c))) → top#(f(f(f(proper(_x51), f(ok(c), proper(_x62), proper(_x63)), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(c, b, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(c), ok(b), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), _x62, c), f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), ok(c)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, b))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(b)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, _x42, c), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), ok(c)), ok(c), proper(_x23)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, c, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), ok(c), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(b, _x82, b), _x62, c), f(b, _x72, f(_x111, c, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(b), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(f(_x111, _x112, _x113), _x92, _x93), _x63), f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(f(proper(_x111), proper(_x112), proper(_x113)), proper(_x92), proper(_x93)), proper(_x63)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, _x93), c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(c, f(_x61, f(_x91, _x92, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(ok(c), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(c, _x82, b), c, c), f(b, _x72, f(_x111, c, c))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), ok(c), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, c, b), _x62, c), f(b, _x72, f(_x111, _x112, c))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, b, _x63), _x53), c, b), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), ok(b), proper(_x63)), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(b, b, _x43), c, c))) → top#(f(f(ok(b), ok(b), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, f(_x101, f(_x131, _x132, _x133), _x103), _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), f(proper(_x131), proper(_x132), proper(_x133)), proper(_x103)), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), f(_x71, f(_x101, _x102, _x103), _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x71), f(proper(_x101), proper(_x102), proper(_x103)), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x121, _x122, _x123)), c, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x121), proper(_x122), proper(_x123))), ok(c), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, b, c))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, _x113))), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, b, c), f(b, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), ok(b), ok(c)), f(ok(b), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(c, _x62, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(ok(c), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(c, _x82, b), b, c), f(b, _x72, f(_x111, c, c))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, c), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x101, _x102, _x103)), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x101), proper(_x102), proper(_x103))), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(f(_x151, _x152, _x153), b, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(f(proper(_x151), proper(_x152), proper(_x153)), ok(b), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, f(_x71, _x72, _x73), _x43), c, _x23))) → top#(f(f(proper(_x41), f(proper(_x71), proper(_x72), proper(_x73)), proper(_x43)), ok(c), proper(_x23)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), f(_x141, _x142, _x143), _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), f(proper(_x141), proper(_x142), proper(_x143)), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, _x132, _x133), b, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), ok(b), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, c), _x63), b), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), ok(c)), proper(_x63)), ok(b)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, c, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), ok(c), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(_x81, _x82, b), b, c), f(b, _x72, f(_x111, c, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, _x93), _x63), _x53), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), _x53), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, b), c, c), f(b, _x72, f(_x111, c, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), ok(c), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, b, _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), ok(b), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(_x81, f(_x111, _x112, _x113), b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), f(proper(_x111), proper(_x112), proper(_x113)), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), _x62, c), f(b, _x72, f(_x111, b, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), _x62, c), f(b, _x72, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, f(_x151, f(_x181, _x182, _x183), _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), f(proper(_x181), proper(_x182), proper(_x183)), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(c, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(c), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, _x93), _x63), b), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63)), ok(b)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(b, c, f(_x61, f(_x91, _x92, _x93), _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, b))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(b)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, b, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(b), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, f(f(_x81, _x82, _x83), c, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(c), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, f(_x101, _x102, _x103), f(f(_x131, _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, b), _x62, c), f(b, _x72, f(_x111, _x112, b))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(b)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, f(_x91, _x92, _x93), _x83), b, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, c, c))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), f(b, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), f(ok(b), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, f(_x141, _x142, _x143), _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), f(proper(_x141), proper(_x142), proper(_x143)), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(c, c, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(c), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, b, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), ok(b), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, b))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), ok(b)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, b, c), c, c))) → top#(f(f(proper(_x41), ok(b), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), f(c, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), f(ok(c), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, b), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), ok(b)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(b, c, f(_x61, _x62, b)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), proper(_x62), ok(b))), ok(c), ok(c)))top#(ok(c)) → top#(mark(b))
top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, _x93), _x63), c), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63)), ok(c)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(c, c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(ok(c), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(f(_x91, _x92, _x93), _x82, _x83), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(f(proper(_x91), proper(_x92), proper(_x93)), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, c, f(f(_x131, _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), ok(c), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, c), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, b, c), f(b, _x72, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(f(_x101, _x102, _x103), _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(f(proper(_x101), proper(_x102), proper(_x103)), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, _x93), _x63), _x53), c, c), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(c, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(c), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, c, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), ok(c), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, b, b), _x62, c), f(b, _x72, f(_x111, c, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), ok(b), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, f(_x141, _x142, _x143), _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), f(proper(_x141), proper(_x142), proper(_x143)), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(b, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(b), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, _x72, f(_x111, _x112, b))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(b)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, _x72, f(_x111, b, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, c, c), f(b, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), ok(c), ok(c)), f(ok(b), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, c, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(c, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(c), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, f(_x121, _x122, _x123)), c, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(proper(_x121), proper(_x122), proper(_x123))), ok(c), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(b, c, b), c, c))) → top#(f(f(ok(b), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(b, f(_x61, _x62, c), f(b, f(_x101, _x102, _x103), _x73)), c, _x43), c, c))) → top#(f(f(f(ok(b), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(_x81, c, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), ok(c), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(b, c, c), c, c))) → top#(f(f(ok(b), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, c, _x83), b, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), ok(c), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, _x82, f(_x101, _x102, _x103)), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), f(proper(_x101), proper(_x102), proper(_x103))), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, _x113))), c, c), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(b, c, f(b, _x62, c)), c, c))) → top#(f(f(ok(b), ok(c), f(ok(b), proper(_x62), ok(c))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, _x72, f(_x111, f(_x141, _x142, _x143), c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), f(proper(_x141), proper(_x142), proper(_x143)), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(_x21, b, b))) → top#(f(proper(_x21), ok(b), ok(b)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), _x62, c), f(b, _x72, f(_x111, _x112, b))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(b)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, c, _x113))), c, b), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), b, c), f(b, _x72, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, f(_x61, c, c)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(c), ok(c))), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, b, f(f(_x131, _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), ok(b), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(f(_x111, _x112, _x113), _x92, _x93), _x63), _x53), c, c), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(f(proper(_x111), proper(_x112), proper(_x113)), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, _x72, f(_x111, _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, c, f(f(_x131, b, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), ok(c), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(_x61, _x62, _x63), _x53), c, b), c, c))) → top#(f(f(f(ok(b), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(c, c, f(_x61, c, _x63)), c, c))) → top#(f(f(ok(c), ok(c), f(proper(_x61), ok(c), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, _x72, _x73)), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), proper(_x73))), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, c), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, f(_x101, _x102, _x103), f(f(_x131, b, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(f(_x111, _x112, _x113), f(_x121, _x122, _x123), _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(f(proper(_x111), proper(_x112), proper(_x113)), f(proper(_x121), proper(_x122), proper(_x123)), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, _x83), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), proper(_x83)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, c, c))), c, b), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), ok(c)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(_x81, _x82, b), c, c), f(b, _x72, f(_x111, c, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), ok(c), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, f(b, _x102, _x103), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(ok(b), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(f(_x61, _x62, _x63), f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, _x52, c), c, _x43), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), ok(c)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(b, b, _x133), _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(ok(b), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(c, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(ok(c), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, f(_x151, _x152, c)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), proper(_x152), ok(c))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(c)) → top#(ok(c))top#(mark(f(f(f(_x51, f(f(_x81, f(_x111, _x112, _x113), b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), f(proper(_x111), proper(_x112), proper(_x113)), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, c), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(f(_x101, _x102, _x103), _x82, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(f(proper(_x101), proper(_x102), proper(_x103)), proper(_x82), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(b)) → top#(ok(b))top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, f(_x101, _x102, _x103), _x73)), c, b), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), proper(_x73))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(c, f(_x61, _x62, c), f(b, f(_x101, _x102, _x103), _x73)), c, _x43), c, c))) → top#(f(f(f(ok(c), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(_x61, c, b)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(c), ok(b))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, c, f(_x121, c, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(proper(_x121), ok(c), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, f(f(_x171, _x172, _x173), _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(f(proper(_x171), proper(_x172), proper(_x173)), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(_x81, c, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(b, b, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(ok(b), ok(b), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, b), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), ok(b)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, _x72, f(_x111, f(_x141, _x142, _x143), _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), f(proper(_x141), proper(_x142), proper(_x143)), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, f(b, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(ok(b), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(c, f(_x61, _x62, _x63), f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(ok(c), f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(c, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(c), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, _x82, c), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), ok(c)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, b, f(_x111, c, c))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), ok(b), f(proper(_x111), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, b), c, c), f(b, _x72, f(_x111, b, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), ok(c), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), b, c), f(b, _x72, f(_x111, c, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), _x62, c), f(b, _x72, f(_x111, c, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, f(_x101, b, _x103), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), ok(b), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(c, _x62, c), f(b, _x72, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(ok(c), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(c, _x62, c), f(b, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(ok(c), proper(_x62), ok(c)), f(ok(b), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, c), _x63), _x53), c, b), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), ok(c)), proper(_x63)), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, f(c, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(ok(c), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, c, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), _x62, _x63), f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), proper(_x63)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(f(_x101, _x102, _x103), c, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(f(proper(_x101), proper(_x102), proper(_x103)), ok(c), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, b), c, c), f(b, _x72, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), ok(c), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, _x72, f(_x111, _x112, c))), c, c), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, _x72, f(_x111, c, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x121, _x122, _x123)), _x62, c), f(b, c, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), ok(c), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, b, _x43), c, _x23))) → top#(f(f(proper(_x41), ok(b), proper(_x43)), ok(c), proper(_x23)))top#(mark(f(f(f(_x51, f(_x61, f(f(_x111, _x112, b), _x92, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(f(proper(_x111), proper(_x112), ok(b)), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, _x72, f(b, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(b), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), _x62, _x63), _x53), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), proper(_x63)), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, f(_x121, _x122, _x123)), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(proper(_x121), proper(_x122), proper(_x123))), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(c, f(f(_x81, _x82, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(c), f(f(proper(_x81), proper(_x82), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, c, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, c, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), ok(c), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, f(_x101, b, _x103), _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), ok(b), proper(_x103)), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, c, _x113))), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), proper(_x113)))), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, b, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, b, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), ok(b), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(_x21, c, b))) → top#(f(proper(_x21), ok(c), ok(b)))top#(mark(f(_x21, _x22, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), proper(_x22), f(proper(_x61), proper(_x62), proper(_x63))))
top#(mark(f(f(_x41, c, f(_x61, f(_x91, _x92, _x93), _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, b, c))), c, c), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), ok(c)))), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, c, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), ok(c), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), c, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(c), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(c, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(ok(c), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(b, c, f(b, _x62, f(_x101, _x102, _x103))), c, c))) → top#(f(f(ok(b), ok(c), f(ok(b), proper(_x62), f(proper(_x101), proper(_x102), proper(_x103)))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, c, b), _x62, c), f(b, _x72, f(b, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(b), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, f(f(_x111, _x112, _x113), _x92, _x93), _x63), _x53), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(f(proper(_x111), proper(_x112), proper(_x113)), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, c), b, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(c)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, _x72, f(_x111, _x112, b))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(b)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, f(_x151, _x152, _x153)))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(_x81, f(_x111, _x112, _x113), b), _x62, c), f(b, _x72, f(_x111, c, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), f(proper(_x111), proper(_x112), proper(_x113)), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(f(_x61, _x62, _x63), f(_x61, f(_x91, _x92, c), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x61), f(proper(_x91), proper(_x92), ok(c)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, c, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, c, f(_x121, _x122, _x123)), f(_x91, _x92, _x93), c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(proper(_x121), proper(_x122), proper(_x123))), f(proper(_x91), proper(_x92), proper(_x93)), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(f(_x91, _x92, _x93), _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(f(proper(_x91), proper(_x92), proper(_x93)), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, f(_x161, _x162, _x163), _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), f(proper(_x161), proper(_x162), proper(_x163)), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x121, _x122, _x123)), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x121), proper(_x122), proper(_x123))), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, b, b), _x62, c), f(b, _x72, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), ok(b), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, _x132, c), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), ok(c)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(_x81, _x82, b), f(_x91, _x92, _x93), c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), f(proper(_x91), proper(_x92), proper(_x93)), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x121, c, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x121), ok(c), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, b), _x62, c), f(b, _x72, f(c, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(c), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, b, _x83), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(b), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(f(_x151, _x152, _x153), _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(f(proper(_x151), proper(_x152), proper(_x153)), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, _x82, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(c, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(c), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, _x72, f(b, c, c))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(b), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x101, _x102, _x103)), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x101), proper(_x102), proper(_x103))), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(f(_x101, _x102, _x103), c, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(f(proper(_x101), proper(_x102), proper(_x103)), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(c, _x22, _x23))) → top#(f(ok(c), proper(_x22), proper(_x23)))
top#(mark(f(f(f(_x51, f(f(f(_x91, _x92, _x93), _x82, _x83), b, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(f(proper(_x91), proper(_x92), proper(_x93)), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(b, c, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(b), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(f(_x151, _x152, _x153), b, _x133), _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(f(proper(_x151), proper(_x152), proper(_x153)), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, f(_x111, _x112, _x113), f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), f(proper(_x111), proper(_x112), proper(_x113)), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(b, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(b), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, b))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), ok(b)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(f(_x61, _x62, _x63), f(_x61, _x62, c), f(b, _x72, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(b, b, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(b), ok(b), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, b, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(b), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(b, c, f(_x61, c, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), ok(c), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, b, c))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), ok(c)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, c, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(c, _x92, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(ok(c), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, _x52, _x53), c, b), c, c))) → top#(f(f(f(proper(_x51), proper(_x52), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, b, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), ok(b), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), f(_x71, c, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x71), ok(c), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(f(_x91, _x92, _x93), _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(f(proper(_x91), proper(_x92), proper(_x93)), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, f(_x61, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(f(_x111, _x112, _x113), _x92, f(_x131, _x132, _x133)), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(f(proper(_x111), proper(_x112), proper(_x113)), proper(_x92), f(proper(_x131), proper(_x132), proper(_x133))), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, f(_x151, _x152, b)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), proper(_x152), ok(b))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, c, b), c, c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), ok(b)), ok(c), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, b))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), ok(b)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(_x71, c, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(proper(_x71), ok(c), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, f(f(_x111, _x112, _x113), _x92, _x93), b), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(f(proper(_x111), proper(_x112), proper(_x113)), proper(_x92), proper(_x93)), ok(b)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(_x91, b, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), ok(b), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(c, f(_x61, f(_x91, _x92, c), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(ok(c), f(proper(_x61), f(proper(_x91), proper(_x92), ok(c)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, c, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, f(_x111, _x112, _x113), b), _x62, c), f(b, _x72, f(_x111, c, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), f(proper(_x111), proper(_x112), proper(_x113)), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(b, _x82, _x83), b, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, f(_x101, _x102, _x103), f(c, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(ok(c), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(_x61, _x62, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(ok(b), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(b, c, f(b, c, _x63)), c, c))) → top#(f(f(ok(b), ok(c), f(ok(b), ok(c), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(_x71, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(proper(_x71), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, b), _x53), c, b), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(b)), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(_x111, _x112, b))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(b)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, _x72, f(b, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(ok(b), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), c, c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), ok(c), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, f(_x101, _x102, _x103), _x73)), c, c), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), proper(_x73))), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, b, f(_x111, c, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), ok(b), f(proper(_x111), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, b, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(b), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, _x132, _x133), f(_x141, _x142, _x143), _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), f(proper(_x141), proper(_x142), proper(_x143)), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, f(_x121, _x122, b)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(proper(_x121), proper(_x122), ok(b))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(c, _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(ok(c), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), _x62, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, f(_x61, b, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(proper(_x61), ok(b), proper(_x63))), ok(c), ok(c)))top#(ok(f(_x21, c, _x23))) → top#(f(_x21, mark(b), _x23))
top#(mark(f(f(f(f(_x61, _x62, _x63), f(_x61, f(f(_x111, _x112, _x113), _x92, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x61), f(f(proper(_x111), proper(_x112), proper(_x113)), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, f(_x151, b, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), ok(b), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, c, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), ok(c), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, f(_x131, _x132, _x133)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), f(proper(_x131), proper(_x132), proper(_x133))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(_x111, b, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(c, c, _x23))) → top#(f(ok(c), ok(c), proper(_x23)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), _x53), c, b), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, f(_x91, _x92, _x93), _x83), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, f(_x91, c, c), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), ok(c), ok(c)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), f(f(_x111, _x112, _x113), _x92, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), f(f(proper(_x111), proper(_x112), proper(_x113)), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(_x41, c, f(b, _x62, _x63)), c, c))) → top#(f(f(proper(_x41), ok(c), f(ok(b), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(b, f(f(_x111, _x112, _x113), _x92, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(ok(b), f(f(proper(_x111), proper(_x112), proper(_x113)), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), f(_x71, _x72, c)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x71), proper(_x72), ok(c))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(b, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(b), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(f(_x61, _x62, _x63), _x52, _x53), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), proper(_x52), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, b), _x62, c), f(b, b, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), ok(b), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(f(_x111, _x112, f(_x151, _x152, _x153)), _x92, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(f(proper(_x111), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, b, _x63), f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), ok(b), proper(_x63)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, c, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, c, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, b, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), ok(b), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, c, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, f(_x141, _x142, _x143), _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), f(proper(_x141), proper(_x142), proper(_x143)), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(f(_x61, _x62, _x63), f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, f(_x101, c, _x103), _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), ok(c), proper(_x103)), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(_x81, _x82, b), f(_x91, _x92, _x93), c), f(b, _x72, f(_x111, c, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), f(proper(_x91), proper(_x92), proper(_x93)), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, _x132, f(_x171, _x172, _x173)), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), f(proper(_x171), proper(_x172), proper(_x173))), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, b, f(f(_x131, b, _x133), _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), ok(b), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, b), _x62, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(f(_x61, _x62, _x63), f(f(_x81, _x82, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(f(proper(_x81), proper(_x82), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, c))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(c, f(f(_x81, c, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(c), f(f(proper(_x81), ok(c), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, f(_x111, _x112, _x113), b), _x62, c), f(b, _x72, f(_x111, b, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), f(proper(_x111), proper(_x112), proper(_x113)), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(c, f(_x91, _x92, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(ok(c), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(b, _x62, c), f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(ok(b), proper(_x62), ok(c)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(_x71, _x72, _x73)), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, f(_x151, _x152, _x153)))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(f(_x61, _x62, _x63), f(_x61, f(_x91, _x92, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, f(c, _x102, _x103), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(ok(c), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(ok(f(b, _x21, c))) → top#(mark(f(_x21, c, _x21)))top#(mark(f(f(f(_x51, f(f(_x81, f(_x91, _x92, _x93), _x83), b, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, f(_x151, _x152, _x153)))), c, c), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), f(f(_x91, _x92, _x93), _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), f(f(proper(_x91), proper(_x92), proper(_x93)), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(f(_x61, _x62, _x63), f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, c, c))), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(b, c, f(_x61, _x62, c)), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), proper(_x62), ok(c))), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, c, b), _x62, c), f(b, _x72, f(_x111, c, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(c, c, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(c), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(_x61, _x62, c), f(b, _x72, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, f(_x101, _x102, _x103), f(f(_x131, b, _x133), _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, f(_x91, f(_x121, _x122, _x123), _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), f(proper(_x121), proper(_x122), proper(_x123)), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(_x81, _x82, b), c, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), ok(c), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(f(_x61, _x62, _x63), f(_x61, _x62, _x63), _x53), c, _x43), c, c))) → top#(f(f(f(f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x61), proper(_x62), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, b), f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(b)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(c, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, _x72, f(_x111, c, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, f(_x101, _x102, _x103), f(_x111, c, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, b, _x83), b, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(b), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, f(_x91, _x92, _x93), _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(_x81, _x82, b), _x62, c), f(b, _x72, f(b, c, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(b), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(b, _x92, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(ok(b), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, b, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(_x81, _x82, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), proper(_x82), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(_x81, b, b), _x62, c), f(b, _x72, f(_x111, c, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(proper(_x81), ok(b), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, f(_x101, _x102, _x103), f(_x111, c, c))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, _x72, f(_x111, b, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, c, _x63), f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), ok(c), proper(_x63)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x121, _x122, c)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x121), proper(_x122), ok(c))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, c), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, c, c), f(b, _x72, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), ok(c), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(_x91, c, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), ok(c), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x121, f(_x151, _x152, _x153), _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x121), f(proper(_x151), proper(_x152), proper(_x153)), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, f(_x101, _x102, b), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), ok(b)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, c, c), f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), ok(c), ok(c)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, c, _x63), _x53), c, b), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), ok(c), proper(_x63)), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), _x62, c), f(b, _x72, f(_x111, f(_x141, _x142, _x143), _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), f(proper(_x141), proper(_x142), proper(_x143)), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, _x72, f(_x111, _x112, c))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(b, _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(ok(b), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, _x62, _x63), f(_x71, _x72, _x73)), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), proper(_x63)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, b), f(_x91, _x92, _x93), c), f(b, _x72, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), f(proper(_x91), proper(_x92), proper(_x93)), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, _x72, f(_x111, f(_x141, _x142, _x143), _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), f(proper(_x141), proper(_x142), proper(_x143)), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, c, b), _x62, c), f(b, _x72, f(_x111, b, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(b, _x42, b), c, c))) → top#(f(f(ok(b), proper(_x42), ok(b)), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, f(_x81, _x82, _x83)), c, _x23))) → top#(f(f(proper(_x41), proper(_x42), f(proper(_x81), proper(_x82), proper(_x83))), ok(c), proper(_x23)))top#(mark(f(f(f(_x51, f(f(_x81, c, f(_x121, f(_x151, _x152, _x153), _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(proper(_x121), f(proper(_x151), proper(_x152), proper(_x153)), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(f(_x111, _x112, _x113), _x92, b), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(f(proper(_x111), proper(_x112), proper(_x113)), proper(_x92), ok(b)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(c, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(ok(c), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(_x41, _x42, b), c, c))) → top#(f(f(proper(_x41), proper(_x42), ok(b)), ok(c), ok(c)))top#(mark(f(f(b, c, f(_x61, _x62, f(_x101, _x102, _x103))), c, c))) → top#(f(f(ok(b), ok(c), f(proper(_x61), proper(_x62), f(proper(_x101), proper(_x102), proper(_x103)))), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, c, c))), c, b), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), ok(c)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, f(_x101, _x102, _x103), f(b, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(ok(b), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(c, _x42, c), c, c))) → top#(f(f(ok(c), proper(_x42), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, c), b, c), f(b, _x72, f(f(_x131, b, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(c)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(c, f(_x61, f(f(_x111, _x112, _x113), _x92, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(ok(c), f(proper(_x61), f(f(proper(_x111), proper(_x112), proper(_x113)), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, c, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(b, _x72, f(_x111, c, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(c, c, _x43), c, c))) → top#(f(f(ok(c), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(_x61, _x62, c), f(b, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(ok(b), f(proper(_x61), proper(_x62), ok(c)), f(ok(b), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, b), _x62, c), f(b, b, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), ok(b), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(_x21, c, f(_x61, _x62, _x63)))) → top#(f(proper(_x21), ok(c), f(proper(_x61), proper(_x62), proper(_x63))))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), f(_x91, _x92, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, f(_x101, _x102, _x103)), _x53), c, b), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), f(proper(_x101), proper(_x102), proper(_x103))), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(_x21, b, _x23))) → top#(f(proper(_x21), ok(b), proper(_x23)))
top#(mark(f(f(f(_x51, f(_x61, f(f(f(_x131, _x132, _x133), _x112, _x113), _x92, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, f(_x121, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, f(_x141, _x142, _x143), _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), f(proper(_x121), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), f(proper(_x141), proper(_x142), proper(_x143)), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, c), b), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), ok(c)), ok(b)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), _x62, c), f(b, _x72, f(b, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(b), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(b, _x42, c), c, c))) → top#(f(f(ok(b), proper(_x42), ok(c)), ok(c), ok(c)))top#(mark(f(f(_x41, f(_x51, _x52, _x53), c), c, c))) → top#(f(f(proper(_x41), f(proper(_x51), proper(_x52), proper(_x53)), ok(c)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, c))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, f(_x91, _x92, _x93), _x63), _x53), c, b), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(proper(_x91), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), ok(b)), ok(c), ok(c)))
top#(mark(f(f(_x41, c, b), c, c))) → top#(f(f(proper(_x41), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, c, _x83), b, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, f(_x101, _x102, f(_x121, _x122, _x123)), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), f(proper(_x121), proper(_x122), proper(_x123))), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(b, _x82, _x83), b, c), f(b, _x72, f(c, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(ok(b), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(ok(c), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, c, f(c, _x122, _x123)), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), ok(c), f(ok(c), proper(_x122), proper(_x123))), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(_x61, f(f(c, _x112, _x113), _x92, _x93), _x63), _x53), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), f(f(ok(c), proper(_x112), proper(_x113)), proper(_x92), proper(_x93)), proper(_x63)), proper(_x53)), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(_x61, _x62, c), f(_x71, f(_x101, _x102, _x103), _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(proper(_x61), proper(_x62), ok(c)), f(proper(_x71), f(proper(_x101), proper(_x102), proper(_x103)), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(c, _x62, c), f(_x71, _x72, _x73)), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(ok(c), proper(_x62), ok(c)), f(proper(_x71), proper(_x72), proper(_x73))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), b, c), f(b, _x72, f(f(_x131, b, b), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), ok(b), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), ok(b), ok(b)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(_x51, f(f(_x81, _x82, _x83), _x62, c), f(b, _x72, f(c, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(proper(_x51), f(f(proper(_x81), proper(_x82), proper(_x83)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(c), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, mark, ok, proper, top

Strategy

The right-hand side of the rule top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c))) is 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
top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(b), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(c), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(ok(b), f(f(ok(c), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), ok(c), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), ok(b), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(b)))), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(c)), ok(c), ok(c))) 
top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), ok(c), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(ok(b), f(f(ok(c), ok(b), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c))) 
top#(f(f(f(ok(b), f(f(ok(c), f(proper(_x111), proper(_x112), proper(_x113)), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c))) 
top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), f(proper(_x141), proper(_x142), proper(_x143)), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c))) 
top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), f(proper(_x91), proper(_x92), proper(_x93)), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c))) 
Thus, the rule top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c))) is replaced by the following rules:
top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, c), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(c)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(c, _x82, b), f(_x91, _x92, _x93), c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), f(proper(_x91), proper(_x92), proper(_x93)), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, f(_x61, _x62, _x63)), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), f(proper(_x61), proper(_x62), proper(_x63))), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, c, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(c), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, f(_x151, _x152, _x153)))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), f(proper(_x151), proper(_x152), proper(_x153))))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(c, f(_x111, _x112, _x113), b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), f(proper(_x111), proper(_x112), proper(_x113)), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, b), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), ok(b)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, _x72, f(c, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(c), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(c, c, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), ok(c), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, f(_x141, _x142, _x143), _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), f(proper(_x141), proper(_x142), proper(_x143)), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, f(_x101, _x102, _x103), f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), f(proper(_x101), proper(_x102), proper(_x103)), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, b, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), ok(b), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, b))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(b)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(c, _x82, b), b, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), ok(b), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, _x72, f(_x111, _x112, c))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), ok(c)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, c, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), ok(c), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(c, _x82, b), c, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), ok(c), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, b, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), ok(b), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(c, b, b), _x62, c), f(b, _x72, f(_x111, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), ok(b), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(proper(_x111), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, _x72, f(f(_x131, _x132, _x133), _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(f(proper(_x131), proper(_x132), proper(_x133)), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))
top#(mark(f(f(f(b, f(f(c, _x82, b), _x62, c), f(b, _x72, f(b, _x112, _x113))), c, _x43), c, c))) → top#(f(f(f(ok(b), f(f(ok(c), proper(_x82), ok(b)), proper(_x62), ok(c)), f(ok(b), proper(_x72), f(ok(b), proper(_x112), proper(_x113)))), ok(c), proper(_x43)), ok(c), ok(c)))

Problem 4: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

active#(f(X1, X2, X3)) → active#(X2)

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, mark, ok, proper, top

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

active#(f(X1, X2, X3)) → active#(X2)

Problem 5: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

f#(X1, mark(X2), X3) → f#(X1, X2, X3)f#(ok(X1), ok(X2), ok(X3)) → f#(X1, X2, X3)

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, mark, ok, proper, top

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

f#(ok(X1), ok(X2), ok(X3)) → f#(X1, X2, X3)

Problem 6: PolynomialLinearRange4iUR

Dependency Pair Problem

Dependency Pairs

f#(X1, mark(X2), X3) → f#(X1, X2, X3)

Rewrite Rules

active(f(b, X, c)) → mark(f(X, c, X))active(c) → mark(b)
active(f(X1, X2, X3)) → f(X1, active(X2), X3)f(X1, mark(X2), X3) → mark(f(X1, X2, X3))
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3))proper(b) → ok(b)
proper(c) → ok(c)f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, b, c, active, ok, mark, proper, top

Strategy

Polynomial Interpretation

There are no usable rules

The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed:

f#(X1, mark(X2), X3) → f#(X1, X2, X3)