TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60001 ms.

The following DP Processors were used


Problem 1 was processed with processor DependencyGraph (973ms).
 | – Problem 2 was processed with processor SubtermCriterion (2ms).
 | – Problem 3 was processed with processor ForwardNarrowing (8ms).
 |    | – Problem 10 was processed with processor ForwardNarrowing (7ms).
 |    |    | – Problem 11 was processed with processor ForwardNarrowing (12ms).
 |    |    |    | – Problem 12 was processed with processor ForwardNarrowing (12ms).
 |    |    |    |    | – Problem 13 was processed with processor ForwardNarrowing (40ms).
 |    |    |    |    |    | – Problem 14 was processed with processor ForwardNarrowing (7ms).
 |    |    |    |    |    |    | – Problem 15 was processed with processor ForwardNarrowing (10ms).
 |    |    |    |    |    |    |    | – Problem 16 was processed with processor ForwardNarrowing (12ms).
 |    |    |    |    |    |    |    |    | – Problem 17 was processed with processor ForwardNarrowing (19ms).
 |    |    |    |    |    |    |    |    |    | – Problem 18 was processed with processor ForwardNarrowing (11ms).
 |    |    |    |    |    |    |    |    |    |    | – Problem 19 was processed with processor ForwardNarrowing (11ms).
 |    |    |    |    |    |    |    |    |    |    |    | – Problem 20 was processed with processor ForwardNarrowing (7ms).
 |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 21 was processed with processor ForwardNarrowing (10ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 22 was processed with processor ForwardNarrowing (8ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 23 was processed with processor ForwardNarrowing (12ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 24 was processed with processor ForwardNarrowing (14ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 25 was processed with processor ForwardNarrowing (53ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 26 was processed with processor ForwardNarrowing (16ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 27 was processed with processor ForwardNarrowing (15ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 28 was processed with processor ForwardNarrowing (11ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 29 was processed with processor ForwardNarrowing (33ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 30 was processed with processor ForwardNarrowing (141ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 31 was processed with processor ForwardNarrowing (195ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 32 remains open; application of the following processors failed [ForwardNarrowing (80ms), ForwardNarrowing (80ms), ForwardNarrowing (80ms), ForwardNarrowing (102ms), ForwardNarrowing (218ms), ForwardNarrowing (117ms), ForwardNarrowing (119ms), ForwardNarrowing (118ms), ForwardNarrowing (109ms), ForwardNarrowing (238ms), ForwardNarrowing (110ms), ForwardNarrowing (224ms), ForwardNarrowing (83ms), ForwardNarrowing (213ms), ForwardNarrowing (83ms), ForwardNarrowing (86ms), ForwardNarrowing (74ms), ForwardNarrowing (94ms), ForwardNarrowing (85ms), ForwardNarrowing (97ms), ForwardNarrowing (113ms), ForwardNarrowing (96ms), ForwardNarrowing (96ms), ForwardNarrowing (75ms), ForwardNarrowing (209ms), ForwardNarrowing (97ms), ForwardNarrowing (228ms), ForwardNarrowing (109ms), ForwardNarrowing (246ms), ForwardNarrowing (102ms), ForwardNarrowing (235ms), ForwardNarrowing (124ms), ForwardNarrowing (260ms), ForwardNarrowing (115ms), ForwardNarrowing (210ms), ForwardNarrowing (105ms), ForwardNarrowing (95ms), ForwardNarrowing (95ms), ForwardNarrowing (103ms), ForwardNarrowing (236ms), ForwardNarrowing (106ms), ForwardNarrowing (233ms), ForwardNarrowing (105ms), ForwardNarrowing (timeout)].
 | – Problem 4 was processed with processor SubtermCriterion (1ms).
 | – Problem 5 was processed with processor SubtermCriterion (1ms).
 | – Problem 6 was processed with processor SubtermCriterion (1ms).
 |    | – Problem 8 was processed with processor ReductionPairSAT (118ms).
 |    |    | – Problem 9 was processed with processor ReductionPairSAT (77ms).
 | – Problem 7 was processed with processor SubtermCriterion (0ms).

The following open problems remain:

Open Dependency Pair Problem 3

Dependency Pairs

active#(tail(cons(X, XS))) → mark#(XS)mark#(cons(X1, X2)) → active#(cons(mark(X1), X2))
mark#(0) → active#(0)mark#(head(X)) → active#(head(mark(X)))
active#(nats) → mark#(cons(0, incr(nats)))mark#(s(X)) → active#(s(mark(X)))
active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))mark#(nats) → active#(nats)
mark#(cons(X1, X2)) → mark#(X1)mark#(incr(X)) → active#(incr(mark(X)))
mark#(incr(X)) → mark#(X)mark#(pairs) → active#(pairs)
active#(pairs) → mark#(cons(0, incr(odds)))mark#(odds) → active#(odds)
mark#(tail(X)) → active#(tail(mark(X)))mark#(head(X)) → mark#(X)
mark#(tail(X)) → mark#(X)mark#(s(X)) → mark#(X)
active#(head(cons(X, XS))) → mark#(X)active#(odds) → mark#(incr(pairs))

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, s, pairs, active, mark, incr, head, tail, odds, cons

Problem 1: DependencyGraph

Dependency Pair Problem

Dependency Pairs

mark#(cons(X1, X2)) → active#(cons(mark(X1), X2))active#(pairs) → cons#(0, incr(odds))
mark#(head(X)) → active#(head(mark(X)))incr#(active(X)) → incr#(X)
cons#(mark(X1), X2) → cons#(X1, X2)mark#(tail(X)) → tail#(mark(X))
active#(pairs) → incr#(odds)active#(nats) → cons#(0, incr(nats))
mark#(pairs) → active#(pairs)mark#(s(X)) → s#(mark(X))
active#(pairs) → mark#(cons(0, incr(odds)))mark#(tail(X)) → active#(tail(mark(X)))
mark#(head(X)) → mark#(X)tail#(active(X)) → tail#(X)
incr#(mark(X)) → incr#(X)cons#(X1, mark(X2)) → cons#(X1, X2)
mark#(s(X)) → mark#(X)mark#(incr(X)) → incr#(mark(X))
mark#(cons(X1, X2)) → cons#(mark(X1), X2)active#(tail(cons(X, XS))) → mark#(XS)
active#(nats) → mark#(cons(0, incr(nats)))mark#(0) → active#(0)
mark#(s(X)) → active#(s(mark(X)))active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))
mark#(nats) → active#(nats)active#(incr(cons(X, XS))) → cons#(s(X), incr(XS))
head#(mark(X)) → head#(X)mark#(cons(X1, X2)) → mark#(X1)
active#(nats) → incr#(nats)cons#(active(X1), X2) → cons#(X1, X2)
tail#(mark(X)) → tail#(X)mark#(incr(X)) → active#(incr(mark(X)))
mark#(incr(X)) → mark#(X)mark#(head(X)) → head#(mark(X))
active#(incr(cons(X, XS))) → s#(X)mark#(odds) → active#(odds)
s#(mark(X)) → s#(X)cons#(X1, active(X2)) → cons#(X1, X2)
mark#(tail(X)) → mark#(X)active#(odds) → incr#(pairs)
head#(active(X)) → head#(X)active#(odds) → mark#(incr(pairs))
active#(head(cons(X, XS))) → mark#(X)s#(active(X)) → s#(X)
active#(incr(cons(X, XS))) → incr#(XS)

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, pairs, s, active, mark, incr, head, odds, tail, cons

Strategy

The following SCCs where found

tail#(active(X)) → tail#(X)tail#(mark(X)) → tail#(X)
active#(tail(cons(X, XS))) → mark#(XS)active#(nats) → mark#(cons(0, incr(nats)))
mark#(head(X)) → active#(head(mark(X)))mark#(0) → active#(0)
mark#(cons(X1, X2)) → active#(cons(mark(X1), X2))mark#(s(X)) → active#(s(mark(X)))
active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))mark#(nats) → active#(nats)
mark#(cons(X1, X2)) → mark#(X1)mark#(incr(X)) → active#(incr(mark(X)))
mark#(incr(X)) → mark#(X)mark#(pairs) → active#(pairs)
active#(pairs) → mark#(cons(0, incr(odds)))mark#(odds) → active#(odds)
mark#(tail(X)) → active#(tail(mark(X)))mark#(head(X)) → mark#(X)
mark#(tail(X)) → mark#(X)active#(odds) → mark#(incr(pairs))
active#(head(cons(X, XS))) → mark#(X)mark#(s(X)) → mark#(X)
cons#(X1, active(X2)) → cons#(X1, X2)cons#(mark(X1), X2) → cons#(X1, X2)
cons#(X1, mark(X2)) → cons#(X1, X2)cons#(active(X1), X2) → cons#(X1, X2)
s#(mark(X)) → s#(X)s#(active(X)) → s#(X)
incr#(active(X)) → incr#(X)incr#(mark(X)) → incr#(X)
head#(mark(X)) → head#(X)head#(active(X)) → head#(X)

Problem 2: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

tail#(active(X)) → tail#(X)tail#(mark(X)) → tail#(X)

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, pairs, s, active, mark, incr, head, odds, tail, cons

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

tail#(active(X)) → tail#(X)tail#(mark(X)) → tail#(X)

Problem 3: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

active#(tail(cons(X, XS))) → mark#(XS)mark#(cons(X1, X2)) → active#(cons(mark(X1), X2))
mark#(0) → active#(0)mark#(head(X)) → active#(head(mark(X)))
active#(nats) → mark#(cons(0, incr(nats)))mark#(s(X)) → active#(s(mark(X)))
active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))mark#(nats) → active#(nats)
mark#(cons(X1, X2)) → mark#(X1)mark#(incr(X)) → active#(incr(mark(X)))
mark#(incr(X)) → mark#(X)mark#(pairs) → active#(pairs)
active#(pairs) → mark#(cons(0, incr(odds)))mark#(odds) → active#(odds)
mark#(tail(X)) → active#(tail(mark(X)))mark#(head(X)) → mark#(X)
mark#(tail(X)) → mark#(X)active#(odds) → mark#(incr(pairs))
active#(head(cons(X, XS))) → mark#(X)mark#(s(X)) → mark#(X)

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, pairs, s, active, mark, incr, head, odds, tail, cons

Strategy

The right-hand side of the rule mark#(cons(X1, X2)) → active#(cons(mark(X1), X2)) 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
active#(cons(active(s(mark(_x31))), X2)) 
active#(cons(active(pairs), X2)) 
active#(cons(active(cons(mark(_x31), _x32)), X2)) 
active#(cons(active(nats), X2)) 
active#(cons(_x21, _x22)) 
active#(cons(active(incr(mark(_x31))), X2)) 
active#(cons(mark(X1), _x22)) 
active#(cons(active(odds), X2)) 
active#(cons(active(0), X2)) 
active#(cons(active(tail(mark(_x31))), X2)) 
active#(cons(active(head(mark(_x31))), X2)) 
Thus, the rule mark#(cons(X1, X2)) → active#(cons(mark(X1), X2)) is replaced by the following rules:
mark#(cons(X1, mark(_x22))) → active#(cons(mark(X1), _x22))mark#(cons(cons(_x31, _x32), X2)) → active#(cons(active(cons(mark(_x31), _x32)), X2))
mark#(cons(incr(_x31), X2)) → active#(cons(active(incr(mark(_x31))), X2))mark#(cons(s(_x31), X2)) → active#(cons(active(s(mark(_x31))), X2))
mark#(cons(odds, X2)) → active#(cons(active(odds), X2))mark#(cons(tail(_x31), X2)) → active#(cons(active(tail(mark(_x31))), X2))
mark#(cons(head(_x31), X2)) → active#(cons(active(head(mark(_x31))), X2))mark#(cons(nats, X2)) → active#(cons(active(nats), X2))
mark#(cons(_x21, _x22)) → active#(cons(_x21, _x22))mark#(cons(pairs, X2)) → active#(cons(active(pairs), X2))
mark#(cons(0, X2)) → active#(cons(active(0), X2))mark#(cons(X1, active(_x22))) → active#(cons(mark(X1), _x22))

Problem 10: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(head(X)) → active#(head(mark(X)))mark#(cons(tail(_x31), X2)) → active#(cons(active(tail(mark(_x31))), X2))
mark#(pairs) → active#(pairs)active#(pairs) → mark#(cons(0, incr(odds)))
mark#(cons(incr(_x31), X2)) → active#(cons(active(incr(mark(_x31))), X2))mark#(cons(X1, mark(_x22))) → active#(cons(mark(X1), _x22))
mark#(tail(X)) → active#(tail(mark(X)))mark#(head(X)) → mark#(X)
mark#(s(X)) → mark#(X)mark#(cons(cons(_x31, _x32), X2)) → active#(cons(active(cons(mark(_x31), _x32)), X2))
active#(tail(cons(X, XS))) → mark#(XS)mark#(0) → active#(0)
active#(nats) → mark#(cons(0, incr(nats)))mark#(s(X)) → active#(s(mark(X)))
active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))mark#(cons(s(_x31), X2)) → active#(cons(active(s(mark(_x31))), X2))
mark#(nats) → active#(nats)mark#(cons(odds, X2)) → active#(cons(active(odds), X2))
mark#(cons(X1, X2)) → mark#(X1)mark#(cons(nats, X2)) → active#(cons(active(nats), X2))
mark#(incr(X)) → active#(incr(mark(X)))mark#(incr(X)) → mark#(X)
mark#(cons(pairs, X2)) → active#(cons(active(pairs), X2))mark#(cons(X1, active(_x22))) → active#(cons(mark(X1), _x22))
mark#(cons(0, X2)) → active#(cons(active(0), X2))mark#(odds) → active#(odds)
mark#(tail(X)) → mark#(X)mark#(cons(head(_x31), X2)) → active#(cons(active(head(mark(_x31))), X2))
active#(odds) → mark#(incr(pairs))active#(head(cons(X, XS))) → mark#(X)
mark#(cons(_x21, _x22)) → active#(cons(_x21, _x22))

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, s, pairs, active, mark, incr, head, tail, odds, cons

Strategy

The right-hand side of the rule mark#(head(X)) → active#(head(mark(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
active#(head(_x21)) 
active#(head(active(nats))) 
active#(head(active(incr(mark(_x31))))) 
active#(head(active(cons(mark(_x31), _x32)))) 
active#(head(active(tail(mark(_x31))))) 
active#(head(active(pairs))) 
active#(head(active(odds))) 
active#(head(active(0))) 
active#(head(active(head(mark(_x31))))) 
active#(head(active(s(mark(_x31))))) 
Thus, the rule mark#(head(X)) → active#(head(mark(X))) is replaced by the following rules:
mark#(head(incr(_x31))) → active#(head(active(incr(mark(_x31)))))mark#(head(cons(_x31, _x32))) → active#(head(active(cons(mark(_x31), _x32))))
mark#(head(pairs)) → active#(head(active(pairs)))mark#(head(head(_x31))) → active#(head(active(head(mark(_x31)))))
mark#(head(0)) → active#(head(active(0)))mark#(head(s(_x31))) → active#(head(active(s(mark(_x31)))))
mark#(head(_x21)) → active#(head(_x21))mark#(head(nats)) → active#(head(active(nats)))
mark#(head(tail(_x31))) → active#(head(active(tail(mark(_x31)))))mark#(head(odds)) → active#(head(active(odds)))

Problem 11: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(head(incr(_x31))) → active#(head(active(incr(mark(_x31)))))mark#(cons(tail(_x31), X2)) → active#(cons(active(tail(mark(_x31))), X2))
mark#(head(s(_x31))) → active#(head(active(s(mark(_x31)))))mark#(head(tail(_x31))) → active#(head(active(tail(mark(_x31)))))
mark#(pairs) → active#(pairs)active#(pairs) → mark#(cons(0, incr(odds)))
mark#(cons(X1, mark(_x22))) → active#(cons(mark(X1), _x22))mark#(cons(incr(_x31), X2)) → active#(cons(active(incr(mark(_x31))), X2))
mark#(tail(X)) → active#(tail(mark(X)))mark#(head(X)) → mark#(X)
mark#(head(head(_x31))) → active#(head(active(head(mark(_x31)))))mark#(head(0)) → active#(head(active(0)))
mark#(head(nats)) → active#(head(active(nats)))mark#(head(_x21)) → active#(head(_x21))
mark#(s(X)) → mark#(X)mark#(cons(cons(_x31, _x32), X2)) → active#(cons(active(cons(mark(_x31), _x32)), X2))
active#(tail(cons(X, XS))) → mark#(XS)mark#(0) → active#(0)
active#(nats) → mark#(cons(0, incr(nats)))mark#(head(cons(_x31, _x32))) → active#(head(active(cons(mark(_x31), _x32))))
mark#(s(X)) → active#(s(mark(X)))active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))
mark#(cons(s(_x31), X2)) → active#(cons(active(s(mark(_x31))), X2))mark#(nats) → active#(nats)
mark#(cons(odds, X2)) → active#(cons(active(odds), X2))mark#(cons(X1, X2)) → mark#(X1)
mark#(cons(nats, X2)) → active#(cons(active(nats), X2))mark#(incr(X)) → active#(incr(mark(X)))
mark#(incr(X)) → mark#(X)mark#(cons(pairs, X2)) → active#(cons(active(pairs), X2))
mark#(cons(0, X2)) → active#(cons(active(0), X2))mark#(cons(X1, active(_x22))) → active#(cons(mark(X1), _x22))
mark#(odds) → active#(odds)mark#(head(pairs)) → active#(head(active(pairs)))
mark#(tail(X)) → mark#(X)mark#(cons(head(_x31), X2)) → active#(cons(active(head(mark(_x31))), X2))
active#(head(cons(X, XS))) → mark#(X)active#(odds) → mark#(incr(pairs))
mark#(cons(_x21, _x22)) → active#(cons(_x21, _x22))mark#(head(odds)) → active#(head(active(odds)))

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, pairs, s, active, mark, incr, head, odds, tail, cons

Strategy

The right-hand side of the rule mark#(head(incr(_x31))) → active#(head(active(incr(mark(_x31))))) 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
active#(head(active(incr(active(tail(mark(_x61))))))) 
active#(head(active(incr(active(0))))) 
active#(head(active(incr(active(pairs))))) 
active#(head(active(incr(active(odds))))) 
active#(head(incr(mark(_x31)))) 
active#(head(active(incr(active(head(mark(_x61))))))) 
active#(head(active(incr(active(nats))))) 
active#(head(active(incr(active(incr(mark(_x61))))))) 
active#(head(active(incr(_x51)))) 
active#(head(active(incr(active(s(mark(_x61))))))) 
active#(head(active(incr(active(cons(mark(_x61), _x62)))))) 
Thus, the rule mark#(head(incr(_x31))) → active#(head(active(incr(mark(_x31))))) is replaced by the following rules:
mark#(head(incr(_x31))) → active#(head(incr(mark(_x31))))mark#(head(incr(nats))) → active#(head(active(incr(active(nats)))))
mark#(head(incr(head(_x61)))) → active#(head(active(incr(active(head(mark(_x61)))))))mark#(head(incr(cons(_x61, _x62)))) → active#(head(active(incr(active(cons(mark(_x61), _x62))))))
mark#(head(incr(s(_x61)))) → active#(head(active(incr(active(s(mark(_x61)))))))mark#(head(incr(odds))) → active#(head(active(incr(active(odds)))))
mark#(head(incr(pairs))) → active#(head(active(incr(active(pairs)))))mark#(head(incr(_x51))) → active#(head(active(incr(_x51))))
mark#(head(incr(tail(_x61)))) → active#(head(active(incr(active(tail(mark(_x61)))))))mark#(head(incr(incr(_x61)))) → active#(head(active(incr(active(incr(mark(_x61)))))))
mark#(head(incr(0))) → active#(head(active(incr(active(0)))))

Problem 12: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(head(incr(cons(_x61, _x62)))) → active#(head(active(incr(active(cons(mark(_x61), _x62))))))mark#(head(s(_x31))) → active#(head(active(s(mark(_x31)))))
mark#(head(tail(_x31))) → active#(head(active(tail(mark(_x31)))))mark#(head(incr(odds))) → active#(head(active(incr(active(odds)))))
mark#(pairs) → active#(pairs)mark#(head(incr(pairs))) → active#(head(active(incr(active(pairs)))))
active#(pairs) → mark#(cons(0, incr(odds)))mark#(cons(incr(_x31), X2)) → active#(cons(active(incr(mark(_x31))), X2))
mark#(tail(X)) → active#(tail(mark(X)))mark#(head(incr(_x31))) → active#(head(incr(mark(_x31))))
mark#(head(head(_x31))) → active#(head(active(head(mark(_x31)))))mark#(head(0)) → active#(head(active(0)))
mark#(head(nats)) → active#(head(active(nats)))mark#(head(_x21)) → active#(head(_x21))
mark#(s(X)) → mark#(X)mark#(head(incr(tail(_x61)))) → active#(head(active(incr(active(tail(mark(_x61)))))))
mark#(cons(cons(_x31, _x32), X2)) → active#(cons(active(cons(mark(_x31), _x32)), X2))mark#(head(cons(_x31, _x32))) → active#(head(active(cons(mark(_x31), _x32))))
active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))mark#(cons(s(_x31), X2)) → active#(cons(active(s(mark(_x31))), X2))
mark#(cons(odds, X2)) → active#(cons(active(odds), X2))mark#(cons(X1, X2)) → mark#(X1)
mark#(cons(nats, X2)) → active#(cons(active(nats), X2))mark#(incr(X)) → active#(incr(mark(X)))
mark#(cons(X1, active(_x22))) → active#(cons(mark(X1), _x22))mark#(cons(0, X2)) → active#(cons(active(0), X2))
mark#(tail(X)) → mark#(X)mark#(cons(head(_x31), X2)) → active#(cons(active(head(mark(_x31))), X2))
active#(odds) → mark#(incr(pairs))mark#(head(incr(_x51))) → active#(head(active(incr(_x51))))
mark#(head(incr(incr(_x61)))) → active#(head(active(incr(active(incr(mark(_x61)))))))mark#(cons(tail(_x31), X2)) → active#(cons(active(tail(mark(_x31))), X2))
mark#(head(incr(s(_x61)))) → active#(head(active(incr(active(s(mark(_x61)))))))mark#(cons(X1, mark(_x22))) → active#(cons(mark(X1), _x22))
mark#(head(X)) → mark#(X)mark#(head(incr(nats))) → active#(head(active(incr(active(nats)))))
mark#(head(incr(0))) → active#(head(active(incr(active(0)))))active#(tail(cons(X, XS))) → mark#(XS)
active#(nats) → mark#(cons(0, incr(nats)))mark#(0) → active#(0)
mark#(s(X)) → active#(s(mark(X)))mark#(nats) → active#(nats)
mark#(head(incr(head(_x61)))) → active#(head(active(incr(active(head(mark(_x61)))))))mark#(incr(X)) → mark#(X)
mark#(cons(pairs, X2)) → active#(cons(active(pairs), X2))mark#(odds) → active#(odds)
mark#(head(pairs)) → active#(head(active(pairs)))active#(head(cons(X, XS))) → mark#(X)
mark#(cons(_x21, _x22)) → active#(cons(_x21, _x22))mark#(head(odds)) → active#(head(active(odds)))

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, s, pairs, active, mark, incr, head, tail, odds, cons

Strategy

The right-hand side of the rule mark#(head(incr(cons(_x61, _x62)))) → active#(head(active(incr(active(cons(mark(_x61), _x62)))))) 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
active#(head(active(incr(active(cons(active(head(mark(_x81))), _x62)))))) 
active#(head(active(incr(active(cons(active(nats), _x62)))))) 
active#(head(active(incr(active(cons(active(tail(mark(_x81))), _x62)))))) 
active#(head(incr(active(cons(mark(_x61), _x62))))) 
active#(head(active(incr(cons(mark(_x61), _x62))))) 
active#(head(active(incr(active(cons(active(incr(mark(_x81))), _x62)))))) 
active#(head(active(incr(active(cons(active(0), _x62)))))) 
active#(head(active(incr(active(cons(active(pairs), _x62)))))) 
active#(head(active(incr(active(cons(_x71, _x72)))))) 
active#(head(active(incr(active(cons(mark(_x61), _x72)))))) 
active#(head(active(incr(active(cons(active(odds), _x62)))))) 
active#(head(active(incr(active(cons(active(cons(mark(_x81), _x82)), _x62)))))) 
active#(head(active(incr(active(cons(active(s(mark(_x81))), _x62)))))) 
Thus, the rule mark#(head(incr(cons(_x61, _x62)))) → active#(head(active(incr(active(cons(mark(_x61), _x62)))))) is replaced by the following rules:
mark#(head(incr(cons(cons(_x81, _x82), _x62)))) → active#(head(active(incr(active(cons(active(cons(mark(_x81), _x82)), _x62))))))mark#(head(incr(cons(_x61, mark(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))
mark#(head(incr(cons(head(_x81), _x62)))) → active#(head(active(incr(active(cons(active(head(mark(_x81))), _x62))))))mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(active(cons(active(pairs), _x62))))))
mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(active(cons(active(nats), _x62))))))mark#(head(incr(cons(_x61, active(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))
mark#(head(incr(cons(_x61, _x62)))) → active#(head(active(incr(cons(mark(_x61), _x62)))))mark#(head(incr(cons(tail(_x81), _x62)))) → active#(head(active(incr(active(cons(active(tail(mark(_x81))), _x62))))))
mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(active(cons(active(odds), _x62))))))mark#(head(incr(cons(s(_x81), _x62)))) → active#(head(active(incr(active(cons(active(s(mark(_x81))), _x62))))))
mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(active(cons(active(0), _x62))))))mark#(head(incr(cons(_x71, _x72)))) → active#(head(active(incr(active(cons(_x71, _x72))))))
mark#(head(incr(cons(incr(_x81), _x62)))) → active#(head(active(incr(active(cons(active(incr(mark(_x81))), _x62))))))mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(active(cons(mark(_x61), _x62)))))

Problem 13: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(head(s(_x31))) → active#(head(active(s(mark(_x31)))))mark#(head(tail(_x31))) → active#(head(active(tail(mark(_x31)))))
mark#(head(incr(odds))) → active#(head(active(incr(active(odds)))))mark#(pairs) → active#(pairs)
mark#(head(incr(pairs))) → active#(head(active(incr(active(pairs)))))mark#(head(incr(cons(_x61, _x62)))) → active#(head(active(incr(cons(mark(_x61), _x62)))))
active#(pairs) → mark#(cons(0, incr(odds)))mark#(cons(incr(_x31), X2)) → active#(cons(active(incr(mark(_x31))), X2))
mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(active(cons(active(odds), _x62))))))mark#(tail(X)) → active#(tail(mark(X)))
mark#(head(incr(_x31))) → active#(head(incr(mark(_x31))))mark#(head(head(_x31))) → active#(head(active(head(mark(_x31)))))
mark#(head(0)) → active#(head(active(0)))mark#(head(_x21)) → active#(head(_x21))
mark#(head(nats)) → active#(head(active(nats)))mark#(s(X)) → mark#(X)
mark#(head(incr(cons(incr(_x81), _x62)))) → active#(head(active(incr(active(cons(active(incr(mark(_x81))), _x62))))))mark#(head(incr(tail(_x61)))) → active#(head(active(incr(active(tail(mark(_x61)))))))
mark#(cons(cons(_x31, _x32), X2)) → active#(cons(active(cons(mark(_x31), _x32)), X2))mark#(head(cons(_x31, _x32))) → active#(head(active(cons(mark(_x31), _x32))))
mark#(cons(s(_x31), X2)) → active#(cons(active(s(mark(_x31))), X2))active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))
mark#(cons(odds, X2)) → active#(cons(active(odds), X2))mark#(cons(X1, X2)) → mark#(X1)
mark#(cons(nats, X2)) → active#(cons(active(nats), X2))mark#(incr(X)) → active#(incr(mark(X)))
mark#(head(incr(cons(_x61, active(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(active(cons(active(nats), _x62))))))
mark#(head(incr(cons(tail(_x81), _x62)))) → active#(head(active(incr(active(cons(active(tail(mark(_x81))), _x62))))))mark#(cons(X1, active(_x22))) → active#(cons(mark(X1), _x22))
mark#(cons(0, X2)) → active#(cons(active(0), X2))mark#(tail(X)) → mark#(X)
mark#(head(incr(cons(_x71, _x72)))) → active#(head(active(incr(active(cons(_x71, _x72))))))mark#(cons(head(_x31), X2)) → active#(cons(active(head(mark(_x31))), X2))
active#(odds) → mark#(incr(pairs))mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(active(cons(mark(_x61), _x62)))))
mark#(head(incr(_x51))) → active#(head(active(incr(_x51))))mark#(head(incr(incr(_x61)))) → active#(head(active(incr(active(incr(mark(_x61)))))))
mark#(head(incr(cons(cons(_x81, _x82), _x62)))) → active#(head(active(incr(active(cons(active(cons(mark(_x81), _x82)), _x62))))))mark#(head(incr(cons(head(_x81), _x62)))) → active#(head(active(incr(active(cons(active(head(mark(_x81))), _x62))))))
mark#(cons(tail(_x31), X2)) → active#(cons(active(tail(mark(_x31))), X2))mark#(head(incr(s(_x61)))) → active#(head(active(incr(active(s(mark(_x61)))))))
mark#(cons(X1, mark(_x22))) → active#(cons(mark(X1), _x22))mark#(head(incr(cons(s(_x81), _x62)))) → active#(head(active(incr(active(cons(active(s(mark(_x81))), _x62))))))
mark#(head(X)) → mark#(X)mark#(head(incr(nats))) → active#(head(active(incr(active(nats)))))
mark#(head(incr(0))) → active#(head(active(incr(active(0)))))active#(tail(cons(X, XS))) → mark#(XS)
mark#(0) → active#(0)active#(nats) → mark#(cons(0, incr(nats)))
mark#(s(X)) → active#(s(mark(X)))mark#(nats) → active#(nats)
mark#(head(incr(cons(_x61, mark(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))mark#(head(incr(head(_x61)))) → active#(head(active(incr(active(head(mark(_x61)))))))
mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(active(cons(active(pairs), _x62))))))mark#(incr(X)) → mark#(X)
mark#(cons(pairs, X2)) → active#(cons(active(pairs), X2))mark#(odds) → active#(odds)
mark#(head(pairs)) → active#(head(active(pairs)))mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(active(cons(active(0), _x62))))))
active#(head(cons(X, XS))) → mark#(X)mark#(cons(_x21, _x22)) → active#(cons(_x21, _x22))
mark#(head(odds)) → active#(head(active(odds)))

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, pairs, s, active, mark, incr, head, odds, tail, cons

Strategy

The right-hand side of the rule mark#(head(s(_x31))) → active#(head(active(s(mark(_x31))))) 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
active#(head(active(s(active(tail(mark(_x61))))))) 
active#(head(active(s(active(pairs))))) 
active#(head(active(s(active(nats))))) 
active#(head(s(mark(_x31)))) 
active#(head(active(s(active(0))))) 
active#(head(active(s(active(incr(mark(_x61))))))) 
active#(head(active(s(active(cons(mark(_x61), _x62)))))) 
active#(head(active(s(active(odds))))) 
active#(head(active(s(_x51)))) 
active#(head(active(s(active(s(mark(_x61))))))) 
active#(head(active(s(active(head(mark(_x61))))))) 
Thus, the rule mark#(head(s(_x31))) → active#(head(active(s(mark(_x31))))) is replaced by the following rules:
mark#(head(s(nats))) → active#(head(active(s(active(nats)))))mark#(head(s(incr(_x61)))) → active#(head(active(s(active(incr(mark(_x61)))))))
mark#(head(s(pairs))) → active#(head(active(s(active(pairs)))))mark#(head(s(_x51))) → active#(head(active(s(_x51))))
mark#(head(s(tail(_x61)))) → active#(head(active(s(active(tail(mark(_x61)))))))mark#(head(s(_x31))) → active#(head(s(mark(_x31))))
mark#(head(s(cons(_x61, _x62)))) → active#(head(active(s(active(cons(mark(_x61), _x62))))))mark#(head(s(head(_x61)))) → active#(head(active(s(active(head(mark(_x61)))))))
mark#(head(s(0))) → active#(head(active(s(active(0)))))mark#(head(s(s(_x61)))) → active#(head(active(s(active(s(mark(_x61)))))))
mark#(head(s(odds))) → active#(head(active(s(active(odds)))))

Problem 14: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(head(s(nats))) → active#(head(active(s(active(nats)))))mark#(head(tail(_x31))) → active#(head(active(tail(mark(_x31)))))
mark#(head(s(s(_x61)))) → active#(head(active(s(active(s(mark(_x61)))))))mark#(head(incr(odds))) → active#(head(active(incr(active(odds)))))
mark#(pairs) → active#(pairs)mark#(head(incr(pairs))) → active#(head(active(incr(active(pairs)))))
mark#(head(incr(cons(_x61, _x62)))) → active#(head(active(incr(cons(mark(_x61), _x62)))))active#(pairs) → mark#(cons(0, incr(odds)))
mark#(cons(incr(_x31), X2)) → active#(cons(active(incr(mark(_x31))), X2))mark#(head(incr(_x31))) → active#(head(incr(mark(_x31))))
mark#(head(s(pairs))) → active#(head(active(s(active(pairs)))))mark#(head(s(incr(_x61)))) → active#(head(active(s(active(incr(mark(_x61)))))))
mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(active(cons(active(odds), _x62))))))mark#(tail(X)) → active#(tail(mark(X)))
mark#(head(head(_x31))) → active#(head(active(head(mark(_x31)))))mark#(head(s(_x51))) → active#(head(active(s(_x51))))
mark#(head(0)) → active#(head(active(0)))mark#(head(s(cons(_x61, _x62)))) → active#(head(active(s(active(cons(mark(_x61), _x62))))))
mark#(head(nats)) → active#(head(active(nats)))mark#(head(_x21)) → active#(head(_x21))
mark#(s(X)) → mark#(X)mark#(head(incr(cons(incr(_x81), _x62)))) → active#(head(active(incr(active(cons(active(incr(mark(_x81))), _x62))))))
mark#(head(incr(tail(_x61)))) → active#(head(active(incr(active(tail(mark(_x61)))))))mark#(cons(cons(_x31, _x32), X2)) → active#(cons(active(cons(mark(_x31), _x32)), X2))
mark#(head(cons(_x31, _x32))) → active#(head(active(cons(mark(_x31), _x32))))mark#(cons(s(_x31), X2)) → active#(cons(active(s(mark(_x31))), X2))
active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))mark#(cons(odds, X2)) → active#(cons(active(odds), X2))
mark#(cons(X1, X2)) → mark#(X1)mark#(cons(nats, X2)) → active#(cons(active(nats), X2))
mark#(head(s(0))) → active#(head(active(s(active(0)))))mark#(incr(X)) → active#(incr(mark(X)))
mark#(head(incr(cons(_x61, active(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(active(cons(active(nats), _x62))))))
mark#(head(incr(cons(tail(_x81), _x62)))) → active#(head(active(incr(active(cons(active(tail(mark(_x81))), _x62))))))mark#(cons(X1, active(_x22))) → active#(cons(mark(X1), _x22))
mark#(cons(0, X2)) → active#(cons(active(0), X2))mark#(head(s(tail(_x61)))) → active#(head(active(s(active(tail(mark(_x61)))))))
mark#(tail(X)) → mark#(X)mark#(head(incr(cons(_x71, _x72)))) → active#(head(active(incr(active(cons(_x71, _x72))))))
mark#(cons(head(_x31), X2)) → active#(cons(active(head(mark(_x31))), X2))active#(odds) → mark#(incr(pairs))
mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(active(cons(mark(_x61), _x62)))))mark#(head(incr(_x51))) → active#(head(active(incr(_x51))))
mark#(head(incr(incr(_x61)))) → active#(head(active(incr(active(incr(mark(_x61)))))))mark#(head(incr(cons(cons(_x81, _x82), _x62)))) → active#(head(active(incr(active(cons(active(cons(mark(_x81), _x82)), _x62))))))
mark#(head(incr(cons(head(_x81), _x62)))) → active#(head(active(incr(active(cons(active(head(mark(_x81))), _x62))))))mark#(head(s(head(_x61)))) → active#(head(active(s(active(head(mark(_x61)))))))
mark#(cons(tail(_x31), X2)) → active#(cons(active(tail(mark(_x31))), X2))mark#(head(incr(s(_x61)))) → active#(head(active(incr(active(s(mark(_x61)))))))
mark#(cons(X1, mark(_x22))) → active#(cons(mark(X1), _x22))mark#(head(X)) → mark#(X)
mark#(head(incr(cons(s(_x81), _x62)))) → active#(head(active(incr(active(cons(active(s(mark(_x81))), _x62))))))mark#(head(incr(nats))) → active#(head(active(incr(active(nats)))))
mark#(head(incr(0))) → active#(head(active(incr(active(0)))))active#(tail(cons(X, XS))) → mark#(XS)
active#(nats) → mark#(cons(0, incr(nats)))mark#(0) → active#(0)
mark#(s(X)) → active#(s(mark(X)))mark#(head(incr(cons(_x61, mark(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))
mark#(nats) → active#(nats)mark#(head(incr(head(_x61)))) → active#(head(active(incr(active(head(mark(_x61)))))))
mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(active(cons(active(pairs), _x62))))))mark#(incr(X)) → mark#(X)
mark#(cons(pairs, X2)) → active#(cons(active(pairs), X2))mark#(odds) → active#(odds)
mark#(head(pairs)) → active#(head(active(pairs)))mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(active(cons(active(0), _x62))))))
mark#(head(s(_x31))) → active#(head(s(mark(_x31))))active#(head(cons(X, XS))) → mark#(X)
mark#(cons(_x21, _x22)) → active#(cons(_x21, _x22))mark#(head(odds)) → active#(head(active(odds)))
mark#(head(s(odds))) → active#(head(active(s(active(odds)))))

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, s, pairs, active, mark, incr, head, tail, odds, cons

Strategy

The right-hand side of the rule mark#(head(s(nats))) → active#(head(active(s(active(nats))))) 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
active#(head(s(active(nats)))) 
active#(head(active(s(nats)))) 
active#(head(active(s(mark(cons(0, incr(nats))))))) 
Thus, the rule mark#(head(s(nats))) → active#(head(active(s(active(nats))))) is replaced by the following rules:
mark#(head(s(nats))) → active#(head(active(s(mark(cons(0, incr(nats)))))))mark#(head(s(nats))) → active#(head(active(s(nats))))
mark#(head(s(nats))) → active#(head(s(active(nats))))

Problem 15: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(head(tail(_x31))) → active#(head(active(tail(mark(_x31)))))mark#(head(s(s(_x61)))) → active#(head(active(s(active(s(mark(_x61)))))))
mark#(head(incr(odds))) → active#(head(active(incr(active(odds)))))mark#(pairs) → active#(pairs)
mark#(head(incr(pairs))) → active#(head(active(incr(active(pairs)))))mark#(head(incr(cons(_x61, _x62)))) → active#(head(active(incr(cons(mark(_x61), _x62)))))
active#(pairs) → mark#(cons(0, incr(odds)))mark#(cons(incr(_x31), X2)) → active#(cons(active(incr(mark(_x31))), X2))
mark#(head(incr(_x31))) → active#(head(incr(mark(_x31))))mark#(head(s(pairs))) → active#(head(active(s(active(pairs)))))
mark#(head(s(incr(_x61)))) → active#(head(active(s(active(incr(mark(_x61)))))))mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(active(cons(active(odds), _x62))))))
mark#(tail(X)) → active#(tail(mark(X)))mark#(head(s(_x51))) → active#(head(active(s(_x51))))
mark#(head(head(_x31))) → active#(head(active(head(mark(_x31)))))mark#(head(0)) → active#(head(active(0)))
mark#(head(s(cons(_x61, _x62)))) → active#(head(active(s(active(cons(mark(_x61), _x62))))))mark#(head(_x21)) → active#(head(_x21))
mark#(head(nats)) → active#(head(active(nats)))mark#(s(X)) → mark#(X)
mark#(head(incr(cons(incr(_x81), _x62)))) → active#(head(active(incr(active(cons(active(incr(mark(_x81))), _x62))))))mark#(head(incr(tail(_x61)))) → active#(head(active(incr(active(tail(mark(_x61)))))))
mark#(cons(cons(_x31, _x32), X2)) → active#(cons(active(cons(mark(_x31), _x32)), X2))mark#(head(cons(_x31, _x32))) → active#(head(active(cons(mark(_x31), _x32))))
mark#(cons(s(_x31), X2)) → active#(cons(active(s(mark(_x31))), X2))active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))
mark#(cons(odds, X2)) → active#(cons(active(odds), X2))mark#(cons(X1, X2)) → mark#(X1)
mark#(cons(nats, X2)) → active#(cons(active(nats), X2))mark#(head(s(0))) → active#(head(active(s(active(0)))))
mark#(incr(X)) → active#(incr(mark(X)))mark#(head(incr(cons(_x61, active(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))
mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(active(cons(active(nats), _x62))))))mark#(head(incr(cons(tail(_x81), _x62)))) → active#(head(active(incr(active(cons(active(tail(mark(_x81))), _x62))))))
mark#(cons(X1, active(_x22))) → active#(cons(mark(X1), _x22))mark#(cons(0, X2)) → active#(cons(active(0), X2))
mark#(head(s(tail(_x61)))) → active#(head(active(s(active(tail(mark(_x61)))))))mark#(tail(X)) → mark#(X)
mark#(head(incr(cons(_x71, _x72)))) → active#(head(active(incr(active(cons(_x71, _x72))))))mark#(cons(head(_x31), X2)) → active#(cons(active(head(mark(_x31))), X2))
active#(odds) → mark#(incr(pairs))mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(active(cons(mark(_x61), _x62)))))
mark#(head(incr(_x51))) → active#(head(active(incr(_x51))))mark#(head(incr(incr(_x61)))) → active#(head(active(incr(active(incr(mark(_x61)))))))
mark#(head(incr(cons(cons(_x81, _x82), _x62)))) → active#(head(active(incr(active(cons(active(cons(mark(_x81), _x82)), _x62))))))mark#(head(incr(cons(head(_x81), _x62)))) → active#(head(active(incr(active(cons(active(head(mark(_x81))), _x62))))))
mark#(head(s(head(_x61)))) → active#(head(active(s(active(head(mark(_x61)))))))mark#(cons(tail(_x31), X2)) → active#(cons(active(tail(mark(_x31))), X2))
mark#(head(incr(s(_x61)))) → active#(head(active(incr(active(s(mark(_x61)))))))mark#(head(s(nats))) → active#(head(s(active(nats))))
mark#(cons(X1, mark(_x22))) → active#(cons(mark(X1), _x22))mark#(head(incr(cons(s(_x81), _x62)))) → active#(head(active(incr(active(cons(active(s(mark(_x81))), _x62))))))
mark#(head(X)) → mark#(X)mark#(head(incr(nats))) → active#(head(active(incr(active(nats)))))
mark#(head(incr(0))) → active#(head(active(incr(active(0)))))active#(tail(cons(X, XS))) → mark#(XS)
mark#(0) → active#(0)active#(nats) → mark#(cons(0, incr(nats)))
mark#(s(X)) → active#(s(mark(X)))mark#(head(s(nats))) → active#(head(active(s(mark(cons(0, incr(nats)))))))
mark#(nats) → active#(nats)mark#(head(incr(cons(_x61, mark(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))
mark#(head(incr(head(_x61)))) → active#(head(active(incr(active(head(mark(_x61)))))))mark#(head(s(nats))) → active#(head(active(s(nats))))
mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(active(cons(active(pairs), _x62))))))mark#(incr(X)) → mark#(X)
mark#(cons(pairs, X2)) → active#(cons(active(pairs), X2))mark#(odds) → active#(odds)
mark#(head(pairs)) → active#(head(active(pairs)))mark#(head(s(_x31))) → active#(head(s(mark(_x31))))
mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(active(cons(active(0), _x62))))))active#(head(cons(X, XS))) → mark#(X)
mark#(cons(_x21, _x22)) → active#(cons(_x21, _x22))mark#(head(odds)) → active#(head(active(odds)))
mark#(head(s(odds))) → active#(head(active(s(active(odds)))))

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, pairs, s, active, mark, incr, head, odds, tail, cons

Strategy

The right-hand side of the rule mark#(head(tail(_x31))) → active#(head(active(tail(mark(_x31))))) 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
active#(head(active(tail(active(nats))))) 
active#(head(active(tail(active(odds))))) 
active#(head(active(tail(active(head(mark(_x61))))))) 
active#(head(active(tail(_x51)))) 
active#(head(active(tail(active(pairs))))) 
active#(head(active(tail(active(tail(mark(_x61))))))) 
active#(head(active(tail(active(incr(mark(_x61))))))) 
active#(head(active(tail(active(cons(mark(_x61), _x62)))))) 
active#(head(tail(mark(_x31)))) 
active#(head(active(tail(active(s(mark(_x61))))))) 
active#(head(active(tail(active(0))))) 
Thus, the rule mark#(head(tail(_x31))) → active#(head(active(tail(mark(_x31))))) is replaced by the following rules:
mark#(head(tail(incr(_x61)))) → active#(head(active(tail(active(incr(mark(_x61)))))))mark#(head(tail(0))) → active#(head(active(tail(active(0)))))
mark#(head(tail(_x51))) → active#(head(active(tail(_x51))))mark#(head(tail(head(_x61)))) → active#(head(active(tail(active(head(mark(_x61)))))))
mark#(head(tail(s(_x61)))) → active#(head(active(tail(active(s(mark(_x61)))))))mark#(head(tail(nats))) → active#(head(active(tail(active(nats)))))
mark#(head(tail(tail(_x61)))) → active#(head(active(tail(active(tail(mark(_x61)))))))mark#(head(tail(_x31))) → active#(head(tail(mark(_x31))))
mark#(head(tail(cons(_x61, _x62)))) → active#(head(active(tail(active(cons(mark(_x61), _x62))))))mark#(head(tail(odds))) → active#(head(active(tail(active(odds)))))
mark#(head(tail(pairs))) → active#(head(active(tail(active(pairs)))))

Problem 16: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(head(s(s(_x61)))) → active#(head(active(s(active(s(mark(_x61)))))))mark#(head(incr(odds))) → active#(head(active(incr(active(odds)))))
mark#(pairs) → active#(pairs)mark#(head(incr(pairs))) → active#(head(active(incr(active(pairs)))))
mark#(head(incr(cons(_x61, _x62)))) → active#(head(active(incr(cons(mark(_x61), _x62)))))active#(pairs) → mark#(cons(0, incr(odds)))
mark#(cons(incr(_x31), X2)) → active#(cons(active(incr(mark(_x31))), X2))mark#(head(incr(_x31))) → active#(head(incr(mark(_x31))))
mark#(head(s(pairs))) → active#(head(active(s(active(pairs)))))mark#(head(s(incr(_x61)))) → active#(head(active(s(active(incr(mark(_x61)))))))
mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(active(cons(active(odds), _x62))))))mark#(tail(X)) → active#(tail(mark(X)))
mark#(head(head(_x31))) → active#(head(active(head(mark(_x31)))))mark#(head(s(_x51))) → active#(head(active(s(_x51))))
mark#(head(tail(_x51))) → active#(head(active(tail(_x51))))mark#(head(0)) → active#(head(active(0)))
mark#(head(s(cons(_x61, _x62)))) → active#(head(active(s(active(cons(mark(_x61), _x62))))))mark#(head(nats)) → active#(head(active(nats)))
mark#(head(_x21)) → active#(head(_x21))mark#(s(X)) → mark#(X)
mark#(head(incr(cons(incr(_x81), _x62)))) → active#(head(active(incr(active(cons(active(incr(mark(_x81))), _x62))))))mark#(head(incr(tail(_x61)))) → active#(head(active(incr(active(tail(mark(_x61)))))))
mark#(cons(cons(_x31, _x32), X2)) → active#(cons(active(cons(mark(_x31), _x32)), X2))mark#(head(tail(0))) → active#(head(active(tail(active(0)))))
mark#(head(cons(_x31, _x32))) → active#(head(active(cons(mark(_x31), _x32))))mark#(cons(s(_x31), X2)) → active#(cons(active(s(mark(_x31))), X2))
active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))mark#(cons(odds, X2)) → active#(cons(active(odds), X2))
mark#(cons(X1, X2)) → mark#(X1)mark#(cons(nats, X2)) → active#(cons(active(nats), X2))
mark#(head(s(0))) → active#(head(active(s(active(0)))))mark#(incr(X)) → active#(incr(mark(X)))
mark#(head(tail(odds))) → active#(head(active(tail(active(odds)))))mark#(head(incr(cons(_x61, active(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))
mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(active(cons(active(nats), _x62))))))mark#(head(incr(cons(tail(_x81), _x62)))) → active#(head(active(incr(active(cons(active(tail(mark(_x81))), _x62))))))
mark#(cons(X1, active(_x22))) → active#(cons(mark(X1), _x22))mark#(cons(0, X2)) → active#(cons(active(0), X2))
mark#(head(s(tail(_x61)))) → active#(head(active(s(active(tail(mark(_x61)))))))mark#(tail(X)) → mark#(X)
mark#(head(incr(cons(_x71, _x72)))) → active#(head(active(incr(active(cons(_x71, _x72))))))mark#(head(tail(_x31))) → active#(head(tail(mark(_x31))))
mark#(cons(head(_x31), X2)) → active#(cons(active(head(mark(_x31))), X2))active#(odds) → mark#(incr(pairs))
mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(active(cons(mark(_x61), _x62)))))mark#(head(incr(_x51))) → active#(head(active(incr(_x51))))
mark#(head(incr(incr(_x61)))) → active#(head(active(incr(active(incr(mark(_x61)))))))mark#(head(incr(cons(cons(_x81, _x82), _x62)))) → active#(head(active(incr(active(cons(active(cons(mark(_x81), _x82)), _x62))))))
mark#(head(tail(head(_x61)))) → active#(head(active(tail(active(head(mark(_x61)))))))mark#(head(incr(cons(head(_x81), _x62)))) → active#(head(active(incr(active(cons(active(head(mark(_x81))), _x62))))))
mark#(head(tail(s(_x61)))) → active#(head(active(tail(active(s(mark(_x61)))))))mark#(head(s(head(_x61)))) → active#(head(active(s(active(head(mark(_x61)))))))
mark#(cons(tail(_x31), X2)) → active#(cons(active(tail(mark(_x31))), X2))mark#(head(incr(s(_x61)))) → active#(head(active(incr(active(s(mark(_x61)))))))
mark#(head(s(nats))) → active#(head(s(active(nats))))mark#(cons(X1, mark(_x22))) → active#(cons(mark(X1), _x22))
mark#(head(X)) → mark#(X)mark#(head(incr(cons(s(_x81), _x62)))) → active#(head(active(incr(active(cons(active(s(mark(_x81))), _x62))))))
mark#(head(incr(nats))) → active#(head(active(incr(active(nats)))))mark#(head(tail(nats))) → active#(head(active(tail(active(nats)))))
mark#(head(incr(0))) → active#(head(active(incr(active(0)))))active#(tail(cons(X, XS))) → mark#(XS)
active#(nats) → mark#(cons(0, incr(nats)))mark#(0) → active#(0)
mark#(head(tail(incr(_x61)))) → active#(head(active(tail(active(incr(mark(_x61)))))))mark#(head(s(nats))) → active#(head(active(s(mark(cons(0, incr(nats)))))))
mark#(s(X)) → active#(s(mark(X)))mark#(head(incr(cons(_x61, mark(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))
mark#(nats) → active#(nats)mark#(head(s(nats))) → active#(head(active(s(nats))))
mark#(head(incr(head(_x61)))) → active#(head(active(incr(active(head(mark(_x61)))))))mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(active(cons(active(pairs), _x62))))))
mark#(head(tail(cons(_x61, _x62)))) → active#(head(active(tail(active(cons(mark(_x61), _x62))))))mark#(incr(X)) → mark#(X)
mark#(cons(pairs, X2)) → active#(cons(active(pairs), X2))mark#(odds) → active#(odds)
mark#(head(pairs)) → active#(head(active(pairs)))mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(active(cons(active(0), _x62))))))
mark#(head(s(_x31))) → active#(head(s(mark(_x31))))mark#(head(tail(tail(_x61)))) → active#(head(active(tail(active(tail(mark(_x61)))))))
active#(head(cons(X, XS))) → mark#(X)mark#(cons(_x21, _x22)) → active#(cons(_x21, _x22))
mark#(head(odds)) → active#(head(active(odds)))mark#(head(s(odds))) → active#(head(active(s(active(odds)))))
mark#(head(tail(pairs))) → active#(head(active(tail(active(pairs)))))

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, s, pairs, active, mark, incr, head, tail, odds, cons

Strategy

The right-hand side of the rule mark#(head(s(s(_x61)))) → active#(head(active(s(active(s(mark(_x61))))))) 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
active#(head(active(s(active(s(active(s(mark(_x81))))))))) 
active#(head(active(s(active(s(active(head(mark(_x81))))))))) 
active#(head(active(s(active(s(active(tail(mark(_x81))))))))) 
active#(head(active(s(active(s(active(pairs))))))) 
active#(head(active(s(active(s(active(incr(mark(_x81))))))))) 
active#(head(active(s(active(s(active(cons(mark(_x81), _x82)))))))) 
active#(head(s(active(s(mark(_x61)))))) 
active#(head(active(s(active(s(active(odds))))))) 
active#(head(active(s(active(s(_x71)))))) 
active#(head(active(s(active(s(active(nats))))))) 
active#(head(active(s(active(s(active(0))))))) 
active#(head(active(s(s(mark(_x61)))))) 
Thus, the rule mark#(head(s(s(_x61)))) → active#(head(active(s(active(s(mark(_x61))))))) is replaced by the following rules:
mark#(head(s(s(nats)))) → active#(head(active(s(active(s(active(nats)))))))mark#(head(s(s(_x61)))) → active#(head(s(active(s(mark(_x61))))))
mark#(head(s(s(incr(_x81))))) → active#(head(active(s(active(s(active(incr(mark(_x81)))))))))mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(active(pairs)))))))
mark#(head(s(s(s(_x81))))) → active#(head(active(s(active(s(active(s(mark(_x81)))))))))mark#(head(s(s(cons(_x81, _x82))))) → active#(head(active(s(active(s(active(cons(mark(_x81), _x82))))))))
mark#(head(s(s(0)))) → active#(head(active(s(active(s(active(0)))))))mark#(head(s(s(odds)))) → active#(head(active(s(active(s(active(odds)))))))
mark#(head(s(s(tail(_x81))))) → active#(head(active(s(active(s(active(tail(mark(_x81)))))))))mark#(head(s(s(_x71)))) → active#(head(active(s(active(s(_x71))))))
mark#(head(s(s(_x61)))) → active#(head(active(s(s(mark(_x61))))))mark#(head(s(s(head(_x81))))) → active#(head(active(s(active(s(active(head(mark(_x81)))))))))

Problem 17: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(head(s(s(incr(_x81))))) → active#(head(active(s(active(s(active(incr(mark(_x81)))))))))mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(active(pairs)))))))
mark#(head(s(s(odds)))) → active#(head(active(s(active(s(active(odds)))))))mark#(head(incr(odds))) → active#(head(active(incr(active(odds)))))
mark#(pairs) → active#(pairs)mark#(head(incr(pairs))) → active#(head(active(incr(active(pairs)))))
mark#(head(incr(cons(_x61, _x62)))) → active#(head(active(incr(cons(mark(_x61), _x62)))))active#(pairs) → mark#(cons(0, incr(odds)))
mark#(cons(incr(_x31), X2)) → active#(cons(active(incr(mark(_x31))), X2))mark#(tail(X)) → active#(tail(mark(X)))
mark#(head(incr(_x31))) → active#(head(incr(mark(_x31))))mark#(head(s(pairs))) → active#(head(active(s(active(pairs)))))
mark#(head(s(incr(_x61)))) → active#(head(active(s(active(incr(mark(_x61)))))))mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(active(cons(active(odds), _x62))))))
mark#(head(tail(_x51))) → active#(head(active(tail(_x51))))mark#(head(s(_x51))) → active#(head(active(s(_x51))))
mark#(head(head(_x31))) → active#(head(active(head(mark(_x31)))))mark#(head(0)) → active#(head(active(0)))
mark#(head(s(cons(_x61, _x62)))) → active#(head(active(s(active(cons(mark(_x61), _x62))))))mark#(head(_x21)) → active#(head(_x21))
mark#(head(nats)) → active#(head(active(nats)))mark#(s(X)) → mark#(X)
mark#(head(incr(cons(incr(_x81), _x62)))) → active#(head(active(incr(active(cons(active(incr(mark(_x81))), _x62))))))mark#(head(incr(tail(_x61)))) → active#(head(active(incr(active(tail(mark(_x61)))))))
mark#(head(s(s(head(_x81))))) → active#(head(active(s(active(s(active(head(mark(_x81)))))))))mark#(cons(cons(_x31, _x32), X2)) → active#(cons(active(cons(mark(_x31), _x32)), X2))
mark#(head(tail(0))) → active#(head(active(tail(active(0)))))mark#(head(cons(_x31, _x32))) → active#(head(active(cons(mark(_x31), _x32))))
mark#(cons(s(_x31), X2)) → active#(cons(active(s(mark(_x31))), X2))active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))
mark#(cons(odds, X2)) → active#(cons(active(odds), X2))mark#(head(s(s(s(_x81))))) → active#(head(active(s(active(s(active(s(mark(_x81)))))))))
mark#(cons(X1, X2)) → mark#(X1)mark#(head(s(s(cons(_x81, _x82))))) → active#(head(active(s(active(s(active(cons(mark(_x81), _x82))))))))
mark#(cons(nats, X2)) → active#(cons(active(nats), X2))mark#(head(s(0))) → active#(head(active(s(active(0)))))
mark#(incr(X)) → active#(incr(mark(X)))mark#(head(tail(odds))) → active#(head(active(tail(active(odds)))))
mark#(head(incr(cons(_x61, active(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(active(cons(active(nats), _x62))))))
mark#(head(incr(cons(tail(_x81), _x62)))) → active#(head(active(incr(active(cons(active(tail(mark(_x81))), _x62))))))mark#(cons(X1, active(_x22))) → active#(cons(mark(X1), _x22))
mark#(cons(0, X2)) → active#(cons(active(0), X2))mark#(head(s(tail(_x61)))) → active#(head(active(s(active(tail(mark(_x61)))))))
mark#(tail(X)) → mark#(X)mark#(head(incr(cons(_x71, _x72)))) → active#(head(active(incr(active(cons(_x71, _x72))))))
mark#(head(tail(_x31))) → active#(head(tail(mark(_x31))))mark#(cons(head(_x31), X2)) → active#(cons(active(head(mark(_x31))), X2))
active#(odds) → mark#(incr(pairs))mark#(head(incr(_x51))) → active#(head(active(incr(_x51))))
mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(active(cons(mark(_x61), _x62)))))mark#(head(incr(incr(_x61)))) → active#(head(active(incr(active(incr(mark(_x61)))))))
mark#(head(s(s(_x61)))) → active#(head(active(s(s(mark(_x61))))))mark#(head(incr(cons(cons(_x81, _x82), _x62)))) → active#(head(active(incr(active(cons(active(cons(mark(_x81), _x82)), _x62))))))
mark#(head(tail(head(_x61)))) → active#(head(active(tail(active(head(mark(_x61)))))))mark#(head(tail(s(_x61)))) → active#(head(active(tail(active(s(mark(_x61)))))))
mark#(head(incr(cons(head(_x81), _x62)))) → active#(head(active(incr(active(cons(active(head(mark(_x81))), _x62))))))mark#(head(s(head(_x61)))) → active#(head(active(s(active(head(mark(_x61)))))))
mark#(cons(tail(_x31), X2)) → active#(cons(active(tail(mark(_x31))), X2))mark#(head(incr(s(_x61)))) → active#(head(active(incr(active(s(mark(_x61)))))))
mark#(head(s(nats))) → active#(head(s(active(nats))))mark#(cons(X1, mark(_x22))) → active#(cons(mark(X1), _x22))
mark#(head(s(s(nats)))) → active#(head(active(s(active(s(active(nats)))))))mark#(head(incr(cons(s(_x81), _x62)))) → active#(head(active(incr(active(cons(active(s(mark(_x81))), _x62))))))
mark#(head(X)) → mark#(X)mark#(head(s(s(_x61)))) → active#(head(s(active(s(mark(_x61))))))
mark#(head(incr(nats))) → active#(head(active(incr(active(nats)))))mark#(head(tail(nats))) → active#(head(active(tail(active(nats)))))
mark#(head(incr(0))) → active#(head(active(incr(active(0)))))mark#(head(s(s(_x71)))) → active#(head(active(s(active(s(_x71))))))
active#(tail(cons(X, XS))) → mark#(XS)mark#(head(tail(incr(_x61)))) → active#(head(active(tail(active(incr(mark(_x61)))))))
mark#(0) → active#(0)active#(nats) → mark#(cons(0, incr(nats)))
mark#(s(X)) → active#(s(mark(X)))mark#(head(s(nats))) → active#(head(active(s(mark(cons(0, incr(nats)))))))
mark#(nats) → active#(nats)mark#(head(incr(cons(_x61, mark(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))
mark#(head(incr(head(_x61)))) → active#(head(active(incr(active(head(mark(_x61)))))))mark#(head(s(nats))) → active#(head(active(s(nats))))
mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(active(cons(active(pairs), _x62))))))mark#(head(tail(cons(_x61, _x62)))) → active#(head(active(tail(active(cons(mark(_x61), _x62))))))
mark#(incr(X)) → mark#(X)mark#(cons(pairs, X2)) → active#(cons(active(pairs), X2))
mark#(odds) → active#(odds)mark#(head(pairs)) → active#(head(active(pairs)))
mark#(head(s(_x31))) → active#(head(s(mark(_x31))))mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(active(cons(active(0), _x62))))))
mark#(head(tail(tail(_x61)))) → active#(head(active(tail(active(tail(mark(_x61)))))))active#(head(cons(X, XS))) → mark#(X)
mark#(head(s(s(0)))) → active#(head(active(s(active(s(active(0)))))))mark#(cons(_x21, _x22)) → active#(cons(_x21, _x22))
mark#(head(s(s(tail(_x81))))) → active#(head(active(s(active(s(active(tail(mark(_x81)))))))))mark#(head(odds)) → active#(head(active(odds)))
mark#(head(s(odds))) → active#(head(active(s(active(odds)))))mark#(head(tail(pairs))) → active#(head(active(tail(active(pairs)))))

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, pairs, s, active, mark, incr, head, odds, tail, cons

Strategy

The right-hand side of the rule mark#(head(s(s(incr(_x81))))) → active#(head(active(s(active(s(active(incr(mark(_x81))))))))) 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
active#(head(active(s(active(s(active(incr(active(head(mark(_x101))))))))))) 
active#(head(active(s(active(s(active(incr(active(s(mark(_x101))))))))))) 
active#(head(active(s(active(s(active(incr(active(incr(mark(_x101))))))))))) 
active#(head(active(s(active(s(active(incr(active(tail(mark(_x101))))))))))) 
active#(head(active(s(active(s(active(incr(active(0))))))))) 
active#(head(active(s(active(s(active(incr(active(pairs))))))))) 
active#(head(s(active(s(active(incr(mark(_x81)))))))) 
active#(head(active(s(active(s(active(incr(active(cons(mark(_x101), _x102)))))))))) 
active#(head(active(s(s(active(incr(mark(_x81)))))))) 
active#(head(active(s(active(s(incr(mark(_x81)))))))) 
active#(head(active(s(active(s(active(incr(active(odds))))))))) 
active#(head(active(s(active(s(active(incr(active(nats))))))))) 
active#(head(active(s(active(s(active(incr(_x91)))))))) 
Thus, the rule mark#(head(s(s(incr(_x81))))) → active#(head(active(s(active(s(active(incr(mark(_x81))))))))) is replaced by the following rules:
mark#(head(s(s(incr(_x81))))) → active#(head(active(s(s(active(incr(mark(_x81))))))))mark#(head(s(s(incr(s(_x101)))))) → active#(head(active(s(active(s(active(incr(active(s(mark(_x101)))))))))))
mark#(head(s(s(incr(tail(_x101)))))) → active#(head(active(s(active(s(active(incr(active(tail(mark(_x101)))))))))))mark#(head(s(s(incr(_x91))))) → active#(head(active(s(active(s(active(incr(_x91))))))))
mark#(head(s(s(incr(cons(_x101, _x102)))))) → active#(head(active(s(active(s(active(incr(active(cons(mark(_x101), _x102))))))))))mark#(head(s(s(incr(incr(_x101)))))) → active#(head(active(s(active(s(active(incr(active(incr(mark(_x101)))))))))))
mark#(head(s(s(incr(odds))))) → active#(head(active(s(active(s(active(incr(active(odds)))))))))mark#(head(s(s(incr(_x81))))) → active#(head(s(active(s(active(incr(mark(_x81))))))))
mark#(head(s(s(incr(head(_x101)))))) → active#(head(active(s(active(s(active(incr(active(head(mark(_x101)))))))))))mark#(head(s(s(incr(pairs))))) → active#(head(active(s(active(s(active(incr(active(pairs)))))))))
mark#(head(s(s(incr(nats))))) → active#(head(active(s(active(s(active(incr(active(nats)))))))))mark#(head(s(s(incr(_x81))))) → active#(head(active(s(active(s(incr(mark(_x81))))))))
mark#(head(s(s(incr(0))))) → active#(head(active(s(active(s(active(incr(active(0)))))))))

Problem 18: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(active(pairs)))))))mark#(head(s(s(odds)))) → active#(head(active(s(active(s(active(odds)))))))
mark#(head(incr(odds))) → active#(head(active(incr(active(odds)))))mark#(pairs) → active#(pairs)
mark#(head(incr(pairs))) → active#(head(active(incr(active(pairs)))))mark#(head(incr(cons(_x61, _x62)))) → active#(head(active(incr(cons(mark(_x61), _x62)))))
active#(pairs) → mark#(cons(0, incr(odds)))mark#(head(incr(_x31))) → active#(head(incr(mark(_x31))))
mark#(head(s(incr(_x61)))) → active#(head(active(s(active(incr(mark(_x61)))))))mark#(head(head(_x31))) → active#(head(active(head(mark(_x31)))))
mark#(head(s(cons(_x61, _x62)))) → active#(head(active(s(active(cons(mark(_x61), _x62))))))mark#(head(s(s(incr(pairs))))) → active#(head(active(s(active(s(active(incr(active(pairs)))))))))
mark#(head(s(s(incr(nats))))) → active#(head(active(s(active(s(active(incr(active(nats)))))))))mark#(s(X)) → mark#(X)
mark#(head(incr(tail(_x61)))) → active#(head(active(incr(active(tail(mark(_x61)))))))mark#(head(s(s(head(_x81))))) → active#(head(active(s(active(s(active(head(mark(_x81)))))))))
mark#(head(s(s(incr(_x81))))) → active#(head(active(s(s(active(incr(mark(_x81))))))))mark#(head(tail(0))) → active#(head(active(tail(active(0)))))
mark#(head(s(s(incr(s(_x101)))))) → active#(head(active(s(active(s(active(incr(active(s(mark(_x101)))))))))))mark#(head(cons(_x31, _x32))) → active#(head(active(cons(mark(_x31), _x32))))
active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))mark#(head(s(s(s(_x81))))) → active#(head(active(s(active(s(active(s(mark(_x81)))))))))
mark#(cons(X1, X2)) → mark#(X1)mark#(head(s(s(cons(_x81, _x82))))) → active#(head(active(s(active(s(active(cons(mark(_x81), _x82))))))))
mark#(head(s(0))) → active#(head(active(s(active(0)))))mark#(head(s(s(incr(cons(_x101, _x102)))))) → active#(head(active(s(active(s(active(incr(active(cons(mark(_x101), _x102))))))))))
mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(active(cons(active(nats), _x62))))))mark#(cons(0, X2)) → active#(cons(active(0), X2))
mark#(head(s(tail(_x61)))) → active#(head(active(s(active(tail(mark(_x61)))))))mark#(tail(X)) → mark#(X)
mark#(head(tail(_x31))) → active#(head(tail(mark(_x31))))active#(odds) → mark#(incr(pairs))
mark#(head(incr(incr(_x61)))) → active#(head(active(incr(active(incr(mark(_x61)))))))mark#(head(s(s(_x61)))) → active#(head(active(s(s(mark(_x61))))))
mark#(head(incr(cons(cons(_x81, _x82), _x62)))) → active#(head(active(incr(active(cons(active(cons(mark(_x81), _x82)), _x62))))))mark#(head(incr(cons(head(_x81), _x62)))) → active#(head(active(incr(active(cons(active(head(mark(_x81))), _x62))))))
mark#(head(s(head(_x61)))) → active#(head(active(s(active(head(mark(_x61)))))))mark#(head(incr(cons(s(_x81), _x62)))) → active#(head(active(incr(active(cons(active(s(mark(_x81))), _x62))))))
mark#(head(X)) → mark#(X)mark#(head(s(s(_x61)))) → active#(head(s(active(s(mark(_x61))))))
mark#(head(tail(nats))) → active#(head(active(tail(active(nats)))))mark#(0) → active#(0)
active#(nats) → mark#(cons(0, incr(nats)))mark#(s(X)) → active#(s(mark(X)))
mark#(nats) → active#(nats)mark#(head(incr(head(_x61)))) → active#(head(active(incr(active(head(mark(_x61)))))))
mark#(head(s(nats))) → active#(head(active(s(nats))))mark#(head(tail(cons(_x61, _x62)))) → active#(head(active(tail(active(cons(mark(_x61), _x62))))))
mark#(incr(X)) → mark#(X)mark#(head(pairs)) → active#(head(active(pairs)))
mark#(head(s(s(incr(head(_x101)))))) → active#(head(active(s(active(s(active(incr(active(head(mark(_x101)))))))))))mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(active(cons(active(0), _x62))))))
active#(head(cons(X, XS))) → mark#(X)mark#(head(tail(pairs))) → active#(head(active(tail(active(pairs)))))
mark#(head(s(s(incr(tail(_x101)))))) → active#(head(active(s(active(s(active(incr(active(tail(mark(_x101)))))))))))mark#(cons(incr(_x31), X2)) → active#(cons(active(incr(mark(_x31))), X2))
mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(active(cons(active(odds), _x62))))))mark#(head(s(pairs))) → active#(head(active(s(active(pairs)))))
mark#(tail(X)) → active#(tail(mark(X)))mark#(head(s(_x51))) → active#(head(active(s(_x51))))
mark#(head(tail(_x51))) → active#(head(active(tail(_x51))))mark#(head(0)) → active#(head(active(0)))
mark#(head(nats)) → active#(head(active(nats)))mark#(head(_x21)) → active#(head(_x21))
mark#(head(incr(cons(incr(_x81), _x62)))) → active#(head(active(incr(active(cons(active(incr(mark(_x81))), _x62))))))mark#(head(s(s(incr(0))))) → active#(head(active(s(active(s(active(incr(active(0)))))))))
mark#(cons(cons(_x31, _x32), X2)) → active#(cons(active(cons(mark(_x31), _x32)), X2))mark#(cons(s(_x31), X2)) → active#(cons(active(s(mark(_x31))), X2))
mark#(cons(odds, X2)) → active#(cons(active(odds), X2))mark#(cons(nats, X2)) → active#(cons(active(nats), X2))
mark#(incr(X)) → active#(incr(mark(X)))mark#(head(tail(odds))) → active#(head(active(tail(active(odds)))))
mark#(head(incr(cons(_x61, active(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))mark#(cons(X1, active(_x22))) → active#(cons(mark(X1), _x22))
mark#(head(incr(cons(tail(_x81), _x62)))) → active#(head(active(incr(active(cons(active(tail(mark(_x81))), _x62))))))mark#(head(incr(cons(_x71, _x72)))) → active#(head(active(incr(active(cons(_x71, _x72))))))
mark#(cons(head(_x31), X2)) → active#(cons(active(head(mark(_x31))), X2))mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(active(cons(mark(_x61), _x62)))))
mark#(head(incr(_x51))) → active#(head(active(incr(_x51))))mark#(head(tail(head(_x61)))) → active#(head(active(tail(active(head(mark(_x61)))))))
mark#(head(tail(s(_x61)))) → active#(head(active(tail(active(s(mark(_x61)))))))mark#(cons(tail(_x31), X2)) → active#(cons(active(tail(mark(_x31))), X2))
mark#(head(incr(s(_x61)))) → active#(head(active(incr(active(s(mark(_x61)))))))mark#(head(s(nats))) → active#(head(s(active(nats))))
mark#(head(s(s(nats)))) → active#(head(active(s(active(s(active(nats)))))))mark#(cons(X1, mark(_x22))) → active#(cons(mark(X1), _x22))
mark#(head(s(s(incr(_x81))))) → active#(head(s(active(s(active(incr(mark(_x81))))))))mark#(head(s(s(incr(odds))))) → active#(head(active(s(active(s(active(incr(active(odds)))))))))
mark#(head(incr(nats))) → active#(head(active(incr(active(nats)))))mark#(head(s(s(_x71)))) → active#(head(active(s(active(s(_x71))))))
mark#(head(incr(0))) → active#(head(active(incr(active(0)))))active#(tail(cons(X, XS))) → mark#(XS)
mark#(head(tail(incr(_x61)))) → active#(head(active(tail(active(incr(mark(_x61)))))))mark#(head(s(nats))) → active#(head(active(s(mark(cons(0, incr(nats)))))))
mark#(head(incr(cons(_x61, mark(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(active(cons(active(pairs), _x62))))))
mark#(head(s(s(incr(_x91))))) → active#(head(active(s(active(s(active(incr(_x91))))))))mark#(cons(pairs, X2)) → active#(cons(active(pairs), X2))
mark#(odds) → active#(odds)mark#(head(s(s(incr(incr(_x101)))))) → active#(head(active(s(active(s(active(incr(active(incr(mark(_x101)))))))))))
mark#(head(s(_x31))) → active#(head(s(mark(_x31))))mark#(head(tail(tail(_x61)))) → active#(head(active(tail(active(tail(mark(_x61)))))))
mark#(head(s(s(0)))) → active#(head(active(s(active(s(active(0)))))))mark#(cons(_x21, _x22)) → active#(cons(_x21, _x22))
mark#(head(s(s(tail(_x81))))) → active#(head(active(s(active(s(active(tail(mark(_x81)))))))))mark#(head(odds)) → active#(head(active(odds)))
mark#(head(s(s(incr(_x81))))) → active#(head(active(s(active(s(incr(mark(_x81))))))))mark#(head(s(odds))) → active#(head(active(s(active(odds)))))

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, s, pairs, active, mark, incr, head, tail, odds, cons

Strategy

The right-hand side of the rule mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(active(pairs))))))) 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
active#(head(active(s(active(s(pairs)))))) 
active#(head(active(s(active(s(mark(cons(0, incr(odds))))))))) 
active#(head(active(s(s(active(pairs)))))) 
active#(head(s(active(s(active(pairs)))))) 
Thus, the rule mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(active(pairs))))))) is replaced by the following rules:
mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(mark(cons(0, incr(odds)))))))))mark#(head(s(s(pairs)))) → active#(head(active(s(s(active(pairs))))))
mark#(head(s(s(pairs)))) → active#(head(s(active(s(active(pairs))))))mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(pairs))))))

Problem 19: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(head(incr(odds))) → active#(head(active(incr(active(odds)))))mark#(head(s(s(odds)))) → active#(head(active(s(active(s(active(odds)))))))
mark#(head(incr(pairs))) → active#(head(active(incr(active(pairs)))))mark#(pairs) → active#(pairs)
mark#(head(incr(cons(_x61, _x62)))) → active#(head(active(incr(cons(mark(_x61), _x62)))))active#(pairs) → mark#(cons(0, incr(odds)))
mark#(head(s(incr(_x61)))) → active#(head(active(s(active(incr(mark(_x61)))))))mark#(head(incr(_x31))) → active#(head(incr(mark(_x31))))
mark#(head(head(_x31))) → active#(head(active(head(mark(_x31)))))mark#(head(s(cons(_x61, _x62)))) → active#(head(active(s(active(cons(mark(_x61), _x62))))))
mark#(head(s(s(incr(pairs))))) → active#(head(active(s(active(s(active(incr(active(pairs)))))))))mark#(s(X)) → mark#(X)
mark#(head(s(s(incr(nats))))) → active#(head(active(s(active(s(active(incr(active(nats)))))))))mark#(head(incr(tail(_x61)))) → active#(head(active(incr(active(tail(mark(_x61)))))))
mark#(head(s(s(head(_x81))))) → active#(head(active(s(active(s(active(head(mark(_x81)))))))))mark#(head(s(s(incr(_x81))))) → active#(head(active(s(s(active(incr(mark(_x81))))))))
mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(mark(cons(0, incr(odds)))))))))mark#(head(tail(0))) → active#(head(active(tail(active(0)))))
mark#(head(s(s(incr(s(_x101)))))) → active#(head(active(s(active(s(active(incr(active(s(mark(_x101)))))))))))mark#(head(cons(_x31, _x32))) → active#(head(active(cons(mark(_x31), _x32))))
active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))mark#(head(s(s(s(_x81))))) → active#(head(active(s(active(s(active(s(mark(_x81)))))))))
mark#(cons(X1, X2)) → mark#(X1)mark#(head(s(s(cons(_x81, _x82))))) → active#(head(active(s(active(s(active(cons(mark(_x81), _x82))))))))
mark#(head(s(0))) → active#(head(active(s(active(0)))))mark#(head(s(s(incr(cons(_x101, _x102)))))) → active#(head(active(s(active(s(active(incr(active(cons(mark(_x101), _x102))))))))))
mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(active(cons(active(nats), _x62))))))mark#(cons(0, X2)) → active#(cons(active(0), X2))
mark#(tail(X)) → mark#(X)mark#(head(s(tail(_x61)))) → active#(head(active(s(active(tail(mark(_x61)))))))
mark#(head(tail(_x31))) → active#(head(tail(mark(_x31))))active#(odds) → mark#(incr(pairs))
mark#(head(s(s(_x61)))) → active#(head(active(s(s(mark(_x61))))))mark#(head(incr(incr(_x61)))) → active#(head(active(incr(active(incr(mark(_x61)))))))
mark#(head(incr(cons(cons(_x81, _x82), _x62)))) → active#(head(active(incr(active(cons(active(cons(mark(_x81), _x82)), _x62))))))mark#(head(incr(cons(head(_x81), _x62)))) → active#(head(active(incr(active(cons(active(head(mark(_x81))), _x62))))))
mark#(head(s(head(_x61)))) → active#(head(active(s(active(head(mark(_x61)))))))mark#(head(s(s(_x61)))) → active#(head(s(active(s(mark(_x61))))))
mark#(head(X)) → mark#(X)mark#(head(incr(cons(s(_x81), _x62)))) → active#(head(active(incr(active(cons(active(s(mark(_x81))), _x62))))))
mark#(head(tail(nats))) → active#(head(active(tail(active(nats)))))active#(nats) → mark#(cons(0, incr(nats)))
mark#(0) → active#(0)mark#(s(X)) → active#(s(mark(X)))
mark#(nats) → active#(nats)mark#(head(s(s(pairs)))) → active#(head(s(active(s(active(pairs))))))
mark#(head(s(nats))) → active#(head(active(s(nats))))mark#(head(incr(head(_x61)))) → active#(head(active(incr(active(head(mark(_x61)))))))
mark#(head(tail(cons(_x61, _x62)))) → active#(head(active(tail(active(cons(mark(_x61), _x62))))))mark#(incr(X)) → mark#(X)
mark#(head(pairs)) → active#(head(active(pairs)))mark#(head(s(s(incr(head(_x101)))))) → active#(head(active(s(active(s(active(incr(active(head(mark(_x101)))))))))))
mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(active(cons(active(0), _x62))))))active#(head(cons(X, XS))) → mark#(X)
mark#(head(tail(pairs))) → active#(head(active(tail(active(pairs)))))mark#(head(s(s(incr(tail(_x101)))))) → active#(head(active(s(active(s(active(incr(active(tail(mark(_x101)))))))))))
mark#(cons(incr(_x31), X2)) → active#(cons(active(incr(mark(_x31))), X2))mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(active(cons(active(odds), _x62))))))
mark#(head(s(pairs))) → active#(head(active(s(active(pairs)))))mark#(tail(X)) → active#(tail(mark(X)))
mark#(head(s(_x51))) → active#(head(active(s(_x51))))mark#(head(tail(_x51))) → active#(head(active(tail(_x51))))
mark#(head(0)) → active#(head(active(0)))mark#(head(nats)) → active#(head(active(nats)))
mark#(head(_x21)) → active#(head(_x21))mark#(head(incr(cons(incr(_x81), _x62)))) → active#(head(active(incr(active(cons(active(incr(mark(_x81))), _x62))))))
mark#(head(s(s(incr(0))))) → active#(head(active(s(active(s(active(incr(active(0)))))))))mark#(cons(cons(_x31, _x32), X2)) → active#(cons(active(cons(mark(_x31), _x32)), X2))
mark#(cons(s(_x31), X2)) → active#(cons(active(s(mark(_x31))), X2))mark#(cons(odds, X2)) → active#(cons(active(odds), X2))
mark#(cons(nats, X2)) → active#(cons(active(nats), X2))mark#(incr(X)) → active#(incr(mark(X)))
mark#(head(tail(odds))) → active#(head(active(tail(active(odds)))))mark#(head(incr(cons(_x61, active(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))
mark#(cons(X1, active(_x22))) → active#(cons(mark(X1), _x22))mark#(head(incr(cons(tail(_x81), _x62)))) → active#(head(active(incr(active(cons(active(tail(mark(_x81))), _x62))))))
mark#(head(incr(cons(_x71, _x72)))) → active#(head(active(incr(active(cons(_x71, _x72))))))mark#(cons(head(_x31), X2)) → active#(cons(active(head(mark(_x31))), X2))
mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(pairs))))))mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(active(cons(mark(_x61), _x62)))))
mark#(head(incr(_x51))) → active#(head(active(incr(_x51))))mark#(head(tail(head(_x61)))) → active#(head(active(tail(active(head(mark(_x61)))))))
mark#(head(s(s(pairs)))) → active#(head(active(s(s(active(pairs))))))mark#(head(tail(s(_x61)))) → active#(head(active(tail(active(s(mark(_x61)))))))
mark#(cons(tail(_x31), X2)) → active#(cons(active(tail(mark(_x31))), X2))mark#(head(incr(s(_x61)))) → active#(head(active(incr(active(s(mark(_x61)))))))
mark#(head(s(nats))) → active#(head(s(active(nats))))mark#(head(s(s(nats)))) → active#(head(active(s(active(s(active(nats)))))))
mark#(cons(X1, mark(_x22))) → active#(cons(mark(X1), _x22))mark#(head(s(s(incr(_x81))))) → active#(head(s(active(s(active(incr(mark(_x81))))))))
mark#(head(s(s(incr(odds))))) → active#(head(active(s(active(s(active(incr(active(odds)))))))))mark#(head(incr(nats))) → active#(head(active(incr(active(nats)))))
mark#(head(s(s(_x71)))) → active#(head(active(s(active(s(_x71))))))mark#(head(incr(0))) → active#(head(active(incr(active(0)))))
active#(tail(cons(X, XS))) → mark#(XS)mark#(head(tail(incr(_x61)))) → active#(head(active(tail(active(incr(mark(_x61)))))))
mark#(head(s(nats))) → active#(head(active(s(mark(cons(0, incr(nats)))))))mark#(head(incr(cons(_x61, mark(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))
mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(active(cons(active(pairs), _x62))))))mark#(head(s(s(incr(_x91))))) → active#(head(active(s(active(s(active(incr(_x91))))))))
mark#(cons(pairs, X2)) → active#(cons(active(pairs), X2))mark#(odds) → active#(odds)
mark#(head(s(s(incr(incr(_x101)))))) → active#(head(active(s(active(s(active(incr(active(incr(mark(_x101)))))))))))mark#(head(s(_x31))) → active#(head(s(mark(_x31))))
mark#(head(tail(tail(_x61)))) → active#(head(active(tail(active(tail(mark(_x61)))))))mark#(head(s(s(0)))) → active#(head(active(s(active(s(active(0)))))))
mark#(head(s(s(tail(_x81))))) → active#(head(active(s(active(s(active(tail(mark(_x81)))))))))mark#(cons(_x21, _x22)) → active#(cons(_x21, _x22))
mark#(head(s(s(incr(_x81))))) → active#(head(active(s(active(s(incr(mark(_x81))))))))mark#(head(odds)) → active#(head(active(odds)))
mark#(head(s(odds))) → active#(head(active(s(active(odds)))))

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, pairs, s, active, mark, incr, head, odds, tail, cons

Strategy

The right-hand side of the rule mark#(head(s(s(odds)))) → active#(head(active(s(active(s(active(odds))))))) 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
active#(head(active(s(s(active(odds)))))) 
active#(head(active(s(active(s(odds)))))) 
active#(head(active(s(active(s(mark(incr(pairs)))))))) 
active#(head(s(active(s(active(odds)))))) 
Thus, the rule mark#(head(s(s(odds)))) → active#(head(active(s(active(s(active(odds))))))) is replaced by the following rules:
mark#(head(s(s(odds)))) → active#(head(s(active(s(active(odds))))))mark#(head(s(s(odds)))) → active#(head(active(s(active(s(mark(incr(pairs))))))))
mark#(head(s(s(odds)))) → active#(head(active(s(active(s(odds))))))mark#(head(s(s(odds)))) → active#(head(active(s(s(active(odds))))))

Problem 20: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(head(incr(odds))) → active#(head(active(incr(active(odds)))))mark#(pairs) → active#(pairs)
mark#(head(incr(pairs))) → active#(head(active(incr(active(pairs)))))mark#(head(incr(cons(_x61, _x62)))) → active#(head(active(incr(cons(mark(_x61), _x62)))))
active#(pairs) → mark#(cons(0, incr(odds)))mark#(head(incr(_x31))) → active#(head(incr(mark(_x31))))
mark#(head(s(incr(_x61)))) → active#(head(active(s(active(incr(mark(_x61)))))))mark#(head(head(_x31))) → active#(head(active(head(mark(_x31)))))
mark#(head(s(cons(_x61, _x62)))) → active#(head(active(s(active(cons(mark(_x61), _x62))))))mark#(head(s(s(incr(pairs))))) → active#(head(active(s(active(s(active(incr(active(pairs)))))))))
mark#(head(s(s(incr(nats))))) → active#(head(active(s(active(s(active(incr(active(nats)))))))))mark#(s(X)) → mark#(X)
mark#(head(incr(tail(_x61)))) → active#(head(active(incr(active(tail(mark(_x61)))))))mark#(head(s(s(head(_x81))))) → active#(head(active(s(active(s(active(head(mark(_x81)))))))))
mark#(head(s(s(incr(_x81))))) → active#(head(active(s(s(active(incr(mark(_x81))))))))mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(mark(cons(0, incr(odds)))))))))
mark#(head(tail(0))) → active#(head(active(tail(active(0)))))mark#(head(s(s(incr(s(_x101)))))) → active#(head(active(s(active(s(active(incr(active(s(mark(_x101)))))))))))
mark#(head(cons(_x31, _x32))) → active#(head(active(cons(mark(_x31), _x32))))active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))
mark#(head(s(s(s(_x81))))) → active#(head(active(s(active(s(active(s(mark(_x81)))))))))mark#(cons(X1, X2)) → mark#(X1)
mark#(head(s(s(cons(_x81, _x82))))) → active#(head(active(s(active(s(active(cons(mark(_x81), _x82))))))))mark#(head(s(0))) → active#(head(active(s(active(0)))))
mark#(head(s(s(incr(cons(_x101, _x102)))))) → active#(head(active(s(active(s(active(incr(active(cons(mark(_x101), _x102))))))))))mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(active(cons(active(nats), _x62))))))
mark#(cons(0, X2)) → active#(cons(active(0), X2))mark#(head(s(tail(_x61)))) → active#(head(active(s(active(tail(mark(_x61)))))))
mark#(tail(X)) → mark#(X)mark#(head(tail(_x31))) → active#(head(tail(mark(_x31))))
active#(odds) → mark#(incr(pairs))mark#(head(s(s(odds)))) → active#(head(active(s(s(active(odds))))))
mark#(head(incr(incr(_x61)))) → active#(head(active(incr(active(incr(mark(_x61)))))))mark#(head(s(s(_x61)))) → active#(head(active(s(s(mark(_x61))))))
mark#(head(incr(cons(cons(_x81, _x82), _x62)))) → active#(head(active(incr(active(cons(active(cons(mark(_x81), _x82)), _x62))))))mark#(head(incr(cons(head(_x81), _x62)))) → active#(head(active(incr(active(cons(active(head(mark(_x81))), _x62))))))
mark#(head(s(head(_x61)))) → active#(head(active(s(active(head(mark(_x61)))))))mark#(head(incr(cons(s(_x81), _x62)))) → active#(head(active(incr(active(cons(active(s(mark(_x81))), _x62))))))
mark#(head(X)) → mark#(X)mark#(head(s(s(_x61)))) → active#(head(s(active(s(mark(_x61))))))
mark#(head(s(s(odds)))) → active#(head(active(s(active(s(mark(incr(pairs))))))))mark#(head(tail(nats))) → active#(head(active(tail(active(nats)))))
mark#(0) → active#(0)active#(nats) → mark#(cons(0, incr(nats)))
mark#(s(X)) → active#(s(mark(X)))mark#(nats) → active#(nats)
mark#(head(s(s(pairs)))) → active#(head(s(active(s(active(pairs))))))mark#(head(incr(head(_x61)))) → active#(head(active(incr(active(head(mark(_x61)))))))
mark#(head(s(nats))) → active#(head(active(s(nats))))mark#(head(tail(cons(_x61, _x62)))) → active#(head(active(tail(active(cons(mark(_x61), _x62))))))
mark#(incr(X)) → mark#(X)mark#(head(pairs)) → active#(head(active(pairs)))
mark#(head(s(s(incr(head(_x101)))))) → active#(head(active(s(active(s(active(incr(active(head(mark(_x101)))))))))))mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(active(cons(active(0), _x62))))))
active#(head(cons(X, XS))) → mark#(X)mark#(head(tail(pairs))) → active#(head(active(tail(active(pairs)))))
mark#(head(s(s(incr(tail(_x101)))))) → active#(head(active(s(active(s(active(incr(active(tail(mark(_x101)))))))))))mark#(cons(incr(_x31), X2)) → active#(cons(active(incr(mark(_x31))), X2))
mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(active(cons(active(odds), _x62))))))mark#(head(s(pairs))) → active#(head(active(s(active(pairs)))))
mark#(tail(X)) → active#(tail(mark(X)))mark#(head(s(s(odds)))) → active#(head(s(active(s(active(odds))))))
mark#(head(s(_x51))) → active#(head(active(s(_x51))))mark#(head(tail(_x51))) → active#(head(active(tail(_x51))))
mark#(head(0)) → active#(head(active(0)))mark#(head(nats)) → active#(head(active(nats)))
mark#(head(_x21)) → active#(head(_x21))mark#(head(incr(cons(incr(_x81), _x62)))) → active#(head(active(incr(active(cons(active(incr(mark(_x81))), _x62))))))
mark#(head(s(s(incr(0))))) → active#(head(active(s(active(s(active(incr(active(0)))))))))mark#(cons(cons(_x31, _x32), X2)) → active#(cons(active(cons(mark(_x31), _x32)), X2))
mark#(cons(s(_x31), X2)) → active#(cons(active(s(mark(_x31))), X2))mark#(cons(odds, X2)) → active#(cons(active(odds), X2))
mark#(head(s(s(odds)))) → active#(head(active(s(active(s(odds))))))mark#(cons(nats, X2)) → active#(cons(active(nats), X2))
mark#(incr(X)) → active#(incr(mark(X)))mark#(head(tail(odds))) → active#(head(active(tail(active(odds)))))
mark#(head(incr(cons(_x61, active(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))mark#(cons(X1, active(_x22))) → active#(cons(mark(X1), _x22))
mark#(head(incr(cons(tail(_x81), _x62)))) → active#(head(active(incr(active(cons(active(tail(mark(_x81))), _x62))))))mark#(head(incr(cons(_x71, _x72)))) → active#(head(active(incr(active(cons(_x71, _x72))))))
mark#(cons(head(_x31), X2)) → active#(cons(active(head(mark(_x31))), X2))mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(pairs))))))
mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(active(cons(mark(_x61), _x62)))))mark#(head(incr(_x51))) → active#(head(active(incr(_x51))))
mark#(head(tail(head(_x61)))) → active#(head(active(tail(active(head(mark(_x61)))))))mark#(head(s(s(pairs)))) → active#(head(active(s(s(active(pairs))))))
mark#(head(tail(s(_x61)))) → active#(head(active(tail(active(s(mark(_x61)))))))mark#(cons(tail(_x31), X2)) → active#(cons(active(tail(mark(_x31))), X2))
mark#(head(incr(s(_x61)))) → active#(head(active(incr(active(s(mark(_x61)))))))mark#(head(s(nats))) → active#(head(s(active(nats))))
mark#(head(s(s(nats)))) → active#(head(active(s(active(s(active(nats)))))))mark#(cons(X1, mark(_x22))) → active#(cons(mark(X1), _x22))
mark#(head(s(s(incr(_x81))))) → active#(head(s(active(s(active(incr(mark(_x81))))))))mark#(head(s(s(incr(odds))))) → active#(head(active(s(active(s(active(incr(active(odds)))))))))
mark#(head(incr(nats))) → active#(head(active(incr(active(nats)))))mark#(head(s(s(_x71)))) → active#(head(active(s(active(s(_x71))))))
mark#(head(incr(0))) → active#(head(active(incr(active(0)))))active#(tail(cons(X, XS))) → mark#(XS)
mark#(head(tail(incr(_x61)))) → active#(head(active(tail(active(incr(mark(_x61)))))))mark#(head(s(nats))) → active#(head(active(s(mark(cons(0, incr(nats)))))))
mark#(head(incr(cons(_x61, mark(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(active(cons(active(pairs), _x62))))))
mark#(head(s(s(incr(_x91))))) → active#(head(active(s(active(s(active(incr(_x91))))))))mark#(cons(pairs, X2)) → active#(cons(active(pairs), X2))
mark#(odds) → active#(odds)mark#(head(s(s(incr(incr(_x101)))))) → active#(head(active(s(active(s(active(incr(active(incr(mark(_x101)))))))))))
mark#(head(s(_x31))) → active#(head(s(mark(_x31))))mark#(head(tail(tail(_x61)))) → active#(head(active(tail(active(tail(mark(_x61)))))))
mark#(head(s(s(0)))) → active#(head(active(s(active(s(active(0)))))))mark#(cons(_x21, _x22)) → active#(cons(_x21, _x22))
mark#(head(s(s(tail(_x81))))) → active#(head(active(s(active(s(active(tail(mark(_x81)))))))))mark#(head(odds)) → active#(head(active(odds)))
mark#(head(s(s(incr(_x81))))) → active#(head(active(s(active(s(incr(mark(_x81))))))))mark#(head(s(odds))) → active#(head(active(s(active(odds)))))

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, s, pairs, active, mark, incr, head, tail, odds, cons

Strategy

The right-hand side of the rule mark#(head(incr(odds))) → active#(head(active(incr(active(odds))))) 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
active#(head(incr(active(odds)))) 
active#(head(active(incr(odds)))) 
active#(head(active(incr(mark(incr(pairs)))))) 
Thus, the rule mark#(head(incr(odds))) → active#(head(active(incr(active(odds))))) is replaced by the following rules:
mark#(head(incr(odds))) → active#(head(active(incr(odds))))mark#(head(incr(odds))) → active#(head(active(incr(mark(incr(pairs))))))
mark#(head(incr(odds))) → active#(head(incr(active(odds))))

Problem 21: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(head(incr(pairs))) → active#(head(active(incr(active(pairs)))))mark#(pairs) → active#(pairs)
mark#(head(incr(cons(_x61, _x62)))) → active#(head(active(incr(cons(mark(_x61), _x62)))))active#(pairs) → mark#(cons(0, incr(odds)))
mark#(head(s(incr(_x61)))) → active#(head(active(s(active(incr(mark(_x61)))))))mark#(head(incr(_x31))) → active#(head(incr(mark(_x31))))
mark#(head(head(_x31))) → active#(head(active(head(mark(_x31)))))mark#(head(s(cons(_x61, _x62)))) → active#(head(active(s(active(cons(mark(_x61), _x62))))))
mark#(head(s(s(incr(pairs))))) → active#(head(active(s(active(s(active(incr(active(pairs)))))))))mark#(s(X)) → mark#(X)
mark#(head(s(s(incr(nats))))) → active#(head(active(s(active(s(active(incr(active(nats)))))))))mark#(head(incr(tail(_x61)))) → active#(head(active(incr(active(tail(mark(_x61)))))))
mark#(head(s(s(head(_x81))))) → active#(head(active(s(active(s(active(head(mark(_x81)))))))))mark#(head(s(s(incr(_x81))))) → active#(head(active(s(s(active(incr(mark(_x81))))))))
mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(mark(cons(0, incr(odds)))))))))mark#(head(tail(0))) → active#(head(active(tail(active(0)))))
mark#(head(s(s(incr(s(_x101)))))) → active#(head(active(s(active(s(active(incr(active(s(mark(_x101)))))))))))mark#(head(cons(_x31, _x32))) → active#(head(active(cons(mark(_x31), _x32))))
active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))mark#(head(s(s(s(_x81))))) → active#(head(active(s(active(s(active(s(mark(_x81)))))))))
mark#(cons(X1, X2)) → mark#(X1)mark#(head(s(s(cons(_x81, _x82))))) → active#(head(active(s(active(s(active(cons(mark(_x81), _x82))))))))
mark#(head(s(0))) → active#(head(active(s(active(0)))))mark#(head(s(s(incr(cons(_x101, _x102)))))) → active#(head(active(s(active(s(active(incr(active(cons(mark(_x101), _x102))))))))))
mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(active(cons(active(nats), _x62))))))mark#(cons(0, X2)) → active#(cons(active(0), X2))
mark#(tail(X)) → mark#(X)mark#(head(s(tail(_x61)))) → active#(head(active(s(active(tail(mark(_x61)))))))
mark#(head(tail(_x31))) → active#(head(tail(mark(_x31))))active#(odds) → mark#(incr(pairs))
mark#(head(s(s(odds)))) → active#(head(active(s(s(active(odds))))))mark#(head(s(s(_x61)))) → active#(head(active(s(s(mark(_x61))))))
mark#(head(incr(incr(_x61)))) → active#(head(active(incr(active(incr(mark(_x61)))))))mark#(head(incr(cons(cons(_x81, _x82), _x62)))) → active#(head(active(incr(active(cons(active(cons(mark(_x81), _x82)), _x62))))))
mark#(head(incr(cons(head(_x81), _x62)))) → active#(head(active(incr(active(cons(active(head(mark(_x81))), _x62))))))mark#(head(s(head(_x61)))) → active#(head(active(s(active(head(mark(_x61)))))))
mark#(head(s(s(_x61)))) → active#(head(s(active(s(mark(_x61))))))mark#(head(X)) → mark#(X)
mark#(head(incr(cons(s(_x81), _x62)))) → active#(head(active(incr(active(cons(active(s(mark(_x81))), _x62))))))mark#(head(s(s(odds)))) → active#(head(active(s(active(s(mark(incr(pairs))))))))
mark#(head(tail(nats))) → active#(head(active(tail(active(nats)))))active#(nats) → mark#(cons(0, incr(nats)))
mark#(0) → active#(0)mark#(s(X)) → active#(s(mark(X)))
mark#(nats) → active#(nats)mark#(head(s(s(pairs)))) → active#(head(s(active(s(active(pairs))))))
mark#(head(s(nats))) → active#(head(active(s(nats))))mark#(head(incr(head(_x61)))) → active#(head(active(incr(active(head(mark(_x61)))))))
mark#(head(tail(cons(_x61, _x62)))) → active#(head(active(tail(active(cons(mark(_x61), _x62))))))mark#(incr(X)) → mark#(X)
mark#(head(pairs)) → active#(head(active(pairs)))mark#(head(s(s(incr(head(_x101)))))) → active#(head(active(s(active(s(active(incr(active(head(mark(_x101)))))))))))
mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(active(cons(active(0), _x62))))))active#(head(cons(X, XS))) → mark#(X)
mark#(head(tail(pairs))) → active#(head(active(tail(active(pairs)))))mark#(head(incr(odds))) → active#(head(active(incr(odds))))
mark#(head(s(s(incr(tail(_x101)))))) → active#(head(active(s(active(s(active(incr(active(tail(mark(_x101)))))))))))mark#(cons(incr(_x31), X2)) → active#(cons(active(incr(mark(_x31))), X2))
mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(active(cons(active(odds), _x62))))))mark#(head(s(pairs))) → active#(head(active(s(active(pairs)))))
mark#(tail(X)) → active#(tail(mark(X)))mark#(head(s(s(odds)))) → active#(head(s(active(s(active(odds))))))
mark#(head(s(_x51))) → active#(head(active(s(_x51))))mark#(head(tail(_x51))) → active#(head(active(tail(_x51))))
mark#(head(0)) → active#(head(active(0)))mark#(head(nats)) → active#(head(active(nats)))
mark#(head(_x21)) → active#(head(_x21))mark#(head(incr(cons(incr(_x81), _x62)))) → active#(head(active(incr(active(cons(active(incr(mark(_x81))), _x62))))))
mark#(head(s(s(incr(0))))) → active#(head(active(s(active(s(active(incr(active(0)))))))))mark#(cons(cons(_x31, _x32), X2)) → active#(cons(active(cons(mark(_x31), _x32)), X2))
mark#(cons(s(_x31), X2)) → active#(cons(active(s(mark(_x31))), X2))mark#(cons(odds, X2)) → active#(cons(active(odds), X2))
mark#(head(s(s(odds)))) → active#(head(active(s(active(s(odds))))))mark#(cons(nats, X2)) → active#(cons(active(nats), X2))
mark#(incr(X)) → active#(incr(mark(X)))mark#(head(tail(odds))) → active#(head(active(tail(active(odds)))))
mark#(head(incr(cons(_x61, active(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))mark#(cons(X1, active(_x22))) → active#(cons(mark(X1), _x22))
mark#(head(incr(cons(tail(_x81), _x62)))) → active#(head(active(incr(active(cons(active(tail(mark(_x81))), _x62))))))mark#(head(incr(cons(_x71, _x72)))) → active#(head(active(incr(active(cons(_x71, _x72))))))
mark#(cons(head(_x31), X2)) → active#(cons(active(head(mark(_x31))), X2))mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(pairs))))))
mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(active(cons(mark(_x61), _x62)))))mark#(head(incr(_x51))) → active#(head(active(incr(_x51))))
mark#(head(tail(head(_x61)))) → active#(head(active(tail(active(head(mark(_x61)))))))mark#(head(s(s(pairs)))) → active#(head(active(s(s(active(pairs))))))
mark#(head(tail(s(_x61)))) → active#(head(active(tail(active(s(mark(_x61)))))))mark#(cons(tail(_x31), X2)) → active#(cons(active(tail(mark(_x31))), X2))
mark#(head(incr(s(_x61)))) → active#(head(active(incr(active(s(mark(_x61)))))))mark#(head(s(nats))) → active#(head(s(active(nats))))
mark#(head(s(s(nats)))) → active#(head(active(s(active(s(active(nats)))))))mark#(cons(X1, mark(_x22))) → active#(cons(mark(X1), _x22))
mark#(head(s(s(incr(_x81))))) → active#(head(s(active(s(active(incr(mark(_x81))))))))mark#(head(s(s(incr(odds))))) → active#(head(active(s(active(s(active(incr(active(odds)))))))))
mark#(head(incr(odds))) → active#(head(active(incr(mark(incr(pairs))))))mark#(head(incr(nats))) → active#(head(active(incr(active(nats)))))
mark#(head(incr(odds))) → active#(head(incr(active(odds))))mark#(head(incr(0))) → active#(head(active(incr(active(0)))))
mark#(head(s(s(_x71)))) → active#(head(active(s(active(s(_x71))))))active#(tail(cons(X, XS))) → mark#(XS)
mark#(head(tail(incr(_x61)))) → active#(head(active(tail(active(incr(mark(_x61)))))))mark#(head(s(nats))) → active#(head(active(s(mark(cons(0, incr(nats)))))))
mark#(head(incr(cons(_x61, mark(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(active(cons(active(pairs), _x62))))))
mark#(head(s(s(incr(_x91))))) → active#(head(active(s(active(s(active(incr(_x91))))))))mark#(cons(pairs, X2)) → active#(cons(active(pairs), X2))
mark#(odds) → active#(odds)mark#(head(s(s(incr(incr(_x101)))))) → active#(head(active(s(active(s(active(incr(active(incr(mark(_x101)))))))))))
mark#(head(s(_x31))) → active#(head(s(mark(_x31))))mark#(head(tail(tail(_x61)))) → active#(head(active(tail(active(tail(mark(_x61)))))))
mark#(head(s(s(0)))) → active#(head(active(s(active(s(active(0)))))))mark#(head(s(s(tail(_x81))))) → active#(head(active(s(active(s(active(tail(mark(_x81)))))))))
mark#(cons(_x21, _x22)) → active#(cons(_x21, _x22))mark#(head(s(s(incr(_x81))))) → active#(head(active(s(active(s(incr(mark(_x81))))))))
mark#(head(odds)) → active#(head(active(odds)))mark#(head(s(odds))) → active#(head(active(s(active(odds)))))

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, pairs, s, active, mark, incr, head, odds, tail, cons

Strategy

The right-hand side of the rule mark#(head(incr(pairs))) → active#(head(active(incr(active(pairs))))) 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
active#(head(active(incr(mark(cons(0, incr(odds))))))) 
active#(head(active(incr(pairs)))) 
active#(head(incr(active(pairs)))) 
Thus, the rule mark#(head(incr(pairs))) → active#(head(active(incr(active(pairs))))) is replaced by the following rules:
mark#(head(incr(pairs))) → active#(head(incr(active(pairs))))mark#(head(incr(pairs))) → active#(head(active(incr(mark(cons(0, incr(odds)))))))
mark#(head(incr(pairs))) → active#(head(active(incr(pairs))))

Problem 22: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(head(incr(pairs))) → active#(head(incr(active(pairs))))mark#(pairs) → active#(pairs)
mark#(head(incr(cons(_x61, _x62)))) → active#(head(active(incr(cons(mark(_x61), _x62)))))active#(pairs) → mark#(cons(0, incr(odds)))
mark#(head(incr(_x31))) → active#(head(incr(mark(_x31))))mark#(head(s(incr(_x61)))) → active#(head(active(s(active(incr(mark(_x61)))))))
mark#(head(head(_x31))) → active#(head(active(head(mark(_x31)))))mark#(head(s(cons(_x61, _x62)))) → active#(head(active(s(active(cons(mark(_x61), _x62))))))
mark#(head(s(s(incr(pairs))))) → active#(head(active(s(active(s(active(incr(active(pairs)))))))))mark#(head(s(s(incr(nats))))) → active#(head(active(s(active(s(active(incr(active(nats)))))))))
mark#(s(X)) → mark#(X)mark#(head(incr(tail(_x61)))) → active#(head(active(incr(active(tail(mark(_x61)))))))
mark#(head(s(s(head(_x81))))) → active#(head(active(s(active(s(active(head(mark(_x81)))))))))mark#(head(s(s(incr(_x81))))) → active#(head(active(s(s(active(incr(mark(_x81))))))))
mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(mark(cons(0, incr(odds)))))))))mark#(head(tail(0))) → active#(head(active(tail(active(0)))))
mark#(head(s(s(incr(s(_x101)))))) → active#(head(active(s(active(s(active(incr(active(s(mark(_x101)))))))))))mark#(head(cons(_x31, _x32))) → active#(head(active(cons(mark(_x31), _x32))))
active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))mark#(head(s(s(s(_x81))))) → active#(head(active(s(active(s(active(s(mark(_x81)))))))))
mark#(cons(X1, X2)) → mark#(X1)mark#(head(s(s(cons(_x81, _x82))))) → active#(head(active(s(active(s(active(cons(mark(_x81), _x82))))))))
mark#(head(s(0))) → active#(head(active(s(active(0)))))mark#(head(s(s(incr(cons(_x101, _x102)))))) → active#(head(active(s(active(s(active(incr(active(cons(mark(_x101), _x102))))))))))
mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(active(cons(active(nats), _x62))))))mark#(cons(0, X2)) → active#(cons(active(0), X2))
mark#(head(incr(pairs))) → active#(head(active(incr(pairs))))mark#(head(s(tail(_x61)))) → active#(head(active(s(active(tail(mark(_x61)))))))
mark#(tail(X)) → mark#(X)mark#(head(tail(_x31))) → active#(head(tail(mark(_x31))))
active#(odds) → mark#(incr(pairs))mark#(head(s(s(odds)))) → active#(head(active(s(s(active(odds))))))
mark#(head(incr(incr(_x61)))) → active#(head(active(incr(active(incr(mark(_x61)))))))mark#(head(s(s(_x61)))) → active#(head(active(s(s(mark(_x61))))))
mark#(head(incr(cons(cons(_x81, _x82), _x62)))) → active#(head(active(incr(active(cons(active(cons(mark(_x81), _x82)), _x62))))))mark#(head(incr(cons(head(_x81), _x62)))) → active#(head(active(incr(active(cons(active(head(mark(_x81))), _x62))))))
mark#(head(s(head(_x61)))) → active#(head(active(s(active(head(mark(_x61)))))))mark#(head(incr(cons(s(_x81), _x62)))) → active#(head(active(incr(active(cons(active(s(mark(_x81))), _x62))))))
mark#(head(X)) → mark#(X)mark#(head(s(s(_x61)))) → active#(head(s(active(s(mark(_x61))))))
mark#(head(s(s(odds)))) → active#(head(active(s(active(s(mark(incr(pairs))))))))mark#(head(tail(nats))) → active#(head(active(tail(active(nats)))))
mark#(0) → active#(0)active#(nats) → mark#(cons(0, incr(nats)))
mark#(s(X)) → active#(s(mark(X)))mark#(nats) → active#(nats)
mark#(head(s(s(pairs)))) → active#(head(s(active(s(active(pairs))))))mark#(head(incr(head(_x61)))) → active#(head(active(incr(active(head(mark(_x61)))))))
mark#(head(s(nats))) → active#(head(active(s(nats))))mark#(head(tail(cons(_x61, _x62)))) → active#(head(active(tail(active(cons(mark(_x61), _x62))))))
mark#(incr(X)) → mark#(X)mark#(head(pairs)) → active#(head(active(pairs)))
mark#(head(s(s(incr(head(_x101)))))) → active#(head(active(s(active(s(active(incr(active(head(mark(_x101)))))))))))mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(active(cons(active(0), _x62))))))
active#(head(cons(X, XS))) → mark#(X)mark#(head(tail(pairs))) → active#(head(active(tail(active(pairs)))))
mark#(head(incr(odds))) → active#(head(active(incr(odds))))mark#(head(s(s(incr(tail(_x101)))))) → active#(head(active(s(active(s(active(incr(active(tail(mark(_x101)))))))))))
mark#(cons(incr(_x31), X2)) → active#(cons(active(incr(mark(_x31))), X2))mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(active(cons(active(odds), _x62))))))
mark#(head(s(pairs))) → active#(head(active(s(active(pairs)))))mark#(tail(X)) → active#(tail(mark(X)))
mark#(head(s(s(odds)))) → active#(head(s(active(s(active(odds))))))mark#(head(s(_x51))) → active#(head(active(s(_x51))))
mark#(head(tail(_x51))) → active#(head(active(tail(_x51))))mark#(head(0)) → active#(head(active(0)))
mark#(head(nats)) → active#(head(active(nats)))mark#(head(_x21)) → active#(head(_x21))
mark#(head(incr(cons(incr(_x81), _x62)))) → active#(head(active(incr(active(cons(active(incr(mark(_x81))), _x62))))))mark#(head(s(s(incr(0))))) → active#(head(active(s(active(s(active(incr(active(0)))))))))
mark#(cons(cons(_x31, _x32), X2)) → active#(cons(active(cons(mark(_x31), _x32)), X2))mark#(cons(s(_x31), X2)) → active#(cons(active(s(mark(_x31))), X2))
mark#(cons(odds, X2)) → active#(cons(active(odds), X2))mark#(head(s(s(odds)))) → active#(head(active(s(active(s(odds))))))
mark#(cons(nats, X2)) → active#(cons(active(nats), X2))mark#(incr(X)) → active#(incr(mark(X)))
mark#(head(tail(odds))) → active#(head(active(tail(active(odds)))))mark#(head(incr(cons(_x61, active(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))
mark#(cons(X1, active(_x22))) → active#(cons(mark(X1), _x22))mark#(head(incr(cons(tail(_x81), _x62)))) → active#(head(active(incr(active(cons(active(tail(mark(_x81))), _x62))))))
mark#(head(incr(cons(_x71, _x72)))) → active#(head(active(incr(active(cons(_x71, _x72))))))mark#(cons(head(_x31), X2)) → active#(cons(active(head(mark(_x31))), X2))
mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(pairs))))))mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(active(cons(mark(_x61), _x62)))))
mark#(head(incr(_x51))) → active#(head(active(incr(_x51))))mark#(head(tail(head(_x61)))) → active#(head(active(tail(active(head(mark(_x61)))))))
mark#(head(s(s(pairs)))) → active#(head(active(s(s(active(pairs))))))mark#(head(tail(s(_x61)))) → active#(head(active(tail(active(s(mark(_x61)))))))
mark#(cons(tail(_x31), X2)) → active#(cons(active(tail(mark(_x31))), X2))mark#(head(incr(s(_x61)))) → active#(head(active(incr(active(s(mark(_x61)))))))
mark#(head(s(nats))) → active#(head(s(active(nats))))mark#(head(s(s(nats)))) → active#(head(active(s(active(s(active(nats)))))))
mark#(cons(X1, mark(_x22))) → active#(cons(mark(X1), _x22))mark#(head(s(s(incr(_x81))))) → active#(head(s(active(s(active(incr(mark(_x81))))))))
mark#(head(s(s(incr(odds))))) → active#(head(active(s(active(s(active(incr(active(odds)))))))))mark#(head(incr(odds))) → active#(head(active(incr(mark(incr(pairs))))))
mark#(head(incr(nats))) → active#(head(active(incr(active(nats)))))mark#(head(incr(pairs))) → active#(head(active(incr(mark(cons(0, incr(odds)))))))
mark#(head(incr(odds))) → active#(head(incr(active(odds))))mark#(head(s(s(_x71)))) → active#(head(active(s(active(s(_x71))))))
mark#(head(incr(0))) → active#(head(active(incr(active(0)))))active#(tail(cons(X, XS))) → mark#(XS)
mark#(head(tail(incr(_x61)))) → active#(head(active(tail(active(incr(mark(_x61)))))))mark#(head(s(nats))) → active#(head(active(s(mark(cons(0, incr(nats)))))))
mark#(head(incr(cons(_x61, mark(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(active(cons(active(pairs), _x62))))))
mark#(head(s(s(incr(_x91))))) → active#(head(active(s(active(s(active(incr(_x91))))))))mark#(cons(pairs, X2)) → active#(cons(active(pairs), X2))
mark#(odds) → active#(odds)mark#(head(s(s(incr(incr(_x101)))))) → active#(head(active(s(active(s(active(incr(active(incr(mark(_x101)))))))))))
mark#(head(s(_x31))) → active#(head(s(mark(_x31))))mark#(head(tail(tail(_x61)))) → active#(head(active(tail(active(tail(mark(_x61)))))))
mark#(head(s(s(0)))) → active#(head(active(s(active(s(active(0)))))))mark#(cons(_x21, _x22)) → active#(cons(_x21, _x22))
mark#(head(s(s(tail(_x81))))) → active#(head(active(s(active(s(active(tail(mark(_x81)))))))))mark#(head(odds)) → active#(head(active(odds)))
mark#(head(s(s(incr(_x81))))) → active#(head(active(s(active(s(incr(mark(_x81))))))))mark#(head(s(odds))) → active#(head(active(s(active(odds)))))

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, s, pairs, active, mark, incr, head, tail, odds, cons

Strategy

The right-hand side of the rule mark#(head(incr(pairs))) → active#(head(incr(active(pairs)))) 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
active#(head(incr(pairs))) 
active#(head(incr(mark(cons(0, incr(odds)))))) 
Thus, the rule mark#(head(incr(pairs))) → active#(head(incr(active(pairs)))) is replaced by the following rules:
mark#(head(incr(pairs))) → active#(head(incr(pairs)))mark#(head(incr(pairs))) → active#(head(incr(mark(cons(0, incr(odds))))))

Problem 23: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(pairs) → active#(pairs)mark#(head(incr(cons(_x61, _x62)))) → active#(head(active(incr(cons(mark(_x61), _x62)))))
active#(pairs) → mark#(cons(0, incr(odds)))mark#(head(s(incr(_x61)))) → active#(head(active(s(active(incr(mark(_x61)))))))
mark#(head(incr(_x31))) → active#(head(incr(mark(_x31))))mark#(head(head(_x31))) → active#(head(active(head(mark(_x31)))))
mark#(head(s(cons(_x61, _x62)))) → active#(head(active(s(active(cons(mark(_x61), _x62))))))mark#(head(s(s(incr(pairs))))) → active#(head(active(s(active(s(active(incr(active(pairs)))))))))
mark#(s(X)) → mark#(X)mark#(head(s(s(incr(nats))))) → active#(head(active(s(active(s(active(incr(active(nats)))))))))
mark#(head(incr(tail(_x61)))) → active#(head(active(incr(active(tail(mark(_x61)))))))mark#(head(s(s(head(_x81))))) → active#(head(active(s(active(s(active(head(mark(_x81)))))))))
mark#(head(s(s(incr(_x81))))) → active#(head(active(s(s(active(incr(mark(_x81))))))))mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(mark(cons(0, incr(odds)))))))))
mark#(head(tail(0))) → active#(head(active(tail(active(0)))))mark#(head(s(s(incr(s(_x101)))))) → active#(head(active(s(active(s(active(incr(active(s(mark(_x101)))))))))))
mark#(head(cons(_x31, _x32))) → active#(head(active(cons(mark(_x31), _x32))))active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))
mark#(head(s(s(s(_x81))))) → active#(head(active(s(active(s(active(s(mark(_x81)))))))))mark#(cons(X1, X2)) → mark#(X1)
mark#(head(s(s(cons(_x81, _x82))))) → active#(head(active(s(active(s(active(cons(mark(_x81), _x82))))))))mark#(head(s(0))) → active#(head(active(s(active(0)))))
mark#(head(s(s(incr(cons(_x101, _x102)))))) → active#(head(active(s(active(s(active(incr(active(cons(mark(_x101), _x102))))))))))mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(active(cons(active(nats), _x62))))))
mark#(head(incr(pairs))) → active#(head(active(incr(pairs))))mark#(cons(0, X2)) → active#(cons(active(0), X2))
mark#(tail(X)) → mark#(X)mark#(head(s(tail(_x61)))) → active#(head(active(s(active(tail(mark(_x61)))))))
mark#(head(incr(pairs))) → active#(head(incr(pairs)))mark#(head(tail(_x31))) → active#(head(tail(mark(_x31))))
active#(odds) → mark#(incr(pairs))mark#(head(s(s(odds)))) → active#(head(active(s(s(active(odds))))))
mark#(head(s(s(_x61)))) → active#(head(active(s(s(mark(_x61))))))mark#(head(incr(incr(_x61)))) → active#(head(active(incr(active(incr(mark(_x61)))))))
mark#(head(incr(cons(cons(_x81, _x82), _x62)))) → active#(head(active(incr(active(cons(active(cons(mark(_x81), _x82)), _x62))))))mark#(head(incr(cons(head(_x81), _x62)))) → active#(head(active(incr(active(cons(active(head(mark(_x81))), _x62))))))
mark#(head(s(head(_x61)))) → active#(head(active(s(active(head(mark(_x61)))))))mark#(head(s(s(_x61)))) → active#(head(s(active(s(mark(_x61))))))
mark#(head(X)) → mark#(X)mark#(head(incr(cons(s(_x81), _x62)))) → active#(head(active(incr(active(cons(active(s(mark(_x81))), _x62))))))
mark#(head(s(s(odds)))) → active#(head(active(s(active(s(mark(incr(pairs))))))))mark#(head(tail(nats))) → active#(head(active(tail(active(nats)))))
active#(nats) → mark#(cons(0, incr(nats)))mark#(0) → active#(0)
mark#(s(X)) → active#(s(mark(X)))mark#(nats) → active#(nats)
mark#(head(s(s(pairs)))) → active#(head(s(active(s(active(pairs))))))mark#(head(s(nats))) → active#(head(active(s(nats))))
mark#(head(incr(head(_x61)))) → active#(head(active(incr(active(head(mark(_x61)))))))mark#(head(tail(cons(_x61, _x62)))) → active#(head(active(tail(active(cons(mark(_x61), _x62))))))
mark#(incr(X)) → mark#(X)mark#(head(pairs)) → active#(head(active(pairs)))
mark#(head(s(s(incr(head(_x101)))))) → active#(head(active(s(active(s(active(incr(active(head(mark(_x101)))))))))))mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(active(cons(active(0), _x62))))))
active#(head(cons(X, XS))) → mark#(X)mark#(head(tail(pairs))) → active#(head(active(tail(active(pairs)))))
mark#(head(incr(odds))) → active#(head(active(incr(odds))))mark#(head(s(s(incr(tail(_x101)))))) → active#(head(active(s(active(s(active(incr(active(tail(mark(_x101)))))))))))
mark#(cons(incr(_x31), X2)) → active#(cons(active(incr(mark(_x31))), X2))mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(active(cons(active(odds), _x62))))))
mark#(head(s(pairs))) → active#(head(active(s(active(pairs)))))mark#(tail(X)) → active#(tail(mark(X)))
mark#(head(s(s(odds)))) → active#(head(s(active(s(active(odds))))))mark#(head(s(_x51))) → active#(head(active(s(_x51))))
mark#(head(tail(_x51))) → active#(head(active(tail(_x51))))mark#(head(0)) → active#(head(active(0)))
mark#(head(nats)) → active#(head(active(nats)))mark#(head(_x21)) → active#(head(_x21))
mark#(head(incr(cons(incr(_x81), _x62)))) → active#(head(active(incr(active(cons(active(incr(mark(_x81))), _x62))))))mark#(head(s(s(incr(0))))) → active#(head(active(s(active(s(active(incr(active(0)))))))))
mark#(cons(cons(_x31, _x32), X2)) → active#(cons(active(cons(mark(_x31), _x32)), X2))mark#(cons(s(_x31), X2)) → active#(cons(active(s(mark(_x31))), X2))
mark#(cons(odds, X2)) → active#(cons(active(odds), X2))mark#(head(s(s(odds)))) → active#(head(active(s(active(s(odds))))))
mark#(cons(nats, X2)) → active#(cons(active(nats), X2))mark#(head(incr(pairs))) → active#(head(incr(mark(cons(0, incr(odds))))))
mark#(incr(X)) → active#(incr(mark(X)))mark#(head(tail(odds))) → active#(head(active(tail(active(odds)))))
mark#(head(incr(cons(_x61, active(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))mark#(cons(X1, active(_x22))) → active#(cons(mark(X1), _x22))
mark#(head(incr(cons(tail(_x81), _x62)))) → active#(head(active(incr(active(cons(active(tail(mark(_x81))), _x62))))))mark#(head(incr(cons(_x71, _x72)))) → active#(head(active(incr(active(cons(_x71, _x72))))))
mark#(cons(head(_x31), X2)) → active#(cons(active(head(mark(_x31))), X2))mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(pairs))))))
mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(active(cons(mark(_x61), _x62)))))mark#(head(incr(_x51))) → active#(head(active(incr(_x51))))
mark#(head(tail(head(_x61)))) → active#(head(active(tail(active(head(mark(_x61)))))))mark#(head(s(s(pairs)))) → active#(head(active(s(s(active(pairs))))))
mark#(head(tail(s(_x61)))) → active#(head(active(tail(active(s(mark(_x61)))))))mark#(cons(tail(_x31), X2)) → active#(cons(active(tail(mark(_x31))), X2))
mark#(head(incr(s(_x61)))) → active#(head(active(incr(active(s(mark(_x61)))))))mark#(head(s(nats))) → active#(head(s(active(nats))))
mark#(head(s(s(nats)))) → active#(head(active(s(active(s(active(nats)))))))mark#(cons(X1, mark(_x22))) → active#(cons(mark(X1), _x22))
mark#(head(s(s(incr(_x81))))) → active#(head(s(active(s(active(incr(mark(_x81))))))))mark#(head(s(s(incr(odds))))) → active#(head(active(s(active(s(active(incr(active(odds)))))))))
mark#(head(incr(odds))) → active#(head(active(incr(mark(incr(pairs))))))mark#(head(incr(nats))) → active#(head(active(incr(active(nats)))))
mark#(head(incr(pairs))) → active#(head(active(incr(mark(cons(0, incr(odds)))))))mark#(head(incr(odds))) → active#(head(incr(active(odds))))
mark#(head(incr(0))) → active#(head(active(incr(active(0)))))mark#(head(s(s(_x71)))) → active#(head(active(s(active(s(_x71))))))
active#(tail(cons(X, XS))) → mark#(XS)mark#(head(tail(incr(_x61)))) → active#(head(active(tail(active(incr(mark(_x61)))))))
mark#(head(s(nats))) → active#(head(active(s(mark(cons(0, incr(nats)))))))mark#(head(incr(cons(_x61, mark(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))
mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(active(cons(active(pairs), _x62))))))mark#(head(s(s(incr(_x91))))) → active#(head(active(s(active(s(active(incr(_x91))))))))
mark#(cons(pairs, X2)) → active#(cons(active(pairs), X2))mark#(odds) → active#(odds)
mark#(head(s(s(incr(incr(_x101)))))) → active#(head(active(s(active(s(active(incr(active(incr(mark(_x101)))))))))))mark#(head(s(_x31))) → active#(head(s(mark(_x31))))
mark#(head(tail(tail(_x61)))) → active#(head(active(tail(active(tail(mark(_x61)))))))mark#(head(s(s(0)))) → active#(head(active(s(active(s(active(0)))))))
mark#(head(s(s(tail(_x81))))) → active#(head(active(s(active(s(active(tail(mark(_x81)))))))))mark#(cons(_x21, _x22)) → active#(cons(_x21, _x22))
mark#(head(s(s(incr(_x81))))) → active#(head(active(s(active(s(incr(mark(_x81))))))))mark#(head(odds)) → active#(head(active(odds)))
mark#(head(s(odds))) → active#(head(active(s(active(odds)))))

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, pairs, s, active, mark, incr, head, odds, tail, cons

Strategy

The right-hand side of the rule mark#(head(incr(cons(_x61, _x62)))) → active#(head(active(incr(cons(mark(_x61), _x62))))) 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
active#(head(active(incr(cons(active(nats), _x62))))) 
active#(head(mark(cons(s(mark(_x61)), incr(_x31))))) 
active#(head(incr(cons(mark(_x61), _x62)))) 
active#(head(active(incr(cons(mark(_x61), _x52))))) 
active#(head(active(incr(cons(active(head(mark(_x71))), _x62))))) 
active#(head(active(incr(cons(active(0), _x62))))) 
active#(head(active(incr(cons(active(pairs), _x62))))) 
active#(head(active(incr(cons(active(tail(mark(_x71))), _x62))))) 
active#(head(active(incr(cons(active(s(mark(_x71))), _x62))))) 
active#(head(active(incr(cons(active(incr(mark(_x71))), _x62))))) 
active#(head(active(incr(cons(_x51, _x52))))) 
active#(head(active(incr(cons(active(cons(mark(_x71), _x72)), _x62))))) 
active#(head(active(incr(cons(active(odds), _x62))))) 
Thus, the rule mark#(head(incr(cons(_x61, _x62)))) → active#(head(active(incr(cons(mark(_x61), _x62))))) is replaced by the following rules:
mark#(head(incr(cons(incr(_x71), _x62)))) → active#(head(active(incr(cons(active(incr(mark(_x71))), _x62)))))mark#(head(incr(cons(_x51, _x52)))) → active#(head(active(incr(cons(_x51, _x52)))))
mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(cons(active(0), _x62)))))mark#(head(incr(cons(_x61, _x31)))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))
mark#(head(incr(cons(_x61, active(_x52))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))mark#(head(incr(cons(tail(_x71), _x62)))) → active#(head(active(incr(cons(active(tail(mark(_x71))), _x62)))))
mark#(head(incr(cons(s(_x71), _x62)))) → active#(head(active(incr(cons(active(s(mark(_x71))), _x62)))))mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(cons(active(nats), _x62)))))
mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(cons(active(pairs), _x62)))))mark#(head(incr(cons(head(_x71), _x62)))) → active#(head(active(incr(cons(active(head(mark(_x71))), _x62)))))
mark#(head(incr(cons(cons(_x71, _x72), _x62)))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x72)), _x62)))))mark#(head(incr(cons(_x61, mark(_x52))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))
mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(cons(mark(_x61), _x62))))mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(cons(active(odds), _x62)))))

Problem 24: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(pairs) → active#(pairs)mark#(head(incr(cons(_x61, active(_x52))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))
active#(pairs) → mark#(cons(0, incr(odds)))mark#(head(incr(_x31))) → active#(head(incr(mark(_x31))))
mark#(head(s(incr(_x61)))) → active#(head(active(s(active(incr(mark(_x61)))))))mark#(head(head(_x31))) → active#(head(active(head(mark(_x31)))))
mark#(head(incr(cons(tail(_x71), _x62)))) → active#(head(active(incr(cons(active(tail(mark(_x71))), _x62)))))mark#(head(s(cons(_x61, _x62)))) → active#(head(active(s(active(cons(mark(_x61), _x62))))))
mark#(head(s(s(incr(pairs))))) → active#(head(active(s(active(s(active(incr(active(pairs)))))))))mark#(head(s(s(incr(nats))))) → active#(head(active(s(active(s(active(incr(active(nats)))))))))
mark#(s(X)) → mark#(X)mark#(head(incr(cons(cons(_x71, _x72), _x62)))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x72)), _x62)))))
mark#(head(incr(cons(_x61, mark(_x52))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(cons(active(odds), _x62)))))
mark#(head(incr(tail(_x61)))) → active#(head(active(incr(active(tail(mark(_x61)))))))mark#(head(s(s(head(_x81))))) → active#(head(active(s(active(s(active(head(mark(_x81)))))))))
mark#(head(s(s(incr(_x81))))) → active#(head(active(s(s(active(incr(mark(_x81))))))))mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(mark(cons(0, incr(odds)))))))))
mark#(head(tail(0))) → active#(head(active(tail(active(0)))))mark#(head(s(s(incr(s(_x101)))))) → active#(head(active(s(active(s(active(incr(active(s(mark(_x101)))))))))))
mark#(head(cons(_x31, _x32))) → active#(head(active(cons(mark(_x31), _x32))))active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))
mark#(head(s(s(s(_x81))))) → active#(head(active(s(active(s(active(s(mark(_x81)))))))))mark#(cons(X1, X2)) → mark#(X1)
mark#(head(s(s(cons(_x81, _x82))))) → active#(head(active(s(active(s(active(cons(mark(_x81), _x82))))))))mark#(head(s(0))) → active#(head(active(s(active(0)))))
mark#(head(s(s(incr(cons(_x101, _x102)))))) → active#(head(active(s(active(s(active(incr(active(cons(mark(_x101), _x102))))))))))mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(active(cons(active(nats), _x62))))))
mark#(cons(0, X2)) → active#(cons(active(0), X2))mark#(head(incr(pairs))) → active#(head(active(incr(pairs))))
mark#(head(incr(pairs))) → active#(head(incr(pairs)))mark#(head(s(tail(_x61)))) → active#(head(active(s(active(tail(mark(_x61)))))))
mark#(tail(X)) → mark#(X)mark#(head(incr(cons(s(_x71), _x62)))) → active#(head(active(incr(cons(active(s(mark(_x71))), _x62)))))
mark#(head(tail(_x31))) → active#(head(tail(mark(_x31))))mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(cons(active(pairs), _x62)))))
active#(odds) → mark#(incr(pairs))mark#(head(s(s(odds)))) → active#(head(active(s(s(active(odds))))))
mark#(head(incr(incr(_x61)))) → active#(head(active(incr(active(incr(mark(_x61)))))))mark#(head(s(s(_x61)))) → active#(head(active(s(s(mark(_x61))))))
mark#(head(incr(cons(cons(_x81, _x82), _x62)))) → active#(head(active(incr(active(cons(active(cons(mark(_x81), _x82)), _x62))))))mark#(head(incr(cons(head(_x81), _x62)))) → active#(head(active(incr(active(cons(active(head(mark(_x81))), _x62))))))
mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(cons(active(0), _x62)))))mark#(head(s(head(_x61)))) → active#(head(active(s(active(head(mark(_x61)))))))
mark#(head(incr(cons(s(_x81), _x62)))) → active#(head(active(incr(active(cons(active(s(mark(_x81))), _x62))))))mark#(head(X)) → mark#(X)
mark#(head(s(s(_x61)))) → active#(head(s(active(s(mark(_x61))))))mark#(head(s(s(odds)))) → active#(head(active(s(active(s(mark(incr(pairs))))))))
mark#(head(tail(nats))) → active#(head(active(tail(active(nats)))))active#(nats) → mark#(cons(0, incr(nats)))
mark#(0) → active#(0)mark#(s(X)) → active#(s(mark(X)))
mark#(nats) → active#(nats)mark#(head(incr(cons(_x51, _x52)))) → active#(head(active(incr(cons(_x51, _x52)))))
mark#(head(s(s(pairs)))) → active#(head(s(active(s(active(pairs))))))mark#(head(s(nats))) → active#(head(active(s(nats))))
mark#(head(incr(head(_x61)))) → active#(head(active(incr(active(head(mark(_x61)))))))mark#(head(tail(cons(_x61, _x62)))) → active#(head(active(tail(active(cons(mark(_x61), _x62))))))
mark#(incr(X)) → mark#(X)mark#(head(pairs)) → active#(head(active(pairs)))
mark#(head(s(s(incr(head(_x101)))))) → active#(head(active(s(active(s(active(incr(active(head(mark(_x101)))))))))))mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(active(cons(active(0), _x62))))))
mark#(head(incr(cons(head(_x71), _x62)))) → active#(head(active(incr(cons(active(head(mark(_x71))), _x62)))))active#(head(cons(X, XS))) → mark#(X)
mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(cons(mark(_x61), _x62))))mark#(head(tail(pairs))) → active#(head(active(tail(active(pairs)))))
mark#(head(incr(odds))) → active#(head(active(incr(odds))))mark#(head(incr(cons(incr(_x71), _x62)))) → active#(head(active(incr(cons(active(incr(mark(_x71))), _x62)))))
mark#(head(s(s(incr(tail(_x101)))))) → active#(head(active(s(active(s(active(incr(active(tail(mark(_x101)))))))))))mark#(cons(incr(_x31), X2)) → active#(cons(active(incr(mark(_x31))), X2))
mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(active(cons(active(odds), _x62))))))mark#(head(s(pairs))) → active#(head(active(s(active(pairs)))))
mark#(tail(X)) → active#(tail(mark(X)))mark#(head(s(s(odds)))) → active#(head(s(active(s(active(odds))))))
mark#(head(s(_x51))) → active#(head(active(s(_x51))))mark#(head(tail(_x51))) → active#(head(active(tail(_x51))))
mark#(head(0)) → active#(head(active(0)))mark#(head(nats)) → active#(head(active(nats)))
mark#(head(_x21)) → active#(head(_x21))mark#(head(incr(cons(incr(_x81), _x62)))) → active#(head(active(incr(active(cons(active(incr(mark(_x81))), _x62))))))
mark#(head(s(s(incr(0))))) → active#(head(active(s(active(s(active(incr(active(0)))))))))mark#(cons(cons(_x31, _x32), X2)) → active#(cons(active(cons(mark(_x31), _x32)), X2))
mark#(cons(s(_x31), X2)) → active#(cons(active(s(mark(_x31))), X2))mark#(cons(odds, X2)) → active#(cons(active(odds), X2))
mark#(head(s(s(odds)))) → active#(head(active(s(active(s(odds))))))mark#(cons(nats, X2)) → active#(cons(active(nats), X2))
mark#(head(incr(pairs))) → active#(head(incr(mark(cons(0, incr(odds))))))mark#(incr(X)) → active#(incr(mark(X)))
mark#(head(tail(odds))) → active#(head(active(tail(active(odds)))))mark#(head(incr(cons(_x61, active(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))
mark#(cons(X1, active(_x22))) → active#(cons(mark(X1), _x22))mark#(head(incr(cons(tail(_x81), _x62)))) → active#(head(active(incr(active(cons(active(tail(mark(_x81))), _x62))))))
mark#(head(incr(cons(_x71, _x72)))) → active#(head(active(incr(active(cons(_x71, _x72))))))mark#(cons(head(_x31), X2)) → active#(cons(active(head(mark(_x31))), X2))
mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(pairs))))))mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(active(cons(mark(_x61), _x62)))))
mark#(head(incr(_x51))) → active#(head(active(incr(_x51))))mark#(head(tail(head(_x61)))) → active#(head(active(tail(active(head(mark(_x61)))))))
mark#(head(tail(s(_x61)))) → active#(head(active(tail(active(s(mark(_x61)))))))mark#(head(s(s(pairs)))) → active#(head(active(s(s(active(pairs))))))
mark#(cons(tail(_x31), X2)) → active#(cons(active(tail(mark(_x31))), X2))mark#(head(incr(cons(_x61, _x31)))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))
mark#(head(incr(s(_x61)))) → active#(head(active(incr(active(s(mark(_x61)))))))mark#(head(s(nats))) → active#(head(s(active(nats))))
mark#(cons(X1, mark(_x22))) → active#(cons(mark(X1), _x22))mark#(head(s(s(nats)))) → active#(head(active(s(active(s(active(nats)))))))
mark#(head(s(s(incr(odds))))) → active#(head(active(s(active(s(active(incr(active(odds)))))))))mark#(head(s(s(incr(_x81))))) → active#(head(s(active(s(active(incr(mark(_x81))))))))
mark#(head(incr(odds))) → active#(head(active(incr(mark(incr(pairs))))))mark#(head(incr(nats))) → active#(head(active(incr(active(nats)))))
mark#(head(incr(pairs))) → active#(head(active(incr(mark(cons(0, incr(odds)))))))mark#(head(incr(odds))) → active#(head(incr(active(odds))))
mark#(head(s(s(_x71)))) → active#(head(active(s(active(s(_x71))))))mark#(head(incr(0))) → active#(head(active(incr(active(0)))))
active#(tail(cons(X, XS))) → mark#(XS)mark#(head(tail(incr(_x61)))) → active#(head(active(tail(active(incr(mark(_x61)))))))
mark#(head(s(nats))) → active#(head(active(s(mark(cons(0, incr(nats)))))))mark#(head(incr(cons(_x61, mark(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))
mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(active(cons(active(pairs), _x62))))))mark#(head(s(s(incr(_x91))))) → active#(head(active(s(active(s(active(incr(_x91))))))))
mark#(cons(pairs, X2)) → active#(cons(active(pairs), X2))mark#(odds) → active#(odds)
mark#(head(s(s(incr(incr(_x101)))))) → active#(head(active(s(active(s(active(incr(active(incr(mark(_x101)))))))))))mark#(head(s(_x31))) → active#(head(s(mark(_x31))))
mark#(head(tail(tail(_x61)))) → active#(head(active(tail(active(tail(mark(_x61)))))))mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(cons(active(nats), _x62)))))
mark#(head(s(s(0)))) → active#(head(active(s(active(s(active(0)))))))mark#(cons(_x21, _x22)) → active#(cons(_x21, _x22))
mark#(head(s(s(tail(_x81))))) → active#(head(active(s(active(s(active(tail(mark(_x81)))))))))mark#(head(odds)) → active#(head(active(odds)))
mark#(head(s(s(incr(_x81))))) → active#(head(active(s(active(s(incr(mark(_x81))))))))mark#(head(s(odds))) → active#(head(active(s(active(odds)))))

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, s, pairs, active, mark, incr, head, tail, odds, cons

Strategy

The right-hand side of the rule mark#(head(incr(cons(_x61, active(_x52))))) → active#(head(active(incr(cons(mark(_x61), _x52))))) 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
active#(head(active(incr(cons(active(incr(mark(_x81))), _x52))))) 
active#(head(active(incr(cons(active(tail(mark(_x81))), _x52))))) 
active#(head(mark(cons(s(mark(_x61)), incr(_x31))))) 
active#(head(active(incr(cons(active(nats), _x52))))) 
active#(head(incr(cons(mark(_x61), _x52)))) 
active#(head(active(incr(cons(active(head(mark(_x81))), _x52))))) 
active#(head(active(incr(cons(active(odds), _x52))))) 
active#(head(active(incr(cons(mark(_x61), _x72))))) 
active#(head(active(incr(cons(_x71, _x72))))) 
active#(head(active(incr(cons(active(pairs), _x52))))) 
active#(head(active(incr(cons(active(cons(mark(_x81), _x82)), _x52))))) 
active#(head(active(incr(cons(active(s(mark(_x81))), _x52))))) 
active#(head(active(incr(cons(active(0), _x52))))) 
Thus, the rule mark#(head(incr(cons(_x61, active(_x52))))) → active#(head(active(incr(cons(mark(_x61), _x52))))) is replaced by the following rules:
mark#(head(incr(cons(s(_x81), active(_x52))))) → active#(head(active(incr(cons(active(s(mark(_x81))), _x52)))))mark#(head(incr(cons(_x61, active(mark(_x72)))))) → active#(head(active(incr(cons(mark(_x61), _x72)))))
mark#(head(incr(cons(head(_x81), active(_x52))))) → active#(head(active(incr(cons(active(head(mark(_x81))), _x52)))))mark#(head(incr(cons(tail(_x81), active(_x52))))) → active#(head(active(incr(cons(active(tail(mark(_x81))), _x52)))))
mark#(head(incr(cons(_x71, active(_x72))))) → active#(head(active(incr(cons(_x71, _x72)))))mark#(head(incr(cons(_x61, active(_x31))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))
mark#(head(incr(cons(pairs, active(_x52))))) → active#(head(active(incr(cons(active(pairs), _x52)))))mark#(head(incr(cons(nats, active(_x52))))) → active#(head(active(incr(cons(active(nats), _x52)))))
mark#(head(incr(cons(0, active(_x52))))) → active#(head(active(incr(cons(active(0), _x52)))))mark#(head(incr(cons(incr(_x81), active(_x52))))) → active#(head(active(incr(cons(active(incr(mark(_x81))), _x52)))))
mark#(head(incr(cons(odds, active(_x52))))) → active#(head(active(incr(cons(active(odds), _x52)))))mark#(head(incr(cons(cons(_x81, _x82), active(_x52))))) → active#(head(active(incr(cons(active(cons(mark(_x81), _x82)), _x52)))))
mark#(head(incr(cons(_x61, active(active(_x72)))))) → active#(head(active(incr(cons(mark(_x61), _x72)))))mark#(head(incr(cons(_x61, active(_x52))))) → active#(head(incr(cons(mark(_x61), _x52))))

Problem 25: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(head(incr(cons(_x61, active(mark(_x72)))))) → active#(head(active(incr(cons(mark(_x61), _x72)))))mark#(pairs) → active#(pairs)
active#(pairs) → mark#(cons(0, incr(odds)))mark#(head(s(incr(_x61)))) → active#(head(active(s(active(incr(mark(_x61)))))))
mark#(head(incr(_x31))) → active#(head(incr(mark(_x31))))mark#(head(incr(cons(tail(_x71), _x62)))) → active#(head(active(incr(cons(active(tail(mark(_x71))), _x62)))))
mark#(head(head(_x31))) → active#(head(active(head(mark(_x31)))))mark#(head(s(cons(_x61, _x62)))) → active#(head(active(s(active(cons(mark(_x61), _x62))))))
mark#(head(s(s(incr(pairs))))) → active#(head(active(s(active(s(active(incr(active(pairs)))))))))mark#(head(incr(cons(cons(_x71, _x72), _x62)))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x72)), _x62)))))
mark#(s(X)) → mark#(X)mark#(head(s(s(incr(nats))))) → active#(head(active(s(active(s(active(incr(active(nats)))))))))
mark#(head(incr(cons(_x61, mark(_x52))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(cons(active(odds), _x62)))))
mark#(head(incr(tail(_x61)))) → active#(head(active(incr(active(tail(mark(_x61)))))))mark#(head(s(s(head(_x81))))) → active#(head(active(s(active(s(active(head(mark(_x81)))))))))
mark#(head(s(s(incr(_x81))))) → active#(head(active(s(s(active(incr(mark(_x81))))))))mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(mark(cons(0, incr(odds)))))))))
mark#(head(tail(0))) → active#(head(active(tail(active(0)))))mark#(head(s(s(incr(s(_x101)))))) → active#(head(active(s(active(s(active(incr(active(s(mark(_x101)))))))))))
mark#(head(cons(_x31, _x32))) → active#(head(active(cons(mark(_x31), _x32))))active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))
mark#(head(s(s(s(_x81))))) → active#(head(active(s(active(s(active(s(mark(_x81)))))))))mark#(cons(X1, X2)) → mark#(X1)
mark#(head(s(s(cons(_x81, _x82))))) → active#(head(active(s(active(s(active(cons(mark(_x81), _x82))))))))mark#(head(s(0))) → active#(head(active(s(active(0)))))
mark#(head(incr(cons(tail(_x81), active(_x52))))) → active#(head(active(incr(cons(active(tail(mark(_x81))), _x52)))))mark#(head(s(s(incr(cons(_x101, _x102)))))) → active#(head(active(s(active(s(active(incr(active(cons(mark(_x101), _x102))))))))))
mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(active(cons(active(nats), _x62))))))mark#(head(incr(pairs))) → active#(head(active(incr(pairs))))
mark#(cons(0, X2)) → active#(cons(active(0), X2))mark#(head(incr(cons(incr(_x81), active(_x52))))) → active#(head(active(incr(cons(active(incr(mark(_x81))), _x52)))))
mark#(head(incr(cons(s(_x71), _x62)))) → active#(head(active(incr(cons(active(s(mark(_x71))), _x62)))))mark#(tail(X)) → mark#(X)
mark#(head(s(tail(_x61)))) → active#(head(active(s(active(tail(mark(_x61)))))))mark#(head(incr(pairs))) → active#(head(incr(pairs)))
mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(cons(active(pairs), _x62)))))mark#(head(tail(_x31))) → active#(head(tail(mark(_x31))))
active#(odds) → mark#(incr(pairs))mark#(head(s(s(odds)))) → active#(head(active(s(s(active(odds))))))
mark#(head(s(s(_x61)))) → active#(head(active(s(s(mark(_x61))))))mark#(head(incr(incr(_x61)))) → active#(head(active(incr(active(incr(mark(_x61)))))))
mark#(head(incr(cons(cons(_x81, _x82), _x62)))) → active#(head(active(incr(active(cons(active(cons(mark(_x81), _x82)), _x62))))))mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(cons(active(0), _x62)))))
mark#(head(incr(cons(head(_x81), _x62)))) → active#(head(active(incr(active(cons(active(head(mark(_x81))), _x62))))))mark#(head(s(head(_x61)))) → active#(head(active(s(active(head(mark(_x61)))))))
mark#(head(incr(cons(_x71, active(_x72))))) → active#(head(active(incr(cons(_x71, _x72)))))mark#(head(X)) → mark#(X)
mark#(head(incr(cons(s(_x81), _x62)))) → active#(head(active(incr(active(cons(active(s(mark(_x81))), _x62))))))mark#(head(s(s(_x61)))) → active#(head(s(active(s(mark(_x61))))))
mark#(head(s(s(odds)))) → active#(head(active(s(active(s(mark(incr(pairs))))))))mark#(head(tail(nats))) → active#(head(active(tail(active(nats)))))
active#(nats) → mark#(cons(0, incr(nats)))mark#(0) → active#(0)
mark#(s(X)) → active#(s(mark(X)))mark#(nats) → active#(nats)
mark#(head(incr(cons(_x51, _x52)))) → active#(head(active(incr(cons(_x51, _x52)))))mark#(head(s(s(pairs)))) → active#(head(s(active(s(active(pairs))))))
mark#(head(s(nats))) → active#(head(active(s(nats))))mark#(head(incr(head(_x61)))) → active#(head(active(incr(active(head(mark(_x61)))))))
mark#(head(tail(cons(_x61, _x62)))) → active#(head(active(tail(active(cons(mark(_x61), _x62))))))mark#(head(incr(cons(_x61, active(_x31))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))
mark#(incr(X)) → mark#(X)mark#(head(pairs)) → active#(head(active(pairs)))
mark#(head(incr(cons(_x61, active(active(_x72)))))) → active#(head(active(incr(cons(mark(_x61), _x72)))))mark#(head(s(s(incr(head(_x101)))))) → active#(head(active(s(active(s(active(incr(active(head(mark(_x101)))))))))))
mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(active(cons(active(0), _x62))))))mark#(head(incr(cons(head(_x71), _x62)))) → active#(head(active(incr(cons(active(head(mark(_x71))), _x62)))))
active#(head(cons(X, XS))) → mark#(X)mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(cons(mark(_x61), _x62))))
mark#(head(tail(pairs))) → active#(head(active(tail(active(pairs)))))mark#(head(incr(odds))) → active#(head(active(incr(odds))))
mark#(head(incr(cons(incr(_x71), _x62)))) → active#(head(active(incr(cons(active(incr(mark(_x71))), _x62)))))mark#(head(s(s(incr(tail(_x101)))))) → active#(head(active(s(active(s(active(incr(active(tail(mark(_x101)))))))))))
mark#(cons(incr(_x31), X2)) → active#(cons(active(incr(mark(_x31))), X2))mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(active(cons(active(odds), _x62))))))
mark#(head(s(pairs))) → active#(head(active(s(active(pairs)))))mark#(tail(X)) → active#(tail(mark(X)))
mark#(head(s(s(odds)))) → active#(head(s(active(s(active(odds))))))mark#(head(incr(cons(cons(_x81, _x82), active(_x52))))) → active#(head(active(incr(cons(active(cons(mark(_x81), _x82)), _x52)))))
mark#(head(s(_x51))) → active#(head(active(s(_x51))))mark#(head(tail(_x51))) → active#(head(active(tail(_x51))))
mark#(head(0)) → active#(head(active(0)))mark#(head(nats)) → active#(head(active(nats)))
mark#(head(_x21)) → active#(head(_x21))mark#(head(incr(cons(incr(_x81), _x62)))) → active#(head(active(incr(active(cons(active(incr(mark(_x81))), _x62))))))
mark#(head(s(s(incr(0))))) → active#(head(active(s(active(s(active(incr(active(0)))))))))mark#(cons(cons(_x31, _x32), X2)) → active#(cons(active(cons(mark(_x31), _x32)), X2))
mark#(head(incr(cons(s(_x81), active(_x52))))) → active#(head(active(incr(cons(active(s(mark(_x81))), _x52)))))mark#(cons(s(_x31), X2)) → active#(cons(active(s(mark(_x31))), X2))
mark#(cons(odds, X2)) → active#(cons(active(odds), X2))mark#(head(s(s(odds)))) → active#(head(active(s(active(s(odds))))))
mark#(cons(nats, X2)) → active#(cons(active(nats), X2))mark#(head(incr(cons(head(_x81), active(_x52))))) → active#(head(active(incr(cons(active(head(mark(_x81))), _x52)))))
mark#(head(incr(pairs))) → active#(head(incr(mark(cons(0, incr(odds))))))mark#(incr(X)) → active#(incr(mark(X)))
mark#(head(tail(odds))) → active#(head(active(tail(active(odds)))))mark#(head(incr(cons(_x61, active(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))
mark#(head(incr(cons(nats, active(_x52))))) → active#(head(active(incr(cons(active(nats), _x52)))))mark#(head(incr(cons(tail(_x81), _x62)))) → active#(head(active(incr(active(cons(active(tail(mark(_x81))), _x62))))))
mark#(cons(X1, active(_x22))) → active#(cons(mark(X1), _x22))mark#(head(incr(cons(0, active(_x52))))) → active#(head(active(incr(cons(active(0), _x52)))))
mark#(head(incr(cons(odds, active(_x52))))) → active#(head(active(incr(cons(active(odds), _x52)))))mark#(head(incr(cons(_x71, _x72)))) → active#(head(active(incr(active(cons(_x71, _x72))))))
mark#(cons(head(_x31), X2)) → active#(cons(active(head(mark(_x31))), X2))mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(pairs))))))
mark#(head(incr(_x51))) → active#(head(active(incr(_x51))))mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(active(cons(mark(_x61), _x62)))))
mark#(head(tail(head(_x61)))) → active#(head(active(tail(active(head(mark(_x61)))))))mark#(head(s(s(pairs)))) → active#(head(active(s(s(active(pairs))))))
mark#(head(tail(s(_x61)))) → active#(head(active(tail(active(s(mark(_x61)))))))mark#(head(incr(cons(_x61, _x31)))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))
mark#(cons(tail(_x31), X2)) → active#(cons(active(tail(mark(_x31))), X2))mark#(head(incr(s(_x61)))) → active#(head(active(incr(active(s(mark(_x61)))))))
mark#(head(incr(cons(pairs, active(_x52))))) → active#(head(active(incr(cons(active(pairs), _x52)))))mark#(head(s(nats))) → active#(head(s(active(nats))))
mark#(head(s(s(nats)))) → active#(head(active(s(active(s(active(nats)))))))mark#(cons(X1, mark(_x22))) → active#(cons(mark(X1), _x22))
mark#(head(s(s(incr(_x81))))) → active#(head(s(active(s(active(incr(mark(_x81))))))))mark#(head(s(s(incr(odds))))) → active#(head(active(s(active(s(active(incr(active(odds)))))))))
mark#(head(incr(odds))) → active#(head(active(incr(mark(incr(pairs))))))mark#(head(incr(nats))) → active#(head(active(incr(active(nats)))))
mark#(head(incr(pairs))) → active#(head(active(incr(mark(cons(0, incr(odds)))))))mark#(head(incr(odds))) → active#(head(incr(active(odds))))
mark#(head(incr(cons(_x61, active(_x52))))) → active#(head(incr(cons(mark(_x61), _x52))))mark#(head(incr(0))) → active#(head(active(incr(active(0)))))
mark#(head(s(s(_x71)))) → active#(head(active(s(active(s(_x71))))))active#(tail(cons(X, XS))) → mark#(XS)
mark#(head(tail(incr(_x61)))) → active#(head(active(tail(active(incr(mark(_x61)))))))mark#(head(s(nats))) → active#(head(active(s(mark(cons(0, incr(nats)))))))
mark#(head(incr(cons(_x61, mark(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(active(cons(active(pairs), _x62))))))
mark#(head(s(s(incr(_x91))))) → active#(head(active(s(active(s(active(incr(_x91))))))))mark#(cons(pairs, X2)) → active#(cons(active(pairs), X2))
mark#(odds) → active#(odds)mark#(head(s(s(incr(incr(_x101)))))) → active#(head(active(s(active(s(active(incr(active(incr(mark(_x101)))))))))))
mark#(head(s(_x31))) → active#(head(s(mark(_x31))))mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(cons(active(nats), _x62)))))
mark#(head(tail(tail(_x61)))) → active#(head(active(tail(active(tail(mark(_x61)))))))mark#(head(s(s(0)))) → active#(head(active(s(active(s(active(0)))))))
mark#(head(s(s(tail(_x81))))) → active#(head(active(s(active(s(active(tail(mark(_x81)))))))))mark#(cons(_x21, _x22)) → active#(cons(_x21, _x22))
mark#(head(s(s(incr(_x81))))) → active#(head(active(s(active(s(incr(mark(_x81))))))))mark#(head(odds)) → active#(head(active(odds)))
mark#(head(s(odds))) → active#(head(active(s(active(odds)))))

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, pairs, s, active, mark, incr, head, odds, tail, cons

Strategy

The right-hand side of the rule mark#(head(incr(cons(_x61, active(mark(_x72)))))) → active#(head(active(incr(cons(mark(_x61), _x72))))) 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
active#(head(active(incr(cons(active(odds), _x72))))) 
active#(head(incr(cons(mark(_x61), _x72)))) 
active#(head(mark(cons(s(mark(_x61)), incr(_x31))))) 
active#(head(active(incr(cons(mark(_x61), _x52))))) 
active#(head(active(incr(cons(active(0), _x72))))) 
active#(head(active(incr(cons(active(tail(mark(_x71))), _x72))))) 
active#(head(active(incr(cons(active(incr(mark(_x71))), _x72))))) 
active#(head(active(incr(cons(active(s(mark(_x71))), _x72))))) 
active#(head(active(incr(cons(active(head(mark(_x71))), _x72))))) 
active#(head(active(incr(cons(active(nats), _x72))))) 
active#(head(active(incr(cons(active(cons(mark(_x71), _x72)), _x72))))) 
active#(head(active(incr(cons(active(pairs), _x72))))) 
active#(head(active(incr(cons(_x51, _x52))))) 
Thus, the rule mark#(head(incr(cons(_x61, active(mark(_x72)))))) → active#(head(active(incr(cons(mark(_x61), _x72))))) is replaced by the following rules:
mark#(head(incr(cons(incr(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(incr(mark(_x71))), _x72)))))mark#(head(incr(cons(odds, active(mark(_x72)))))) → active#(head(active(incr(cons(active(odds), _x72)))))
mark#(head(incr(cons(_x61, active(mark(mark(_x52))))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))mark#(head(incr(cons(cons(_x71, _x72), active(mark(_x72)))))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x72)), _x72)))))
mark#(head(incr(cons(head(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(head(mark(_x71))), _x72)))))mark#(head(incr(cons(nats, active(mark(_x72)))))) → active#(head(active(incr(cons(active(nats), _x72)))))
mark#(head(incr(cons(_x61, active(mark(_x72)))))) → active#(head(incr(cons(mark(_x61), _x72))))mark#(head(incr(cons(pairs, active(mark(_x72)))))) → active#(head(active(incr(cons(active(pairs), _x72)))))
mark#(head(incr(cons(_x61, active(mark(_x31)))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))mark#(head(incr(cons(_x51, active(mark(_x52)))))) → active#(head(active(incr(cons(_x51, _x52)))))
mark#(head(incr(cons(tail(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(tail(mark(_x71))), _x72)))))mark#(head(incr(cons(_x61, active(mark(active(_x52))))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))
mark#(head(incr(cons(s(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(s(mark(_x71))), _x72)))))mark#(head(incr(cons(0, active(mark(_x72)))))) → active#(head(active(incr(cons(active(0), _x72)))))

Problem 26: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(pairs) → active#(pairs)active#(pairs) → mark#(cons(0, incr(odds)))
mark#(head(incr(_x31))) → active#(head(incr(mark(_x31))))mark#(head(s(incr(_x61)))) → active#(head(active(s(active(incr(mark(_x61)))))))
mark#(head(incr(cons(_x61, active(mark(active(_x52))))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))mark#(head(head(_x31))) → active#(head(active(head(mark(_x31)))))
mark#(head(incr(cons(tail(_x71), _x62)))) → active#(head(active(incr(cons(active(tail(mark(_x71))), _x62)))))mark#(head(s(cons(_x61, _x62)))) → active#(head(active(s(active(cons(mark(_x61), _x62))))))
mark#(head(s(s(incr(pairs))))) → active#(head(active(s(active(s(active(incr(active(pairs)))))))))mark#(head(s(s(incr(nats))))) → active#(head(active(s(active(s(active(incr(active(nats)))))))))
mark#(s(X)) → mark#(X)mark#(head(incr(cons(cons(_x71, _x72), _x62)))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x72)), _x62)))))
mark#(head(incr(cons(_x61, mark(_x52))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(cons(active(odds), _x62)))))
mark#(head(incr(tail(_x61)))) → active#(head(active(incr(active(tail(mark(_x61)))))))mark#(head(s(s(head(_x81))))) → active#(head(active(s(active(s(active(head(mark(_x81)))))))))
mark#(head(s(s(incr(_x81))))) → active#(head(active(s(s(active(incr(mark(_x81))))))))mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(mark(cons(0, incr(odds)))))))))
mark#(head(tail(0))) → active#(head(active(tail(active(0)))))mark#(head(s(s(incr(s(_x101)))))) → active#(head(active(s(active(s(active(incr(active(s(mark(_x101)))))))))))
mark#(head(cons(_x31, _x32))) → active#(head(active(cons(mark(_x31), _x32))))active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))
mark#(head(incr(cons(_x61, active(mark(mark(_x52))))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))mark#(head(s(s(s(_x81))))) → active#(head(active(s(active(s(active(s(mark(_x81)))))))))
mark#(cons(X1, X2)) → mark#(X1)mark#(head(s(s(cons(_x81, _x82))))) → active#(head(active(s(active(s(active(cons(mark(_x81), _x82))))))))
mark#(head(s(0))) → active#(head(active(s(active(0)))))mark#(head(incr(cons(tail(_x81), active(_x52))))) → active#(head(active(incr(cons(active(tail(mark(_x81))), _x52)))))
mark#(head(s(s(incr(cons(_x101, _x102)))))) → active#(head(active(s(active(s(active(incr(active(cons(mark(_x101), _x102))))))))))mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(active(cons(active(nats), _x62))))))
mark#(cons(0, X2)) → active#(cons(active(0), X2))mark#(head(incr(pairs))) → active#(head(active(incr(pairs))))
mark#(head(incr(cons(pairs, active(mark(_x72)))))) → active#(head(active(incr(cons(active(pairs), _x72)))))mark#(head(incr(cons(_x51, active(mark(_x52)))))) → active#(head(active(incr(cons(_x51, _x52)))))
mark#(head(incr(cons(incr(_x81), active(_x52))))) → active#(head(active(incr(cons(active(incr(mark(_x81))), _x52)))))mark#(head(incr(pairs))) → active#(head(incr(pairs)))
mark#(head(s(tail(_x61)))) → active#(head(active(s(active(tail(mark(_x61)))))))mark#(tail(X)) → mark#(X)
mark#(head(incr(cons(s(_x71), _x62)))) → active#(head(active(incr(cons(active(s(mark(_x71))), _x62)))))mark#(head(tail(_x31))) → active#(head(tail(mark(_x31))))
mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(cons(active(pairs), _x62)))))active#(odds) → mark#(incr(pairs))
mark#(head(s(s(odds)))) → active#(head(active(s(s(active(odds))))))mark#(head(incr(incr(_x61)))) → active#(head(active(incr(active(incr(mark(_x61)))))))
mark#(head(s(s(_x61)))) → active#(head(active(s(s(mark(_x61))))))mark#(head(incr(cons(incr(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(incr(mark(_x71))), _x72)))))
mark#(head(incr(cons(cons(_x81, _x82), _x62)))) → active#(head(active(incr(active(cons(active(cons(mark(_x81), _x82)), _x62))))))mark#(head(incr(cons(head(_x81), _x62)))) → active#(head(active(incr(active(cons(active(head(mark(_x81))), _x62))))))
mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(cons(active(0), _x62)))))mark#(head(incr(cons(cons(_x71, _x72), active(mark(_x72)))))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x72)), _x72)))))
mark#(head(incr(cons(head(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(head(mark(_x71))), _x72)))))mark#(head(s(head(_x61)))) → active#(head(active(s(active(head(mark(_x61)))))))
mark#(head(incr(cons(_x71, active(_x72))))) → active#(head(active(incr(cons(_x71, _x72)))))mark#(head(X)) → mark#(X)
mark#(head(incr(cons(s(_x81), _x62)))) → active#(head(active(incr(active(cons(active(s(mark(_x81))), _x62))))))mark#(head(s(s(_x61)))) → active#(head(s(active(s(mark(_x61))))))
mark#(head(s(s(odds)))) → active#(head(active(s(active(s(mark(incr(pairs))))))))mark#(head(tail(nats))) → active#(head(active(tail(active(nats)))))
active#(nats) → mark#(cons(0, incr(nats)))mark#(0) → active#(0)
mark#(s(X)) → active#(s(mark(X)))mark#(nats) → active#(nats)
mark#(head(incr(cons(_x51, _x52)))) → active#(head(active(incr(cons(_x51, _x52)))))mark#(head(s(s(pairs)))) → active#(head(s(active(s(active(pairs))))))
mark#(head(s(nats))) → active#(head(active(s(nats))))mark#(head(incr(head(_x61)))) → active#(head(active(incr(active(head(mark(_x61)))))))
mark#(head(tail(cons(_x61, _x62)))) → active#(head(active(tail(active(cons(mark(_x61), _x62))))))mark#(head(incr(cons(_x61, active(_x31))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))
mark#(incr(X)) → mark#(X)mark#(head(incr(cons(_x61, active(mark(_x31)))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))
mark#(head(incr(cons(tail(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(tail(mark(_x71))), _x72)))))mark#(head(pairs)) → active#(head(active(pairs)))
mark#(head(incr(cons(_x61, active(active(_x72)))))) → active#(head(active(incr(cons(mark(_x61), _x72)))))mark#(head(s(s(incr(head(_x101)))))) → active#(head(active(s(active(s(active(incr(active(head(mark(_x101)))))))))))
mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(active(cons(active(0), _x62))))))mark#(head(incr(cons(head(_x71), _x62)))) → active#(head(active(incr(cons(active(head(mark(_x71))), _x62)))))
active#(head(cons(X, XS))) → mark#(X)mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(cons(mark(_x61), _x62))))
mark#(head(incr(cons(0, active(mark(_x72)))))) → active#(head(active(incr(cons(active(0), _x72)))))mark#(head(tail(pairs))) → active#(head(active(tail(active(pairs)))))
mark#(head(incr(odds))) → active#(head(active(incr(odds))))mark#(head(incr(cons(incr(_x71), _x62)))) → active#(head(active(incr(cons(active(incr(mark(_x71))), _x62)))))
mark#(head(s(s(incr(tail(_x101)))))) → active#(head(active(s(active(s(active(incr(active(tail(mark(_x101)))))))))))mark#(head(incr(cons(_x61, active(mark(_x72)))))) → active#(head(incr(cons(mark(_x61), _x72))))
mark#(cons(incr(_x31), X2)) → active#(cons(active(incr(mark(_x31))), X2))mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(active(cons(active(odds), _x62))))))
mark#(head(s(pairs))) → active#(head(active(s(active(pairs)))))mark#(tail(X)) → active#(tail(mark(X)))
mark#(head(s(s(odds)))) → active#(head(s(active(s(active(odds))))))mark#(head(incr(cons(cons(_x81, _x82), active(_x52))))) → active#(head(active(incr(cons(active(cons(mark(_x81), _x82)), _x52)))))
mark#(head(s(_x51))) → active#(head(active(s(_x51))))mark#(head(tail(_x51))) → active#(head(active(tail(_x51))))
mark#(head(0)) → active#(head(active(0)))mark#(head(nats)) → active#(head(active(nats)))
mark#(head(_x21)) → active#(head(_x21))mark#(head(incr(cons(incr(_x81), _x62)))) → active#(head(active(incr(active(cons(active(incr(mark(_x81))), _x62))))))
mark#(head(s(s(incr(0))))) → active#(head(active(s(active(s(active(incr(active(0)))))))))mark#(cons(cons(_x31, _x32), X2)) → active#(cons(active(cons(mark(_x31), _x32)), X2))
mark#(head(incr(cons(s(_x81), active(_x52))))) → active#(head(active(incr(cons(active(s(mark(_x81))), _x52)))))mark#(cons(s(_x31), X2)) → active#(cons(active(s(mark(_x31))), X2))
mark#(cons(odds, X2)) → active#(cons(active(odds), X2))mark#(head(s(s(odds)))) → active#(head(active(s(active(s(odds))))))
mark#(cons(nats, X2)) → active#(cons(active(nats), X2))mark#(head(incr(cons(head(_x81), active(_x52))))) → active#(head(active(incr(cons(active(head(mark(_x81))), _x52)))))
mark#(incr(X)) → active#(incr(mark(X)))mark#(head(incr(pairs))) → active#(head(incr(mark(cons(0, incr(odds))))))
mark#(head(tail(odds))) → active#(head(active(tail(active(odds)))))mark#(head(incr(cons(_x61, active(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))
mark#(head(incr(cons(nats, active(_x52))))) → active#(head(active(incr(cons(active(nats), _x52)))))mark#(head(incr(cons(0, active(_x52))))) → active#(head(active(incr(cons(active(0), _x52)))))
mark#(cons(X1, active(_x22))) → active#(cons(mark(X1), _x22))mark#(head(incr(cons(tail(_x81), _x62)))) → active#(head(active(incr(active(cons(active(tail(mark(_x81))), _x62))))))
mark#(head(incr(cons(odds, active(_x52))))) → active#(head(active(incr(cons(active(odds), _x52)))))mark#(head(incr(cons(_x71, _x72)))) → active#(head(active(incr(active(cons(_x71, _x72))))))
mark#(cons(head(_x31), X2)) → active#(cons(active(head(mark(_x31))), X2))mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(pairs))))))
mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(active(cons(mark(_x61), _x62)))))mark#(head(incr(_x51))) → active#(head(active(incr(_x51))))
mark#(head(tail(head(_x61)))) → active#(head(active(tail(active(head(mark(_x61)))))))mark#(head(tail(s(_x61)))) → active#(head(active(tail(active(s(mark(_x61)))))))
mark#(head(s(s(pairs)))) → active#(head(active(s(s(active(pairs))))))mark#(cons(tail(_x31), X2)) → active#(cons(active(tail(mark(_x31))), X2))
mark#(head(incr(cons(_x61, _x31)))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))mark#(head(incr(s(_x61)))) → active#(head(active(incr(active(s(mark(_x61)))))))
mark#(head(incr(cons(pairs, active(_x52))))) → active#(head(active(incr(cons(active(pairs), _x52)))))mark#(head(s(nats))) → active#(head(s(active(nats))))
mark#(cons(X1, mark(_x22))) → active#(cons(mark(X1), _x22))mark#(head(s(s(nats)))) → active#(head(active(s(active(s(active(nats)))))))
mark#(head(s(s(incr(odds))))) → active#(head(active(s(active(s(active(incr(active(odds)))))))))mark#(head(s(s(incr(_x81))))) → active#(head(s(active(s(active(incr(mark(_x81))))))))
mark#(head(incr(odds))) → active#(head(active(incr(mark(incr(pairs))))))mark#(head(incr(nats))) → active#(head(active(incr(active(nats)))))
mark#(head(incr(pairs))) → active#(head(active(incr(mark(cons(0, incr(odds)))))))mark#(head(incr(odds))) → active#(head(incr(active(odds))))
mark#(head(incr(cons(s(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(s(mark(_x71))), _x72)))))mark#(head(incr(cons(_x61, active(_x52))))) → active#(head(incr(cons(mark(_x61), _x52))))
mark#(head(s(s(_x71)))) → active#(head(active(s(active(s(_x71))))))mark#(head(incr(0))) → active#(head(active(incr(active(0)))))
active#(tail(cons(X, XS))) → mark#(XS)mark#(head(tail(incr(_x61)))) → active#(head(active(tail(active(incr(mark(_x61)))))))
mark#(head(s(nats))) → active#(head(active(s(mark(cons(0, incr(nats)))))))mark#(head(incr(cons(_x61, mark(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))
mark#(head(incr(cons(odds, active(mark(_x72)))))) → active#(head(active(incr(cons(active(odds), _x72)))))mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(active(cons(active(pairs), _x62))))))
mark#(head(s(s(incr(_x91))))) → active#(head(active(s(active(s(active(incr(_x91))))))))mark#(head(incr(cons(nats, active(mark(_x72)))))) → active#(head(active(incr(cons(active(nats), _x72)))))
mark#(cons(pairs, X2)) → active#(cons(active(pairs), X2))mark#(odds) → active#(odds)
mark#(head(s(s(incr(incr(_x101)))))) → active#(head(active(s(active(s(active(incr(active(incr(mark(_x101)))))))))))mark#(head(s(_x31))) → active#(head(s(mark(_x31))))
mark#(head(tail(tail(_x61)))) → active#(head(active(tail(active(tail(mark(_x61)))))))mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(cons(active(nats), _x62)))))
mark#(head(s(s(0)))) → active#(head(active(s(active(s(active(0)))))))mark#(cons(_x21, _x22)) → active#(cons(_x21, _x22))
mark#(head(s(s(tail(_x81))))) → active#(head(active(s(active(s(active(tail(mark(_x81)))))))))mark#(head(odds)) → active#(head(active(odds)))
mark#(head(s(s(incr(_x81))))) → active#(head(active(s(active(s(incr(mark(_x81))))))))mark#(head(s(odds))) → active#(head(active(s(active(odds)))))

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, s, pairs, active, mark, incr, head, tail, odds, cons

Strategy

The right-hand side of the rule mark#(head(s(incr(_x61)))) → active#(head(active(s(active(incr(mark(_x61))))))) 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
active#(head(active(s(active(incr(active(odds))))))) 
active#(head(active(s(active(incr(active(tail(mark(_x81))))))))) 
active#(head(s(active(incr(mark(_x61)))))) 
active#(head(active(s(active(incr(active(pairs))))))) 
active#(head(active(s(active(incr(active(incr(mark(_x81))))))))) 
active#(head(active(s(active(incr(active(head(mark(_x81))))))))) 
active#(head(active(s(incr(mark(_x61)))))) 
active#(head(active(s(active(incr(active(s(mark(_x81))))))))) 
active#(head(active(s(active(incr(active(nats))))))) 
active#(head(active(s(active(incr(active(0))))))) 
active#(head(active(s(active(incr(active(cons(mark(_x81), _x82)))))))) 
active#(head(active(s(active(incr(_x71)))))) 
Thus, the rule mark#(head(s(incr(_x61)))) → active#(head(active(s(active(incr(mark(_x61))))))) is replaced by the following rules:
mark#(head(s(incr(0)))) → active#(head(active(s(active(incr(active(0)))))))mark#(head(s(incr(tail(_x81))))) → active#(head(active(s(active(incr(active(tail(mark(_x81)))))))))
mark#(head(s(incr(odds)))) → active#(head(active(s(active(incr(active(odds)))))))mark#(head(s(incr(head(_x81))))) → active#(head(active(s(active(incr(active(head(mark(_x81)))))))))
mark#(head(s(incr(cons(_x81, _x82))))) → active#(head(active(s(active(incr(active(cons(mark(_x81), _x82))))))))mark#(head(s(incr(incr(_x81))))) → active#(head(active(s(active(incr(active(incr(mark(_x81)))))))))
mark#(head(s(incr(_x61)))) → active#(head(s(active(incr(mark(_x61))))))mark#(head(s(incr(pairs)))) → active#(head(active(s(active(incr(active(pairs)))))))
mark#(head(s(incr(s(_x81))))) → active#(head(active(s(active(incr(active(s(mark(_x81)))))))))mark#(head(s(incr(nats)))) → active#(head(active(s(active(incr(active(nats)))))))
mark#(head(s(incr(_x61)))) → active#(head(active(s(incr(mark(_x61))))))mark#(head(s(incr(_x71)))) → active#(head(active(s(active(incr(_x71))))))

Problem 27: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(pairs) → active#(pairs)active#(pairs) → mark#(cons(0, incr(odds)))
mark#(head(incr(_x31))) → active#(head(incr(mark(_x31))))mark#(head(incr(cons(_x61, active(mark(active(_x52))))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))
mark#(head(incr(cons(tail(_x71), _x62)))) → active#(head(active(incr(cons(active(tail(mark(_x71))), _x62)))))mark#(head(head(_x31))) → active#(head(active(head(mark(_x31)))))
mark#(head(s(incr(odds)))) → active#(head(active(s(active(incr(active(odds)))))))mark#(head(s(cons(_x61, _x62)))) → active#(head(active(s(active(cons(mark(_x61), _x62))))))
mark#(head(s(s(incr(pairs))))) → active#(head(active(s(active(s(active(incr(active(pairs)))))))))mark#(head(incr(cons(cons(_x71, _x72), _x62)))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x72)), _x62)))))
mark#(s(X)) → mark#(X)mark#(head(s(s(incr(nats))))) → active#(head(active(s(active(s(active(incr(active(nats)))))))))
mark#(head(s(incr(s(_x81))))) → active#(head(active(s(active(incr(active(s(mark(_x81)))))))))mark#(head(incr(cons(_x61, mark(_x52))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))
mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(cons(active(odds), _x62)))))mark#(head(incr(tail(_x61)))) → active#(head(active(incr(active(tail(mark(_x61)))))))
mark#(head(s(s(head(_x81))))) → active#(head(active(s(active(s(active(head(mark(_x81)))))))))mark#(head(s(s(incr(_x81))))) → active#(head(active(s(s(active(incr(mark(_x81))))))))
mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(mark(cons(0, incr(odds)))))))))mark#(head(tail(0))) → active#(head(active(tail(active(0)))))
mark#(head(s(s(incr(s(_x101)))))) → active#(head(active(s(active(s(active(incr(active(s(mark(_x101)))))))))))mark#(head(cons(_x31, _x32))) → active#(head(active(cons(mark(_x31), _x32))))
active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))mark#(head(incr(cons(_x61, active(mark(mark(_x52))))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))
mark#(head(s(s(s(_x81))))) → active#(head(active(s(active(s(active(s(mark(_x81)))))))))mark#(cons(X1, X2)) → mark#(X1)
mark#(head(s(s(cons(_x81, _x82))))) → active#(head(active(s(active(s(active(cons(mark(_x81), _x82))))))))mark#(head(s(0))) → active#(head(active(s(active(0)))))
mark#(head(incr(cons(tail(_x81), active(_x52))))) → active#(head(active(incr(cons(active(tail(mark(_x81))), _x52)))))mark#(head(s(s(incr(cons(_x101, _x102)))))) → active#(head(active(s(active(s(active(incr(active(cons(mark(_x101), _x102))))))))))
mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(active(cons(active(nats), _x62))))))mark#(head(incr(pairs))) → active#(head(active(incr(pairs))))
mark#(cons(0, X2)) → active#(cons(active(0), X2))mark#(head(incr(cons(_x51, active(mark(_x52)))))) → active#(head(active(incr(cons(_x51, _x52)))))
mark#(head(incr(cons(pairs, active(mark(_x72)))))) → active#(head(active(incr(cons(active(pairs), _x72)))))mark#(head(incr(cons(incr(_x81), active(_x52))))) → active#(head(active(incr(cons(active(incr(mark(_x81))), _x52)))))
mark#(head(incr(cons(s(_x71), _x62)))) → active#(head(active(incr(cons(active(s(mark(_x71))), _x62)))))mark#(tail(X)) → mark#(X)
mark#(head(s(tail(_x61)))) → active#(head(active(s(active(tail(mark(_x61)))))))mark#(head(incr(pairs))) → active#(head(incr(pairs)))
mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(cons(active(pairs), _x62)))))mark#(head(tail(_x31))) → active#(head(tail(mark(_x31))))
mark#(head(s(incr(cons(_x81, _x82))))) → active#(head(active(s(active(incr(active(cons(mark(_x81), _x82))))))))active#(odds) → mark#(incr(pairs))
mark#(head(s(s(odds)))) → active#(head(active(s(s(active(odds))))))mark#(head(s(s(_x61)))) → active#(head(active(s(s(mark(_x61))))))
mark#(head(incr(incr(_x61)))) → active#(head(active(incr(active(incr(mark(_x61)))))))mark#(head(incr(cons(incr(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(incr(mark(_x71))), _x72)))))
mark#(head(s(incr(tail(_x81))))) → active#(head(active(s(active(incr(active(tail(mark(_x81)))))))))mark#(head(incr(cons(cons(_x81, _x82), _x62)))) → active#(head(active(incr(active(cons(active(cons(mark(_x81), _x82)), _x62))))))
mark#(head(incr(cons(head(_x81), _x62)))) → active#(head(active(incr(active(cons(active(head(mark(_x81))), _x62))))))mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(cons(active(0), _x62)))))
mark#(head(incr(cons(cons(_x71, _x72), active(mark(_x72)))))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x72)), _x72)))))mark#(head(incr(cons(head(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(head(mark(_x71))), _x72)))))
mark#(head(s(head(_x61)))) → active#(head(active(s(active(head(mark(_x61)))))))mark#(head(incr(cons(_x71, active(_x72))))) → active#(head(active(incr(cons(_x71, _x72)))))
mark#(head(X)) → mark#(X)mark#(head(incr(cons(s(_x81), _x62)))) → active#(head(active(incr(active(cons(active(s(mark(_x81))), _x62))))))
mark#(head(s(s(_x61)))) → active#(head(s(active(s(mark(_x61))))))mark#(head(s(s(odds)))) → active#(head(active(s(active(s(mark(incr(pairs))))))))
mark#(head(tail(nats))) → active#(head(active(tail(active(nats)))))active#(nats) → mark#(cons(0, incr(nats)))
mark#(0) → active#(0)mark#(s(X)) → active#(s(mark(X)))
mark#(nats) → active#(nats)mark#(head(incr(cons(_x51, _x52)))) → active#(head(active(incr(cons(_x51, _x52)))))
mark#(head(s(s(pairs)))) → active#(head(s(active(s(active(pairs))))))mark#(head(s(nats))) → active#(head(active(s(nats))))
mark#(head(incr(head(_x61)))) → active#(head(active(incr(active(head(mark(_x61)))))))mark#(head(tail(cons(_x61, _x62)))) → active#(head(active(tail(active(cons(mark(_x61), _x62))))))
mark#(head(incr(cons(_x61, active(_x31))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))mark#(incr(X)) → mark#(X)
mark#(head(s(incr(nats)))) → active#(head(active(s(active(incr(active(nats)))))))mark#(head(incr(cons(_x61, active(mark(_x31)))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))
mark#(head(incr(cons(tail(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(tail(mark(_x71))), _x72)))))mark#(head(pairs)) → active#(head(active(pairs)))
mark#(head(incr(cons(_x61, active(active(_x72)))))) → active#(head(active(incr(cons(mark(_x61), _x72)))))mark#(head(s(s(incr(head(_x101)))))) → active#(head(active(s(active(s(active(incr(active(head(mark(_x101)))))))))))
mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(active(cons(active(0), _x62))))))mark#(head(incr(cons(head(_x71), _x62)))) → active#(head(active(incr(cons(active(head(mark(_x71))), _x62)))))
active#(head(cons(X, XS))) → mark#(X)mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(cons(mark(_x61), _x62))))
mark#(head(incr(cons(0, active(mark(_x72)))))) → active#(head(active(incr(cons(active(0), _x72)))))mark#(head(tail(pairs))) → active#(head(active(tail(active(pairs)))))
mark#(head(incr(odds))) → active#(head(active(incr(odds))))mark#(head(incr(cons(incr(_x71), _x62)))) → active#(head(active(incr(cons(active(incr(mark(_x71))), _x62)))))
mark#(head(s(s(incr(tail(_x101)))))) → active#(head(active(s(active(s(active(incr(active(tail(mark(_x101)))))))))))mark#(head(s(incr(incr(_x81))))) → active#(head(active(s(active(incr(active(incr(mark(_x81)))))))))
mark#(head(incr(cons(_x61, active(mark(_x72)))))) → active#(head(incr(cons(mark(_x61), _x72))))mark#(head(s(incr(_x71)))) → active#(head(active(s(active(incr(_x71))))))
mark#(cons(incr(_x31), X2)) → active#(cons(active(incr(mark(_x31))), X2))mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(active(cons(active(odds), _x62))))))
mark#(head(s(pairs))) → active#(head(active(s(active(pairs)))))mark#(tail(X)) → active#(tail(mark(X)))
mark#(head(s(s(odds)))) → active#(head(s(active(s(active(odds))))))mark#(head(tail(_x51))) → active#(head(active(tail(_x51))))
mark#(head(incr(cons(cons(_x81, _x82), active(_x52))))) → active#(head(active(incr(cons(active(cons(mark(_x81), _x82)), _x52)))))mark#(head(s(_x51))) → active#(head(active(s(_x51))))
mark#(head(0)) → active#(head(active(0)))mark#(head(_x21)) → active#(head(_x21))
mark#(head(nats)) → active#(head(active(nats)))mark#(head(incr(cons(incr(_x81), _x62)))) → active#(head(active(incr(active(cons(active(incr(mark(_x81))), _x62))))))
mark#(head(s(s(incr(0))))) → active#(head(active(s(active(s(active(incr(active(0)))))))))mark#(cons(cons(_x31, _x32), X2)) → active#(cons(active(cons(mark(_x31), _x32)), X2))
mark#(head(incr(cons(s(_x81), active(_x52))))) → active#(head(active(incr(cons(active(s(mark(_x81))), _x52)))))mark#(cons(s(_x31), X2)) → active#(cons(active(s(mark(_x31))), X2))
mark#(cons(odds, X2)) → active#(cons(active(odds), X2))mark#(head(s(s(odds)))) → active#(head(active(s(active(s(odds))))))
mark#(cons(nats, X2)) → active#(cons(active(nats), X2))mark#(head(incr(cons(head(_x81), active(_x52))))) → active#(head(active(incr(cons(active(head(mark(_x81))), _x52)))))
mark#(head(incr(pairs))) → active#(head(incr(mark(cons(0, incr(odds))))))mark#(incr(X)) → active#(incr(mark(X)))
mark#(head(tail(odds))) → active#(head(active(tail(active(odds)))))mark#(head(incr(cons(_x61, active(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))
mark#(head(incr(cons(nats, active(_x52))))) → active#(head(active(incr(cons(active(nats), _x52)))))mark#(head(incr(cons(tail(_x81), _x62)))) → active#(head(active(incr(active(cons(active(tail(mark(_x81))), _x62))))))
mark#(cons(X1, active(_x22))) → active#(cons(mark(X1), _x22))mark#(head(incr(cons(0, active(_x52))))) → active#(head(active(incr(cons(active(0), _x52)))))
mark#(head(s(incr(0)))) → active#(head(active(s(active(incr(active(0)))))))mark#(head(incr(cons(odds, active(_x52))))) → active#(head(active(incr(cons(active(odds), _x52)))))
mark#(head(incr(cons(_x71, _x72)))) → active#(head(active(incr(active(cons(_x71, _x72))))))mark#(cons(head(_x31), X2)) → active#(cons(active(head(mark(_x31))), X2))
mark#(head(s(incr(pairs)))) → active#(head(active(s(active(incr(active(pairs)))))))mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(pairs))))))
mark#(head(incr(_x51))) → active#(head(active(incr(_x51))))mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(active(cons(mark(_x61), _x62)))))
mark#(head(tail(head(_x61)))) → active#(head(active(tail(active(head(mark(_x61)))))))mark#(head(s(s(pairs)))) → active#(head(active(s(s(active(pairs))))))
mark#(head(tail(s(_x61)))) → active#(head(active(tail(active(s(mark(_x61)))))))mark#(head(incr(cons(_x61, _x31)))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))
mark#(cons(tail(_x31), X2)) → active#(cons(active(tail(mark(_x31))), X2))mark#(head(incr(s(_x61)))) → active#(head(active(incr(active(s(mark(_x61)))))))
mark#(head(incr(cons(pairs, active(_x52))))) → active#(head(active(incr(cons(active(pairs), _x52)))))mark#(head(s(nats))) → active#(head(s(active(nats))))
mark#(head(s(s(nats)))) → active#(head(active(s(active(s(active(nats)))))))mark#(cons(X1, mark(_x22))) → active#(cons(mark(X1), _x22))
mark#(head(s(s(incr(_x81))))) → active#(head(s(active(s(active(incr(mark(_x81))))))))mark#(head(s(s(incr(odds))))) → active#(head(active(s(active(s(active(incr(active(odds)))))))))
mark#(head(incr(odds))) → active#(head(active(incr(mark(incr(pairs))))))mark#(head(incr(nats))) → active#(head(active(incr(active(nats)))))
mark#(head(s(incr(head(_x81))))) → active#(head(active(s(active(incr(active(head(mark(_x81)))))))))mark#(head(incr(pairs))) → active#(head(active(incr(mark(cons(0, incr(odds)))))))
mark#(head(incr(cons(s(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(s(mark(_x71))), _x72)))))mark#(head(incr(odds))) → active#(head(incr(active(odds))))
mark#(head(incr(cons(_x61, active(_x52))))) → active#(head(incr(cons(mark(_x61), _x52))))mark#(head(incr(0))) → active#(head(active(incr(active(0)))))
mark#(head(s(s(_x71)))) → active#(head(active(s(active(s(_x71))))))active#(tail(cons(X, XS))) → mark#(XS)
mark#(head(tail(incr(_x61)))) → active#(head(active(tail(active(incr(mark(_x61)))))))mark#(head(s(nats))) → active#(head(active(s(mark(cons(0, incr(nats)))))))
mark#(head(incr(cons(odds, active(mark(_x72)))))) → active#(head(active(incr(cons(active(odds), _x72)))))mark#(head(incr(cons(_x61, mark(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))
mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(active(cons(active(pairs), _x62))))))mark#(head(incr(cons(nats, active(mark(_x72)))))) → active#(head(active(incr(cons(active(nats), _x72)))))
mark#(head(s(s(incr(_x91))))) → active#(head(active(s(active(s(active(incr(_x91))))))))mark#(cons(pairs, X2)) → active#(cons(active(pairs), X2))
mark#(odds) → active#(odds)mark#(head(s(s(incr(incr(_x101)))))) → active#(head(active(s(active(s(active(incr(active(incr(mark(_x101)))))))))))
mark#(head(s(_x31))) → active#(head(s(mark(_x31))))mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(cons(active(nats), _x62)))))
mark#(head(tail(tail(_x61)))) → active#(head(active(tail(active(tail(mark(_x61)))))))mark#(head(s(incr(_x61)))) → active#(head(s(active(incr(mark(_x61))))))
mark#(head(s(s(0)))) → active#(head(active(s(active(s(active(0)))))))mark#(head(s(s(tail(_x81))))) → active#(head(active(s(active(s(active(tail(mark(_x81)))))))))
mark#(cons(_x21, _x22)) → active#(cons(_x21, _x22))mark#(head(s(s(incr(_x81))))) → active#(head(active(s(active(s(incr(mark(_x81))))))))
mark#(head(odds)) → active#(head(active(odds)))mark#(head(s(odds))) → active#(head(active(s(active(odds)))))
mark#(head(s(incr(_x61)))) → active#(head(active(s(incr(mark(_x61))))))

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, pairs, s, active, mark, incr, head, odds, tail, cons

Strategy

The right-hand side of the rule mark#(head(incr(_x31))) → active#(head(incr(mark(_x31)))) 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
active#(head(incr(active(cons(mark(_x51), _x52))))) 
active#(head(incr(active(odds)))) 
active#(head(incr(active(nats)))) 
active#(head(incr(active(incr(mark(_x51)))))) 
active#(head(incr(_x41))) 
active#(head(incr(active(s(mark(_x51)))))) 
active#(head(incr(active(head(mark(_x51)))))) 
active#(head(incr(active(0)))) 
active#(head(incr(active(tail(mark(_x51)))))) 
active#(head(incr(active(pairs)))) 
Thus, the rule mark#(head(incr(_x31))) → active#(head(incr(mark(_x31)))) is replaced by the following rules:
mark#(head(incr(incr(_x51)))) → active#(head(incr(active(incr(mark(_x51))))))mark#(head(incr(pairs))) → active#(head(incr(active(pairs))))
mark#(head(incr(cons(_x51, _x52)))) → active#(head(incr(active(cons(mark(_x51), _x52)))))mark#(head(incr(tail(_x51)))) → active#(head(incr(active(tail(mark(_x51))))))
mark#(head(incr(_x41))) → active#(head(incr(_x41)))mark#(head(incr(head(_x51)))) → active#(head(incr(active(head(mark(_x51))))))
mark#(head(incr(odds))) → active#(head(incr(active(odds))))mark#(head(incr(s(_x51)))) → active#(head(incr(active(s(mark(_x51))))))
mark#(head(incr(0))) → active#(head(incr(active(0))))mark#(head(incr(nats))) → active#(head(incr(active(nats))))

Problem 28: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(head(incr(pairs))) → active#(head(incr(active(pairs))))mark#(pairs) → active#(pairs)
active#(pairs) → mark#(cons(0, incr(odds)))mark#(head(incr(incr(_x51)))) → active#(head(incr(active(incr(mark(_x51))))))
mark#(head(incr(cons(_x61, active(mark(active(_x52))))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))mark#(head(s(incr(odds)))) → active#(head(active(s(active(incr(active(odds)))))))
mark#(head(head(_x31))) → active#(head(active(head(mark(_x31)))))mark#(head(incr(cons(tail(_x71), _x62)))) → active#(head(active(incr(cons(active(tail(mark(_x71))), _x62)))))
mark#(head(s(cons(_x61, _x62)))) → active#(head(active(s(active(cons(mark(_x61), _x62))))))mark#(head(s(s(incr(pairs))))) → active#(head(active(s(active(s(active(incr(active(pairs)))))))))
mark#(head(s(s(incr(nats))))) → active#(head(active(s(active(s(active(incr(active(nats)))))))))mark#(s(X)) → mark#(X)
mark#(head(incr(cons(cons(_x71, _x72), _x62)))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x72)), _x62)))))mark#(head(s(incr(s(_x81))))) → active#(head(active(s(active(incr(active(s(mark(_x81)))))))))
mark#(head(incr(cons(_x61, mark(_x52))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(cons(active(odds), _x62)))))
mark#(head(incr(tail(_x61)))) → active#(head(active(incr(active(tail(mark(_x61)))))))mark#(head(s(s(head(_x81))))) → active#(head(active(s(active(s(active(head(mark(_x81)))))))))
mark#(head(s(s(incr(_x81))))) → active#(head(active(s(s(active(incr(mark(_x81))))))))mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(mark(cons(0, incr(odds)))))))))
mark#(head(tail(0))) → active#(head(active(tail(active(0)))))mark#(head(s(s(incr(s(_x101)))))) → active#(head(active(s(active(s(active(incr(active(s(mark(_x101)))))))))))
mark#(head(cons(_x31, _x32))) → active#(head(active(cons(mark(_x31), _x32))))active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))
mark#(head(s(s(s(_x81))))) → active#(head(active(s(active(s(active(s(mark(_x81)))))))))mark#(head(incr(cons(_x61, active(mark(mark(_x52))))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))
mark#(cons(X1, X2)) → mark#(X1)mark#(head(s(s(cons(_x81, _x82))))) → active#(head(active(s(active(s(active(cons(mark(_x81), _x82))))))))
mark#(head(s(0))) → active#(head(active(s(active(0)))))mark#(head(incr(cons(tail(_x81), active(_x52))))) → active#(head(active(incr(cons(active(tail(mark(_x81))), _x52)))))
mark#(head(s(s(incr(cons(_x101, _x102)))))) → active#(head(active(s(active(s(active(incr(active(cons(mark(_x101), _x102))))))))))mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(active(cons(active(nats), _x62))))))
mark#(cons(0, X2)) → active#(cons(active(0), X2))mark#(head(incr(pairs))) → active#(head(active(incr(pairs))))
mark#(head(incr(cons(pairs, active(mark(_x72)))))) → active#(head(active(incr(cons(active(pairs), _x72)))))mark#(head(incr(cons(_x51, active(mark(_x52)))))) → active#(head(active(incr(cons(_x51, _x52)))))
mark#(head(incr(cons(incr(_x81), active(_x52))))) → active#(head(active(incr(cons(active(incr(mark(_x81))), _x52)))))mark#(head(incr(pairs))) → active#(head(incr(pairs)))
mark#(head(s(tail(_x61)))) → active#(head(active(s(active(tail(mark(_x61)))))))mark#(tail(X)) → mark#(X)
mark#(head(incr(cons(s(_x71), _x62)))) → active#(head(active(incr(cons(active(s(mark(_x71))), _x62)))))mark#(head(s(incr(cons(_x81, _x82))))) → active#(head(active(s(active(incr(active(cons(mark(_x81), _x82))))))))
mark#(head(tail(_x31))) → active#(head(tail(mark(_x31))))mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(cons(active(pairs), _x62)))))
mark#(head(incr(head(_x51)))) → active#(head(incr(active(head(mark(_x51))))))active#(odds) → mark#(incr(pairs))
mark#(head(s(s(odds)))) → active#(head(active(s(s(active(odds))))))mark#(head(incr(incr(_x61)))) → active#(head(active(incr(active(incr(mark(_x61)))))))
mark#(head(s(s(_x61)))) → active#(head(active(s(s(mark(_x61))))))mark#(head(incr(cons(incr(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(incr(mark(_x71))), _x72)))))
mark#(head(s(incr(tail(_x81))))) → active#(head(active(s(active(incr(active(tail(mark(_x81)))))))))mark#(head(incr(cons(cons(_x81, _x82), _x62)))) → active#(head(active(incr(active(cons(active(cons(mark(_x81), _x82)), _x62))))))
mark#(head(incr(cons(head(_x81), _x62)))) → active#(head(active(incr(active(cons(active(head(mark(_x81))), _x62))))))mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(cons(active(0), _x62)))))
mark#(head(incr(cons(cons(_x71, _x72), active(mark(_x72)))))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x72)), _x72)))))mark#(head(incr(cons(head(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(head(mark(_x71))), _x72)))))
mark#(head(s(head(_x61)))) → active#(head(active(s(active(head(mark(_x61)))))))mark#(head(incr(cons(_x71, active(_x72))))) → active#(head(active(incr(cons(_x71, _x72)))))
mark#(head(X)) → mark#(X)mark#(head(incr(cons(s(_x81), _x62)))) → active#(head(active(incr(active(cons(active(s(mark(_x81))), _x62))))))
mark#(head(s(s(_x61)))) → active#(head(s(active(s(mark(_x61))))))mark#(head(s(s(odds)))) → active#(head(active(s(active(s(mark(incr(pairs))))))))
mark#(head(incr(tail(_x51)))) → active#(head(incr(active(tail(mark(_x51))))))mark#(head(tail(nats))) → active#(head(active(tail(active(nats)))))
mark#(head(incr(_x41))) → active#(head(incr(_x41)))active#(nats) → mark#(cons(0, incr(nats)))
mark#(0) → active#(0)mark#(s(X)) → active#(s(mark(X)))
mark#(nats) → active#(nats)mark#(head(incr(cons(_x51, _x52)))) → active#(head(active(incr(cons(_x51, _x52)))))
mark#(head(s(s(pairs)))) → active#(head(s(active(s(active(pairs))))))mark#(head(incr(cons(_x51, _x52)))) → active#(head(incr(active(cons(mark(_x51), _x52)))))
mark#(head(s(nats))) → active#(head(active(s(nats))))mark#(head(incr(head(_x61)))) → active#(head(active(incr(active(head(mark(_x61)))))))
mark#(head(tail(cons(_x61, _x62)))) → active#(head(active(tail(active(cons(mark(_x61), _x62))))))mark#(head(incr(cons(_x61, active(_x31))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))
mark#(incr(X)) → mark#(X)mark#(head(s(incr(nats)))) → active#(head(active(s(active(incr(active(nats)))))))
mark#(head(incr(cons(_x61, active(mark(_x31)))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))mark#(head(incr(cons(tail(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(tail(mark(_x71))), _x72)))))
mark#(head(pairs)) → active#(head(active(pairs)))mark#(head(incr(cons(_x61, active(active(_x72)))))) → active#(head(active(incr(cons(mark(_x61), _x72)))))
mark#(head(s(s(incr(head(_x101)))))) → active#(head(active(s(active(s(active(incr(active(head(mark(_x101)))))))))))mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(active(cons(active(0), _x62))))))
mark#(head(incr(cons(head(_x71), _x62)))) → active#(head(active(incr(cons(active(head(mark(_x71))), _x62)))))active#(head(cons(X, XS))) → mark#(X)
mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(cons(mark(_x61), _x62))))mark#(head(incr(cons(0, active(mark(_x72)))))) → active#(head(active(incr(cons(active(0), _x72)))))
mark#(head(tail(pairs))) → active#(head(active(tail(active(pairs)))))mark#(head(incr(odds))) → active#(head(active(incr(odds))))
mark#(head(incr(cons(incr(_x71), _x62)))) → active#(head(active(incr(cons(active(incr(mark(_x71))), _x62)))))mark#(head(s(s(incr(tail(_x101)))))) → active#(head(active(s(active(s(active(incr(active(tail(mark(_x101)))))))))))
mark#(head(s(incr(incr(_x81))))) → active#(head(active(s(active(incr(active(incr(mark(_x81)))))))))mark#(head(incr(cons(_x61, active(mark(_x72)))))) → active#(head(incr(cons(mark(_x61), _x72))))
mark#(head(s(incr(_x71)))) → active#(head(active(s(active(incr(_x71))))))mark#(cons(incr(_x31), X2)) → active#(cons(active(incr(mark(_x31))), X2))
mark#(tail(X)) → active#(tail(mark(X)))mark#(head(s(pairs))) → active#(head(active(s(active(pairs)))))
mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(active(cons(active(odds), _x62))))))mark#(head(s(s(odds)))) → active#(head(s(active(s(active(odds))))))
mark#(head(s(_x51))) → active#(head(active(s(_x51))))mark#(head(incr(cons(cons(_x81, _x82), active(_x52))))) → active#(head(active(incr(cons(active(cons(mark(_x81), _x82)), _x52)))))
mark#(head(tail(_x51))) → active#(head(active(tail(_x51))))mark#(head(0)) → active#(head(active(0)))
mark#(head(nats)) → active#(head(active(nats)))mark#(head(_x21)) → active#(head(_x21))
mark#(head(incr(cons(incr(_x81), _x62)))) → active#(head(active(incr(active(cons(active(incr(mark(_x81))), _x62))))))mark#(head(incr(s(_x51)))) → active#(head(incr(active(s(mark(_x51))))))
mark#(head(s(s(incr(0))))) → active#(head(active(s(active(s(active(incr(active(0)))))))))mark#(cons(cons(_x31, _x32), X2)) → active#(cons(active(cons(mark(_x31), _x32)), X2))
mark#(head(incr(cons(s(_x81), active(_x52))))) → active#(head(active(incr(cons(active(s(mark(_x81))), _x52)))))mark#(cons(s(_x31), X2)) → active#(cons(active(s(mark(_x31))), X2))
mark#(cons(odds, X2)) → active#(cons(active(odds), X2))mark#(head(s(s(odds)))) → active#(head(active(s(active(s(odds))))))
mark#(cons(nats, X2)) → active#(cons(active(nats), X2))mark#(head(incr(cons(head(_x81), active(_x52))))) → active#(head(active(incr(cons(active(head(mark(_x81))), _x52)))))
mark#(incr(X)) → active#(incr(mark(X)))mark#(head(incr(pairs))) → active#(head(incr(mark(cons(0, incr(odds))))))
mark#(head(tail(odds))) → active#(head(active(tail(active(odds)))))mark#(head(incr(cons(_x61, active(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))
mark#(head(incr(cons(nats, active(_x52))))) → active#(head(active(incr(cons(active(nats), _x52)))))mark#(head(incr(cons(0, active(_x52))))) → active#(head(active(incr(cons(active(0), _x52)))))
mark#(cons(X1, active(_x22))) → active#(cons(mark(X1), _x22))mark#(head(incr(cons(tail(_x81), _x62)))) → active#(head(active(incr(active(cons(active(tail(mark(_x81))), _x62))))))
mark#(head(s(incr(0)))) → active#(head(active(s(active(incr(active(0)))))))mark#(head(incr(cons(odds, active(_x52))))) → active#(head(active(incr(cons(active(odds), _x52)))))
mark#(head(incr(cons(_x71, _x72)))) → active#(head(active(incr(active(cons(_x71, _x72))))))mark#(cons(head(_x31), X2)) → active#(cons(active(head(mark(_x31))), X2))
mark#(head(s(incr(pairs)))) → active#(head(active(s(active(incr(active(pairs)))))))mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(pairs))))))
mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(active(cons(mark(_x61), _x62)))))mark#(head(incr(_x51))) → active#(head(active(incr(_x51))))
mark#(head(incr(0))) → active#(head(incr(active(0))))mark#(head(tail(head(_x61)))) → active#(head(active(tail(active(head(mark(_x61)))))))
mark#(head(tail(s(_x61)))) → active#(head(active(tail(active(s(mark(_x61)))))))mark#(head(s(s(pairs)))) → active#(head(active(s(s(active(pairs))))))
mark#(cons(tail(_x31), X2)) → active#(cons(active(tail(mark(_x31))), X2))mark#(head(incr(cons(_x61, _x31)))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))
mark#(head(incr(s(_x61)))) → active#(head(active(incr(active(s(mark(_x61)))))))mark#(head(incr(cons(pairs, active(_x52))))) → active#(head(active(incr(cons(active(pairs), _x52)))))
mark#(head(s(nats))) → active#(head(s(active(nats))))mark#(cons(X1, mark(_x22))) → active#(cons(mark(X1), _x22))
mark#(head(s(s(nats)))) → active#(head(active(s(active(s(active(nats)))))))mark#(head(s(s(incr(odds))))) → active#(head(active(s(active(s(active(incr(active(odds)))))))))
mark#(head(s(s(incr(_x81))))) → active#(head(s(active(s(active(incr(mark(_x81))))))))mark#(head(incr(odds))) → active#(head(active(incr(mark(incr(pairs))))))
mark#(head(s(incr(head(_x81))))) → active#(head(active(s(active(incr(active(head(mark(_x81)))))))))mark#(head(incr(nats))) → active#(head(active(incr(active(nats)))))
mark#(head(incr(pairs))) → active#(head(active(incr(mark(cons(0, incr(odds)))))))mark#(head(incr(odds))) → active#(head(incr(active(odds))))
mark#(head(incr(cons(s(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(s(mark(_x71))), _x72)))))mark#(head(incr(cons(_x61, active(_x52))))) → active#(head(incr(cons(mark(_x61), _x52))))
mark#(head(s(s(_x71)))) → active#(head(active(s(active(s(_x71))))))mark#(head(incr(0))) → active#(head(active(incr(active(0)))))
active#(tail(cons(X, XS))) → mark#(XS)mark#(head(tail(incr(_x61)))) → active#(head(active(tail(active(incr(mark(_x61)))))))
mark#(head(s(nats))) → active#(head(active(s(mark(cons(0, incr(nats)))))))mark#(head(incr(cons(_x61, mark(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))
mark#(head(incr(cons(odds, active(mark(_x72)))))) → active#(head(active(incr(cons(active(odds), _x72)))))mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(active(cons(active(pairs), _x62))))))
mark#(head(s(s(incr(_x91))))) → active#(head(active(s(active(s(active(incr(_x91))))))))mark#(head(incr(cons(nats, active(mark(_x72)))))) → active#(head(active(incr(cons(active(nats), _x72)))))
mark#(cons(pairs, X2)) → active#(cons(active(pairs), X2))mark#(head(incr(nats))) → active#(head(incr(active(nats))))
mark#(odds) → active#(odds)mark#(head(s(s(incr(incr(_x101)))))) → active#(head(active(s(active(s(active(incr(active(incr(mark(_x101)))))))))))
mark#(head(s(_x31))) → active#(head(s(mark(_x31))))mark#(head(tail(tail(_x61)))) → active#(head(active(tail(active(tail(mark(_x61)))))))
mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(cons(active(nats), _x62)))))mark#(head(s(incr(_x61)))) → active#(head(s(active(incr(mark(_x61))))))
mark#(head(s(s(0)))) → active#(head(active(s(active(s(active(0)))))))mark#(cons(_x21, _x22)) → active#(cons(_x21, _x22))
mark#(head(s(s(tail(_x81))))) → active#(head(active(s(active(s(active(tail(mark(_x81)))))))))mark#(head(odds)) → active#(head(active(odds)))
mark#(head(s(s(incr(_x81))))) → active#(head(active(s(active(s(incr(mark(_x81))))))))mark#(head(s(incr(_x61)))) → active#(head(active(s(incr(mark(_x61))))))
mark#(head(s(odds))) → active#(head(active(s(active(odds)))))

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, s, pairs, active, mark, incr, head, tail, odds, cons

Strategy

The right-hand side of the rule mark#(head(incr(pairs))) → active#(head(incr(active(pairs)))) 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
active#(head(incr(pairs))) 
active#(head(incr(mark(cons(0, incr(odds)))))) 
Thus, the rule mark#(head(incr(pairs))) → active#(head(incr(active(pairs)))) is replaced by the following rules:
mark#(head(incr(pairs))) → active#(head(incr(pairs)))mark#(head(incr(pairs))) → active#(head(incr(mark(cons(0, incr(odds))))))

Problem 29: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(s(X)) → mark#(X)mark#(head(s(s(s(_x81))))) → active#(head(active(s(active(s(active(s(mark(_x81)))))))))
mark#(head(s(incr(s(incr(incr(_x121))))))) → active#(head(s(active(incr(active(s(active(incr(active(incr(mark(_x121))))))))))))mark#(head(incr(cons(tail(cons(_x91, _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(mark(_x91), _x92)))), _x62)))))
mark#(head(s(incr(s(tail(s(0))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(active(0)))))))))))))mark#(head(incr(incr(tail(cons(_x81, _x82)))))) → active#(head(incr(incr(tail(active(cons(mark(_x81), _x82)))))))
mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(active(cons(active(nats), _x62))))))mark#(head(incr(cons(cons(incr(_x91), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(incr(mark(_x91))), _x72)), _x62)))))
mark#(head(incr(cons(pairs, active(mark(_x72)))))) → active#(head(active(incr(cons(active(pairs), _x72)))))mark#(head(incr(incr(tail(odds))))) → active#(head(incr(incr(tail(active(odds))))))
mark#(head(incr(cons(cons(active(_x71), _x72), mark(_x52))))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x52)))))mark#(head(incr(incr(_x51)))) → active#(head(incr(incr(mark(_x51)))))
mark#(head(incr(cons(s(_x71), _x62)))) → active#(head(active(incr(cons(active(s(mark(_x71))), _x62)))))mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(cons(active(pairs), _x62)))))
mark#(head(incr(head(_x51)))) → active#(head(incr(active(head(mark(_x51))))))mark#(head(incr(incr(_x61)))) → active#(head(active(incr(active(incr(mark(_x61)))))))
mark#(head(s(incr(s(incr(tail(incr(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(incr(mark(_x141)))))))))))))))mark#(head(incr(cons(cons(_x71, active(_x72)), _x62)))) → active#(head(incr(cons(active(cons(_x71, _x72)), _x62))))
mark#(head(s(incr(tail(_x81))))) → active#(head(active(s(active(incr(active(tail(mark(_x81)))))))))mark#(head(s(incr(s(incr(incr(_x121))))))) → active#(head(active(s(active(incr(active(s(incr(active(incr(mark(_x121))))))))))))
mark#(head(incr(cons(incr(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(incr(mark(_x71))), _x72)))))mark#(head(s(incr(s(s(_x101)))))) → active#(head(active(s(active(incr(active(s(active(s(mark(_x101)))))))))))
mark#(head(s(incr(s(tail(_x101)))))) → active#(head(active(s(active(incr(s(active(tail(mark(_x101))))))))))mark#(head(incr(cons(cons(_x71, _x72), _x31)))) → active#(head(mark(cons(s(active(cons(mark(_x71), _x72))), incr(_x31)))))
mark#(head(s(s(odds)))) → active#(head(active(s(active(s(mark(incr(pairs))))))))mark#(head(incr(cons(tail(odds), _x62)))) → active#(head(active(incr(cons(active(tail(active(odds))), _x62)))))
mark#(head(s(incr(s(tail(incr(_x121))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(incr(mark(_x121)))))))))))))mark#(head(incr(incr(tail(cons(_x81, mark(_x92))))))) → active#(head(incr(incr(active(tail(active(cons(mark(_x81), _x92))))))))
mark#(head(incr(cons(_x61, mark(active(_x72)))))) → active#(head(active(incr(cons(mark(_x61), _x72)))))mark#(head(incr(cons(_x61, mark(mark(_x72)))))) → active#(head(active(incr(cons(mark(_x61), _x72)))))
mark#(head(incr(cons(_x51, _x52)))) → active#(head(active(incr(cons(_x51, _x52)))))mark#(head(s(incr(s(tail(s(_x121))))))) → active#(head(active(s(active(incr(s(active(tail(active(s(mark(_x121))))))))))))
mark#(head(incr(cons(_x71, mark(_x72))))) → active#(head(active(incr(cons(_x71, _x72)))))mark#(head(tail(cons(_x61, _x62)))) → active#(head(active(tail(active(cons(mark(_x61), _x62))))))
mark#(head(incr(cons(odds, _x52)))) → active#(head(active(incr(cons(odds, _x52)))))mark#(head(s(incr(s(incr(incr(pairs))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(pairs)))))))))))))
mark#(head(s(cons(0, _x62)))) → active#(head(active(s(active(cons(active(0), _x62))))))mark#(head(incr(cons(_x61, active(active(_x72)))))) → active#(head(active(incr(cons(mark(_x61), _x72)))))
mark#(head(s(s(incr(nats))))) → active#(head(s(s(active(incr(active(nats)))))))mark#(head(s(s(incr(head(_x101)))))) → active#(head(active(s(active(s(active(incr(active(head(mark(_x101)))))))))))
mark#(head(incr(cons(odds, _x62)))) → active#(head(incr(cons(mark(incr(pairs)), _x62))))mark#(head(incr(cons(head(_x71), _x62)))) → active#(head(active(incr(cons(active(head(mark(_x71))), _x62)))))
mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(cons(mark(_x61), _x62))))mark#(head(s(incr(s(tail(tail(_x121))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(tail(mark(_x121)))))))))))))
mark#(head(incr(cons(incr(_x71), _x62)))) → active#(head(active(incr(cons(active(incr(mark(_x71))), _x62)))))mark#(head(s(incr(s(tail(cons(_x121, _x122))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(cons(mark(_x121), _x122))))))))))))
mark#(head(s(s(incr(tail(_x101)))))) → active#(head(active(s(active(s(active(incr(active(tail(mark(_x101)))))))))))mark#(head(s(incr(incr(_x81))))) → active#(head(active(s(active(incr(active(incr(mark(_x81)))))))))
mark#(head(incr(cons(incr(_x81), mark(_x52))))) → active#(head(active(incr(cons(active(incr(mark(_x81))), _x52)))))mark#(head(s(incr(s(incr(tail(_x121))))))) → active#(head(active(s(active(incr(active(s(active(incr(tail(mark(_x121))))))))))))
mark#(head(s(pairs))) → active#(head(active(s(active(pairs)))))mark#(tail(X)) → active#(tail(mark(X)))
mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(active(cons(active(odds), _x62))))))mark#(head(cons(_x31, active(_x52)))) → active#(head(active(cons(mark(_x31), _x52))))
mark#(head(incr(incr(tail(pairs))))) → active#(head(incr(active(incr(active(tail(active(pairs))))))))mark#(head(incr(incr(tail(s(_x81)))))) → active#(head(incr(incr(active(tail(active(s(mark(_x81)))))))))
mark#(head(s(incr(s(incr(pairs)))))) → active#(head(active(s(active(incr(active(s(active(incr(active(pairs)))))))))))mark#(head(s(s(incr(nats))))) → active#(head(s(active(s(active(incr(active(nats))))))))
mark#(head(incr(incr(tail(odds))))) → active#(head(incr(active(incr(active(tail(active(odds))))))))mark#(cons(cons(_x31, _x32), X2)) → active#(cons(active(cons(mark(_x31), _x32)), X2))
mark#(head(incr(cons(cons(head(_x91), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(head(mark(_x91))), _x72)), _x62)))))mark#(head(incr(incr(tail(cons(0, _x82)))))) → active#(head(incr(incr(active(tail(cons(active(0), _x82)))))))
mark#(head(s(cons(tail(_x81), _x62)))) → active#(head(active(s(active(cons(active(tail(mark(_x81))), _x62))))))mark#(cons(nats, X2)) → active#(cons(active(nats), X2))
mark#(head(incr(cons(head(_x81), active(_x52))))) → active#(head(active(incr(cons(active(head(mark(_x81))), _x52)))))mark#(head(tail(odds))) → active#(head(active(tail(active(odds)))))
mark#(head(s(incr(s(tail(s(_x121))))))) → active#(head(active(s(incr(active(s(active(tail(active(s(mark(_x121))))))))))))mark#(head(s(incr(s(tail(_x101)))))) → active#(head(s(active(incr(active(s(active(tail(mark(_x101))))))))))
mark#(head(s(incr(0)))) → active#(head(active(s(active(incr(active(0)))))))mark#(head(incr(incr(tail(nats))))) → active#(head(incr(incr(tail(active(nats))))))
mark#(head(s(incr(s(tail(s(_x131))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(_x131))))))))))))mark#(head(incr(cons(tail(_x81), mark(_x52))))) → active#(head(active(incr(cons(active(tail(mark(_x81))), _x52)))))
mark#(head(incr(cons(cons(_x81, _x82), _x52)))) → active#(head(active(incr(cons(cons(_x81, _x82), _x52)))))mark#(head(incr(cons(cons(_x81, active(active(_x82))), _x62)))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x62)))))
mark#(head(s(cons(head(_x81), _x62)))) → active#(head(active(s(active(cons(active(head(mark(_x81))), _x62))))))mark#(head(incr(cons(_x61, _x31)))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))
mark#(head(incr(incr(tail(cons(incr(_x91), _x82)))))) → active#(head(incr(incr(active(tail(cons(active(incr(mark(_x91))), _x82)))))))mark#(head(incr(s(_x61)))) → active#(head(active(incr(active(s(mark(_x61)))))))
mark#(head(incr(incr(tail(incr(_x61)))))) → active#(head(incr(incr(tail(active(incr(mark(_x61))))))))mark#(head(s(incr(s(_x91))))) → active#(head(active(s(active(incr(active(s(_x91))))))))
mark#(head(s(s(nats)))) → active#(head(active(s(active(s(active(nats)))))))mark#(head(incr(cons(tail(incr(_x91)), _x62)))) → active#(head(active(incr(cons(active(tail(active(incr(mark(_x91))))), _x62)))))
mark#(head(incr(nats))) → active#(head(active(incr(active(nats)))))mark#(head(incr(incr(pairs)))) → active#(head(incr(active(incr(active(pairs))))))
mark#(head(incr(pairs))) → active#(head(active(incr(mark(cons(0, incr(odds)))))))mark#(head(incr(incr(s(_x71))))) → active#(head(incr(active(incr(active(s(mark(_x71))))))))
mark#(head(incr(cons(s(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(s(mark(_x71))), _x72)))))mark#(head(incr(odds))) → active#(head(incr(active(odds))))
mark#(head(incr(cons(cons(_x81, _x82), mark(_x52))))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x52)))))mark#(head(incr(cons(nats, mark(_x52))))) → active#(head(active(incr(cons(active(nats), _x52)))))
mark#(head(incr(cons(_x61, active(_x52))))) → active#(head(incr(cons(mark(_x61), _x52))))mark#(head(incr(cons(cons(active(active(_x81)), _x82), _x62)))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x62)))))
mark#(head(cons(incr(_x61), _x32))) → active#(head(active(cons(active(incr(mark(_x61))), _x32))))mark#(head(incr(cons(cons(pairs, _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(pairs), _x72)), _x62)))))
mark#(head(incr(incr(tail(cons(_x81, active(_x92))))))) → active#(head(incr(incr(active(tail(active(cons(mark(_x81), _x92))))))))mark#(head(s(incr(s(0))))) → active#(head(active(s(active(incr(active(s(active(0)))))))))
mark#(head(incr(cons(cons(s(_x91), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(s(mark(_x91))), _x72)), _x62)))))mark#(head(incr(cons(tail(tail(_x91)), _x62)))) → active#(head(active(incr(cons(active(tail(active(tail(mark(_x91))))), _x62)))))
mark#(head(incr(incr(tail(_x81))))) → active#(head(incr(active(incr(active(tail(_x81)))))))mark#(head(tail(tail(_x61)))) → active#(head(active(tail(active(tail(mark(_x61)))))))
mark#(head(incr(cons(cons(active(_x81), mark(_x82)), _x62)))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x62)))))mark#(head(s(s(tail(_x81))))) → active#(head(active(s(active(s(active(tail(mark(_x81)))))))))
mark#(head(s(incr(s(incr(incr(cons(_x141, _x142)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(cons(mark(_x141), _x142))))))))))))))mark#(head(incr(cons(cons(_x71, active(_x72)), _x52)))) → active#(head(active(incr(cons(cons(_x71, _x72), _x52)))))
mark#(head(incr(incr(tail(cons(tail(_x91), _x82)))))) → active#(head(incr(incr(active(tail(cons(active(tail(mark(_x91))), _x82)))))))mark#(pairs) → active#(pairs)
active#(pairs) → mark#(cons(0, incr(odds)))mark#(head(s(incr(s(incr(_x101)))))) → active#(head(active(s(active(incr(active(s(incr(mark(_x101))))))))))
mark#(head(s(incr(s(incr(tail(_x121))))))) → active#(head(active(s(active(incr(s(active(incr(active(tail(mark(_x121))))))))))))mark#(head(s(incr(s(incr(tail(_x121))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(mark(_x121))))))))))))
mark#(head(incr(cons(cons(_x81, active(mark(_x82))), _x52)))) → active#(head(active(incr(cons(cons(_x81, _x82), _x52)))))mark#(head(head(_x31))) → active#(head(active(head(mark(_x31)))))
mark#(head(s(incr(s(incr(s(_x121))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(s(mark(_x121)))))))))))))mark#(head(s(s(incr(pairs))))) → active#(head(active(s(active(s(active(incr(active(pairs)))))))))
mark#(head(incr(cons(cons(_x71, _x72), mark(_x52))))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x72)), _x52)))))mark#(head(incr(cons(pairs, mark(active(_x62)))))) → active#(head(active(incr(cons(active(pairs), _x62)))))
mark#(head(incr(incr(tail(nats))))) → active#(head(incr(active(incr(active(tail(active(nats))))))))mark#(head(s(cons(_x71, _x72)))) → active#(head(active(s(active(cons(_x71, _x72))))))
mark#(head(incr(incr(tail(incr(_x81)))))) → active#(head(incr(incr(active(tail(active(incr(mark(_x81)))))))))mark#(head(tail(0))) → active#(head(active(tail(active(0)))))
mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(mark(cons(0, incr(odds)))))))))mark#(head(incr(incr(0)))) → active#(head(incr(active(incr(active(0))))))
mark#(cons(X1, X2)) → mark#(X1)mark#(head(s(cons(odds, _x62)))) → active#(head(active(s(active(cons(active(odds), _x62))))))
mark#(head(incr(cons(cons(odds, _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(odds), _x72)), _x62)))))mark#(head(s(incr(s(incr(tail(_x121))))))) → active#(head(s(active(incr(active(s(active(incr(active(tail(mark(_x121))))))))))))
mark#(head(incr(incr(tail(head(_x91)))))) → active#(head(incr(incr(active(tail(active(head(_x91))))))))mark#(head(incr(pairs))) → active#(head(active(incr(pairs))))
mark#(head(incr(cons(_x51, active(mark(_x52)))))) → active#(head(active(incr(cons(_x51, _x52)))))mark#(head(incr(cons(cons(mark(_x71), active(mark(_x72))), _x62)))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x62)))))
mark#(head(s(tail(_x61)))) → active#(head(active(s(active(tail(mark(_x61)))))))mark#(head(s(incr(cons(_x81, _x82))))) → active#(head(active(s(active(incr(active(cons(mark(_x81), _x82))))))))
mark#(head(tail(_x31))) → active#(head(tail(mark(_x31))))mark#(head(s(cons(_x61, _x62)))) → active#(head(s(active(cons(mark(_x61), _x62)))))
mark#(head(s(incr(s(incr(cons(_x121, _x122))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(cons(mark(_x121), _x122))))))))))))mark#(head(s(s(odds)))) → active#(head(active(s(s(active(odds))))))
mark#(head(s(incr(s(tail(s(_x121))))))) → active#(head(s(active(incr(active(s(active(tail(active(s(mark(_x121))))))))))))mark#(head(incr(incr(tail(head(_x61)))))) → active#(head(incr(incr(tail(active(head(mark(_x61))))))))
mark#(head(incr(cons(0, mark(_x52))))) → active#(head(active(incr(cons(active(0), _x52)))))mark#(head(incr(cons(head(_x81), _x62)))) → active#(head(active(incr(active(cons(active(head(mark(_x81))), _x62))))))
mark#(head(incr(cons(cons(_x71, _x72), active(mark(_x72)))))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x72)), _x72)))))mark#(head(incr(cons(head(_x81), mark(_x52))))) → active#(head(active(incr(cons(active(head(mark(_x81))), _x52)))))
mark#(head(incr(incr(tail(0))))) → active#(head(incr(incr(active(tail(active(0)))))))mark#(head(incr(incr(tail(cons(_x81, active(_x72))))))) → active#(head(incr(incr(active(tail(cons(mark(_x81), _x72)))))))
mark#(head(incr(incr(incr(_x71))))) → active#(head(incr(active(incr(active(incr(mark(_x71))))))))mark#(head(incr(tail(_x51)))) → active#(head(incr(active(tail(mark(_x51))))))
mark#(head(s(incr(s(cons(_x101, _x102)))))) → active#(head(active(s(active(incr(active(s(active(cons(mark(_x101), _x102))))))))))mark#(head(s(incr(s(incr(incr(odds))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(odds)))))))))))))
mark#(head(s(incr(s(incr(incr(_x131))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(_x131))))))))))))mark#(head(s(incr(s(tail(s(odds))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(active(odds)))))))))))))
mark#(head(cons(tail(_x61), _x32))) → active#(head(active(cons(active(tail(mark(_x61))), _x32))))mark#(0) → active#(0)
active#(nats) → mark#(cons(0, incr(nats)))mark#(head(s(cons(cons(_x81, _x82), _x62)))) → active#(head(active(s(active(cons(active(cons(mark(_x81), _x82)), _x62))))))
mark#(head(s(incr(s(incr(odds)))))) → active#(head(active(s(active(incr(active(s(active(incr(active(odds)))))))))))mark#(head(incr(cons(_x51, _x52)))) → active#(head(incr(active(cons(mark(_x51), _x52)))))
mark#(head(incr(incr(cons(_x71, _x72))))) → active#(head(incr(active(incr(active(cons(mark(_x71), _x72)))))))mark#(head(incr(incr(tail(0))))) → active#(head(incr(active(incr(active(tail(active(0))))))))
mark#(head(incr(cons(cons(mark(_x81), active(_x82)), _x62)))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x62)))))mark#(head(s(s(incr(0))))) → active#(head(active(s(s(active(incr(active(0))))))))
mark#(head(incr(cons(_x61, active(mark(_x31)))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))mark#(head(incr(incr(tail(head(incr(_x101))))))) → active#(head(incr(incr(active(tail(active(head(active(incr(mark(_x101)))))))))))
mark#(head(s(incr(s(incr(tail(0))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(0)))))))))))))mark#(head(s(incr(s(incr(incr(s(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(s(mark(_x141)))))))))))))))
mark#(head(incr(odds))) → active#(head(active(incr(odds))))mark#(head(incr(cons(pairs, mark(_x62))))) → active#(head(active(incr(cons(pairs, _x62)))))
mark#(head(incr(cons(cons(_x71, _x72), _x52)))) → active#(head(active(incr(cons(cons(mark(_x71), _x72), _x52)))))mark#(head(s(incr(_x71)))) → active#(head(active(s(active(incr(_x71))))))
mark#(head(s(incr(s(tail(s(pairs))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(active(pairs)))))))))))))mark#(head(incr(incr(tail(head(0)))))) → active#(head(incr(incr(active(tail(active(head(active(0)))))))))
mark#(head(_x21)) → active#(head(_x21))mark#(head(nats)) → active#(head(active(nats)))
mark#(head(incr(cons(incr(_x81), _x62)))) → active#(head(active(incr(active(cons(active(incr(mark(_x81))), _x62))))))mark#(head(incr(cons(s(_x81), active(_x52))))) → active#(head(active(incr(cons(active(s(mark(_x81))), _x52)))))
mark#(head(cons(head(_x61), _x32))) → active#(head(active(cons(active(head(mark(_x61))), _x32))))mark#(cons(s(_x31), X2)) → active#(cons(active(s(mark(_x31))), X2))
mark#(head(incr(cons(cons(mark(_x71), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x62)))))mark#(head(s(s(odds)))) → active#(head(active(s(active(s(odds))))))
mark#(head(cons(odds, _x32))) → active#(head(active(cons(active(odds), _x32))))mark#(incr(X)) → active#(incr(mark(X)))
mark#(head(incr(cons(nats, active(_x52))))) → active#(head(active(incr(cons(active(nats), _x52)))))mark#(head(incr(cons(0, active(_x52))))) → active#(head(active(incr(cons(active(0), _x52)))))
mark#(head(incr(incr(tail(tail(_x81)))))) → active#(head(incr(incr(active(tail(active(tail(mark(_x81)))))))))mark#(head(incr(cons(cons(_x71, active(_x82)), _x62)))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x82)), _x62)))))
mark#(head(incr(cons(cons(nats, _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(nats), _x72)), _x62)))))mark#(head(s(incr(s(tail(_x101)))))) → active#(head(active(s(incr(active(s(active(tail(mark(_x101))))))))))
mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(pairs))))))mark#(head(incr(_x51))) → active#(head(active(incr(_x51))))
mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(active(cons(mark(_x61), _x62)))))mark#(head(incr(0))) → active#(head(incr(active(0))))
mark#(head(s(incr(s(tail(s(tail(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(active(tail(mark(_x141)))))))))))))))mark#(head(s(s(incr(s(_x91)))))) → active#(head(active(s(s(active(incr(active(s(mark(_x91))))))))))
mark#(head(tail(s(_x61)))) → active#(head(active(tail(active(s(mark(_x61)))))))mark#(head(s(s(pairs)))) → active#(head(active(s(s(active(pairs))))))
mark#(head(incr(incr(tail(cons(incr(_x101), _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(incr(mark(_x101))), _x82))))))))mark#(head(s(incr(s(incr(_x101)))))) → active#(head(s(active(incr(active(s(active(incr(mark(_x101))))))))))
mark#(cons(tail(_x31), X2)) → active#(cons(active(tail(mark(_x31))), X2))mark#(head(s(incr(s(tail(s(s(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(active(s(mark(_x141)))))))))))))))
mark#(head(s(s(incr(nats))))) → active#(head(active(s(active(s(active(incr(nats))))))))mark#(head(incr(cons(cons(_x81, active(mark(_x82))), mark(_x52))))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x52)))))
mark#(head(s(nats))) → active#(head(s(active(nats))))mark#(head(cons(nats, _x32))) → active#(head(active(cons(active(nats), _x32))))
mark#(cons(X1, mark(_x22))) → active#(cons(mark(X1), _x22))mark#(head(s(incr(s(pairs))))) → active#(head(active(s(active(incr(active(s(active(pairs)))))))))
mark#(head(incr(incr(tail(0))))) → active#(head(incr(incr(tail(active(0))))))mark#(head(s(s(incr(_x81))))) → active#(head(s(active(s(active(incr(mark(_x81))))))))
mark#(head(incr(cons(s(_x81), mark(_x52))))) → active#(head(active(incr(cons(active(s(mark(_x81))), _x52)))))mark#(head(s(incr(s(incr(head(_x121))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(head(mark(_x121)))))))))))))
mark#(head(s(incr(s(incr(tail(cons(_x141, _x142)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(cons(mark(_x141), _x142))))))))))))))mark#(head(incr(0))) → active#(head(active(incr(active(0)))))
active#(tail(cons(X, XS))) → mark#(XS)mark#(head(cons(pairs, _x32))) → active#(head(active(cons(active(pairs), _x32))))
mark#(head(tail(incr(_x61)))) → active#(head(active(tail(active(incr(mark(_x61)))))))mark#(head(incr(incr(tail(cons(odds, _x72)))))) → active#(head(incr(incr(active(tail(cons(odds, _x72)))))))
mark#(head(incr(cons(odds, active(mark(_x72)))))) → active#(head(active(incr(cons(active(odds), _x72)))))mark#(head(incr(cons(pairs, mark(_x31))))) → active#(head(mark(cons(s(active(pairs)), incr(_x31)))))
mark#(head(cons(_x31, mark(_x52)))) → active#(head(active(cons(mark(_x31), _x52))))mark#(head(s(incr(s(odds))))) → active#(head(active(s(active(incr(active(s(active(odds)))))))))
mark#(head(incr(cons(cons(_x81, _x82), mark(_x52))))) → active#(head(active(incr(cons(active(cons(mark(_x81), _x82)), _x52)))))mark#(head(s(incr(s(incr(tail(_x131))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(_x131))))))))))))
mark#(head(s(s(incr(incr(_x101)))))) → active#(head(active(s(active(s(active(incr(active(incr(mark(_x101)))))))))))mark#(head(incr(incr(tail(cons(cons(_x91, _x92), _x82)))))) → active#(head(incr(incr(active(tail(cons(active(cons(mark(_x91), _x92)), _x82)))))))
mark#(head(incr(cons(tail(_x71), _x31)))) → active#(head(mark(cons(s(active(tail(mark(_x71)))), incr(_x31)))))mark#(head(s(s(0)))) → active#(head(active(s(active(s(active(0)))))))
mark#(cons(_x21, _x22)) → active#(cons(_x21, _x22))mark#(head(s(s(incr(_x81))))) → active#(head(active(s(active(s(incr(mark(_x81))))))))
mark#(head(s(odds))) → active#(head(active(s(active(odds)))))mark#(head(incr(cons(cons(_x71, active(mark(active(_x72)))), _x62)))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x62)))))
mark#(head(incr(incr(tail(cons(_x91, _x92)))))) → active#(head(incr(incr(active(tail(active(cons(_x91, _x92))))))))mark#(head(s(s(incr(head(_x91)))))) → active#(head(active(s(s(active(incr(active(head(mark(_x91))))))))))
mark#(head(s(s(incr(_x81))))) → active#(head(active(s(s(incr(mark(_x81)))))))mark#(head(incr(incr(tail(head(cons(_x101, _x102))))))) → active#(head(incr(incr(active(tail(active(head(active(cons(mark(_x101), _x102))))))))))
mark#(head(s(s(incr(_x81))))) → active#(head(s(s(active(incr(mark(_x81)))))))mark#(head(incr(tail(_x61)))) → active#(head(active(incr(active(tail(mark(_x61)))))))
mark#(head(incr(incr(tail(cons(odds, _x51)))))) → active#(head(incr(incr(mark(_x51)))))mark#(head(s(s(head(_x81))))) → active#(head(active(s(active(s(active(head(mark(_x81)))))))))
mark#(head(incr(cons(cons(active(_x71), _x72), _x31)))) → active#(head(mark(cons(s(active(cons(_x71, _x72))), incr(_x31)))))mark#(head(incr(incr(_x61)))) → active#(head(incr(active(incr(_x61)))))
mark#(head(incr(incr(tail(incr(_x91)))))) → active#(head(incr(active(incr(active(tail(active(incr(mark(_x91))))))))))mark#(head(incr(incr(tail(cons(odds, mark(_x72))))))) → active#(head(incr(incr(active(tail(cons(active(odds), _x72)))))))
mark#(head(s(s(cons(_x81, _x82))))) → active#(head(active(s(active(s(active(cons(mark(_x81), _x82))))))))mark#(head(s(0))) → active#(head(active(s(active(0)))))
mark#(head(incr(cons(cons(_x81, _x82), active(_x52))))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x52)))))mark#(head(incr(cons(cons(_x81, active(mark(_x82))), _x62)))) → active#(head(incr(cons(active(cons(_x81, _x82)), _x62))))
mark#(head(s(incr(s(_x81))))) → active#(head(active(s(incr(active(s(mark(_x81))))))))mark#(cons(0, X2)) → active#(cons(active(0), X2))
mark#(head(s(incr(s(tail(s(head(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(active(head(mark(_x141)))))))))))))))mark#(head(incr(cons(pairs, mark(_x52))))) → active#(head(incr(cons(active(pairs), _x52))))
mark#(head(incr(incr(tail(cons(s(_x91), _x82)))))) → active#(head(incr(incr(active(tail(cons(active(s(mark(_x91))), _x82)))))))mark#(head(s(cons(pairs, _x62)))) → active#(head(active(s(active(cons(active(pairs), _x62))))))
mark#(head(incr(incr(tail(cons(_x81, _x82)))))) → active#(head(incr(incr(tail(cons(mark(_x81), _x82))))))mark#(head(incr(cons(cons(_x81, _x82), _x62)))) → active#(head(active(incr(active(cons(active(cons(mark(_x81), _x82)), _x62))))))
mark#(head(incr(incr(tail(cons(nats, _x82)))))) → active#(head(incr(incr(active(tail(cons(active(nats), _x82)))))))mark#(head(s(head(_x61)))) → active#(head(active(s(active(head(mark(_x61)))))))
mark#(head(s(incr(s(incr(0)))))) → active#(head(active(s(active(incr(active(s(active(incr(active(0)))))))))))mark#(head(incr(incr(tail(pairs))))) → active#(head(incr(incr(tail(active(pairs))))))
mark#(head(X)) → mark#(X)mark#(head(s(s(_x61)))) → active#(head(s(active(s(mark(_x61))))))
mark#(head(tail(nats))) → active#(head(active(tail(active(nats)))))mark#(head(incr(cons(cons(_x71, mark(_x72)), _x62)))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x62)))))
mark#(head(incr(cons(pairs, mark(mark(_x62)))))) → active#(head(active(incr(cons(active(pairs), _x62)))))mark#(head(incr(cons(odds, _x42)))) → active#(head(incr(cons(odds, _x42))))
mark#(nats) → active#(nats)mark#(head(s(s(pairs)))) → active#(head(s(active(s(active(pairs))))))
mark#(head(s(nats))) → active#(head(active(s(nats))))mark#(head(incr(cons(tail(head(_x91)), _x62)))) → active#(head(active(incr(cons(active(tail(active(head(mark(_x91))))), _x62)))))
mark#(head(incr(cons(cons(_x71, active(_x72)), mark(_x52))))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x52)))))mark#(head(s(cons(_x61, _x62)))) → active#(head(active(s(cons(mark(_x61), _x62)))))
mark#(head(incr(cons(tail(_x71), mark(_x52))))) → active#(head(active(incr(cons(active(tail(mark(_x71))), _x52)))))mark#(head(incr(cons(_x61, mark(_x52))))) → active#(head(incr(cons(mark(_x61), _x52))))
mark#(head(incr(incr(tail(head(odds)))))) → active#(head(incr(incr(active(tail(active(head(active(odds)))))))))mark#(head(incr(cons(_x61, mark(_x31))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))
active#(head(cons(X, XS))) → mark#(X)mark#(head(incr(cons(0, active(mark(_x72)))))) → active#(head(active(incr(cons(active(0), _x72)))))
mark#(head(incr(incr(tail(s(_x61)))))) → active#(head(incr(incr(tail(active(s(mark(_x61))))))))mark#(head(tail(pairs))) → active#(head(active(tail(active(pairs)))))
mark#(head(incr(incr(tail(cons(_x91, _x92)))))) → active#(head(incr(active(incr(active(tail(active(cons(mark(_x91), _x92)))))))))mark#(head(incr(cons(_x61, active(mark(_x72)))))) → active#(head(incr(cons(mark(_x61), _x72))))
mark#(head(incr(cons(cons(_x81, _x82), _x62)))) → active#(head(incr(cons(active(cons(_x81, _x82)), _x62))))mark#(head(incr(cons(cons(_x71, active(_x72)), _x31)))) → active#(head(mark(cons(s(active(cons(_x71, _x72))), incr(_x31)))))
mark#(cons(incr(_x31), X2)) → active#(cons(active(incr(mark(_x31))), X2))mark#(head(cons(_x51, _x52))) → active#(head(active(cons(_x51, _x52))))
mark#(head(s(_x51))) → active#(head(active(s(_x51))))mark#(head(incr(cons(cons(_x81, _x82), active(_x52))))) → active#(head(active(incr(cons(active(cons(mark(_x81), _x82)), _x52)))))
mark#(head(0)) → active#(head(active(0)))mark#(head(incr(cons(cons(active(_x71), _x72), _x52)))) → active#(head(active(incr(cons(cons(_x71, _x72), _x52)))))
mark#(head(s(incr(s(incr(_x111)))))) → active#(head(active(s(active(incr(active(s(active(incr(_x111))))))))))mark#(head(s(incr(s(incr(incr(head(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(head(mark(_x141)))))))))))))))
mark#(head(incr(cons(odds, mark(_x42))))) → active#(head(incr(cons(active(odds), _x42))))mark#(head(s(s(incr(0))))) → active#(head(active(s(active(s(active(incr(active(0)))))))))
mark#(cons(odds, X2)) → active#(cons(active(odds), X2))mark#(head(s(incr(s(incr(nats)))))) → active#(head(active(s(active(incr(active(s(active(incr(active(nats)))))))))))
mark#(head(incr(incr(tail(odds))))) → active#(head(incr(incr(active(tail(active(odds)))))))mark#(head(incr(cons(cons(_x81, active(mark(_x82))), active(_x52))))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x52)))))
mark#(head(incr(pairs))) → active#(head(incr(mark(cons(0, incr(odds))))))mark#(head(s(incr(s(head(_x101)))))) → active#(head(active(s(active(incr(active(s(active(head(mark(_x101)))))))))))
mark#(head(incr(cons(_x61, active(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(cons(mark(incr(pairs)), _x62)))))
mark#(head(incr(cons(cons(active(_x81), active(_x82)), _x62)))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x62)))))mark#(head(incr(incr(tail(cons(odds, _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(odds), _x82))))))))
mark#(head(s(incr(s(incr(incr(incr(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(incr(mark(_x141)))))))))))))))mark#(head(incr(cons(odds, active(_x52))))) → active#(head(active(incr(cons(active(odds), _x52)))))
mark#(head(incr(cons(tail(_x81), _x62)))) → active#(head(active(incr(cons(active(tail(_x81)), _x62)))))mark#(cons(head(_x31), X2)) → active#(cons(active(head(mark(_x31))), X2))
mark#(head(incr(incr(tail(tail(_x91)))))) → active#(head(incr(active(incr(active(tail(active(tail(mark(_x91))))))))))mark#(head(s(incr(pairs)))) → active#(head(active(s(active(incr(active(pairs)))))))
mark#(head(s(incr(s(incr(tail(nats))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(nats)))))))))))))mark#(head(incr(incr(tail(_x51))))) → active#(head(incr(incr(tail(_x51)))))
mark#(head(s(incr(s(tail(s(nats))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(active(nats)))))))))))))mark#(head(s(incr(s(incr(tail(tail(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(tail(mark(_x141)))))))))))))))
mark#(head(s(s(incr(nats))))) → active#(head(active(s(s(active(incr(nats)))))))mark#(head(incr(incr(tail(cons(_x61, _x62)))))) → active#(head(incr(incr(tail(active(cons(mark(_x61), _x62)))))))
mark#(head(cons(cons(_x61, _x62), _x32))) → active#(head(active(cons(active(cons(mark(_x61), _x62)), _x32))))mark#(head(incr(incr(tail(cons(head(_x91), _x82)))))) → active#(head(incr(incr(active(tail(cons(active(head(mark(_x91))), _x82)))))))
mark#(head(incr(incr(odds)))) → active#(head(incr(active(incr(active(odds))))))mark#(head(s(incr(s(incr(tail(odds))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(odds)))))))))))))
mark#(head(s(s(incr(odds))))) → active#(head(active(s(active(s(active(incr(active(odds)))))))))mark#(head(incr(odds))) → active#(head(active(incr(mark(incr(pairs))))))
mark#(head(incr(incr(tail(s(_x91)))))) → active#(head(incr(active(incr(active(tail(active(s(mark(_x91))))))))))mark#(head(incr(cons(cons(active(_x71), _x72), active(_x52))))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x52)))))
mark#(head(cons(s(_x61), _x32))) → active#(head(active(cons(active(s(mark(_x61))), _x32))))mark#(head(incr(incr(tail(cons(_x81, _x51)))))) → active#(head(incr(incr(mark(_x51)))))
mark#(head(s(incr(s(_x81))))) → active#(head(s(active(incr(active(s(mark(_x81))))))))mark#(head(s(incr(s(tail(s(cons(_x141, _x142)))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(active(cons(mark(_x141), _x142))))))))))))))
mark#(head(incr(incr(tail(tail(_x61)))))) → active#(head(incr(incr(tail(active(tail(mark(_x61))))))))mark#(head(s(s(_x71)))) → active#(head(active(s(active(s(_x71))))))
mark#(head(incr(cons(tail(_x71), _x62)))) → active#(head(incr(cons(active(tail(mark(_x71))), _x62))))mark#(head(s(nats))) → active#(head(active(s(mark(cons(0, incr(nats)))))))
mark#(head(incr(cons(_x61, mark(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))mark#(head(incr(cons(tail(s(_x91)), _x62)))) → active#(head(active(incr(cons(active(tail(active(s(mark(_x91))))), _x62)))))
mark#(head(incr(incr(tail(cons(0, _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(0), _x82))))))))mark#(head(s(incr(s(tail(pairs)))))) → active#(head(active(s(active(incr(active(s(active(tail(active(pairs)))))))))))
mark#(head(s(s(incr(_x91))))) → active#(head(active(s(active(s(active(incr(_x91))))))))mark#(head(incr(nats))) → active#(head(incr(active(nats))))
mark#(odds) → active#(odds)mark#(head(incr(cons(pairs, mark(_x52))))) → active#(head(active(incr(cons(mark(cons(0, incr(odds))), _x52)))))
mark#(head(s(s(incr(cons(_x91, _x92)))))) → active#(head(active(s(s(active(incr(active(cons(mark(_x91), _x92)))))))))mark#(head(incr(incr(tail(cons(cons(_x101, _x102), _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(cons(mark(_x101), _x102)), _x82))))))))
mark#(head(s(incr(s(incr(incr(tail(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(tail(mark(_x141)))))))))))))))mark#(head(incr(incr(tail(pairs))))) → active#(head(incr(incr(active(tail(active(pairs)))))))
mark#(head(s(_x31))) → active#(head(s(mark(_x31))))mark#(head(incr(incr(tail(head(_x91)))))) → active#(head(incr(active(incr(active(tail(active(head(mark(_x91))))))))))
mark#(head(incr(incr(tail(cons(odds, active(_x72))))))) → active#(head(incr(incr(active(tail(cons(active(odds), _x72)))))))mark#(head(s(incr(_x61)))) → active#(head(s(active(incr(mark(_x61))))))
mark#(head(incr(incr(tail(cons(odds, _x82)))))) → active#(head(incr(incr(active(tail(cons(mark(incr(pairs)), _x82)))))))mark#(head(odds)) → active#(head(active(odds)))
mark#(head(s(incr(_x61)))) → active#(head(active(s(incr(mark(_x61))))))mark#(head(s(cons(_x61, mark(_x72))))) → active#(head(active(s(active(cons(mark(_x61), _x72))))))
mark#(head(incr(cons(cons(_x71, active(_x72)), active(_x52))))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x52)))))mark#(head(s(incr(s(incr(incr(0))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(0)))))))))))))
mark#(head(s(s(incr(incr(_x91)))))) → active#(head(active(s(s(active(incr(active(incr(mark(_x91))))))))))mark#(head(incr(cons(cons(_x71, _x72), active(_x52))))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x72)), _x52)))))
mark#(head(s(incr(s(incr(tail(s(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(s(mark(_x141)))))))))))))))mark#(head(s(incr(s(tail(head(_x121))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(head(mark(_x121)))))))))))))
mark#(head(s(cons(s(_x81), _x62)))) → active#(head(active(s(active(cons(active(s(mark(_x81))), _x62))))))mark#(head(incr(cons(cons(_x71, mark(_x82)), _x62)))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x82)), _x62)))))
mark#(head(s(incr(s(tail(s(incr(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(active(incr(mark(_x141)))))))))))))))mark#(head(incr(incr(tail(cons(_x81, mark(_x72))))))) → active#(head(incr(incr(active(tail(cons(mark(_x81), _x72)))))))
mark#(head(incr(cons(_x61, active(mark(active(_x52))))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))mark#(head(s(incr(odds)))) → active#(head(active(s(active(incr(active(odds)))))))
mark#(head(s(incr(s(incr(incr(nats))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(nats)))))))))))))mark#(head(cons(_x31, _x32))) → active#(head(cons(mark(_x31), _x32)))
mark#(head(s(incr(s(tail(odds)))))) → active#(head(active(s(active(incr(active(s(active(tail(active(odds)))))))))))mark#(head(s(incr(s(incr(incr(_x121))))))) → active#(head(active(s(active(incr(s(active(incr(active(incr(mark(_x121))))))))))))
mark#(head(incr(incr(tail(_x61))))) → active#(head(incr(incr(active(tail(_x61))))))mark#(head(incr(cons(cons(active(_x71), _x72), _x62)))) → active#(head(incr(cons(active(cons(_x71, _x72)), _x62))))
mark#(head(s(s(incr(s(_x101)))))) → active#(head(active(s(active(s(active(incr(active(s(mark(_x101)))))))))))active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))
mark#(head(incr(cons(odds, _x31)))) → active#(head(mark(cons(s(active(odds)), incr(_x31)))))mark#(head(incr(cons(_x61, active(mark(mark(_x52))))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))
mark#(head(incr(cons(odds, mark(_x52))))) → active#(head(active(incr(cons(active(odds), _x52)))))mark#(head(incr(cons(tail(nats), _x62)))) → active#(head(active(incr(cons(active(tail(active(nats))), _x62)))))
mark#(head(incr(cons(tail(_x71), active(_x52))))) → active#(head(active(incr(cons(active(tail(mark(_x71))), _x52)))))mark#(head(incr(cons(tail(_x81), active(_x52))))) → active#(head(active(incr(cons(active(tail(mark(_x81))), _x52)))))
mark#(head(s(s(incr(cons(_x101, _x102)))))) → active#(head(active(s(active(s(active(incr(active(cons(mark(_x101), _x102))))))))))mark#(head(incr(incr(tail(head(_x81)))))) → active#(head(incr(incr(tail(active(head(mark(_x81))))))))
mark#(head(incr(cons(incr(_x81), active(_x52))))) → active#(head(active(incr(cons(active(incr(mark(_x81))), _x52)))))mark#(head(incr(incr(tail(cons(odds, _x82)))))) → active#(head(incr(incr(tail(cons(active(odds), _x82))))))
mark#(head(incr(pairs))) → active#(head(incr(pairs)))mark#(tail(X)) → mark#(X)
mark#(head(incr(cons(tail(pairs), _x62)))) → active#(head(active(incr(cons(active(tail(active(pairs))), _x62)))))mark#(head(incr(cons(cons(active(_x71), active(mark(_x72))), _x62)))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x62)))))
mark#(head(incr(cons(cons(_x81, active(mark(_x82))), _x31)))) → active#(head(mark(cons(s(active(cons(_x81, _x82))), incr(_x31)))))active#(odds) → mark#(incr(pairs))
mark#(head(incr(incr(tail(cons(pairs, _x82)))))) → active#(head(incr(incr(active(tail(cons(active(pairs), _x82)))))))mark#(head(s(s(_x61)))) → active#(head(active(s(s(mark(_x61))))))
mark#(head(s(s(incr(nats))))) → active#(head(active(s(active(s(incr(active(nats))))))))mark#(head(s(s(incr(nats))))) → active#(head(active(s(s(active(incr(mark(cons(0, incr(nats))))))))))
mark#(head(s(s(incr(tail(_x91)))))) → active#(head(active(s(s(active(incr(active(tail(mark(_x91))))))))))mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(cons(active(0), _x62)))))
mark#(head(incr(cons(head(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(head(mark(_x71))), _x72)))))mark#(head(incr(cons(_x71, active(_x72))))) → active#(head(active(incr(cons(_x71, _x72)))))
mark#(head(s(incr(s(tail(0)))))) → active#(head(active(s(active(incr(active(s(active(tail(active(0)))))))))))mark#(head(s(incr(s(incr(_x101)))))) → active#(head(active(s(active(incr(s(active(incr(mark(_x101))))))))))
mark#(head(incr(incr(tail(_x71))))) → active#(head(incr(active(incr(tail(mark(_x71)))))))mark#(head(incr(cons(s(_x81), _x62)))) → active#(head(active(incr(active(cons(active(s(mark(_x81))), _x62))))))
mark#(head(s(incr(s(tail(s(_x121))))))) → active#(head(active(s(active(incr(active(s(active(tail(s(mark(_x121))))))))))))mark#(head(s(incr(s(incr(tail(head(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(head(mark(_x141)))))))))))))))
mark#(head(incr(incr(tail(cons(head(_x101), _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(head(mark(_x101))), _x82))))))))mark#(head(incr(incr(head(_x71))))) → active#(head(incr(active(incr(active(head(mark(_x71))))))))
mark#(head(incr(cons(cons(_x71, active(mark(mark(_x72)))), _x62)))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x62)))))mark#(head(incr(_x41))) → active#(head(incr(_x41)))
mark#(head(s(incr(s(_x81))))) → active#(head(active(s(active(incr(s(mark(_x81))))))))mark#(s(X)) → active#(s(mark(X)))
mark#(head(incr(head(_x61)))) → active#(head(active(incr(active(head(mark(_x61)))))))mark#(head(incr(cons(odds, active(_x42))))) → active#(head(incr(cons(active(odds), _x42))))
mark#(head(s(s(incr(odds))))) → active#(head(active(s(s(active(incr(active(odds))))))))mark#(incr(X)) → mark#(X)
mark#(head(incr(cons(_x61, active(_x31))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))mark#(head(s(incr(nats)))) → active#(head(active(s(active(incr(active(nats)))))))
mark#(head(incr(cons(tail(0), _x62)))) → active#(head(active(incr(cons(active(tail(active(0))), _x62)))))mark#(head(incr(incr(tail(head(nats)))))) → active#(head(incr(incr(active(tail(active(head(active(nats)))))))))
mark#(head(incr(cons(tail(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(tail(mark(_x71))), _x72)))))mark#(head(pairs)) → active#(head(active(pairs)))
mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(active(cons(active(0), _x62))))))mark#(head(incr(incr(tail(nats))))) → active#(head(incr(incr(active(tail(active(nats)))))))
mark#(head(incr(cons(cons(0, _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(0), _x72)), _x62)))))mark#(head(incr(incr(tail(cons(nats, _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(nats), _x82))))))))
mark#(head(incr(cons(cons(cons(_x91, _x92), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(cons(mark(_x91), _x92)), _x72)), _x62)))))mark#(head(cons(0, _x32))) → active#(head(active(cons(active(0), _x32))))
mark#(head(s(s(odds)))) → active#(head(s(active(s(active(odds))))))mark#(head(tail(_x51))) → active#(head(active(tail(_x51))))
mark#(head(incr(incr(tail(head(s(_x101))))))) → active#(head(incr(incr(active(tail(active(head(active(s(mark(_x101)))))))))))mark#(head(incr(incr(tail(cons(_x71, _x72)))))) → active#(head(incr(incr(active(tail(cons(_x71, _x72)))))))
mark#(head(incr(s(_x51)))) → active#(head(incr(active(s(mark(_x51))))))mark#(head(incr(incr(tail(head(pairs)))))) → active#(head(incr(incr(active(tail(active(head(active(pairs)))))))))
mark#(head(s(s(incr(_x71))))) → active#(head(active(s(s(active(incr(_x71)))))))mark#(head(incr(incr(tail(head(_x81)))))) → active#(head(incr(incr(active(tail(head(mark(_x81))))))))
mark#(head(s(incr(s(incr(tail(pairs))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(pairs)))))))))))))mark#(head(s(incr(s(incr(incr(_x121))))))) → active#(head(active(s(incr(active(s(active(incr(active(incr(mark(_x121))))))))))))
mark#(head(s(incr(s(incr(tail(_x121))))))) → active#(head(active(s(active(incr(active(s(incr(active(tail(mark(_x121))))))))))))mark#(head(s(incr(s(tail(_x101)))))) → active#(head(active(s(active(incr(active(s(tail(mark(_x101))))))))))
mark#(cons(X1, active(_x22))) → active#(cons(mark(X1), _x22))mark#(head(incr(cons(tail(_x81), _x62)))) → active#(head(active(incr(active(cons(active(tail(mark(_x81))), _x62))))))
mark#(head(incr(cons(_x71, _x72)))) → active#(head(active(incr(active(cons(_x71, _x72))))))mark#(head(incr(incr(tail(cons(pairs, _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(pairs), _x82))))))))
mark#(head(s(incr(s(incr(incr(_x121))))))) → active#(head(active(s(active(incr(active(s(active(incr(incr(mark(_x121))))))))))))mark#(head(tail(head(_x61)))) → active#(head(active(tail(active(head(mark(_x61)))))))
mark#(head(incr(incr(tail(head(tail(_x101))))))) → active#(head(incr(incr(active(tail(active(head(active(tail(mark(_x101)))))))))))mark#(head(incr(cons(pairs, active(_x52))))) → active#(head(active(incr(cons(active(pairs), _x52)))))
mark#(head(incr(cons(tail(_x71), _x52)))) → active#(head(active(incr(cons(tail(mark(_x71)), _x52)))))mark#(head(incr(incr(nats)))) → active#(head(incr(active(incr(active(nats))))))
mark#(head(s(incr(head(_x81))))) → active#(head(active(s(active(incr(active(head(mark(_x81)))))))))mark#(head(incr(incr(tail(head(head(_x101))))))) → active#(head(incr(incr(active(tail(active(head(active(head(mark(_x101)))))))))))
mark#(head(incr(incr(tail(cons(s(_x101), _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(s(mark(_x101))), _x82))))))))mark#(head(incr(cons(cons(active(mark(_x81)), _x82), _x62)))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x62)))))
mark#(head(s(s(incr(nats))))) → active#(head(active(s(active(s(active(incr(mark(cons(0, incr(nats)))))))))))mark#(head(incr(cons(cons(_x71, _x72), _x62)))) → active#(head(incr(cons(active(cons(mark(_x71), _x72)), _x62))))
mark#(head(s(incr(s(tail(nats)))))) → active#(head(active(s(active(incr(active(s(active(tail(active(nats)))))))))))mark#(head(s(s(incr(pairs))))) → active#(head(active(s(s(active(incr(active(pairs))))))))
mark#(head(incr(cons(cons(_x81, _x82), _x31)))) → active#(head(mark(cons(s(active(cons(_x81, _x82))), incr(_x31)))))mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(active(cons(active(pairs), _x62))))))
mark#(head(s(incr(s(incr(_x101)))))) → active#(head(active(s(incr(active(s(active(incr(mark(_x101))))))))))mark#(head(incr(cons(nats, active(mark(_x72)))))) → active#(head(active(incr(cons(active(nats), _x72)))))
mark#(head(incr(cons(cons(tail(_x91), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(tail(mark(_x91))), _x72)), _x62)))))mark#(cons(pairs, X2)) → active#(cons(active(pairs), X2))
mark#(head(s(cons(nats, _x62)))) → active#(head(active(s(active(cons(active(nats), _x62))))))mark#(head(s(incr(s(tail(s(_x121))))))) → active#(head(active(s(active(incr(active(s(tail(active(s(mark(_x121))))))))))))
mark#(head(s(cons(incr(_x81), _x62)))) → active#(head(active(s(active(cons(active(incr(mark(_x81))), _x62))))))mark#(head(s(incr(s(tail(_x111)))))) → active#(head(active(s(active(incr(active(s(active(tail(_x111))))))))))
mark#(head(s(s(incr(nats))))) → active#(head(active(s(s(incr(active(nats)))))))mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(cons(active(nats), _x62)))))
mark#(head(s(cons(_x61, active(_x72))))) → active#(head(active(s(active(cons(mark(_x61), _x72))))))mark#(head(s(incr(s(nats))))) → active#(head(active(s(active(incr(active(s(active(nats)))))))))
mark#(head(incr(incr(tail(cons(tail(_x101), _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(tail(mark(_x101))), _x82))))))))

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, pairs, s, active, mark, incr, head, odds, tail, cons

Strategy

The right-hand side of the rule mark#(head(s(s(s(_x81))))) → active#(head(active(s(active(s(active(s(mark(_x81))))))))) 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
active#(head(active(s(s(active(s(mark(_x81)))))))) 
active#(head(active(s(active(s(active(s(active(0))))))))) 
active#(head(active(s(active(s(active(s(active(head(mark(_x101))))))))))) 
active#(head(active(s(active(s(active(s(active(tail(mark(_x101))))))))))) 
active#(head(active(s(active(s(active(s(_x91)))))))) 
active#(head(active(s(active(s(s(mark(_x81)))))))) 
active#(head(active(s(active(s(active(s(active(nats))))))))) 
active#(head(active(s(active(s(active(s(active(pairs))))))))) 
active#(head(active(s(active(s(active(s(active(cons(mark(_x101), _x102)))))))))) 
active#(head(active(s(active(s(active(s(active(odds))))))))) 
active#(head(active(s(active(s(active(s(active(incr(mark(_x101))))))))))) 
active#(head(s(active(s(active(s(mark(_x81)))))))) 
active#(head(active(s(active(s(active(s(active(s(mark(_x101))))))))))) 
Thus, the rule mark#(head(s(s(s(_x81))))) → active#(head(active(s(active(s(active(s(mark(_x81))))))))) is replaced by the following rules:
mark#(head(s(s(s(tail(_x101)))))) → active#(head(active(s(active(s(active(s(active(tail(mark(_x101)))))))))))mark#(head(s(s(s(_x81))))) → active#(head(active(s(s(active(s(mark(_x81))))))))
mark#(head(s(s(s(_x91))))) → active#(head(active(s(active(s(active(s(_x91))))))))mark#(head(s(s(s(head(_x101)))))) → active#(head(active(s(active(s(active(s(active(head(mark(_x101)))))))))))
mark#(head(s(s(s(nats))))) → active#(head(active(s(active(s(active(s(active(nats)))))))))mark#(head(s(s(s(_x81))))) → active#(head(s(active(s(active(s(mark(_x81))))))))
mark#(head(s(s(s(pairs))))) → active#(head(active(s(active(s(active(s(active(pairs)))))))))mark#(head(s(s(s(incr(_x101)))))) → active#(head(active(s(active(s(active(s(active(incr(mark(_x101)))))))))))
mark#(head(s(s(s(cons(_x101, _x102)))))) → active#(head(active(s(active(s(active(s(active(cons(mark(_x101), _x102))))))))))mark#(head(s(s(s(odds))))) → active#(head(active(s(active(s(active(s(active(odds)))))))))
mark#(head(s(s(s(s(_x101)))))) → active#(head(active(s(active(s(active(s(active(s(mark(_x101)))))))))))mark#(head(s(s(s(_x81))))) → active#(head(active(s(active(s(s(mark(_x81))))))))
mark#(head(s(s(s(0))))) → active#(head(active(s(active(s(active(s(active(0)))))))))

Problem 30: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(s(X)) → mark#(X)mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(mark(_x91), _x92)))), _x72))))
mark#(head(incr(cons(_x51, _x52)))) → active#(head(active(incr(cons(_x51, _x52)))))mark#(head(incr(cons(_x61, mark(active(mark(_x31))))))) → active#(head(cons(s(mark(_x61)), incr(_x31))))
mark#(head(s(incr(s(tail(_x101)))))) → active#(head(active(s(incr(s(active(tail(mark(_x101)))))))))mark#(head(tail(cons(_x61, _x62)))) → active#(head(active(tail(active(cons(mark(_x61), _x62))))))
mark#(head(s(incr(s(incr(incr(pairs))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(pairs)))))))))))))mark#(head(s(incr(s(incr(tail(incr(head(_x151))))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(head(mark(_x151))))))))))))))))
mark#(head(incr(cons(tail(cons(incr(_x101), active(_x82))), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x82))), _x62)))))mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(mark(_x91), _x92)))), _x52)))))
mark#(head(s(cons(0, _x62)))) → active#(head(active(s(active(cons(active(0), _x62))))))mark#(head(incr(cons(_x61, active(active(_x72)))))) → active#(head(active(incr(cons(mark(_x61), _x72)))))
mark#(head(incr(cons(odds, _x62)))) → active#(head(incr(cons(mark(incr(pairs)), _x62))))mark#(head(incr(cons(tail(cons(incr(_x101), _x92)), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x92))), _x52)))))
mark#(head(s(incr(s(incr(tail(incr(nats)))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(nats))))))))))))))mark#(head(s(incr(s(tail(incr(_x121))))))) → active#(head(s(active(incr(active(s(active(tail(active(incr(mark(_x121))))))))))))
mark#(head(incr(incr(odds)))) → active#(head(active(incr(active(incr(active(odds)))))))mark#(head(s(incr(incr(_x81))))) → active#(head(active(s(active(incr(active(incr(mark(_x81)))))))))
mark#(head(incr(cons(incr(_x81), mark(_x52))))) → active#(head(active(incr(cons(active(incr(mark(_x81))), _x52)))))mark#(head(s(incr(s(incr(tail(_x121))))))) → active#(head(active(s(active(incr(active(s(active(incr(tail(mark(_x121))))))))))))
mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(mark(_x91), _x92))), _x52)))))mark#(head(incr(cons(tail(cons(incr(head(incr(_x131))), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(active(incr(mark(_x131))))))), _x92)), _x62)))))
mark#(head(incr(cons(tail(cons(incr(head(_x121)), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(head(mark(_x121))))), _x92))), _x62)))))mark#(tail(X)) → active#(tail(mark(X)))
mark#(head(incr(incr(tail(pairs))))) → active#(head(incr(active(incr(active(tail(active(pairs))))))))mark#(head(incr(cons(tail(cons(_x101, _x102)), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(_x101, _x102)))), _x62)))))
mark#(head(incr(cons(_x71, mark(active(mark(_x31))))))) → active#(head(mark(cons(s(_x71), incr(_x31)))))mark#(head(s(incr(s(incr(pairs)))))) → active#(head(active(s(active(incr(active(s(active(incr(active(pairs)))))))))))
mark#(head(incr(cons(s(cons(0, _x102)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(0, _x102)))), _x72)))))mark#(head(s(s(incr(nats))))) → active#(head(s(active(s(active(incr(active(nats))))))))
mark#(head(incr(cons(tail(cons(nats, _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(nats), _x92))), _x62)))))mark#(head(incr(cons(tail(cons(_x91, _x71)), active(_x52))))) → active#(head(active(incr(cons(mark(_x71), _x52)))))
mark#(head(incr(cons(cons(active(mark(_x81)), mark(_x82)), mark(_x52))))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x52)))))mark#(head(incr(cons(cons(head(_x91), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(head(mark(_x91))), _x72)), _x62)))))
mark#(cons(nats, X2)) → active#(cons(active(nats), X2))mark#(head(incr(incr(tail(cons(s(_x91), _x82)))))) → active#(head(incr(incr(tail(active(cons(active(s(mark(_x91))), _x82)))))))
mark#(head(tail(odds))) → active#(head(active(tail(active(odds)))))mark#(head(incr(cons(tail(cons(_x91, _x92)), _x62)))) → active#(head(incr(cons(active(tail(active(cons(mark(_x91), _x92)))), _x62))))
mark#(head(incr(cons(s(cons(_x91, _x92)), _x62)))) → active#(head(active(incr(cons(active(s(active(cons(mark(_x91), _x92)))), _x62)))))mark#(head(incr(cons(tail(cons(incr(0), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(0))), _x92))), _x62)))))
mark#(head(incr(cons(tail(cons(cons(_x101, _x102), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(cons(mark(_x101), _x102)), _x92))), _x62)))))mark#(head(incr(cons(tail(cons(_x91, active(_x102))), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(mark(_x91), _x102)))), _x62)))))
mark#(head(s(incr(0)))) → active#(head(active(s(active(incr(active(0)))))))mark#(head(s(incr(s(tail(head(_x111))))))) → active#(head(active(s(active(incr(s(active(tail(active(head(mark(_x111))))))))))))
mark#(head(incr(cons(tail(cons(head(_x111), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(head(mark(_x111))), _x92))), _x52)))))mark#(head(incr(cons(cons(incr(odds), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(incr(active(odds))), _x72)), _x62)))))
mark#(head(incr(incr(tail(cons(incr(_x91), _x82)))))) → active#(head(incr(incr(active(tail(cons(active(incr(mark(_x91))), _x82)))))))mark#(head(incr(cons(nats, _x62)))) → active#(head(incr(active(cons(active(nats), _x62)))))
mark#(head(incr(incr(tail(incr(_x61)))))) → active#(head(incr(incr(tail(active(incr(mark(_x61))))))))mark#(head(incr(cons(pairs, mark(active(mark(_x31))))))) → active#(head(mark(cons(s(active(pairs)), incr(_x31)))))
mark#(head(incr(cons(s(cons(0, _x92)), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(0), _x92)))), _x52)))))mark#(head(incr(cons(cons(incr(pairs), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(incr(active(pairs))), _x72)), _x62)))))
mark#(head(s(s(nats)))) → active#(head(active(s(active(s(active(nats)))))))mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(active(active(mark(_x52)))))))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x111))), _x92)), _x52)))))
mark#(head(incr(nats))) → active#(head(active(incr(active(nats)))))mark#(head(s(s(s(s(_x101)))))) → active#(head(active(s(active(s(active(s(active(s(mark(_x101)))))))))))
mark#(head(s(incr(s(incr(incr(nats))))))) → active#(head(s(active(incr(active(s(active(incr(active(incr(active(nats))))))))))))mark#(head(incr(cons(_x61, mark(active(mark(_x52))))))) → active#(head(incr(cons(mark(_x61), _x52))))
mark#(head(incr(cons(cons(active(mark(_x81)), active(_x82)), mark(_x52))))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x52)))))mark#(head(incr(cons(tail(cons(incr(0), _x92)), active(active(mark(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(0))), _x92)), _x62)))))
mark#(head(s(incr(s(s(head(_x121))))))) → active#(head(active(s(active(incr(active(s(active(s(active(head(mark(_x121)))))))))))))mark#(head(cons(incr(_x61), _x32))) → active#(head(active(cons(active(incr(mark(_x61))), _x32))))
mark#(head(incr(cons(cons(pairs, _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(pairs), _x72)), _x62)))))mark#(head(incr(incr(tail(cons(_x81, active(_x92))))))) → active#(head(incr(incr(active(tail(active(cons(mark(_x81), _x92))))))))
mark#(head(s(incr(s(0))))) → active#(head(active(s(active(incr(active(s(active(0)))))))))mark#(head(incr(cons(cons(active(_x91), mark(_x92)), mark(_x52))))) → active#(head(active(incr(cons(active(cons(_x91, _x92)), _x52)))))
mark#(head(incr(cons(s(cons(0, mark(_x102))), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(active(0), _x102)))), _x72)))))mark#(head(incr(cons(cons(s(_x91), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(s(mark(_x91))), _x72)), _x62)))))
mark#(head(tail(tail(_x61)))) → active#(head(active(tail(active(tail(mark(_x61)))))))mark#(head(incr(cons(cons(active(_x91), active(_x92)), mark(_x52))))) → active#(head(active(incr(cons(active(cons(_x91, _x92)), _x52)))))
mark#(head(incr(cons(cons(_x71, active(_x72)), _x52)))) → active#(head(active(incr(cons(cons(_x71, _x72), _x52)))))mark#(head(incr(incr(tail(cons(tail(_x91), _x82)))))) → active#(head(incr(incr(active(tail(cons(active(tail(mark(_x91))), _x82)))))))
mark#(head(incr(cons(tail(cons(_x91, _x92)), _x52)))) → active#(head(active(incr(cons(tail(active(cons(mark(_x91), _x92))), _x52)))))mark#(head(s(incr(s(incr(_x101)))))) → active#(head(active(s(active(incr(active(s(incr(mark(_x101))))))))))
mark#(head(incr(cons(cons(_x81, active(mark(_x82))), _x52)))) → active#(head(active(incr(cons(cons(_x81, _x82), _x52)))))mark#(head(s(incr(s(incr(tail(_x121))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(mark(_x121))))))))))))
mark#(head(s(incr(s(incr(tail(_x121))))))) → active#(head(active(s(active(incr(s(active(incr(active(tail(mark(_x121))))))))))))mark#(head(s(s(s(cons(_x101, _x102)))))) → active#(head(active(s(active(s(active(s(active(cons(mark(_x101), _x102))))))))))
mark#(head(incr(incr(tail(cons(cons(_x91, _x92), _x82)))))) → active#(head(incr(incr(tail(active(cons(active(cons(mark(_x91), _x92)), _x82)))))))mark#(head(s(incr(s(incr(tail(incr(_x151)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(incr(_x151))))))))))))))
mark#(head(incr(cons(cons(_x71, _x72), mark(_x52))))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x72)), _x52)))))mark#(head(incr(cons(s(cons(0, _x92)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(cons(active(0), _x92))), _x72)))))
mark#(head(incr(incr(tail(incr(_x81)))))) → active#(head(incr(incr(active(tail(active(incr(mark(_x81)))))))))mark#(head(incr(incr(tail(cons(odds, _x82)))))) → active#(head(incr(incr(tail(active(cons(active(odds), _x82)))))))
mark#(head(s(s(s(odds))))) → active#(head(s(active(s(active(s(mark(incr(pairs)))))))))mark#(cons(X1, X2)) → mark#(X1)
mark#(head(s(cons(odds, _x62)))) → active#(head(active(s(active(cons(active(odds), _x62))))))mark#(head(s(incr(s(incr(tail(incr(_x141)))))))) → active#(head(active(s(incr(active(s(incr(active(tail(active(incr(mark(_x141)))))))))))))
mark#(head(s(incr(s(incr(tail(_x121))))))) → active#(head(s(active(incr(active(s(active(incr(active(tail(mark(_x121))))))))))))mark#(head(s(s(s(odds))))) → active#(head(active(s(active(s(active(s(mark(incr(pairs))))))))))
mark#(head(incr(incr(tail(head(_x91)))))) → active#(head(incr(incr(active(tail(active(head(_x91))))))))mark#(head(s(incr(s(tail(pairs)))))) → active#(head(active(s(active(incr(s(active(tail(mark(cons(0, incr(odds))))))))))))
mark#(head(incr(cons(_x51, active(mark(_x52)))))) → active#(head(active(incr(cons(_x51, _x52)))))mark#(head(s(incr(s(tail(_x81)))))) → active#(head(active(s(active(incr(s(tail(_x81))))))))
mark#(head(s(incr(s(incr(tail(incr(_x141)))))))) → active#(head(active(s(incr(s(active(incr(active(tail(active(incr(mark(_x141)))))))))))))mark#(head(incr(cons(tail(cons(tail(_x111), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(active(tail(mark(_x111))), _x92)))), _x62)))))
mark#(head(s(s(odds)))) → active#(head(active(s(s(active(odds))))))mark#(head(s(incr(s(tail(s(_x121))))))) → active#(head(s(active(incr(active(s(active(tail(active(s(mark(_x121))))))))))))
mark#(head(incr(cons(0, mark(_x52))))) → active#(head(active(incr(cons(active(0), _x52)))))mark#(head(incr(cons(tail(cons(incr(pairs), _x92)), active(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(pairs))), _x92)), _x62)))))
mark#(head(incr(cons(head(_x81), _x62)))) → active#(head(active(incr(active(cons(active(head(mark(_x81))), _x62))))))mark#(head(s(incr(s(tail(cons(_x111, _x112))))))) → active#(head(active(s(active(incr(s(active(tail(active(cons(mark(_x111), _x112)))))))))))
mark#(head(incr(cons(head(_x81), mark(_x52))))) → active#(head(active(incr(cons(active(head(mark(_x81))), _x52)))))mark#(head(incr(cons(s(_x71), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(mark(_x71))), _x52)))))
mark#(head(incr(cons(_x61, mark(active(mark(_x31))))))) → active#(head(active(cons(mark(s(mark(_x61))), incr(_x31)))))mark#(head(incr(incr(tail(cons(_x81, active(_x72))))))) → active#(head(incr(incr(active(tail(cons(mark(_x81), _x72)))))))
mark#(head(incr(cons(pairs, active(mark(active(_x52))))))) → active#(head(active(incr(cons(mark(cons(0, incr(odds))), _x52)))))mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(active(incr(mark(_x111))), _x92)))), _x62)))))
mark#(head(incr(cons(tail(_x71), mark(active(_x72)))))) → active#(head(active(incr(cons(active(tail(mark(_x71))), _x72)))))mark#(head(incr(cons(cons(incr(incr(_x121)), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(incr(active(incr(mark(_x121))))), _x72)), _x62)))))
mark#(head(incr(incr(incr(_x71))))) → active#(head(incr(active(incr(active(incr(mark(_x71))))))))mark#(head(incr(tail(_x51)))) → active#(head(incr(active(tail(mark(_x51))))))
mark#(head(s(incr(s(incr(incr(odds))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(odds)))))))))))))mark#(head(s(incr(s(incr(incr(_x131))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(_x131))))))))))))
mark#(head(incr(cons(s(cons(_x91, active(_x102))), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(mark(_x91), _x102)))), _x72)))))mark#(head(s(incr(s(tail(_x91)))))) → active#(head(active(s(active(incr(s(active(tail(_x91)))))))))
active#(nats) → mark#(cons(0, incr(nats)))mark#(0) → active#(0)
mark#(head(cons(tail(_x61), _x32))) → active#(head(active(cons(active(tail(mark(_x61))), _x32))))mark#(head(s(incr(s(incr(incr(pairs))))))) → active#(head(s(active(incr(active(s(active(incr(active(incr(active(pairs))))))))))))
mark#(head(incr(cons(tail(cons(incr(head(_x121)), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(_x121)))), _x92)), _x62)))))mark#(head(incr(cons(s(tail(_x91)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(tail(mark(_x91))))), _x72)))))
mark#(head(incr(head(tail(_x71))))) → active#(head(incr(active(head(active(tail(mark(_x71))))))))mark#(head(s(incr(s(incr(odds)))))) → active#(head(active(s(active(incr(active(s(active(incr(active(odds)))))))))))
mark#(head(incr(cons(cons(_x61, active(mark(_x62))), _x42)))) → active#(head(incr(cons(cons(_x61, _x62), _x42))))mark#(head(incr(incr(tail(0))))) → active#(head(incr(active(incr(active(tail(active(0))))))))
mark#(head(incr(cons(cons(mark(_x81), active(_x82)), _x62)))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x62)))))mark#(head(incr(cons(tail(cons(incr(0), _x92)), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(0)), _x92)), _x52)))))
mark#(head(s(s(incr(0))))) → active#(head(active(s(s(active(incr(active(0))))))))mark#(head(incr(cons(tail(cons(incr(0), _x82)), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(incr(active(0)), _x82)), _x52)))))
mark#(head(incr(cons(tail(cons(incr(tail(_x121)), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(tail(mark(_x121))))), _x92))), _x62)))))mark#(head(incr(cons(cons(active(_x61), active(_x62)), _x62)))) → active#(head(incr(cons(active(cons(_x61, _x62)), _x62))))
mark#(head(s(incr(s(incr(incr(s(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(s(mark(_x141)))))))))))))))mark#(head(incr(cons(s(cons(nats, _x92)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(active(nats), _x92)))), _x72)))))
mark#(head(incr(cons(s(nats), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(nats))), _x72)))))mark#(head(incr(cons(pairs, mark(_x62))))) → active#(head(active(incr(cons(pairs, _x62)))))
mark#(head(incr(cons(tail(cons(0, _x92)), _x31)))) → active#(head(mark(cons(s(active(tail(active(cons(active(0), _x92))))), incr(_x31)))))mark#(head(incr(cons(cons(_x71, _x72), _x52)))) → active#(head(active(incr(cons(cons(mark(_x71), _x72), _x52)))))
mark#(head(incr(cons(pairs, active(mark(mark(_x52))))))) → active#(head(active(incr(cons(mark(cons(0, incr(odds))), _x52)))))mark#(head(incr(cons(tail(cons(incr(_x111), _x71)), active(_x52))))) → active#(head(active(incr(cons(mark(_x71), _x52)))))
mark#(head(s(incr(s(s(incr(_x121))))))) → active#(head(active(s(active(incr(active(s(active(s(active(incr(mark(_x121)))))))))))))mark#(head(incr(head(head(_x71))))) → active#(head(incr(active(head(active(head(mark(_x71))))))))
mark#(head(nats)) → active#(head(active(nats)))mark#(head(incr(cons(tail(cons(incr(s(_x101)), _x92)), active(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(s(mark(_x101))))), _x92)), _x62)))))
mark#(head(incr(cons(incr(_x81), _x62)))) → active#(head(active(incr(active(cons(active(incr(mark(_x81))), _x62))))))mark#(head(s(incr(s(incr(tail(incr(incr(_x161))))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(incr(active(incr(mark(_x161)))))))))))))))))
mark#(head(incr(incr(tail(cons(incr(_x91), _x82)))))) → active#(head(incr(incr(tail(active(cons(active(incr(mark(_x91))), _x82)))))))mark#(head(incr(cons(tail(cons(tail(_x111), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(tail(mark(_x111))), _x92))), _x52)))))
mark#(head(incr(cons(s(_x81), active(_x52))))) → active#(head(active(incr(cons(active(s(mark(_x81))), _x52)))))mark#(head(cons(head(_x61), _x32))) → active#(head(active(cons(active(head(mark(_x61))), _x32))))
mark#(head(incr(cons(cons(mark(_x71), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x62)))))mark#(head(incr(cons(tail(cons(incr(_x111), active(_x82))), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x111))), _x82)), _x52)))))
mark#(head(incr(cons(pairs, active(mark(active(_x42))))))) → active#(head(incr(cons(active(pairs), _x42))))mark#(incr(X)) → active#(incr(mark(X)))
mark#(head(incr(cons(cons(mark(_x61), active(_x62)), _x62)))) → active#(head(incr(cons(active(cons(_x61, _x62)), _x62))))mark#(head(incr(incr(tail(tail(_x81)))))) → active#(head(incr(incr(active(tail(active(tail(mark(_x81)))))))))
mark#(head(incr(cons(s(odds), _x62)))) → active#(head(active(incr(cons(active(s(odds)), _x62)))))mark#(head(incr(cons(cons(_x71, active(_x82)), _x62)))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x82)), _x62)))))
mark#(head(incr(cons(cons(nats, _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(nats), _x72)), _x62)))))mark#(head(s(incr(s(incr(tail(incr(0)))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(0))))))))))))))
mark#(head(s(incr(s(tail(_x101)))))) → active#(head(active(s(incr(active(s(active(tail(mark(_x101))))))))))mark#(head(s(incr(s(tail(s(0))))))) → active#(head(active(s(active(incr(active(s(tail(active(s(active(0))))))))))))
mark#(head(incr(cons(s(_x71), mark(_x52))))) → active#(head(active(incr(cons(active(s(mark(_x71))), _x52)))))mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(pairs))))))
mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(active(cons(mark(_x61), _x62)))))mark#(head(incr(_x51))) → active#(head(active(incr(_x51))))
mark#(head(s(incr(s(incr(incr(tail(_x131)))))))) → active#(head(s(active(incr(active(s(active(incr(active(incr(active(tail(mark(_x131))))))))))))))mark#(head(incr(0))) → active#(head(incr(active(0))))
mark#(head(s(incr(s(incr(tail(incr(_x141)))))))) → active#(head(active(s(active(incr(s(active(incr(active(tail(active(incr(mark(_x141))))))))))))))mark#(head(incr(cons(s(_x81), mark(active(mark(_x31))))))) → active#(head(mark(cons(s(active(s(mark(_x81)))), incr(_x31)))))
mark#(head(incr(incr(tail(cons(incr(_x101), _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(incr(mark(_x101))), _x82))))))))mark#(head(incr(cons(tail(cons(incr(_x111), active(_x72))), active(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x111))), _x72)), _x62)))))
mark#(head(s(incr(s(incr(incr(cons(_x131, _x132)))))))) → active#(head(s(active(incr(active(s(active(incr(active(incr(active(cons(mark(_x131), _x132)))))))))))))mark#(head(incr(cons(tail(cons(incr(_x131), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(_x131)), _x92))), _x52)))))
mark#(head(incr(cons(tail(cons(_x91, _x61)), mark(_x91))))) → active#(head(active(incr(cons(mark(_x61), _x62)))))mark#(head(incr(cons(cons(_x81, active(mark(_x82))), mark(_x52))))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x52)))))
mark#(head(s(nats))) → active#(head(s(active(nats))))mark#(cons(X1, mark(_x22))) → active#(cons(mark(X1), _x22))
mark#(head(cons(nats, _x32))) → active#(head(active(cons(active(nats), _x32))))mark#(head(incr(cons(tail(cons(incr(0), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(0))), _x92)), _x62)))))
mark#(head(incr(incr(tail(0))))) → active#(head(incr(incr(tail(active(0))))))mark#(head(s(s(incr(_x81))))) → active#(head(s(active(s(active(incr(mark(_x81))))))))
mark#(head(incr(cons(odds, mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(odds), _x52)))))mark#(head(incr(cons(s(_x81), mark(_x52))))) → active#(head(active(incr(cons(active(s(mark(_x81))), _x52)))))
mark#(head(s(incr(s(incr(head(_x121))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(head(mark(_x121)))))))))))))mark#(head(s(incr(s(incr(tail(cons(_x141, _x142)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(cons(mark(_x141), _x142))))))))))))))
mark#(head(incr(cons(tail(cons(incr(head(_x101)), mark(_x72))), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(mark(_x101))))), _x72)), _x62)))))active#(tail(cons(X, XS))) → mark#(XS)
mark#(head(tail(incr(_x61)))) → active#(head(active(tail(active(incr(mark(_x61)))))))mark#(head(cons(pairs, _x32))) → active#(head(active(cons(active(pairs), _x32))))
mark#(head(incr(cons(cons(active(_x71), _x72), mark(_x52))))) → active#(head(incr(cons(active(cons(_x71, _x72)), _x52))))mark#(head(s(incr(s(incr(incr(odds))))))) → active#(head(s(active(incr(active(s(active(incr(active(incr(active(odds))))))))))))
mark#(head(incr(cons(pairs, mark(_x31))))) → active#(head(mark(cons(s(active(pairs)), incr(_x31)))))mark#(head(incr(cons(tail(cons(incr(_x101), _x61)), active(incr(mark(_x101))))))) → active#(head(active(incr(cons(mark(_x61), _x62)))))
mark#(head(incr(incr(cons(_x61, _x62))))) → active#(head(incr(incr(active(cons(mark(_x61), _x62))))))mark#(head(incr(cons(cons(_x81, _x82), mark(_x52))))) → active#(head(active(incr(cons(active(cons(mark(_x81), _x82)), _x52)))))
mark#(head(s(incr(s(s(s(_x121))))))) → active#(head(active(s(active(incr(active(s(active(s(active(s(mark(_x121)))))))))))))mark#(head(s(incr(s(tail(_x101)))))) → active#(head(s(active(incr(s(active(tail(mark(_x101)))))))))
mark#(head(s(s(incr(incr(_x101)))))) → active#(head(active(s(active(s(active(incr(active(incr(mark(_x101)))))))))))mark#(head(incr(cons(cons(active(mark(active(_x81))), _x82), mark(_x52))))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x52)))))
mark#(head(incr(head(cons(_x71, _x72))))) → active#(head(incr(active(head(active(cons(mark(_x71), _x72)))))))mark#(head(incr(incr(tail(cons(cons(_x91, _x92), _x82)))))) → active#(head(incr(incr(active(tail(cons(active(cons(mark(_x91), _x92)), _x82)))))))
mark#(head(incr(incr(tail(cons(_x71, _x72)))))) → active#(head(incr(incr(tail(active(cons(_x71, _x72)))))))mark#(head(incr(cons(cons(incr(_x91), _x72), _x62)))) → active#(head(incr(cons(active(cons(active(incr(mark(_x91))), _x72)), _x62))))
mark#(cons(_x21, _x22)) → active#(cons(_x21, _x22))mark#(head(s(incr(s(s(cons(_x121, _x122))))))) → active#(head(active(s(active(incr(active(s(active(s(active(cons(mark(_x121), _x122))))))))))))
mark#(head(s(s(incr(_x81))))) → active#(head(active(s(active(s(incr(mark(_x81))))))))mark#(head(s(odds))) → active#(head(active(s(active(odds)))))
mark#(head(incr(cons(pairs, active(mark(_x52)))))) → active#(head(active(incr(cons(pairs, _x52)))))mark#(head(s(incr(s(tail(s(_x111))))))) → active#(head(active(s(active(incr(s(active(tail(active(s(mark(_x111))))))))))))
mark#(head(s(incr(s(tail(incr(tail(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(incr(active(tail(mark(_x141)))))))))))))))mark#(head(incr(incr(s(_x81))))) → active#(head(active(incr(active(incr(active(s(mark(_x81)))))))))
mark#(head(incr(cons(incr(_x71), mark(active(_x72)))))) → active#(head(active(incr(cons(active(incr(mark(_x71))), _x72)))))mark#(head(incr(cons(pairs, active(mark(_x52)))))) → active#(head(active(incr(cons(cons(0, incr(odds)), _x52)))))
mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(active(active(_x31))))))) → active#(head(mark(cons(s(tail(cons(active(incr(mark(_x111))), _x92))), incr(_x31)))))mark#(head(s(s(s(_x81))))) → active#(head(active(s(s(active(s(mark(_x81))))))))
mark#(head(s(incr(s(incr(tail(incr(pairs)))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(pairs))))))))))))))mark#(head(incr(cons(s(pairs), _x62)))) → active#(head(active(incr(cons(active(s(active(pairs))), _x62)))))
mark#(head(incr(cons(tail(cons(_x91, _x92)), active(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(mark(_x91), _x92))), _x62)))))mark#(head(s(s(incr(head(_x91)))))) → active#(head(active(s(s(active(incr(active(head(mark(_x91))))))))))
mark#(head(s(incr(s(incr(tail(incr(_x141)))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(incr(mark(_x141)))))))))))))mark#(head(s(s(incr(_x81))))) → active#(head(active(s(s(incr(mark(_x81)))))))
mark#(head(s(s(incr(_x81))))) → active#(head(s(s(active(incr(mark(_x81)))))))mark#(head(incr(cons(tail(cons(incr(head(0)), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(active(0))))), _x92)), _x62)))))
mark#(head(s(incr(s(incr(tail(incr(_x141)))))))) → active#(head(s(incr(active(s(active(incr(active(tail(active(incr(mark(_x141)))))))))))))mark#(head(incr(tail(_x61)))) → active#(head(active(incr(active(tail(mark(_x61)))))))
mark#(head(incr(cons(tail(cons(incr(head(s(_x131))), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(active(s(mark(_x131))))))), _x92)), _x62)))))mark#(head(s(s(head(_x81))))) → active#(head(active(s(active(s(active(head(mark(_x81)))))))))
mark#(head(s(0))) → active#(head(active(s(active(0)))))mark#(head(incr(incr(0)))) → active#(head(incr(incr(active(0)))))
mark#(head(incr(cons(cons(_x81, _x82), active(_x52))))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x52)))))mark#(head(incr(cons(tail(cons(incr(cons(_x121, _x122)), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(cons(mark(_x121), _x122)))), _x92))), _x62)))))
mark#(head(incr(cons(_x61, mark(active(_x31)))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))mark#(head(s(incr(s(_x81))))) → active#(head(active(s(incr(active(s(mark(_x81))))))))
mark#(head(incr(cons(cons(_x81, active(mark(_x82))), _x62)))) → active#(head(incr(cons(active(cons(_x81, _x82)), _x62))))mark#(head(incr(cons(tail(cons(incr(head(_x141)), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(head(mark(_x141))))), _x92))), _x52)))))
mark#(head(incr(cons(s(head(_x91)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(head(mark(_x91))))), _x72)))))mark#(head(incr(cons(tail(cons(incr(_x111), _x82)), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(incr(mark(_x111)), _x82)), _x52)))))
mark#(head(s(incr(s(tail(0)))))) → active#(head(active(s(active(incr(s(active(tail(active(0))))))))))mark#(head(incr(cons(pairs, mark(_x52))))) → active#(head(incr(cons(active(pairs), _x52))))
mark#(head(incr(cons(cons(mark(_x61), active(_x62)), _x42)))) → active#(head(incr(cons(cons(_x61, _x62), _x42))))mark#(head(incr(cons(tail(cons(tail(_x101), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(tail(mark(_x101))), _x92))), _x62)))))
mark#(head(incr(cons(tail(cons(incr(_x91), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(_x91)), _x92)), _x62)))))mark#(head(s(cons(pairs, _x62)))) → active#(head(active(s(active(cons(active(pairs), _x62))))))
mark#(head(incr(cons(cons(_x81, _x82), _x62)))) → active#(head(active(incr(active(cons(active(cons(mark(_x81), _x82)), _x62))))))mark#(head(incr(incr(tail(cons(nats, _x82)))))) → active#(head(incr(incr(active(tail(cons(active(nats), _x82)))))))
mark#(head(incr(cons(s(cons(0, _x92)), mark(active(active(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(0), _x92)))), _x52)))))mark#(head(s(head(_x61)))) → active#(head(active(s(active(head(mark(_x61)))))))
mark#(head(incr(cons(tail(cons(incr(_x111), mark(_x72))), active(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x111))), _x72)), _x62)))))mark#(head(s(incr(s(incr(0)))))) → active#(head(active(s(active(incr(active(s(active(incr(active(0)))))))))))
mark#(head(s(s(_x61)))) → active#(head(s(active(s(mark(_x61))))))mark#(head(X)) → mark#(X)
mark#(head(incr(cons(nats, mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(nats), _x52)))))mark#(head(incr(incr(nats)))) → active#(head(active(incr(active(incr(active(nats)))))))
mark#(head(s(incr(s(s(_x101)))))) → active#(head(s(active(incr(active(s(active(s(mark(_x101))))))))))mark#(head(incr(cons(tail(cons(incr(nats), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(nats))), _x92)), _x62)))))
mark#(head(s(nats))) → active#(head(active(s(nats))))mark#(head(incr(cons(cons(active(_x71), _x72), mark(_x62))))) → active#(head(active(incr(cons(cons(_x71, _x72), _x62)))))
mark#(head(incr(cons(tail(cons(incr(s(_x121)), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(s(mark(_x121))))), _x92))), _x62)))))mark#(head(s(cons(_x61, _x62)))) → active#(head(active(s(cons(mark(_x61), _x62)))))
mark#(head(incr(cons(tail(cons(0, _x102)), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(0, _x102)))), _x62)))))mark#(head(s(s(s(pairs))))) → active#(head(active(s(active(s(active(s(active(pairs)))))))))
mark#(head(incr(head(0)))) → active#(head(incr(active(head(active(0))))))mark#(head(incr(incr(tail(head(odds)))))) → active#(head(incr(incr(active(tail(active(head(active(odds)))))))))
mark#(head(incr(cons(s(_x71), mark(active(active(_x52))))))) → active#(head(active(incr(cons(active(s(mark(_x71))), _x52)))))mark#(head(incr(cons(tail(cons(incr(incr(_x121)), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(incr(mark(_x121))))), _x92))), _x62)))))
mark#(head(incr(incr(incr(_x61))))) → active#(head(incr(incr(active(incr(mark(_x61)))))))mark#(head(incr(cons(0, active(mark(_x72)))))) → active#(head(active(incr(cons(active(0), _x72)))))
mark#(head(incr(cons(tail(cons(incr(_x111), _x102)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(incr(mark(_x111)), _x102))), _x52)))))mark#(head(tail(pairs))) → active#(head(active(tail(active(pairs)))))
mark#(head(incr(incr(tail(cons(_x91, _x92)))))) → active#(head(incr(active(incr(active(tail(active(cons(mark(_x91), _x92)))))))))mark#(head(s(incr(s(tail(s(0))))))) → active#(head(active(s(active(incr(active(s(active(tail(s(active(0))))))))))))
mark#(head(incr(cons(tail(cons(incr(0), _x92)), active(active(_x31)))))) → active#(head(mark(cons(s(tail(cons(active(incr(active(0))), _x92))), incr(_x31)))))mark#(head(incr(cons(s(_x71), mark(active(_x31)))))) → active#(head(mark(cons(s(active(s(mark(_x71)))), incr(_x31)))))
mark#(head(incr(cons(cons(_x71, active(_x72)), _x31)))) → active#(head(mark(cons(s(active(cons(_x71, _x72))), incr(_x31)))))mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(active(odds), _x92)))), _x72)))))
mark#(cons(incr(_x31), X2)) → active#(cons(active(incr(mark(_x31))), X2))mark#(head(incr(cons(cons(_x81, _x82), active(_x52))))) → active#(head(active(incr(cons(active(cons(mark(_x81), _x82)), _x52)))))
mark#(head(0)) → active#(head(active(0)))mark#(head(incr(cons(nats, active(_x72))))) → active#(head(active(incr(active(cons(active(nats), _x72))))))
mark#(head(s(incr(s(incr(_x111)))))) → active#(head(active(s(active(incr(active(s(active(incr(_x111))))))))))mark#(head(incr(cons(tail(cons(_x101, _x102)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(_x101, _x102))), _x52)))))
mark#(head(s(s(s(odds))))) → active#(head(s(active(s(s(odds))))))mark#(head(incr(incr(tail(odds))))) → active#(head(incr(incr(active(tail(active(odds)))))))
mark#(head(incr(cons(cons(_x81, active(mark(_x82))), active(_x52))))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x52)))))mark#(head(incr(pairs))) → active#(head(incr(mark(cons(0, incr(odds))))))
mark#(head(s(incr(s(head(_x101)))))) → active#(head(active(s(active(incr(active(s(active(head(mark(_x101)))))))))))mark#(head(incr(cons(s(_x71), mark(active(_x52)))))) → active#(head(active(incr(cons(s(mark(_x71)), _x52)))))
mark#(head(incr(cons(cons(active(_x81), active(_x82)), _x62)))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x62)))))mark#(head(incr(cons(_x61, mark(active(_x72)))))) → active#(head(incr(cons(mark(_x61), _x72))))
mark#(head(incr(cons(s(odds), _x52)))) → active#(head(active(incr(cons(s(active(odds)), _x52)))))mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(cons(mark(cons(0, incr(odds))), _x62)))))
mark#(head(incr(incr(tail(cons(odds, _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(odds), _x82))))))))mark#(head(s(incr(s(incr(incr(incr(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(incr(mark(_x141)))))))))))))))
mark#(head(s(s(s(incr(_x101)))))) → active#(head(active(s(active(s(active(s(active(incr(mark(_x101)))))))))))mark#(head(incr(incr(incr(_x81))))) → active#(head(active(incr(active(incr(active(incr(mark(_x81)))))))))
mark#(head(incr(cons(tail(cons(_x91, mark(_x102))), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(mark(_x91), _x102))), _x52)))))mark#(head(s(incr(s(tail(s(0))))))) → active#(head(active(s(active(incr(s(active(tail(active(s(active(0))))))))))))
mark#(head(incr(cons(tail(cons(0, active(_x102))), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(active(0), _x102)))), _x62)))))mark#(head(s(incr(s(incr(tail(nats))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(nats)))))))))))))
mark#(head(s(incr(pairs)))) → active#(head(active(s(active(incr(active(pairs)))))))mark#(head(s(incr(s(incr(tail(tail(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(tail(mark(_x141)))))))))))))))
mark#(head(s(s(incr(nats))))) → active#(head(active(s(s(active(incr(nats)))))))mark#(head(cons(cons(_x61, _x62), _x32))) → active#(head(active(cons(active(cons(mark(_x61), _x62)), _x32))))
mark#(head(incr(cons(tail(cons(incr(_x91), _x92)), active(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(_x91)), _x92)), _x62)))))mark#(head(incr(incr(_x61)))) → active#(head(incr(active(incr(mark(_x61))))))
mark#(head(incr(incr(tail(cons(head(_x91), _x82)))))) → active#(head(incr(incr(active(tail(cons(active(head(mark(_x91))), _x82)))))))mark#(head(incr(cons(pairs, mark(active(_x72)))))) → active#(head(active(incr(cons(active(pairs), _x72)))))
mark#(head(incr(cons(pairs, _x52)))) → active#(head(active(incr(cons(pairs, _x52)))))mark#(head(incr(incr(odds)))) → active#(head(incr(active(incr(active(odds))))))
mark#(head(incr(incr(odds)))) → active#(head(incr(incr(active(odds)))))mark#(head(incr(odds))) → active#(head(active(incr(mark(incr(pairs))))))
mark#(head(incr(cons(cons(active(_x71), _x72), active(_x52))))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x52)))))mark#(head(incr(cons(s(_x71), mark(active(_x72)))))) → active#(head(incr(cons(active(s(mark(_x71))), _x72))))
mark#(head(s(s(s(odds))))) → active#(head(active(s(active(s(active(s(odds))))))))mark#(head(s(incr(s(_x81))))) → active#(head(s(active(incr(active(s(mark(_x81))))))))
mark#(head(incr(incr(tail(tail(_x61)))))) → active#(head(incr(incr(tail(active(tail(mark(_x61))))))))mark#(head(s(incr(s(tail(s(cons(_x141, _x142)))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(active(cons(mark(_x141), _x142))))))))))))))
mark#(head(incr(incr(0)))) → active#(head(active(incr(active(incr(active(0)))))))mark#(head(incr(cons(tail(_x71), _x62)))) → active#(head(incr(cons(active(tail(mark(_x71))), _x62))))
mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x111))), _x92))), _x62)))))mark#(head(s(incr(s(s(odds)))))) → active#(head(active(s(active(incr(active(s(active(s(active(odds)))))))))))
mark#(head(s(nats))) → active#(head(active(s(mark(cons(0, incr(nats)))))))mark#(head(incr(cons(_x61, mark(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))
mark#(head(incr(cons(head(_x81), mark(active(mark(_x31))))))) → active#(head(mark(cons(s(active(head(mark(_x81)))), incr(_x31)))))mark#(head(incr(cons(tail(cons(incr(tail(_x101)), _x92)), active(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(tail(mark(_x101))))), _x92)), _x62)))))
mark#(head(s(incr(s(tail(pairs)))))) → active#(head(active(s(active(incr(active(s(active(tail(active(pairs)))))))))))mark#(head(incr(cons(tail(cons(incr(head(_x101)), _x92)), active(active(active(_x31))))))) → active#(head(mark(cons(s(tail(cons(active(incr(active(head(mark(_x101))))), _x92))), incr(_x31)))))
mark#(head(incr(cons(tail(cons(_x91, active(_x82))), _x62)))) → active#(head(active(incr(cons(active(tail(cons(mark(_x91), _x82))), _x62)))))mark#(head(incr(cons(tail(cons(incr(_x101), _x92)), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(_x101)), _x92)), _x52)))))
mark#(head(incr(cons(tail(cons(incr(head(_x101)), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(head(mark(_x101)))), _x92)), _x62)))))mark#(head(incr(cons(pairs, mark(_x52))))) → active#(head(active(incr(cons(mark(cons(0, incr(odds))), _x52)))))
mark#(odds) → active#(odds)mark#(head(incr(head(nats)))) → active#(head(incr(active(head(mark(cons(0, incr(nats))))))))
mark#(head(incr(incr(_x71)))) → active#(head(active(incr(active(incr(_x71))))))mark#(head(s(s(incr(cons(_x91, _x92)))))) → active#(head(active(s(s(active(incr(active(cons(mark(_x91), _x92)))))))))
mark#(head(s(s(s(_x91))))) → active#(head(active(s(s(active(s(_x91)))))))mark#(head(incr(incr(tail(pairs))))) → active#(head(incr(incr(active(tail(active(pairs)))))))
mark#(head(incr(cons(tail(cons(_x91, _x92)), _x31)))) → active#(head(mark(cons(s(active(tail(active(cons(mark(_x91), _x92))))), incr(_x31)))))mark#(head(incr(incr(tail(cons(odds, active(_x72))))))) → active#(head(incr(incr(active(tail(cons(active(odds), _x72)))))))
mark#(head(incr(cons(incr(_x81), mark(active(mark(_x31))))))) → active#(head(mark(cons(s(active(incr(mark(_x81)))), incr(_x31)))))mark#(head(incr(cons(tail(cons(pairs, _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(pairs), _x92))), _x62)))))
mark#(head(s(s(s(odds))))) → active#(head(s(active(s(active(s(odds)))))))mark#(head(s(incr(s(tail(incr(head(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(incr(active(head(mark(_x141)))))))))))))))
mark#(head(incr(cons(tail(cons(incr(tail(_x101)), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(tail(mark(_x101))))), _x92)), _x62)))))mark#(head(s(incr(_x61)))) → active#(head(active(s(incr(mark(_x61))))))
mark#(head(s(s(incr(incr(_x91)))))) → active#(head(active(s(s(active(incr(active(incr(mark(_x91))))))))))mark#(head(incr(cons(_x61, mark(active(mark(active(_x71)))))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x71)))))
mark#(head(s(s(s(head(_x101)))))) → active#(head(active(s(active(s(active(s(active(head(mark(_x101)))))))))))mark#(head(incr(cons(cons(_x71, _x72), active(_x52))))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x72)), _x52)))))
mark#(head(incr(incr(tail(cons(_x81, mark(_x72))))))) → active#(head(incr(incr(tail(active(cons(mark(_x81), _x72)))))))mark#(head(s(incr(s(tail(head(_x121))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(head(mark(_x121)))))))))))))
mark#(head(incr(cons(tail(cons(incr(head(nats)), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(active(nats))))), _x92)), _x62)))))mark#(head(incr(cons(_x61, active(mark(active(_x52))))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))
mark#(head(incr(incr(tail(cons(_x81, mark(_x72))))))) → active#(head(incr(incr(active(tail(cons(mark(_x81), _x72)))))))mark#(head(s(incr(odds)))) → active#(head(active(s(active(incr(active(odds)))))))
mark#(head(incr(cons(tail(cons(incr(nats), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(nats))), _x92))), _x62)))))mark#(head(cons(_x31, _x32))) → active#(head(cons(mark(_x31), _x32)))
mark#(head(s(incr(s(incr(tail(incr(s(_x161))))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(incr(active(s(mark(_x161)))))))))))))))))mark#(head(incr(cons(tail(cons(0, _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(active(cons(active(0), _x92)))), _x52)))))
mark#(head(s(incr(s(tail(odds)))))) → active#(head(active(s(active(incr(active(s(active(tail(active(odds)))))))))))mark#(head(s(incr(s(incr(tail(incr(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(incr(mark(_x141))))))))))))))
mark#(head(incr(cons(pairs, mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(pairs), _x52)))))mark#(head(s(incr(s(tail(tail(_x91))))))) → active#(head(active(s(active(incr(s(tail(active(tail(mark(_x91)))))))))))
mark#(head(incr(incr(tail(_x61))))) → active#(head(incr(incr(active(tail(_x61))))))mark#(head(incr(cons(cons(active(_x71), _x72), _x62)))) → active#(head(incr(cons(active(cons(_x71, _x72)), _x62))))
mark#(head(s(s(incr(s(_x101)))))) → active#(head(active(s(active(s(active(incr(active(s(mark(_x101)))))))))))mark#(head(s(incr(s(incr(tail(incr(odds)))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(odds))))))))))))))
active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))mark#(head(s(s(s(tail(_x101)))))) → active#(head(active(s(active(s(active(s(active(tail(mark(_x101)))))))))))
mark#(head(incr(cons(_x61, active(mark(mark(_x52))))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))mark#(head(incr(cons(tail(_x71), active(_x52))))) → active#(head(active(incr(cons(active(tail(mark(_x71))), _x52)))))
mark#(head(incr(cons(tail(nats), _x62)))) → active#(head(active(incr(cons(active(tail(active(nats))), _x62)))))mark#(head(incr(cons(s(head(_x91)), _x62)))) → active#(head(active(incr(cons(active(s(active(head(mark(_x91))))), _x62)))))
mark#(head(s(s(incr(cons(_x101, _x102)))))) → active#(head(active(s(active(s(active(incr(active(cons(mark(_x101), _x102))))))))))mark#(head(incr(incr(tail(head(_x81)))))) → active#(head(incr(incr(tail(active(head(mark(_x81))))))))
mark#(head(s(incr(s(tail(nats)))))) → active#(head(active(s(active(incr(s(tail(active(nats)))))))))mark#(head(s(incr(s(tail(head(_x91))))))) → active#(head(active(s(active(incr(s(tail(active(head(mark(_x91)))))))))))
mark#(head(incr(cons(incr(_x81), active(_x52))))) → active#(head(active(incr(cons(active(incr(mark(_x81))), _x52)))))mark#(tail(X)) → mark#(X)
mark#(head(incr(incr(tail(cons(odds, _x82)))))) → active#(head(incr(incr(tail(cons(active(odds), _x82))))))mark#(head(s(s(s(odds))))) → active#(head(s(active(s(s(mark(incr(pairs))))))))
mark#(head(incr(cons(tail(pairs), _x62)))) → active#(head(active(incr(cons(active(tail(active(pairs))), _x62)))))active#(odds) → mark#(incr(pairs))
mark#(head(incr(cons(cons(_x81, active(mark(_x82))), _x31)))) → active#(head(mark(cons(s(active(cons(_x81, _x82))), incr(_x31)))))mark#(head(s(incr(s(incr(incr(s(_x131)))))))) → active#(head(s(active(incr(active(s(active(incr(active(incr(active(s(mark(_x131))))))))))))))
mark#(head(incr(cons(pairs, active(mark(_x31)))))) → active#(head(mark(cons(s(mark(cons(0, incr(odds)))), incr(_x31)))))mark#(head(incr(incr(tail(cons(pairs, _x82)))))) → active#(head(incr(incr(active(tail(cons(active(pairs), _x82)))))))
mark#(head(s(s(incr(nats))))) → active#(head(active(s(active(s(incr(active(nats))))))))mark#(head(incr(cons(head(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(head(mark(_x71))), _x72)))))
mark#(head(s(incr(s(tail(0)))))) → active#(head(active(s(active(incr(active(s(active(tail(active(0)))))))))))mark#(head(s(incr(s(incr(_x101)))))) → active#(head(active(s(active(incr(s(active(incr(mark(_x101))))))))))
mark#(head(incr(incr(tail(_x71))))) → active#(head(incr(active(incr(tail(mark(_x71)))))))mark#(head(incr(cons(cons(active(mark(_x91)), _x92), mark(_x62))))) → active#(head(active(incr(cons(cons(_x91, _x92), _x62)))))
mark#(head(s(incr(s(tail(s(_x121))))))) → active#(head(active(s(active(incr(active(s(active(tail(s(mark(_x121))))))))))))mark#(head(s(incr(s(incr(tail(head(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(head(mark(_x141)))))))))))))))
mark#(head(incr(cons(cons(_x71, active(mark(mark(_x72)))), _x62)))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x62)))))mark#(head(incr(_x41))) → active#(head(incr(_x41)))
mark#(head(incr(incr(head(_x71))))) → active#(head(incr(active(incr(active(head(mark(_x71))))))))mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(mark(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x111))), _x92))), _x62)))))
mark#(head(s(incr(s(_x81))))) → active#(head(active(s(active(incr(s(mark(_x81))))))))mark#(head(s(s(s(0))))) → active#(head(active(s(active(s(active(s(active(0)))))))))
mark#(head(incr(cons(_x71, mark(active(mark(_x72))))))) → active#(head(active(incr(cons(_x71, _x72)))))mark#(head(s(incr(s(tail(odds)))))) → active#(head(active(s(active(incr(s(tail(active(odds)))))))))
mark#(s(X)) → active#(s(mark(X)))mark#(head(incr(head(_x61)))) → active#(head(active(incr(active(head(mark(_x61)))))))
mark#(head(incr(cons(tail(cons(odds, _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(odds), _x92))), _x52)))))mark#(incr(X)) → mark#(X)
mark#(head(incr(head(_x51)))) → active#(head(incr(head(mark(_x51)))))mark#(head(incr(incr(tail(head(nats)))))) → active#(head(incr(incr(active(tail(active(head(active(nats)))))))))
mark#(head(incr(cons(cons(_x71, active(_x72)), active(_x42))))) → active#(head(incr(cons(active(cons(_x71, _x72)), _x42))))mark#(head(incr(cons(tail(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(tail(mark(_x71))), _x72)))))
mark#(head(pairs)) → active#(head(active(pairs)))mark#(head(incr(cons(s(s(_x91)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(s(mark(_x91))))), _x72)))))
mark#(head(s(incr(s(tail(pairs)))))) → active#(head(s(active(incr(s(active(tail(active(pairs)))))))))mark#(head(incr(cons(tail(_x81), mark(active(mark(_x31))))))) → active#(head(mark(cons(s(active(tail(mark(_x81)))), incr(_x31)))))
mark#(head(incr(cons(tail(cons(head(_x101), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(head(mark(_x101))), _x92))), _x62)))))mark#(head(incr(cons(cons(0, _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(0), _x72)), _x62)))))
mark#(head(incr(cons(tail(cons(odds, _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(active(odds), _x92)))), _x62)))))mark#(head(incr(cons(cons(cons(_x91, _x92), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(cons(mark(_x91), _x92)), _x72)), _x62)))))
mark#(head(incr(cons(s(cons(pairs, _x92)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(active(pairs), _x92)))), _x72)))))mark#(head(incr(cons(tail(cons(incr(s(_x121)), _x92)), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(s(mark(_x121))))), _x92)), _x52)))))
mark#(head(cons(0, _x32))) → active#(head(active(cons(active(0), _x32))))mark#(head(s(incr(s(s(tail(_x121))))))) → active#(head(active(s(active(incr(active(s(active(s(active(tail(mark(_x121)))))))))))))
mark#(head(incr(incr(_x41)))) → active#(head(incr(incr(_x41))))mark#(head(incr(incr(tail(head(s(_x101))))))) → active#(head(incr(incr(active(tail(active(head(active(s(mark(_x101)))))))))))
mark#(head(incr(incr(tail(cons(_x71, _x72)))))) → active#(head(incr(incr(active(tail(cons(_x71, _x72)))))))mark#(head(incr(incr(tail(head(pairs)))))) → active#(head(incr(incr(active(tail(active(head(active(pairs)))))))))
mark#(head(incr(incr(tail(cons(head(_x91), _x82)))))) → active#(head(incr(incr(tail(active(cons(active(head(mark(_x91))), _x82)))))))mark#(head(incr(cons(cons(active(mark(mark(_x81))), _x82), mark(_x52))))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x52)))))
mark#(head(incr(cons(tail(cons(incr(head(_x101)), _x92)), active(active(active(_x62))))))) → active#(head(incr(cons(tail(cons(active(incr(active(head(mark(_x101))))), _x92)), _x62))))mark#(head(incr(cons(tail(cons(incr(incr(_x121)), _x92)), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(incr(mark(_x121))))), _x92)), _x52)))))
mark#(head(s(s(incr(_x71))))) → active#(head(active(s(s(active(incr(_x71)))))))mark#(head(incr(incr(tail(head(_x81)))))) → active#(head(incr(incr(active(tail(head(mark(_x81))))))))
mark#(head(incr(cons(tail(cons(0, _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(0), _x92))), _x62)))))mark#(head(incr(cons(cons(incr(_x91), _x72), active(_x52))))) → active#(head(active(incr(cons(active(cons(active(incr(mark(_x91))), _x72)), _x52)))))
mark#(head(incr(cons(tail(cons(incr(head(head(_x131))), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(active(head(mark(_x131))))))), _x92)), _x62)))))mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(_x62))))) → active#(head(incr(cons(tail(cons(active(incr(mark(_x111))), _x92)), _x62))))
mark#(head(incr(cons(tail(cons(incr(_x101), mark(_x82))), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x82))), _x62)))))mark#(cons(X1, active(_x22))) → active#(cons(mark(X1), _x22))
mark#(head(incr(cons(tail(cons(odds, _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(odds), _x92))), _x62)))))mark#(head(s(incr(s(tail(pairs)))))) → active#(head(active(s(active(incr(s(active(tail(pairs)))))))))
mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(mark(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x111))), _x92)), _x52)))))mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(active(active(_x62))))))) → active#(head(incr(cons(tail(cons(active(incr(mark(_x111))), _x92)), _x62))))
mark#(head(incr(cons(tail(_x81), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(tail(mark(_x81))), _x52)))))mark#(head(incr(cons(s(incr(_x91)), _x62)))) → active#(head(active(incr(cons(active(s(active(incr(mark(_x91))))), _x62)))))
mark#(head(incr(incr(tail(head(tail(_x101))))))) → active#(head(incr(incr(active(tail(active(head(active(tail(mark(_x101)))))))))))mark#(head(incr(incr(tail(odds))))) → active#(head(incr(incr(tail(odds)))))
mark#(head(incr(cons(0, mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(0), _x52)))))mark#(head(incr(cons(tail(_x71), _x52)))) → active#(head(active(incr(cons(tail(mark(_x71)), _x52)))))
mark#(head(incr(incr(nats)))) → active#(head(incr(active(incr(active(nats))))))mark#(head(incr(cons(s(cons(0, active(_x102))), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(active(0), _x102)))), _x72)))))
mark#(head(incr(cons(cons(incr(s(_x121)), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(incr(active(s(mark(_x121))))), _x72)), _x62)))))mark#(head(incr(cons(cons(_x81, _x82), mark(active(mark(_x31))))))) → active#(head(mark(cons(s(active(cons(mark(_x81), _x82))), incr(_x31)))))
mark#(head(s(incr(head(_x81))))) → active#(head(active(s(active(incr(active(head(mark(_x81)))))))))mark#(head(incr(incr(tail(head(head(_x101))))))) → active#(head(incr(incr(active(tail(active(head(active(head(mark(_x101)))))))))))
mark#(head(incr(cons(tail(cons(_x91, _x92)), _x52)))) → active#(head(active(incr(cons(tail(cons(mark(_x91), _x92)), _x52)))))mark#(head(incr(cons(tail(cons(incr(_x101), _x92)), _x52)))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x101))), _x92)), _x52)))))
mark#(head(incr(incr(tail(cons(s(_x101), _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(s(mark(_x101))), _x82))))))))mark#(head(s(incr(s(tail(cons(_x91, _x92))))))) → active#(head(active(s(active(incr(s(tail(active(cons(mark(_x91), _x92))))))))))
mark#(head(s(incr(s(incr(tail(incr(incr(_x151))))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(incr(mark(_x151))))))))))))))))mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(active(cons(active(pairs), _x62))))))
mark#(head(s(s(s(nats))))) → active#(head(active(s(active(s(active(s(active(nats)))))))))mark#(head(incr(cons(nats, active(mark(_x72)))))) → active#(head(active(incr(cons(active(nats), _x72)))))
mark#(head(s(incr(s(incr(_x101)))))) → active#(head(active(s(incr(active(s(active(incr(mark(_x101))))))))))mark#(cons(pairs, X2)) → active#(cons(active(pairs), X2))
mark#(head(s(cons(nats, _x62)))) → active#(head(active(s(active(cons(active(nats), _x62))))))mark#(head(s(incr(s(tail(incr(_x121))))))) → active#(head(active(s(active(incr(s(active(tail(active(incr(mark(_x121))))))))))))
mark#(head(s(incr(s(incr(incr(_x121))))))) → active#(head(s(active(incr(active(s(incr(active(incr(mark(_x121)))))))))))mark#(head(s(s(incr(nats))))) → active#(head(active(s(s(incr(active(nats)))))))
mark#(head(incr(head(nats)))) → active#(head(incr(active(head(nats)))))mark#(head(s(cons(_x61, active(_x72))))) → active#(head(active(s(active(cons(mark(_x61), _x72))))))
mark#(head(incr(incr(s(_x61))))) → active#(head(incr(incr(active(s(mark(_x61)))))))mark#(head(incr(cons(tail(cons(incr(tail(_x141)), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(tail(mark(_x141))))), _x92))), _x52)))))
mark#(head(incr(cons(tail(cons(0, _x92)), _x62)))) → active#(head(incr(cons(active(tail(active(cons(active(0), _x92)))), _x62))))mark#(head(incr(incr(tail(cons(tail(_x101), _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(tail(mark(_x101))), _x82))))))))
mark#(head(incr(cons(s(0), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(0))), _x72)))))mark#(head(incr(cons(tail(cons(incr(0), active(_x82))), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(0))), _x82)), _x52)))))
mark#(head(s(incr(s(s(_x101)))))) → active#(head(active(s(incr(active(s(active(s(mark(_x101))))))))))mark#(head(incr(cons(0, mark(active(mark(_x31))))))) → active#(head(mark(cons(s(active(0)), incr(_x31)))))
mark#(head(incr(cons(cons(_x71, active(_x72)), mark(_x52))))) → active#(head(incr(cons(cons(_x71, _x72), _x52))))mark#(head(incr(cons(cons(_x71, _x72), mark(active(_x72)))))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x72)), _x72)))))
mark#(head(s(incr(s(tail(0)))))) → active#(head(active(s(active(incr(s(tail(active(0)))))))))mark#(head(incr(cons(_x61, mark(active(active(_x52))))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))
mark#(head(s(incr(s(s(pairs)))))) → active#(head(active(s(active(incr(active(s(active(s(active(pairs)))))))))))mark#(head(s(incr(s(incr(incr(_x121))))))) → active#(head(active(s(active(incr(active(s(incr(active(incr(mark(_x121))))))))))))
mark#(head(s(incr(tail(_x81))))) → active#(head(active(s(active(incr(active(tail(mark(_x81)))))))))mark#(head(incr(cons(cons(incr(nats), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(incr(active(nats))), _x72)), _x62)))))
mark#(head(incr(cons(incr(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(incr(mark(_x71))), _x72)))))mark#(head(s(incr(s(incr(tail(incr(cons(_x151, _x152))))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(cons(mark(_x151), _x152)))))))))))))))
mark#(head(incr(incr(_x61)))) → active#(head(active(incr(incr(mark(_x61))))))mark#(head(s(incr(s(incr(incr(_x111))))))) → active#(head(s(active(incr(active(s(active(incr(active(incr(_x111)))))))))))
mark#(head(incr(cons(s(_x71), _x31)))) → active#(head(mark(cons(s(active(s(mark(_x71)))), incr(_x31)))))mark#(head(incr(cons(cons(_x71, _x72), _x31)))) → active#(head(mark(cons(s(active(cons(mark(_x71), _x72))), incr(_x31)))))
mark#(head(s(s(odds)))) → active#(head(active(s(active(s(mark(incr(pairs))))))))mark#(head(incr(cons(tail(cons(cons(_x111, _x112), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(active(cons(mark(_x111), _x112)), _x92)))), _x62)))))
mark#(head(s(incr(s(tail(incr(_x121))))))) → active#(head(active(s(active(incr(active(s(tail(active(incr(mark(_x121))))))))))))mark#(head(incr(cons(cons(active(mark(_x91)), _x92), mark(active(_x62)))))) → active#(head(active(incr(cons(active(cons(_x91, _x92)), _x62)))))
mark#(head(incr(cons(tail(odds), _x62)))) → active#(head(active(incr(cons(active(tail(active(odds))), _x62)))))mark#(head(s(s(s(_x91))))) → active#(head(active(s(active(s(s(_x91)))))))
mark#(head(incr(incr(tail(cons(_x81, mark(_x92))))))) → active#(head(incr(incr(active(tail(active(cons(mark(_x81), _x92))))))))mark#(head(incr(cons(_x61, mark(mark(_x72)))))) → active#(head(active(incr(cons(mark(_x61), _x72)))))
mark#(head(incr(cons(tail(cons(incr(head(cons(_x131, _x132))), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(active(cons(mark(_x131), _x132)))))), _x92)), _x62)))))mark#(head(s(incr(s(tail(s(_x121))))))) → active#(head(active(s(active(incr(s(active(tail(active(s(mark(_x121))))))))))))
mark#(head(incr(cons(tail(cons(incr(incr(_x101)), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(incr(mark(_x101))))), _x92)), _x62)))))mark#(head(incr(cons(_x71, mark(_x72))))) → active#(head(active(incr(cons(_x71, _x72)))))
mark#(head(incr(cons(s(_x81), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(mark(_x81))), _x52)))))mark#(head(incr(cons(tail(cons(pairs, _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(active(pairs), _x92)))), _x62)))))
mark#(head(incr(cons(odds, _x52)))) → active#(head(active(incr(cons(odds, _x52)))))mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(active(cons(mark(cons(0, incr(nats))), _x62))))))
mark#(head(s(incr(s(s(_x101)))))) → active#(head(active(s(active(incr(s(active(s(mark(_x101))))))))))mark#(head(s(s(incr(nats))))) → active#(head(s(s(active(incr(active(nats)))))))
mark#(head(s(s(incr(head(_x101)))))) → active#(head(active(s(active(s(active(incr(active(head(mark(_x101)))))))))))mark#(head(s(incr(s(s(_x101)))))) → active#(head(active(s(active(incr(active(s(s(mark(_x101))))))))))
mark#(head(incr(cons(head(_x71), _x62)))) → active#(head(active(incr(cons(active(head(mark(_x71))), _x62)))))mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(cons(mark(_x61), _x62))))
mark#(head(s(incr(s(tail(tail(_x121))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(tail(mark(_x121)))))))))))))mark#(head(incr(cons(incr(_x71), _x62)))) → active#(head(active(incr(cons(active(incr(mark(_x71))), _x62)))))
mark#(head(incr(cons(tail(cons(incr(0), _x92)), active(active(_x52)))))) → active#(head(incr(cons(tail(cons(active(incr(active(0))), _x92)), _x52))))mark#(head(incr(cons(tail(cons(incr(incr(_x141)), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(incr(mark(_x141))))), _x92))), _x52)))))
mark#(head(s(incr(s(tail(cons(_x121, _x122))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(cons(mark(_x121), _x122))))))))))))mark#(head(s(s(incr(tail(_x101)))))) → active#(head(active(s(active(s(active(incr(active(tail(mark(_x101)))))))))))
mark#(head(incr(cons(tail(cons(0, _x92)), _x52)))) → active#(head(active(incr(cons(tail(active(cons(active(0), _x92))), _x52)))))mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(active(cons(active(odds), _x62))))))
mark#(head(s(pairs))) → active#(head(active(s(active(pairs)))))mark#(head(cons(_x31, active(_x52)))) → active#(head(active(cons(mark(_x31), _x52))))
mark#(head(incr(cons(tail(cons(_x91, _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(active(cons(mark(_x91), _x92)))), _x52)))))mark#(head(incr(cons(s(cons(s(_x111), _x92)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(active(s(mark(_x111))), _x92)))), _x72)))))
mark#(head(incr(incr(tail(s(_x81)))))) → active#(head(incr(incr(active(tail(active(s(mark(_x81)))))))))mark#(head(incr(incr(tail(odds))))) → active#(head(incr(active(incr(active(tail(active(odds))))))))
mark#(cons(cons(_x31, _x32), X2)) → active#(cons(active(cons(mark(_x31), _x32)), X2))mark#(head(incr(incr(tail(cons(0, _x82)))))) → active#(head(incr(incr(active(tail(cons(active(0), _x82)))))))
mark#(head(incr(cons(tail(cons(s(_x101), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(s(mark(_x101))), _x92))), _x62)))))mark#(head(s(cons(tail(_x81), _x62)))) → active#(head(active(s(active(cons(active(tail(mark(_x81))), _x62))))))
mark#(head(incr(cons(tail(cons(incr(head(_x101)), _x92)), active(active(active(active(_x52)))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(mark(_x101))))), _x92)), _x52)))))mark#(head(incr(cons(s(pairs), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(pairs))), _x72)))))
mark#(head(incr(cons(head(_x81), active(_x52))))) → active#(head(active(incr(cons(active(head(mark(_x81))), _x52)))))mark#(head(incr(cons(cons(active(mark(_x91)), _x92), mark(mark(_x62)))))) → active#(head(active(incr(cons(active(cons(_x91, _x92)), _x62)))))
mark#(head(s(incr(s(tail(s(_x121))))))) → active#(head(active(s(incr(active(s(active(tail(active(s(mark(_x121))))))))))))mark#(head(incr(cons(pairs, active(mark(_x31)))))) → active#(head(mark(cons(s(active(pairs)), incr(_x31)))))
mark#(head(incr(cons(nats, mark(active(_x72)))))) → active#(head(active(incr(cons(active(nats), _x72)))))mark#(head(incr(cons(tail(cons(_x81, _x82)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(_x81, _x82))), _x62)))))
mark#(head(s(incr(s(tail(_x101)))))) → active#(head(s(active(incr(active(s(active(tail(mark(_x101))))))))))mark#(head(s(incr(s(incr(tail(incr(_x141)))))))) → active#(head(active(s(active(incr(active(s(incr(active(tail(active(incr(mark(_x141))))))))))))))
mark#(head(incr(cons(cons(incr(_x91), _x72), _x52)))) → active#(head(active(incr(cons(cons(active(incr(mark(_x91))), _x72), _x52)))))mark#(head(incr(incr(tail(nats))))) → active#(head(incr(incr(tail(active(nats))))))
mark#(head(s(incr(s(tail(s(_x131))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(_x131))))))))))))mark#(head(incr(cons(tail(_x81), mark(_x52))))) → active#(head(active(incr(cons(active(tail(mark(_x81))), _x52)))))
mark#(head(incr(cons(cons(_x81, _x82), _x52)))) → active#(head(active(incr(cons(cons(_x81, _x82), _x52)))))mark#(head(incr(cons(cons(_x81, active(active(_x82))), _x62)))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x62)))))
mark#(head(incr(incr(tail(cons(tail(_x91), _x82)))))) → active#(head(incr(incr(tail(active(cons(active(tail(mark(_x91))), _x82)))))))mark#(head(s(cons(head(_x81), _x62)))) → active#(head(active(s(active(cons(active(head(mark(_x81))), _x62))))))
mark#(head(incr(cons(_x61, _x31)))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(active(active(active(_x52)))))))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x111))), _x92)), _x52)))))
mark#(head(incr(cons(tail(cons(_x91, _x92)), _x31)))) → active#(head(mark(cons(s(active(tail(cons(mark(_x91), _x92)))), incr(_x31)))))mark#(head(incr(s(_x61)))) → active#(head(active(incr(active(s(mark(_x61)))))))
mark#(head(s(incr(s(incr(tail(incr(head(_x161))))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(incr(active(head(mark(_x161)))))))))))))))))mark#(head(s(incr(s(_x91))))) → active#(head(active(s(active(incr(active(s(_x91))))))))
mark#(head(incr(cons(tail(incr(_x91)), _x62)))) → active#(head(active(incr(cons(active(tail(active(incr(mark(_x91))))), _x62)))))mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(_x31)))))) → active#(head(mark(cons(s(active(s(active(cons(mark(_x91), _x92))))), incr(_x31)))))
mark#(head(incr(incr(pairs)))) → active#(head(incr(active(incr(active(pairs))))))mark#(head(incr(cons(s(cons(0, _x92)), mark(active(_x31)))))) → active#(head(mark(cons(s(active(s(active(cons(active(0), _x92))))), incr(_x31)))))
mark#(head(incr(pairs))) → active#(head(active(incr(mark(cons(0, incr(odds)))))))mark#(head(incr(incr(s(_x71))))) → active#(head(incr(active(incr(active(s(mark(_x71))))))))
mark#(head(s(s(s(_x81))))) → active#(head(active(s(active(s(s(mark(_x81))))))))mark#(head(incr(cons(s(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(s(mark(_x71))), _x72)))))
mark#(head(incr(odds))) → active#(head(incr(active(odds))))mark#(head(incr(cons(nats, mark(_x52))))) → active#(head(active(incr(cons(active(nats), _x52)))))
mark#(head(incr(cons(cons(_x81, _x82), mark(_x52))))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x52)))))mark#(head(incr(cons(_x61, active(_x52))))) → active#(head(incr(cons(mark(_x61), _x52))))
mark#(head(incr(cons(tail(cons(incr(_x101), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x92))), _x52)))))mark#(head(incr(cons(cons(active(active(_x81)), _x82), _x62)))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x62)))))
mark#(head(incr(cons(cons(_x61, active(mark(_x62))), _x62)))) → active#(head(incr(cons(active(cons(_x61, _x62)), _x62))))mark#(head(s(incr(s(incr(tail(incr(cons(_x161, _x162))))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(incr(active(cons(mark(_x161), _x162))))))))))))))))
mark#(head(s(incr(s(incr(tail(incr(nats)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(incr(active(nats)))))))))))))))mark#(head(incr(cons(cons(active(mark(_x91)), _x92), mark(_x31))))) → active#(head(mark(cons(s(active(cons(_x91, _x92))), incr(_x31)))))
mark#(head(s(incr(s(tail(incr(_x121))))))) → active#(head(active(s(incr(active(s(active(tail(active(incr(mark(_x121))))))))))))mark#(head(incr(cons(tail(cons(_x91, _x92)), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(mark(_x91), _x92))), _x52)))))
mark#(head(s(incr(s(incr(tail(incr(0)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(incr(active(0)))))))))))))))mark#(head(s(incr(s(tail(incr(odds))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(incr(active(odds)))))))))))))
mark#(head(incr(cons(tail(tail(_x91)), _x62)))) → active#(head(active(incr(cons(active(tail(active(tail(mark(_x91))))), _x62)))))mark#(head(incr(incr(tail(_x81))))) → active#(head(incr(active(incr(active(tail(_x81)))))))
mark#(head(incr(cons(cons(active(_x81), mark(_x82)), _x62)))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x62)))))mark#(head(incr(cons(tail(cons(incr(odds), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(odds))), _x92))), _x62)))))
mark#(head(incr(cons(tail(cons(_x91, mark(_x82))), _x62)))) → active#(head(active(incr(cons(active(tail(cons(mark(_x91), _x82))), _x62)))))mark#(head(s(s(tail(_x81))))) → active#(head(active(s(active(s(active(tail(mark(_x81)))))))))
mark#(head(s(incr(s(incr(incr(cons(_x141, _x142)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(cons(mark(_x141), _x142))))))))))))))mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(active(mark(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x111))), _x92)), _x62)))))
mark#(pairs) → active#(pairs)active#(pairs) → mark#(cons(0, incr(odds)))
mark#(head(incr(cons(tail(cons(incr(head(odds)), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(active(odds))))), _x92)), _x62)))))mark#(head(incr(cons(tail(cons(_x91, _x92)), active(_x31))))) → active#(head(mark(cons(s(active(tail(cons(mark(_x91), _x92)))), incr(_x31)))))
mark#(head(incr(cons(tail(cons(incr(pairs), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(pairs))), _x92))), _x52)))))mark#(head(head(_x31))) → active#(head(active(head(mark(_x31)))))
mark#(head(s(incr(s(incr(s(_x121))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(s(mark(_x121)))))))))))))mark#(head(incr(cons(tail(cons(incr(odds), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(odds))), _x92)), _x62)))))
mark#(head(s(s(incr(pairs))))) → active#(head(active(s(active(s(active(incr(active(pairs)))))))))mark#(head(s(incr(s(incr(incr(head(_x131)))))))) → active#(head(s(active(incr(active(s(active(incr(active(incr(active(head(mark(_x131))))))))))))))
mark#(head(incr(cons(pairs, mark(active(_x62)))))) → active#(head(active(incr(cons(active(pairs), _x62)))))mark#(head(incr(incr(tail(nats))))) → active#(head(incr(active(incr(active(tail(active(nats))))))))
mark#(head(s(cons(_x71, _x72)))) → active#(head(active(s(active(cons(_x71, _x72))))))mark#(head(incr(cons(odds, mark(active(_x72)))))) → active#(head(active(incr(cons(active(odds), _x72)))))
mark#(head(tail(0))) → active#(head(active(tail(active(0)))))mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(mark(cons(0, incr(odds)))))))))
mark#(head(s(s(s(odds))))) → active#(head(s(s(s(active(odds))))))mark#(head(incr(cons(head(_x81), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(head(mark(_x81))), _x52)))))
mark#(head(incr(incr(0)))) → active#(head(incr(active(incr(active(0))))))mark#(head(incr(cons(cons(odds, _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(odds), _x72)), _x62)))))
mark#(head(incr(cons(tail(cons(_x91, active(_x102))), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(mark(_x91), _x102))), _x52)))))mark#(head(incr(incr(tail(cons(_x81, active(_x72))))))) → active#(head(incr(incr(tail(active(cons(mark(_x81), _x72)))))))
mark#(head(incr(pairs))) → active#(head(active(incr(pairs))))mark#(head(incr(cons(cons(mark(_x71), active(mark(_x72))), _x62)))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x62)))))
mark#(head(incr(cons(nats, _x72)))) → active#(head(active(incr(active(cons(nats, _x72))))))mark#(head(s(tail(_x61)))) → active#(head(active(s(active(tail(mark(_x61)))))))
mark#(head(incr(cons(tail(cons(incr(pairs), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(pairs))), _x92))), _x62)))))mark#(head(incr(cons(tail(cons(_x91, _x92)), mark(_x52))))) → active#(head(active(incr(cons(active(tail(active(cons(mark(_x91), _x92)))), _x52)))))
mark#(head(s(incr(cons(_x81, _x82))))) → active#(head(active(s(active(incr(active(cons(mark(_x81), _x82))))))))mark#(head(tail(_x31))) → active#(head(tail(mark(_x31))))
mark#(head(s(cons(_x61, _x62)))) → active#(head(s(active(cons(mark(_x61), _x62)))))mark#(head(s(incr(s(incr(cons(_x121, _x122))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(cons(mark(_x121), _x122))))))))))))
mark#(head(incr(cons(cons(active(_x71), _x72), mark(active(_x62)))))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x62)))))mark#(head(incr(cons(tail(cons(incr(odds), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(odds))), _x92))), _x52)))))
mark#(head(s(incr(s(tail(pairs)))))) → active#(head(active(s(active(incr(s(tail(active(pairs)))))))))mark#(head(incr(incr(tail(head(_x61)))))) → active#(head(incr(incr(tail(active(head(mark(_x61))))))))
mark#(head(s(incr(s(tail(incr(s(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(incr(active(s(mark(_x141)))))))))))))))mark#(head(incr(cons(s(cons(0, _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(active(0), _x92))), _x52)))))
mark#(head(incr(cons(cons(_x71, _x72), active(mark(_x72)))))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x72)), _x72)))))mark#(head(incr(cons(_x61, mark(active(mark(mark(_x72)))))))) → active#(head(active(incr(cons(mark(_x61), _x72)))))
mark#(head(incr(cons(s(cons(_x91, mark(_x102))), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(mark(_x91), _x102)))), _x72)))))mark#(head(incr(incr(tail(0))))) → active#(head(incr(incr(active(tail(active(0)))))))
mark#(head(s(incr(s(tail(s(0))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(0))))))))))))mark#(head(s(incr(s(cons(_x101, _x102)))))) → active#(head(active(s(active(incr(active(s(active(cons(mark(_x101), _x102))))))))))
mark#(head(s(incr(s(tail(s(odds))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(active(odds)))))))))))))mark#(head(incr(cons(s(odds), _x62)))) → active#(head(incr(cons(active(s(active(odds))), _x62))))
mark#(head(s(cons(cons(_x81, _x82), _x62)))) → active#(head(active(s(active(cons(active(cons(mark(_x81), _x82)), _x62))))))mark#(head(incr(cons(_x51, _x52)))) → active#(head(incr(active(cons(mark(_x51), _x52)))))
mark#(head(incr(cons(tail(cons(0, mark(_x102))), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(active(0), _x102)))), _x62)))))mark#(head(s(incr(s(tail(incr(_x111))))))) → active#(head(active(s(active(incr(s(active(tail(active(incr(mark(_x111))))))))))))
mark#(head(incr(incr(cons(_x71, _x72))))) → active#(head(incr(active(incr(active(cons(mark(_x71), _x72)))))))mark#(head(incr(cons(tail(cons(incr(_x101), _x82)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(incr(mark(_x101)), _x82))), _x62)))))
mark#(head(incr(cons(_x61, active(mark(_x31)))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))mark#(head(incr(cons(s(_x71), _x62)))) → active#(head(incr(cons(active(s(mark(_x71))), _x62))))
mark#(head(incr(cons(_x51, mark(active(_x52)))))) → active#(head(active(incr(cons(_x51, _x52)))))mark#(head(incr(cons(tail(cons(incr(cons(_x101, _x102)), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(cons(mark(_x101), _x102)))), _x92)), _x62)))))
mark#(head(incr(cons(incr(_x81), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(incr(mark(_x81))), _x52)))))mark#(head(incr(incr(tail(head(incr(_x101))))))) → active#(head(incr(incr(active(tail(active(head(active(incr(mark(_x101)))))))))))
mark#(head(incr(cons(cons(active(_x61), active(_x62)), _x42)))) → active#(head(incr(cons(cons(_x61, _x62), _x42))))mark#(head(incr(cons(tail(cons(incr(head(tail(_x131))), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(active(tail(mark(_x131))))))), _x92)), _x62)))))
mark#(head(s(incr(s(incr(tail(0))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(0)))))))))))))mark#(head(incr(odds))) → active#(head(active(incr(odds))))
mark#(head(incr(incr(head(_x81))))) → active#(head(active(incr(active(incr(active(head(mark(_x81)))))))))mark#(head(incr(cons(tail(cons(incr(odds), _x92)), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(odds))), _x92)), _x52)))))
mark#(head(incr(cons(tail(cons(_x91, _x92)), active(_x52))))) → active#(head(incr(cons(active(tail(cons(mark(_x91), _x92))), _x52))))mark#(head(incr(cons(tail(cons(incr(cons(_x101, _x102)), _x92)), active(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(cons(mark(_x101), _x102)))), _x92)), _x62)))))
mark#(head(s(incr(s(tail(s(_x91))))))) → active#(head(active(s(active(incr(s(tail(active(s(mark(_x91)))))))))))mark#(head(incr(cons(pairs, active(mark(mark(_x52))))))) → active#(head(active(incr(cons(active(pairs), _x52)))))
mark#(head(incr(cons(s(cons(tail(_x111), _x92)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(active(tail(mark(_x111))), _x92)))), _x72)))))mark#(head(s(incr(_x71)))) → active#(head(active(s(active(incr(_x71))))))
mark#(head(s(incr(s(tail(s(pairs))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(active(pairs)))))))))))))mark#(head(incr(incr(tail(head(0)))))) → active#(head(incr(incr(active(tail(active(head(active(0)))))))))
mark#(head(_x21)) → active#(head(_x21))mark#(head(incr(cons(s(_x81), _x62)))) → active#(head(active(incr(cons(active(s(_x81)), _x62)))))
mark#(head(incr(cons(tail(cons(incr(head(_x101)), active(_x72))), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(mark(_x101))))), _x72)), _x62)))))mark#(cons(s(_x31), X2)) → active#(cons(active(s(mark(_x31))), X2))
mark#(head(s(s(odds)))) → active#(head(active(s(active(s(odds))))))mark#(head(cons(odds, _x32))) → active#(head(active(cons(active(odds), _x32))))
mark#(head(s(incr(s(tail(tail(_x111))))))) → active#(head(active(s(active(incr(s(active(tail(active(tail(mark(_x111))))))))))))mark#(head(incr(cons(s(cons(_x101, _x102)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(_x101, _x102)))), _x72)))))
mark#(head(incr(cons(nats, active(_x52))))) → active#(head(active(incr(cons(active(nats), _x52)))))mark#(head(incr(cons(0, active(_x52))))) → active#(head(active(incr(cons(active(0), _x52)))))
mark#(head(incr(cons(tail(cons(nats, _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(active(nats), _x92)))), _x62)))))mark#(head(incr(cons(s(_x71), _x52)))) → active#(head(active(incr(cons(s(mark(_x71)), _x52)))))
mark#(head(incr(cons(tail(cons(incr(s(_x141)), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(s(mark(_x141))))), _x92))), _x52)))))mark#(head(incr(cons(tail(cons(incr(_x111), _x72)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(incr(mark(_x111)), _x72)), _x62)))))
mark#(head(s(incr(s(tail(s(tail(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(active(tail(mark(_x141)))))))))))))))mark#(head(incr(cons(nats, mark(_x72))))) → active#(head(active(incr(active(cons(active(nats), _x72))))))
mark#(head(s(s(incr(s(_x91)))))) → active#(head(active(s(s(active(incr(active(s(mark(_x91))))))))))mark#(head(incr(cons(tail(cons(incr(head(_x121)), _x92)), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(mark(_x121))))), _x92)), _x52)))))
mark#(head(s(s(pairs)))) → active#(head(active(s(s(active(pairs))))))mark#(head(tail(s(_x61)))) → active#(head(active(tail(active(s(mark(_x61)))))))
mark#(head(incr(cons(pairs, active(mark(_x72)))))) → active#(head(incr(cons(mark(cons(0, incr(odds))), _x72))))mark#(head(s(incr(s(incr(_x101)))))) → active#(head(s(active(incr(active(s(active(incr(mark(_x101))))))))))
mark#(cons(tail(_x31), X2)) → active#(cons(active(tail(mark(_x31))), X2))mark#(head(incr(cons(tail(cons(incr(head(_x101)), _x92)), active(active(active(mark(_x52)))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(mark(_x101))))), _x92)), _x52)))))
mark#(head(s(incr(s(tail(s(s(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(active(s(mark(_x141)))))))))))))))mark#(head(s(incr(s(incr(tail(incr(odds)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(incr(active(odds)))))))))))))))
mark#(head(s(s(incr(nats))))) → active#(head(active(s(active(s(active(incr(nats))))))))mark#(head(s(s(s(odds))))) → active#(head(s(s(active(s(active(odds)))))))
mark#(head(s(s(s(_x91))))) → active#(head(s(active(s(active(s(_x91)))))))mark#(head(incr(cons(s(cons(head(_x111), _x92)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(active(head(mark(_x111))), _x92)))), _x72)))))
mark#(head(incr(cons(pairs, active(mark(mark(_x42))))))) → active#(head(incr(cons(active(pairs), _x42))))mark#(head(s(incr(s(pairs))))) → active#(head(active(s(active(incr(active(s(active(pairs)))))))))
mark#(head(s(incr(s(tail(incr(nats))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(incr(active(nats)))))))))))))mark#(head(incr(incr(nats)))) → active#(head(incr(incr(active(nats)))))
mark#(head(incr(0))) → active#(head(active(incr(active(0)))))mark#(head(s(incr(s(tail(incr(0))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(incr(active(0)))))))))))))
mark#(head(incr(cons(odds, active(mark(_x72)))))) → active#(head(active(incr(cons(active(odds), _x72)))))mark#(head(incr(incr(tail(cons(odds, _x72)))))) → active#(head(incr(incr(active(tail(cons(odds, _x72)))))))
mark#(head(incr(cons(s(tail(_x91)), _x62)))) → active#(head(active(incr(cons(active(s(active(tail(mark(_x91))))), _x62)))))mark#(head(cons(_x31, mark(_x52)))) → active#(head(active(cons(mark(_x31), _x52))))
mark#(head(s(incr(s(odds))))) → active#(head(active(s(active(incr(active(s(active(odds)))))))))mark#(head(s(incr(s(incr(tail(_x131))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(_x131))))))))))))
mark#(head(incr(cons(tail(cons(pairs, _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(pairs), _x92))), _x52)))))mark#(head(incr(cons(tail(cons(incr(odds), _x92)), active(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(odds))), _x92)), _x62)))))
mark#(head(incr(cons(tail(_x71), _x31)))) → active#(head(mark(cons(s(active(tail(mark(_x71)))), incr(_x31)))))mark#(head(incr(cons(s(_x81), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(_x81)), _x72)))))
mark#(head(s(s(0)))) → active#(head(active(s(active(s(active(0)))))))mark#(head(s(incr(s(s(0)))))) → active#(head(active(s(active(incr(active(s(active(s(active(0)))))))))))
mark#(head(s(incr(s(incr(incr(0))))))) → active#(head(s(active(incr(active(s(active(incr(active(incr(active(0))))))))))))mark#(head(incr(cons(tail(cons(incr(_x111), active(_x72))), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x111))), _x72)), _x62)))))
mark#(head(incr(head(odds)))) → active#(head(incr(active(head(active(odds))))))mark#(head(incr(cons(cons(_x71, active(mark(active(_x72)))), _x62)))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x62)))))
mark#(head(incr(cons(s(odds), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(odds))), _x72)))))mark#(head(incr(incr(tail(cons(_x91, _x92)))))) → active#(head(incr(incr(active(tail(active(cons(_x91, _x92))))))))
mark#(head(incr(cons(tail(cons(incr(tail(_x121)), _x92)), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(tail(mark(_x121))))), _x92)), _x52)))))mark#(head(s(incr(s(incr(tail(incr(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(tail(active(incr(mark(_x141))))))))))))))
mark#(head(s(s(s(_x81))))) → active#(head(s(active(s(active(s(mark(_x81))))))))mark#(head(s(incr(s(incr(tail(incr(pairs)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(incr(active(pairs)))))))))))))))
mark#(head(incr(incr(pairs)))) → active#(head(active(incr(active(incr(active(pairs)))))))mark#(head(incr(cons(s(s(_x91)), _x62)))) → active#(head(active(incr(cons(active(s(active(s(mark(_x91))))), _x62)))))
mark#(head(s(incr(s(s(nats)))))) → active#(head(active(s(active(incr(active(s(active(s(active(nats)))))))))))mark#(head(incr(incr(tail(head(cons(_x101, _x102))))))) → active#(head(incr(incr(active(tail(active(head(active(cons(mark(_x101), _x102))))))))))
mark#(head(incr(cons(s(_x71), active(_x52))))) → active#(head(active(incr(cons(active(s(mark(_x71))), _x52)))))mark#(head(incr(cons(s(cons(cons(_x111, _x112), _x92)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(active(cons(mark(_x111), _x112)), _x92)))), _x72)))))
mark#(head(incr(cons(tail(cons(incr(cons(_x121, _x122)), _x92)), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(cons(mark(_x121), _x122)))), _x92)), _x52)))))mark#(head(incr(incr(tail(cons(odds, _x51)))))) → active#(head(incr(incr(mark(_x51)))))
mark#(head(incr(cons(cons(active(_x71), _x72), _x31)))) → active#(head(mark(cons(s(active(cons(_x71, _x72))), incr(_x31)))))mark#(head(incr(incr(tail(incr(_x91)))))) → active#(head(incr(active(incr(active(tail(active(incr(mark(_x91))))))))))
mark#(head(incr(incr(_x61)))) → active#(head(incr(active(incr(_x61)))))mark#(head(incr(cons(odds, mark(active(mark(_x31))))))) → active#(head(mark(cons(s(active(odds)), incr(_x31)))))
mark#(head(incr(incr(tail(cons(odds, mark(_x72))))))) → active#(head(incr(incr(active(tail(cons(active(odds), _x72)))))))mark#(head(s(s(cons(_x81, _x82))))) → active#(head(active(s(active(s(active(cons(mark(_x81), _x82))))))))
mark#(head(incr(head(pairs)))) → active#(head(incr(active(head(active(pairs))))))mark#(cons(0, X2)) → active#(cons(active(0), X2))
mark#(head(s(incr(s(tail(s(head(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(active(head(mark(_x141)))))))))))))))mark#(head(incr(cons(cons(_x71, active(_x72)), mark(_x42))))) → active#(head(incr(cons(active(cons(_x71, _x72)), _x42))))
mark#(head(incr(cons(0, mark(active(_x72)))))) → active#(head(active(incr(cons(active(0), _x72)))))mark#(head(s(incr(s(incr(tail(incr(tail(_x151))))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(tail(mark(_x151))))))))))))))))
mark#(head(s(s(s(odds))))) → active#(head(active(s(s(active(s(active(odds))))))))mark#(head(incr(incr(tail(cons(s(_x91), _x82)))))) → active#(head(incr(incr(active(tail(cons(active(s(mark(_x91))), _x82)))))))
mark#(head(s(incr(s(incr(incr(_x121))))))) → active#(head(s(active(incr(active(s(active(incr(incr(mark(_x121)))))))))))mark#(head(incr(cons(tail(cons(incr(head(_x101)), _x92)), active(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(mark(_x101))))), _x92)), _x62)))))
mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(_x31))))) → active#(head(mark(cons(s(active(tail(cons(active(incr(mark(_x111))), _x92)))), incr(_x31)))))mark#(head(incr(cons(tail(cons(0, _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(0), _x92))), _x52)))))
mark#(head(incr(incr(tail(cons(_x81, _x82)))))) → active#(head(incr(incr(tail(cons(mark(_x81), _x82))))))mark#(head(incr(cons(tail(cons(s(_x111), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(s(mark(_x111))), _x92))), _x52)))))
mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(active(_x52)))))) → active#(head(incr(cons(tail(cons(active(incr(mark(_x111))), _x92)), _x52))))mark#(head(incr(cons(tail(cons(_x91, _x92)), _x62)))) → active#(head(incr(cons(active(tail(cons(mark(_x91), _x92))), _x62))))
mark#(head(s(incr(s(tail(incr(pairs))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(incr(active(pairs)))))))))))))mark#(head(incr(incr(tail(pairs))))) → active#(head(incr(incr(tail(active(pairs))))))
mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(_x111)), _x92))), _x62)))))mark#(head(tail(nats))) → active#(head(active(tail(active(nats)))))
mark#(head(incr(cons(pairs, _x62)))) → active#(head(incr(cons(active(pairs), _x62))))mark#(head(incr(cons(cons(_x71, mark(_x72)), _x62)))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x62)))))
mark#(head(incr(cons(cons(_x61, active(active(_x62))), _x42)))) → active#(head(incr(cons(cons(_x61, _x62), _x42))))mark#(head(incr(cons(pairs, mark(mark(_x62)))))) → active#(head(active(incr(cons(active(pairs), _x62)))))
mark#(head(s(incr(s(tail(incr(incr(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(incr(active(incr(mark(_x141)))))))))))))))mark#(head(incr(cons(odds, _x42)))) → active#(head(incr(cons(odds, _x42))))
mark#(nats) → active#(nats)mark#(head(s(s(pairs)))) → active#(head(s(active(s(active(pairs))))))
mark#(head(incr(cons(tail(head(_x91)), _x62)))) → active#(head(active(incr(cons(active(tail(active(head(mark(_x91))))), _x62)))))mark#(head(incr(cons(cons(_x71, active(_x72)), mark(_x52))))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x52)))))
mark#(head(incr(cons(tail(_x71), mark(_x52))))) → active#(head(active(incr(cons(active(tail(mark(_x71))), _x52)))))mark#(head(incr(cons(_x61, mark(_x52))))) → active#(head(incr(cons(mark(_x61), _x52))))
mark#(head(incr(cons(tail(cons(incr(nats), _x92)), active(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(nats))), _x92)), _x62)))))mark#(head(incr(cons(_x61, mark(_x31))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))
mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(active(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(mark(_x91), _x92)))), _x52)))))active#(head(cons(X, XS))) → mark#(X)
mark#(head(incr(cons(tail(cons(incr(0), _x92)), active(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(0))), _x92)), _x62)))))mark#(head(incr(incr(tail(s(_x61)))))) → active#(head(incr(incr(tail(active(s(mark(_x61))))))))
mark#(head(s(incr(s(incr(tail(incr(_x131)))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(_x131)))))))))))))mark#(head(incr(cons(s(incr(_x91)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(incr(mark(_x91))))), _x72)))))
mark#(head(incr(cons(cons(_x81, _x82), _x62)))) → active#(head(incr(cons(active(cons(_x81, _x82)), _x62))))mark#(head(incr(cons(_x61, active(mark(_x72)))))) → active#(head(incr(cons(mark(_x61), _x72))))
mark#(head(incr(cons(cons(active(_x71), _x72), mark(_x31))))) → active#(head(mark(cons(s(active(cons(_x71, _x72))), incr(_x31)))))mark#(head(incr(incr(tail(_x81))))) → active#(head(active(incr(active(incr(active(tail(mark(_x81)))))))))
mark#(head(incr(cons(tail(cons(0, _x92)), mark(_x52))))) → active#(head(active(incr(cons(active(tail(active(cons(active(0), _x92)))), _x52)))))mark#(head(cons(_x51, _x52))) → active#(head(active(cons(_x51, _x52))))
mark#(head(s(_x51))) → active#(head(active(s(_x51))))mark#(head(incr(head(_x61)))) → active#(head(incr(active(head(_x61)))))
mark#(head(incr(cons(cons(active(_x71), _x72), _x52)))) → active#(head(active(incr(cons(cons(_x71, _x72), _x52)))))mark#(head(s(s(s(odds))))) → active#(head(active(s(active(s(s(active(odds))))))))
mark#(head(s(incr(s(incr(incr(head(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(head(mark(_x141)))))))))))))))mark#(head(incr(cons(odds, mark(_x42))))) → active#(head(incr(cons(active(odds), _x42))))
mark#(head(s(s(incr(0))))) → active#(head(active(s(active(s(active(incr(active(0)))))))))mark#(head(s(incr(s(incr(tail(incr(_x141)))))))) → active#(head(active(s(incr(active(s(active(incr(tail(active(incr(mark(_x141)))))))))))))
mark#(head(incr(cons(s(odds), mark(_x52))))) → active#(head(active(incr(cons(active(s(active(odds))), _x52)))))mark#(head(incr(cons(tail(cons(incr(s(_x101)), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(s(mark(_x101))))), _x92)), _x62)))))
mark#(cons(odds, X2)) → active#(cons(active(odds), X2))mark#(head(s(incr(s(incr(nats)))))) → active#(head(active(s(active(incr(active(s(active(incr(active(nats)))))))))))
mark#(head(incr(cons(_x61, active(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(cons(mark(incr(pairs)), _x62)))))
mark#(head(incr(cons(tail(cons(incr(0), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(0))), _x92))), _x52)))))mark#(head(s(incr(s(tail(s(0))))))) → active#(head(s(active(incr(active(s(active(tail(active(s(active(0))))))))))))
mark#(head(incr(cons(odds, active(_x52))))) → active#(head(active(incr(cons(active(odds), _x52)))))mark#(head(s(incr(s(tail(nats)))))) → active#(head(active(s(active(incr(s(active(tail(active(nats))))))))))
mark#(head(incr(cons(tail(_x81), _x62)))) → active#(head(active(incr(cons(active(tail(_x81)), _x62)))))mark#(head(incr(cons(cons(incr(0), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(incr(active(0))), _x72)), _x62)))))
mark#(cons(head(_x31), X2)) → active#(cons(active(head(mark(_x31))), X2))mark#(head(incr(incr(tail(tail(_x91)))))) → active#(head(incr(active(incr(active(tail(active(tail(mark(_x91))))))))))
mark#(head(incr(cons(cons(incr(_x91), active(_x82)), _x62)))) → active#(head(active(incr(cons(active(cons(active(incr(mark(_x91))), _x82)), _x62)))))mark#(head(incr(incr(tail(_x51))))) → active#(head(incr(incr(tail(_x51)))))
mark#(head(incr(incr(head(_x61))))) → active#(head(incr(incr(active(head(mark(_x61)))))))mark#(head(s(incr(s(tail(s(nats))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(active(nats)))))))))))))
mark#(head(s(incr(s(incr(tail(incr(s(_x151))))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(s(mark(_x151))))))))))))))))mark#(head(incr(incr(tail(cons(_x61, _x62)))))) → active#(head(incr(incr(tail(active(cons(mark(_x61), _x62)))))))
mark#(head(incr(cons(tail(cons(incr(head(pairs)), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(active(pairs))))), _x92)), _x62)))))mark#(head(s(incr(s(tail(incr(cons(_x141, _x142)))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(incr(active(cons(mark(_x141), _x142))))))))))))))
mark#(head(s(incr(s(incr(tail(odds))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(odds)))))))))))))mark#(head(s(s(incr(odds))))) → active#(head(active(s(active(s(active(incr(active(odds)))))))))
mark#(head(incr(incr(tail(s(_x91)))))) → active#(head(incr(active(incr(active(tail(active(s(mark(_x91))))))))))mark#(head(incr(incr(tail(cons(_x81, _x51)))))) → active#(head(incr(incr(mark(_x51)))))
mark#(head(cons(s(_x61), _x32))) → active#(head(active(cons(active(s(mark(_x61))), _x32))))mark#(head(incr(head(nats)))) → active#(head(incr(head(active(nats)))))
mark#(head(incr(cons(tail(cons(incr(incr(_x101)), _x92)), active(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(incr(mark(_x101))))), _x92)), _x62)))))mark#(head(incr(cons(tail(cons(nats, _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(nats), _x92))), _x52)))))
mark#(head(s(s(_x71)))) → active#(head(active(s(active(s(_x71))))))mark#(head(incr(incr(tail(_x61))))) → active#(head(incr(incr(active(tail(mark(_x61)))))))
mark#(head(incr(cons(tail(s(_x91)), _x62)))) → active#(head(active(incr(cons(active(tail(active(s(mark(_x91))))), _x62)))))mark#(head(incr(incr(tail(cons(0, _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(0), _x82))))))))
mark#(head(s(s(incr(_x91))))) → active#(head(active(s(active(s(active(incr(_x91))))))))mark#(head(s(incr(s(tail(s(0))))))) → active#(head(active(s(incr(active(s(active(tail(active(s(active(0))))))))))))
mark#(head(incr(nats))) → active#(head(incr(active(nats))))mark#(head(incr(incr(tail(cons(cons(_x101, _x102), _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(cons(mark(_x101), _x102)), _x82))))))))
mark#(head(s(incr(s(incr(incr(tail(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(tail(mark(_x141)))))))))))))))mark#(head(s(_x31))) → active#(head(s(mark(_x31))))
mark#(head(incr(incr(tail(head(_x91)))))) → active#(head(incr(active(incr(active(tail(active(head(mark(_x91))))))))))mark#(head(s(incr(_x61)))) → active#(head(s(active(incr(mark(_x61))))))
mark#(head(incr(incr(tail(cons(odds, _x82)))))) → active#(head(incr(incr(active(tail(cons(mark(incr(pairs)), _x82)))))))mark#(head(odds)) → active#(head(active(odds)))
mark#(head(s(cons(_x61, mark(_x72))))) → active#(head(active(s(active(cons(mark(_x61), _x72))))))mark#(head(incr(cons(tail(cons(incr(0), mark(_x82))), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(0))), _x82)), _x52)))))
mark#(head(incr(cons(cons(_x71, active(_x72)), active(_x52))))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x52)))))mark#(head(s(incr(s(incr(incr(0))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(0)))))))))))))
mark#(head(incr(cons(tail(cons(incr(_x111), active(_x102))), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x111))), _x102))), _x52)))))mark#(head(s(incr(s(incr(incr(_x121))))))) → active#(head(s(incr(active(s(active(incr(active(incr(mark(_x121)))))))))))
mark#(head(incr(cons(pairs, active(mark(_x42)))))) → active#(head(incr(cons(pairs, _x42))))mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(active(_x31)))))) → active#(head(mark(cons(s(tail(cons(active(incr(mark(_x111))), _x92))), incr(_x31)))))
mark#(head(incr(cons(tail(cons(incr(cons(_x141, _x142)), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(cons(mark(_x141), _x142)))), _x92))), _x52)))))mark#(head(incr(cons(cons(incr(_x111), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(incr(_x111)), _x72)), _x62)))))
mark#(head(s(incr(s(incr(tail(s(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(s(mark(_x141)))))))))))))))mark#(head(s(incr(s(tail(_x101)))))) → active#(head(active(s(incr(s(tail(mark(_x101))))))))
mark#(head(s(cons(s(_x81), _x62)))) → active#(head(active(s(active(cons(active(s(mark(_x81))), _x62))))))mark#(head(s(incr(s(tail(s(incr(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(active(incr(mark(_x141)))))))))))))))
mark#(head(incr(cons(cons(_x71, mark(_x82)), _x62)))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x82)), _x62)))))mark#(head(incr(cons(cons(_x61, active(active(_x62))), _x62)))) → active#(head(incr(cons(active(cons(_x61, _x62)), _x62))))
mark#(head(s(incr(s(incr(incr(nats))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(nats)))))))))))))mark#(head(incr(cons(tail(cons(incr(_x111), _x72)), active(_x62))))) → active#(head(active(incr(cons(tail(cons(incr(mark(_x111)), _x72)), _x62)))))
mark#(head(incr(cons(tail(cons(_x91, mark(_x102))), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(mark(_x91), _x102)))), _x62)))))mark#(head(s(incr(s(incr(incr(_x121))))))) → active#(head(active(s(active(incr(s(active(incr(active(incr(mark(_x121))))))))))))
mark#(head(s(incr(s(incr(tail(incr(_x141)))))))) → active#(head(s(active(incr(active(s(active(incr(active(tail(active(incr(mark(_x141))))))))))))))mark#(head(incr(cons(odds, _x31)))) → active#(head(mark(cons(s(active(odds)), incr(_x31)))))
mark#(head(incr(cons(odds, mark(_x52))))) → active#(head(active(incr(cons(active(odds), _x52)))))mark#(head(incr(cons(tail(cons(incr(pairs), _x92)), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(pairs))), _x92)), _x52)))))
mark#(head(incr(head(incr(_x71))))) → active#(head(incr(active(head(active(incr(mark(_x71))))))))mark#(head(incr(cons(tail(_x81), active(_x52))))) → active#(head(active(incr(cons(active(tail(mark(_x81))), _x52)))))
mark#(head(s(s(s(active(_x81)))))) → active#(head(active(s(active(s(active(s(_x81))))))))mark#(head(incr(cons(tail(cons(incr(nats), _x92)), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(nats))), _x92)), _x52)))))
mark#(head(incr(cons(tail(cons(s(_x111), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(active(s(mark(_x111))), _x92)))), _x62)))))mark#(head(incr(pairs))) → active#(head(incr(pairs)))
mark#(head(incr(cons(tail(cons(incr(_x111), mark(_x72))), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x111))), _x72)), _x62)))))mark#(head(s(incr(s(incr(incr(incr(_x131)))))))) → active#(head(s(active(incr(active(s(active(incr(active(incr(active(incr(mark(_x131))))))))))))))
mark#(head(incr(cons(cons(active(_x71), active(mark(_x72))), _x62)))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x62)))))mark#(head(s(s(_x61)))) → active#(head(active(s(s(mark(_x61))))))
mark#(head(s(s(incr(nats))))) → active#(head(active(s(s(active(incr(mark(cons(0, incr(nats))))))))))mark#(head(incr(cons(head(_x71), mark(active(_x72)))))) → active#(head(active(incr(cons(active(head(mark(_x71))), _x72)))))
mark#(head(incr(cons(cons(incr(tail(_x121)), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(incr(active(tail(mark(_x121))))), _x72)), _x62)))))mark#(head(s(s(incr(tail(_x91)))))) → active#(head(active(s(s(active(incr(active(tail(mark(_x91))))))))))
mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(cons(active(0), _x62)))))mark#(head(s(incr(s(s(_x111)))))) → active#(head(active(s(active(incr(active(s(active(s(_x111))))))))))
mark#(head(incr(cons(_x71, active(_x72))))) → active#(head(active(incr(cons(_x71, _x72)))))mark#(head(incr(cons(cons(incr(head(_x121)), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(incr(active(head(mark(_x121))))), _x72)), _x62)))))
mark#(head(incr(cons(s(_x81), _x62)))) → active#(head(active(incr(active(cons(active(s(mark(_x81))), _x62))))))mark#(head(incr(incr(tail(cons(head(_x101), _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(head(mark(_x101))), _x82))))))))
mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(_x52))))) → active#(head(incr(cons(active(tail(cons(active(incr(mark(_x111))), _x92))), _x52))))mark#(head(incr(cons(tail(cons(incr(_x101), _x92)), _x62)))) → active#(head(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x92))), _x62))))
mark#(head(incr(cons(tail(cons(incr(pairs), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(pairs))), _x92)), _x62)))))mark#(head(incr(incr(tail(cons(0, _x82)))))) → active#(head(incr(incr(tail(active(cons(active(0), _x82)))))))
mark#(head(incr(cons(tail(cons(incr(_x111), mark(_x82))), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x111))), _x82)), _x52)))))mark#(head(incr(cons(tail(cons(incr(_x101), _x92)), _x31)))) → active#(head(mark(cons(s(active(tail(cons(active(incr(mark(_x101))), _x92)))), incr(_x31)))))
mark#(head(incr(cons(odds, active(_x42))))) → active#(head(incr(cons(active(odds), _x42))))mark#(head(s(s(incr(odds))))) → active#(head(active(s(s(active(incr(active(odds))))))))
mark#(head(incr(cons(_x61, active(_x31))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))mark#(head(incr(cons(cons(incr(_x91), _x82), _x62)))) → active#(head(active(incr(cons(active(cons(incr(mark(_x91)), _x82)), _x62)))))
mark#(head(s(incr(nats)))) → active#(head(active(s(active(incr(active(nats)))))))mark#(head(incr(cons(tail(0), _x62)))) → active#(head(active(incr(cons(active(tail(active(0))), _x62)))))
mark#(head(incr(cons(s(odds), active(_x52))))) → active#(head(active(incr(cons(active(s(active(odds))), _x52)))))mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(active(cons(active(0), _x62))))))
mark#(head(s(incr(s(incr(tail(incr(tail(_x161))))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(incr(active(tail(mark(_x161)))))))))))))))))mark#(head(incr(incr(tail(cons(pairs, _x82)))))) → active#(head(incr(incr(tail(active(cons(active(pairs), _x82)))))))
mark#(head(s(incr(s(tail(incr(_x121))))))) → active#(head(active(s(active(incr(active(s(active(tail(incr(mark(_x121))))))))))))mark#(head(incr(incr(tail(nats))))) → active#(head(incr(incr(active(tail(active(nats)))))))
mark#(head(s(incr(s(incr(incr(_x121))))))) → active#(head(s(active(incr(s(active(incr(active(incr(mark(_x121)))))))))))mark#(head(incr(incr(tail(cons(nats, _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(nats), _x82))))))))
mark#(head(incr(cons(cons(incr(_x91), _x72), _x31)))) → active#(head(mark(cons(s(active(cons(active(incr(mark(_x91))), _x72))), incr(_x31)))))mark#(head(s(incr(s(tail(pairs)))))) → active#(head(active(s(incr(s(active(tail(active(pairs)))))))))
mark#(head(s(incr(s(tail(_x101)))))) → active#(head(s(active(incr(s(tail(mark(_x101))))))))mark#(head(incr(cons(tail(cons(cons(_x111, _x112), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(cons(mark(_x111), _x112)), _x92))), _x52)))))
mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(cons(mark(_x91), _x92))), _x72)))))mark#(head(incr(cons(tail(cons(head(_x111), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(active(head(mark(_x111))), _x92)))), _x62)))))
mark#(head(incr(cons(cons(active(_x71), _x72), mark(mark(_x62)))))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x62)))))mark#(head(incr(cons(s(0), _x62)))) → active#(head(active(incr(cons(active(s(active(0))), _x62)))))
mark#(head(incr(cons(cons(active(active(_x91)), _x92), mark(_x52))))) → active#(head(active(incr(cons(active(cons(_x91, _x92)), _x52)))))mark#(head(incr(cons(cons(_x81, _x82), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(cons(mark(_x81), _x82)), _x52)))))
mark#(head(s(s(odds)))) → active#(head(s(active(s(active(odds))))))mark#(head(tail(_x51))) → active#(head(active(tail(_x51))))
mark#(head(incr(cons(nats, mark(active(mark(_x31))))))) → active#(head(mark(cons(s(active(nats)), incr(_x31)))))mark#(head(incr(cons(tail(cons(incr(_x111), mark(_x102))), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x111))), _x102))), _x52)))))
mark#(head(incr(s(_x51)))) → active#(head(incr(active(s(mark(_x51))))))mark#(head(incr(head(s(_x71))))) → active#(head(incr(active(head(active(s(mark(_x71))))))))
mark#(head(s(incr(s(incr(tail(pairs))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(pairs)))))))))))))mark#(head(s(incr(s(incr(incr(_x121))))))) → active#(head(active(s(incr(active(s(active(incr(active(incr(mark(_x121))))))))))))
mark#(head(s(incr(s(incr(tail(_x121))))))) → active#(head(active(s(active(incr(active(s(incr(active(tail(mark(_x121))))))))))))mark#(head(s(incr(s(tail(_x101)))))) → active#(head(active(s(active(incr(active(s(tail(mark(_x101))))))))))
mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(_x31))))) → active#(head(mark(cons(s(tail(cons(active(incr(mark(_x111))), _x92))), incr(_x31)))))mark#(head(incr(cons(tail(_x81), _x62)))) → active#(head(active(incr(active(cons(active(tail(mark(_x81))), _x62))))))
mark#(head(s(s(s(mark(_x81)))))) → active#(head(active(s(active(s(active(s(_x81))))))))mark#(head(incr(incr(cons(_x81, _x82))))) → active#(head(active(incr(active(incr(active(cons(mark(_x81), _x82))))))))
mark#(head(incr(cons(_x71, _x72)))) → active#(head(active(incr(active(cons(_x71, _x72))))))mark#(head(incr(incr(tail(cons(pairs, _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(pairs), _x82))))))))
mark#(head(incr(cons(s(cons(0, _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(0), _x92)))), _x72))))mark#(head(s(incr(s(tail(incr(_x91))))))) → active#(head(active(s(active(incr(s(tail(active(incr(mark(_x91)))))))))))
mark#(head(s(incr(s(incr(incr(_x121))))))) → active#(head(active(s(active(incr(active(s(active(incr(incr(mark(_x121))))))))))))mark#(head(incr(cons(s(odds), _x31)))) → active#(head(mark(cons(s(active(s(active(odds)))), incr(_x31)))))
mark#(head(incr(cons(cons(incr(_x91), mark(_x82)), _x62)))) → active#(head(active(incr(cons(active(cons(active(incr(mark(_x91))), _x82)), _x62)))))mark#(head(incr(cons(_x61, mark(active(mark(mark(_x71)))))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x71)))))
mark#(head(s(incr(s(tail(incr(_x131))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(incr(_x131))))))))))))mark#(head(incr(cons(cons(incr(cons(_x121, _x122)), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(incr(active(cons(mark(_x121), _x122)))), _x72)), _x62)))))
mark#(head(tail(head(_x61)))) → active#(head(active(tail(active(head(mark(_x61)))))))mark#(head(incr(cons(pairs, active(mark(active(_x52))))))) → active#(head(active(incr(cons(active(pairs), _x52)))))
mark#(head(incr(incr(pairs)))) → active#(head(incr(incr(active(pairs)))))mark#(head(incr(cons(s(cons(incr(_x111), _x92)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(active(incr(mark(_x111))), _x92)))), _x72)))))
mark#(head(incr(incr(tail(odds))))) → active#(head(incr(incr(tail(mark(incr(pairs)))))))mark#(head(s(incr(s(tail(odds)))))) → active#(head(active(s(active(incr(s(active(tail(active(odds))))))))))
mark#(head(incr(cons(pairs, active(_x52))))) → active#(head(active(incr(cons(active(pairs), _x52)))))mark#(head(incr(cons(_x61, mark(active(mark(active(_x72)))))))) → active#(head(active(incr(cons(mark(_x61), _x72)))))
mark#(head(incr(cons(tail(cons(_x91, _x92)), active(_x62))))) → active#(head(active(incr(cons(tail(cons(mark(_x91), _x92)), _x62)))))mark#(head(incr(cons(tail(cons(incr(nats), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(nats))), _x92))), _x52)))))
mark#(head(incr(cons(tail(cons(incr(head(_x101)), _x72)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(incr(active(head(mark(_x101)))), _x72)), _x62)))))mark#(head(incr(cons(pairs, _x31)))) → active#(head(mark(cons(s(active(pairs)), incr(_x31)))))
mark#(head(incr(cons(cons(incr(_x91), _x72), mark(_x52))))) → active#(head(active(incr(cons(active(cons(active(incr(mark(_x91))), _x72)), _x52)))))mark#(head(incr(cons(s(nats), _x62)))) → active#(head(active(incr(cons(active(s(active(nats))), _x62)))))
mark#(head(incr(cons(pairs, active(mark(_x72)))))) → active#(head(active(incr(cons(active(cons(mark(0), incr(odds))), _x72)))))mark#(head(incr(cons(cons(active(mark(_x81)), _x82), _x62)))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x62)))))
mark#(head(s(s(incr(nats))))) → active#(head(active(s(active(s(active(incr(mark(cons(0, incr(nats)))))))))))mark#(head(incr(cons(cons(_x71, _x72), _x62)))) → active#(head(incr(cons(active(cons(mark(_x71), _x72)), _x62))))
mark#(head(s(incr(s(tail(nats)))))) → active#(head(active(s(active(incr(active(s(active(tail(active(nats)))))))))))mark#(head(incr(cons(tail(cons(_x91, _x92)), active(mark(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(mark(_x91), _x92))), _x62)))))
mark#(head(s(s(incr(pairs))))) → active#(head(active(s(s(active(incr(active(pairs))))))))mark#(head(incr(cons(cons(_x81, _x82), _x31)))) → active#(head(mark(cons(s(active(cons(_x81, _x82))), incr(_x31)))))
mark#(head(incr(cons(s(odds), _x62)))) → active#(head(active(incr(cons(active(s(mark(incr(pairs)))), _x62)))))mark#(head(incr(cons(cons(active(mark(_x91)), _x92), mark(_x52))))) → active#(head(incr(cons(active(cons(_x91, _x92)), _x52))))
mark#(head(incr(cons(cons(tail(_x91), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(tail(mark(_x91))), _x72)), _x62)))))mark#(head(s(incr(s(tail(s(_x121))))))) → active#(head(active(s(active(incr(active(s(tail(active(s(mark(_x121))))))))))))
mark#(head(s(cons(incr(_x81), _x62)))) → active#(head(active(s(active(cons(active(incr(mark(_x81))), _x62))))))mark#(head(s(incr(s(tail(_x111)))))) → active#(head(active(s(active(incr(active(s(active(tail(_x111))))))))))
mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(cons(active(nats), _x62)))))mark#(head(incr(cons(cons(_x71, active(_x72)), active(_x52))))) → active#(head(incr(cons(cons(_x71, _x72), _x52))))
mark#(head(s(incr(s(nats))))) → active#(head(active(s(active(incr(active(s(active(nats)))))))))mark#(head(incr(incr(tail(cons(nats, _x82)))))) → active#(head(incr(incr(tail(active(cons(active(nats), _x82)))))))

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, pairs, s, active, mark, incr, head, odds, tail, cons

Strategy

The right-hand side of the rule mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(mark(_x91), _x92)))), _x72)))) 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
active#(head(incr(cons(active(s(active(cons(active(incr(mark(_x101))), _x92)))), _x72)))) 
active#(head(incr(cons(active(s(active(cons(active(odds), _x92)))), _x72)))) 
active#(head(incr(cons(active(s(active(cons(active(head(mark(_x101))), _x92)))), _x72)))) 
active#(head(incr(cons(active(s(active(cons(active(cons(mark(_x101), _x102)), _x92)))), _x72)))) 
active#(head(incr(cons(active(s(active(cons(_x81, _x82)))), _x72)))) 
active#(head(incr(cons(active(s(cons(mark(_x91), _x92))), _x72)))) 
active#(head(incr(cons(active(s(active(cons(active(0), _x92)))), _x72)))) 
active#(head(incr(cons(active(s(active(cons(active(pairs), _x92)))), _x72)))) 
active#(head(incr(cons(active(s(active(cons(mark(_x91), _x92)))), _x42)))) 
active#(head(incr(cons(active(s(active(cons(mark(_x91), _x82)))), _x72)))) 
active#(head(incr(cons(active(s(active(cons(active(tail(mark(_x101))), _x92)))), _x72)))) 
active#(head(incr(cons(active(s(active(cons(active(s(mark(_x101))), _x92)))), _x72)))) 
active#(head(incr(cons(active(s(active(cons(active(nats), _x92)))), _x72)))) 
active#(head(incr(cons(s(active(cons(mark(_x91), _x92))), _x42)))) 
Thus, the rule mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(mark(_x91), _x92)))), _x72)))) is replaced by the following rules:
mark#(head(incr(cons(s(cons(s(_x101), _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(s(mark(_x101))), _x92)))), _x72))))mark#(head(incr(cons(s(cons(_x91, active(_x82))), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(mark(_x91), _x82)))), _x72))))
mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(_x42)))))) → active#(head(incr(cons(s(active(cons(mark(_x91), _x92))), _x42))))mark#(head(incr(cons(s(cons(nats, _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(nats), _x92)))), _x72))))
mark#(head(incr(cons(s(cons(_x91, mark(_x82))), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(mark(_x91), _x82)))), _x72))))mark#(head(incr(cons(s(cons(pairs, _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(pairs), _x92)))), _x72))))
mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(active(_x42))))))) → active#(head(incr(cons(active(s(active(cons(mark(_x91), _x92)))), _x42))))mark#(head(incr(cons(s(cons(tail(_x101), _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(tail(mark(_x101))), _x92)))), _x72))))
mark#(head(incr(cons(s(cons(incr(_x101), _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(incr(mark(_x101))), _x92)))), _x72))))mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(odds), _x92)))), _x72))))
mark#(head(incr(cons(s(cons(0, _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(0), _x92)))), _x72))))mark#(head(incr(cons(s(cons(cons(_x101, _x102), _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(cons(mark(_x101), _x102)), _x92)))), _x72))))
mark#(head(incr(cons(s(cons(_x81, _x82)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(_x81, _x82)))), _x72))))mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(cons(mark(_x91), _x92))), _x72))))
mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(mark(_x42))))))) → active#(head(incr(cons(active(s(active(cons(mark(_x91), _x92)))), _x42))))mark#(head(incr(cons(s(cons(head(_x101), _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(head(mark(_x101))), _x92)))), _x72))))

Problem 31: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(s(X)) → mark#(X)mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(mark(incr(pairs)), _x92))), _x52)))))
mark#(head(incr(cons(_x61, mark(active(mark(_x31))))))) → active#(head(cons(s(mark(_x61)), incr(_x31))))mark#(head(incr(cons(tail(cons(incr(head(_x121)), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(head(mark(_x121))))), _x92))), _x62)))))
mark#(head(incr(cons(tail(cons(incr(head(incr(_x131))), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(active(incr(mark(_x131))))))), _x92)), _x62)))))mark#(tail(X)) → active#(tail(mark(X)))
mark#(head(incr(cons(_x61, active(active(mark(active(_x72)))))))) → active#(head(active(incr(cons(mark(_x61), _x72)))))mark#(head(incr(cons(tail(cons(incr(head(_x131)), active(_x82))), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(head(mark(_x131))))), _x82))), _x62)))))
mark#(head(incr(incr(tail(pairs))))) → active#(head(incr(active(incr(active(tail(active(pairs))))))))mark#(head(incr(cons(tail(cons(_x101, _x102)), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(_x101, _x102)))), _x62)))))
mark#(head(incr(cons(incr(_x81), mark(active(_x31)))))) → active#(head(mark(cons(s(incr(mark(_x81))), incr(_x31)))))mark#(head(incr(cons(tail(cons(incr(_x101), mark(nats))), mark(active(active(incr(mark(_x101))))))))) → active#(head(active(incr(cons(active(nats), _x62)))))
mark#(head(incr(cons(s(cons(_x81, _x82)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(_x81, _x82)))), _x72))))mark#(head(s(incr(s(incr(pairs)))))) → active#(head(active(s(active(incr(active(s(active(incr(active(pairs)))))))))))
mark#(head(incr(cons(_x71, mark(active(mark(_x31))))))) → active#(head(mark(cons(s(_x71), incr(_x31)))))mark#(head(incr(cons(s(cons(0, _x102)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(0, _x102)))), _x72)))))
mark#(head(incr(cons(tail(cons(nats, _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(nats), _x92))), _x62)))))mark#(head(incr(cons(s(cons(_x91, active(_x112))), mark(active(mark(_x31))))))) → active#(head(mark(cons(s(active(s(active(cons(mark(_x91), _x112))))), incr(_x31)))))
mark#(head(s(s(incr(nats))))) → active#(head(s(active(s(active(incr(active(nats))))))))mark#(head(incr(cons(cons(active(mark(_x81)), mark(_x82)), mark(_x52))))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x52)))))
mark#(head(incr(cons(tail(cons(_x91, _x71)), active(_x52))))) → active#(head(active(incr(cons(mark(_x71), _x52)))))mark#(head(s(incr(s(incr(tail(mark(_x121)))))))) → active#(head(active(s(active(incr(active(s(active(incr(tail(_x121)))))))))))
mark#(head(incr(cons(tail(cons(incr(s(_x131)), mark(_x112))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(s(mark(_x131))))), _x112))), _x52)))))mark#(head(incr(cons(cons(head(_x91), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(head(mark(_x91))), _x72)), _x62)))))
mark#(cons(nats, X2)) → active#(cons(active(nats), X2))mark#(head(incr(incr(tail(cons(s(_x91), _x82)))))) → active#(head(incr(incr(tail(active(cons(active(s(mark(_x91))), _x82)))))))
mark#(head(incr(cons(tail(cons(incr(cons(_x121, _x122)), mark(_x112))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(cons(mark(_x121), _x122)))), _x112))), _x62)))))mark#(head(tail(odds))) → active#(head(active(tail(active(odds)))))
mark#(head(incr(cons(tail(cons(_x91, _x92)), _x62)))) → active#(head(incr(cons(active(tail(active(cons(mark(_x91), _x92)))), _x62))))mark#(head(incr(cons(s(cons(_x91, _x92)), _x62)))) → active#(head(active(incr(cons(active(s(active(cons(mark(_x91), _x92)))), _x62)))))
mark#(head(incr(cons(tail(cons(incr(0), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(0))), _x92))), _x62)))))mark#(head(incr(cons(tail(cons(cons(_x101, _x102), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(cons(mark(_x101), _x102)), _x92))), _x62)))))
mark#(head(incr(cons(s(cons(cons(_x131, _x132), active(_x112))), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(cons(mark(_x131), _x132)), _x112)))), _x52)))))mark#(head(incr(cons(tail(cons(_x91, active(_x102))), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(mark(_x91), _x102)))), _x62)))))
mark#(head(s(incr(0)))) → active#(head(active(s(active(incr(active(0)))))))mark#(head(incr(cons(s(cons(_x91, active(active(_x122)))), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(mark(_x91), _x122)))), _x52)))))
mark#(head(incr(cons(s(cons(odds, active(_x112))), mark(active(mark(_x52))))))) → active#(head(incr(cons(active(s(active(cons(active(odds), _x112)))), _x52))))mark#(head(tail(cons(s(_x81), _x62)))) → active#(head(active(tail(active(cons(active(s(mark(_x81))), _x62))))))
mark#(head(s(incr(s(tail(head(_x111))))))) → active#(head(active(s(active(incr(s(active(tail(active(head(mark(_x111))))))))))))mark#(head(incr(cons(tail(cons(head(_x111), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(head(mark(_x111))), _x92))), _x52)))))
mark#(head(incr(cons(tail(cons(incr(pairs), _x92)), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(pairs))), _x92))), _x52)))))mark#(head(tail(cons(incr(pairs), _x62)))) → active#(head(active(tail(active(cons(active(incr(active(pairs))), _x62))))))
mark#(head(incr(cons(s(cons(head(_x111), _x92)), mark(active(mark(_x62))))))) → active#(head(active(incr(cons(s(active(cons(active(head(mark(_x111))), _x92))), _x62)))))mark#(head(s(incr(s(tail(incr(_x121))))))) → active#(head(s(active(incr(active(s(active(tail(incr(mark(_x121)))))))))))
mark#(head(s(incr(s(incr(tail(odds))))))) → active#(head(active(s(active(incr(active(s(active(incr(tail(active(odds))))))))))))mark#(head(incr(cons(cons(incr(odds), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(incr(active(odds))), _x72)), _x62)))))
mark#(head(incr(cons(tail(cons(incr(head(_x131)), mark(active(_x82)))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(head(mark(_x131))))), _x82))), _x62)))))mark#(head(s(incr(s(incr(tail(_x121))))))) → active#(head(s(active(incr(s(active(incr(tail(mark(_x121))))))))))
mark#(head(incr(incr(tail(cons(incr(_x91), _x82)))))) → active#(head(incr(incr(active(tail(cons(active(incr(mark(_x91))), _x82)))))))mark#(head(incr(cons(nats, _x62)))) → active#(head(incr(active(cons(active(nats), _x62)))))
mark#(head(incr(incr(tail(incr(_x61)))))) → active#(head(incr(incr(tail(active(incr(mark(_x61))))))))mark#(head(incr(cons(pairs, mark(active(mark(_x31))))))) → active#(head(mark(cons(s(active(pairs)), incr(_x31)))))
mark#(head(incr(incr(odds)))) → active#(head(active(incr(incr(active(odds))))))mark#(head(incr(cons(s(cons(0, _x92)), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(0), _x92)))), _x52)))))
mark#(head(incr(cons(cons(incr(pairs), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(incr(active(pairs))), _x72)), _x62)))))mark#(head(s(s(nats)))) → active#(head(active(s(active(s(active(nats)))))))
mark#(head(tail(cons(incr(0), _x62)))) → active#(head(active(tail(active(cons(active(incr(active(0))), _x62))))))mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(active(active(mark(_x52)))))))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x111))), _x92)), _x52)))))
mark#(head(incr(nats))) → active#(head(active(incr(active(nats)))))mark#(head(s(incr(s(incr(tail(odds))))))) → active#(head(active(s(incr(s(active(incr(tail(active(odds))))))))))
mark#(head(s(s(s(s(_x101)))))) → active#(head(active(s(active(s(active(s(active(s(mark(_x101)))))))))))mark#(head(incr(cons(incr(_x81), mark(active(mark(_x62))))))) → active#(head(active(incr(cons(incr(mark(_x81)), _x62)))))
mark#(head(s(incr(s(incr(tail(pairs))))))) → active#(head(active(s(incr(s(active(incr(tail(active(pairs))))))))))mark#(head(incr(cons(s(cons(nats, _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(nats), _x92)))), _x72))))
mark#(head(s(incr(s(incr(incr(nats))))))) → active#(head(s(active(incr(active(s(active(incr(active(incr(active(nats))))))))))))mark#(head(incr(cons(tail(cons(incr(odds), _x92)), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(odds))), _x92))), _x52)))))
mark#(head(incr(cons(tail(cons(incr(incr(_x121)), mark(_x112))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(incr(mark(_x121))))), _x112))), _x62)))))mark#(head(incr(cons(_x61, mark(active(mark(_x52))))))) → active#(head(incr(cons(mark(_x61), _x52))))
mark#(head(incr(cons(cons(active(mark(_x81)), active(_x82)), mark(_x52))))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x52)))))mark#(head(incr(cons(tail(cons(incr(0), _x92)), active(active(mark(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(0))), _x92)), _x62)))))
mark#(head(incr(cons(_x61, active(_x62))))) → active#(head(active(incr(cons(_x61, _x62)))))mark#(head(s(incr(s(s(head(_x121))))))) → active#(head(active(s(active(incr(active(s(active(s(active(head(mark(_x121)))))))))))))
mark#(head(cons(incr(_x61), _x32))) → active#(head(active(cons(active(incr(mark(_x61))), _x32))))mark#(head(incr(cons(tail(cons(incr(_x101), active(active(_x112)))), _x31)))) → active#(head(mark(cons(s(active(tail(cons(active(incr(mark(_x101))), _x112)))), incr(_x31)))))
mark#(head(incr(cons(cons(pairs, _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(pairs), _x72)), _x62)))))mark#(head(incr(incr(tail(cons(_x81, active(_x92))))))) → active#(head(incr(incr(active(tail(active(cons(mark(_x81), _x92))))))))
mark#(head(incr(cons(tail(cons(incr(_x101), active(_x82))), _x62)))) → active#(head(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x82))), _x62))))mark#(head(s(incr(s(0))))) → active#(head(active(s(active(incr(active(s(active(0)))))))))
mark#(head(incr(cons(cons(active(_x91), mark(_x92)), mark(_x52))))) → active#(head(active(incr(cons(active(cons(_x91, _x92)), _x52)))))mark#(head(incr(cons(s(cons(0, mark(_x102))), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(active(0), _x102)))), _x72)))))
mark#(head(incr(cons(cons(s(_x91), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(s(mark(_x91))), _x72)), _x62)))))mark#(head(incr(cons(tail(cons(incr(_x101), _x92)), mark(mark(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x92))), _x62)))))
mark#(head(tail(tail(_x61)))) → active#(head(active(tail(active(tail(mark(_x61)))))))mark#(head(incr(cons(tail(cons(incr(_x101), mark(_x112))), mark(active(_x31)))))) → active#(head(mark(cons(s(active(tail(cons(active(incr(mark(_x101))), _x112)))), incr(_x31)))))
mark#(head(incr(cons(tail(cons(incr(_x101), mark(cons(_x71, _x72)))), mark(active(active(incr(mark(_x101))))))))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x72)), _x62)))))mark#(head(incr(cons(cons(active(_x91), active(_x92)), mark(_x52))))) → active#(head(active(incr(cons(active(cons(_x91, _x92)), _x52)))))
mark#(head(incr(cons(tail(cons(incr(_x101), mark(active(_x82)))), mark(active(active(_x52))))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x82))), _x52)))))mark#(head(incr(cons(s(cons(_x101, active(_x102))), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(_x101, _x102)))), _x72))))
mark#(head(incr(cons(tail(cons(incr(s(_x141)), _x92)), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(s(mark(_x141))))), _x92))), _x52)))))mark#(head(incr(cons(cons(_x71, active(_x72)), _x52)))) → active#(head(active(incr(cons(cons(_x71, _x72), _x52)))))
mark#(head(incr(incr(tail(cons(tail(_x91), _x82)))))) → active#(head(incr(incr(active(tail(cons(active(tail(mark(_x91))), _x82)))))))mark#(head(incr(cons(tail(cons(_x91, _x92)), _x52)))) → active#(head(active(incr(cons(tail(active(cons(mark(_x91), _x92))), _x52)))))
mark#(head(incr(cons(tail(cons(incr(pairs), mark(active(_x82)))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(pairs))), _x82))), _x62)))))mark#(head(s(incr(s(incr(tail(_x121))))))) → active#(head(active(s(incr(active(s(active(incr(tail(mark(_x121)))))))))))
mark#(head(s(cons(0, mark(_x52))))) → active#(head(s(cons(active(0), _x52))))mark#(head(incr(cons(s(cons(_x91, active(active(_x102)))), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(mark(_x91), _x102)))), _x72))))
mark#(head(s(incr(s(incr(_x101)))))) → active#(head(active(s(active(incr(active(s(incr(mark(_x101))))))))))mark#(head(s(incr(s(incr(tail(_x121))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(mark(_x121))))))))))))
mark#(head(s(incr(s(incr(tail(_x121))))))) → active#(head(active(s(active(incr(s(active(incr(active(tail(mark(_x121))))))))))))mark#(head(incr(cons(cons(_x81, active(mark(_x82))), _x52)))) → active#(head(active(incr(cons(cons(_x81, _x82), _x52)))))
mark#(head(s(s(s(cons(_x101, _x102)))))) → active#(head(active(s(active(s(active(s(active(cons(mark(_x101), _x102))))))))))mark#(head(incr(cons(s(cons(s(odds), _x92)), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(s(active(odds))), _x92)))), _x52)))))
mark#(head(incr(incr(tail(cons(cons(_x91, _x92), _x82)))))) → active#(head(incr(incr(tail(active(cons(active(cons(mark(_x91), _x92)), _x82)))))))mark#(head(s(incr(s(incr(tail(incr(_x151)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(incr(_x151))))))))))))))
mark#(head(incr(cons(cons(_x71, _x72), mark(_x52))))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x72)), _x52)))))mark#(head(incr(cons(s(cons(0, _x92)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(cons(active(0), _x92))), _x72)))))
mark#(head(incr(cons(tail(cons(incr(_x101), mark(active(_x82)))), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x82))), _x52)))))mark#(head(incr(cons(s(cons(s(_x131), active(_x112))), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(s(mark(_x131))), _x112)))), _x52)))))
mark#(head(incr(cons(tail(cons(incr(_x101), incr(_x81))), mark(_x52))))) → active#(head(active(incr(cons(active(incr(mark(_x81))), _x52)))))mark#(head(incr(incr(tail(cons(odds, _x82)))))) → active#(head(incr(incr(tail(active(cons(active(odds), _x82)))))))
mark#(head(incr(incr(tail(incr(_x81)))))) → active#(head(incr(incr(active(tail(active(incr(mark(_x81)))))))))mark#(head(incr(cons(tail(cons(incr(tail(_x131)), mark(active(_x82)))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(tail(mark(_x131))))), _x82))), _x62)))))
mark#(head(s(s(s(odds))))) → active#(head(s(active(s(active(s(mark(incr(pairs)))))))))mark#(cons(X1, X2)) → mark#(X1)
mark#(head(incr(cons(s(cons(head(_x111), _x92)), mark(active(_x31)))))) → active#(head(mark(cons(s(s(active(cons(active(head(mark(_x111))), _x92)))), incr(_x31)))))mark#(head(s(cons(odds, _x62)))) → active#(head(active(s(active(cons(active(odds), _x62))))))
mark#(head(incr(cons(s(cons(cons(_x111, _x112), active(_x82))), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(cons(mark(_x111), _x112)), _x82)))), _x72))))mark#(head(s(incr(s(incr(tail(incr(_x141)))))))) → active#(head(active(s(incr(active(s(incr(active(tail(active(incr(mark(_x141)))))))))))))
mark#(head(incr(cons(pairs, active(active(mark(_x52))))))) → active#(head(active(incr(cons(active(pairs), _x52)))))mark#(head(s(s(s(odds))))) → active#(head(active(s(active(s(active(s(mark(incr(pairs))))))))))
mark#(head(s(incr(s(incr(tail(_x121))))))) → active#(head(s(active(incr(active(s(active(incr(active(tail(mark(_x121))))))))))))mark#(head(s(incr(s(incr(tail(incr(nats)))))))) → active#(head(active(s(incr(s(active(incr(active(tail(active(incr(active(nats)))))))))))))
mark#(head(incr(incr(tail(head(_x91)))))) → active#(head(incr(incr(active(tail(active(head(_x91))))))))mark#(head(incr(cons(tail(cons(incr(_x101), mark(active(_x92)))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x92))), _x62)))))
mark#(head(s(incr(s(tail(pairs)))))) → active#(head(active(s(active(incr(s(active(tail(mark(cons(0, incr(odds))))))))))))mark#(head(incr(cons(_x51, active(mark(_x52)))))) → active#(head(active(incr(cons(_x51, _x52)))))
mark#(head(s(incr(s(tail(incr(nats))))))) → active#(head(s(active(incr(active(s(active(tail(active(incr(mark(cons(0, incr(nats))))))))))))))mark#(head(s(incr(s(tail(_x81)))))) → active#(head(active(s(active(incr(s(tail(_x81))))))))
mark#(head(s(incr(s(incr(tail(incr(_x141)))))))) → active#(head(active(s(incr(s(active(incr(active(tail(active(incr(mark(_x141)))))))))))))mark#(head(incr(cons(tail(cons(tail(_x111), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(active(tail(mark(_x111))), _x92)))), _x62)))))
mark#(head(s(s(odds)))) → active#(head(active(s(s(active(odds))))))mark#(head(s(incr(s(incr(tail(incr(head(s(_x171)))))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(head(active(s(mark(_x171))))))))))))))))))
mark#(head(s(incr(s(tail(s(_x121))))))) → active#(head(s(active(incr(active(s(active(tail(active(s(mark(_x121))))))))))))mark#(head(incr(cons(s(cons(0, active(active(_x102)))), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(0), _x102)))), _x52)))))
mark#(head(incr(cons(s(cons(_x91, active(_x112))), mark(active(mark(_x62))))))) → active#(head(active(incr(cons(s(active(cons(mark(_x91), _x112))), _x62)))))mark#(head(incr(cons(0, mark(_x52))))) → active#(head(active(incr(cons(active(0), _x52)))))
mark#(head(incr(cons(s(cons(tail(_x111), _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(active(tail(mark(_x111))), _x92))), _x52)))))mark#(head(incr(cons(tail(cons(incr(pairs), _x92)), active(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(pairs))), _x92)), _x62)))))
mark#(head(incr(cons(head(_x81), _x62)))) → active#(head(active(incr(active(cons(active(head(mark(_x81))), _x62))))))mark#(head(s(incr(s(tail(cons(_x111, _x112))))))) → active#(head(active(s(active(incr(s(active(tail(active(cons(mark(_x111), _x112)))))))))))
mark#(head(incr(cons(tail(cons(incr(head(_x141)), _x92)), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(head(mark(_x141))))), _x92))), _x52)))))mark#(head(incr(cons(head(_x81), mark(_x52))))) → active#(head(active(incr(cons(active(head(mark(_x81))), _x52)))))
mark#(head(incr(cons(s(_x71), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(mark(_x71))), _x52)))))mark#(head(incr(cons(_x61, mark(active(mark(_x31))))))) → active#(head(active(cons(mark(s(mark(_x61))), incr(_x31)))))
mark#(head(incr(incr(tail(cons(_x81, active(_x72))))))) → active#(head(incr(incr(active(tail(cons(mark(_x81), _x72)))))))mark#(head(s(incr(s(incr(tail(incr(head(0))))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(head(active(0))))))))))))))))
mark#(head(incr(cons(pairs, active(mark(active(_x52))))))) → active#(head(active(incr(cons(mark(cons(0, incr(odds))), _x52)))))mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(active(incr(mark(_x111))), _x92)))), _x62)))))
mark#(head(incr(cons(tail(_x71), mark(active(_x72)))))) → active#(head(active(incr(cons(active(tail(mark(_x71))), _x72)))))mark#(head(incr(cons(cons(incr(incr(_x121)), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(incr(active(incr(mark(_x121))))), _x72)), _x62)))))
mark#(head(incr(cons(tail(cons(incr(s(_x131)), active(_x82))), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(s(mark(_x131))))), _x82))), _x62)))))mark#(head(incr(incr(incr(_x71))))) → active#(head(incr(active(incr(active(incr(mark(_x71))))))))
mark#(head(s(incr(s(incr(tail(_x91))))))) → active#(head(active(s(incr(s(active(incr(tail(_x91)))))))))mark#(head(incr(tail(_x51)))) → active#(head(incr(active(tail(mark(_x51))))))
mark#(head(incr(cons(s(cons(_x111, _x112)), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(_x111, _x112)))), _x52)))))mark#(head(s(incr(s(incr(incr(odds))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(odds)))))))))))))
mark#(head(s(cons(0, mark(mark(_x62)))))) → active#(head(s(active(cons(active(0), _x62)))))mark#(head(incr(cons(tail(cons(incr(_x101), mark(active(_x82)))), mark(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x101))), _x82)), _x52)))))
mark#(head(s(incr(s(incr(incr(_x131))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(_x131))))))))))))mark#(head(incr(cons(s(cons(_x91, active(_x102))), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(mark(_x91), _x102)))), _x72)))))
mark#(head(s(incr(s(tail(_x91)))))) → active#(head(active(s(active(incr(s(active(tail(_x91)))))))))active#(nats) → mark#(cons(0, incr(nats)))
mark#(0) → active#(0)mark#(head(cons(tail(_x61), _x32))) → active#(head(active(cons(active(tail(mark(_x61))), _x32))))
mark#(head(incr(cons(tail(cons(incr(pairs), mark(active(_x92)))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(pairs))), _x92))), _x52)))))mark#(head(s(incr(s(incr(incr(pairs))))))) → active#(head(s(active(incr(active(s(active(incr(active(incr(active(pairs))))))))))))
mark#(head(incr(cons(tail(cons(incr(head(_x121)), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(_x121)))), _x92)), _x62)))))mark#(head(incr(cons(s(tail(_x91)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(tail(mark(_x91))))), _x72)))))
mark#(head(incr(head(tail(_x71))))) → active#(head(incr(active(head(active(tail(mark(_x71))))))))mark#(head(s(incr(s(tail(_x101)))))) → active#(head(s(incr(s(active(tail(mark(_x101))))))))
mark#(head(s(incr(s(incr(odds)))))) → active#(head(active(s(active(incr(active(s(active(incr(active(odds)))))))))))mark#(head(incr(cons(incr(tail(_x91)), mark(active(_x52)))))) → active#(head(active(incr(cons(incr(active(tail(mark(_x91)))), _x52)))))
mark#(head(incr(cons(s(cons(odds, active(_x112))), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(mark(incr(pairs)), _x112)))), _x52)))))mark#(head(incr(cons(cons(_x61, active(mark(_x62))), _x42)))) → active#(head(incr(cons(cons(_x61, _x62), _x42))))
mark#(head(incr(incr(tail(0))))) → active#(head(incr(active(incr(active(tail(active(0))))))))mark#(head(incr(cons(tail(cons(incr(_x101), mark(0))), mark(active(active(incr(mark(_x101))))))))) → active#(head(active(incr(cons(active(0), _x62)))))
mark#(head(incr(cons(cons(mark(_x81), active(_x82)), _x62)))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x62)))))mark#(head(incr(cons(tail(cons(incr(0), _x92)), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(0)), _x92)), _x52)))))
mark#(head(s(s(incr(0))))) → active#(head(active(s(s(active(incr(active(0))))))))mark#(head(incr(cons(s(cons(odds, active(_x82))), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(mark(incr(pairs)), _x82)))), _x72))))
mark#(head(incr(cons(tail(cons(incr(_x101), mark(_x51))), mark(active(active(incr(mark(_x101))))))))) → active#(head(active(incr(cons(_x51, _x52)))))mark#(head(s(incr(s(incr(tail(incr(_x131)))))))) → active#(head(active(s(active(incr(active(s(active(incr(tail(active(incr(mark(_x131))))))))))))))
mark#(head(incr(cons(tail(cons(incr(0), _x82)), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(incr(active(0)), _x82)), _x52)))))mark#(head(s(incr(s(tail(incr(_x121))))))) → active#(head(s(active(incr(s(active(tail(active(incr(mark(_x121)))))))))))
mark#(head(incr(cons(tail(cons(incr(tail(_x121)), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(tail(mark(_x121))))), _x92))), _x62)))))mark#(head(incr(cons(tail(cons(incr(_x101), mark(active(_x61)))), mark(active(active(incr(mark(_x101))))))))) → active#(head(active(incr(cons(mark(_x61), _x62)))))
mark#(head(incr(cons(cons(active(_x61), active(_x62)), _x62)))) → active#(head(incr(cons(active(cons(_x61, _x62)), _x62))))mark#(head(incr(cons(s(cons(odds, active(_x102))), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(odds, _x102)))), _x52)))))
mark#(head(s(incr(s(incr(tail(_x101))))))) → active#(head(active(s(active(incr(s(active(incr(tail(_x101))))))))))mark#(head(incr(cons(incr(_x71), mark(active(_x62)))))) → active#(head(active(incr(cons(active(incr(_x71)), _x62)))))
mark#(head(s(incr(s(incr(incr(s(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(s(mark(_x141)))))))))))))))mark#(head(incr(cons(tail(cons(incr(s(_x141)), mark(active(_x92)))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(s(mark(_x141))))), _x92))), _x52)))))
mark#(head(incr(cons(s(cons(nats, _x92)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(active(nats), _x92)))), _x72)))))mark#(head(tail(cons(_x61, mark(_x72))))) → active#(head(active(tail(active(cons(mark(_x61), _x72))))))
mark#(head(incr(cons(s(nats), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(nats))), _x72)))))mark#(head(incr(cons(s(cons(cons(_x111, _x112), _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(active(cons(mark(_x111), _x112)), _x92))), _x52)))))
mark#(head(incr(cons(pairs, mark(_x62))))) → active#(head(active(incr(cons(pairs, _x62)))))mark#(head(incr(cons(tail(cons(0, _x92)), _x31)))) → active#(head(mark(cons(s(active(tail(active(cons(active(0), _x92))))), incr(_x31)))))
mark#(head(incr(cons(cons(_x71, _x72), _x52)))) → active#(head(active(incr(cons(cons(mark(_x71), _x72), _x52)))))mark#(head(incr(cons(s(cons(head(_x131), active(_x112))), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(head(mark(_x131))), _x112)))), _x52)))))
mark#(head(incr(cons(nats, active(active(_x72)))))) → active#(head(active(incr(cons(mark(cons(0, incr(nats))), _x72)))))mark#(head(s(cons(0, _x62)))) → active#(head(active(s(cons(active(0), _x62)))))
mark#(head(incr(cons(s(cons(odds, mark(_x82))), mark(active(active(_x42))))))) → active#(head(incr(cons(active(s(active(cons(mark(incr(pairs)), _x82)))), _x42))))mark#(head(incr(cons(pairs, active(mark(mark(_x52))))))) → active#(head(active(incr(cons(mark(cons(0, incr(odds))), _x52)))))
mark#(head(incr(cons(s(_x81), active(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(mark(_x81))), _x52)))))mark#(head(incr(cons(tail(cons(incr(_x111), _x71)), active(_x52))))) → active#(head(active(incr(cons(mark(_x71), _x52)))))
mark#(head(incr(cons(tail(cons(incr(_x101), active(_x61))), active(incr(mark(_x101))))))) → active#(head(active(incr(cons(mark(_x61), _x62)))))mark#(head(s(incr(s(s(incr(_x121))))))) → active#(head(active(s(active(incr(active(s(active(s(active(incr(mark(_x121)))))))))))))
mark#(head(incr(head(head(_x71))))) → active#(head(incr(active(head(active(head(mark(_x71))))))))mark#(head(s(incr(s(incr(tail(incr(head(pairs))))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(head(active(pairs))))))))))))))))
mark#(head(incr(cons(s(cons(odds, mark(_x82))), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(incr(mark(pairs))), _x82)))), _x72))))mark#(head(nats)) → active#(head(active(nats)))
mark#(head(incr(cons(tail(cons(incr(s(_x101)), _x92)), active(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(s(mark(_x101))))), _x92)), _x62)))))mark#(head(incr(cons(incr(_x81), _x62)))) → active#(head(active(incr(active(cons(active(incr(mark(_x81))), _x62))))))
mark#(head(incr(cons(tail(cons(incr(_x111), mark(_x112))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(_x111)), _x112))), _x62)))))mark#(head(s(incr(s(incr(tail(incr(incr(_x161))))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(incr(active(incr(mark(_x161)))))))))))))))))
mark#(head(incr(incr(tail(cons(incr(_x91), _x82)))))) → active#(head(incr(incr(tail(active(cons(active(incr(mark(_x91))), _x82)))))))mark#(head(incr(cons(tail(cons(tail(_x111), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(tail(mark(_x111))), _x92))), _x52)))))
mark#(head(incr(cons(s(_x81), active(_x52))))) → active#(head(active(incr(cons(active(s(mark(_x81))), _x52)))))mark#(head(cons(head(_x61), _x32))) → active#(head(active(cons(active(head(mark(_x61))), _x32))))
mark#(head(incr(cons(tail(cons(incr(s(_x131)), mark(active(_x82)))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(s(mark(_x131))))), _x82))), _x62)))))mark#(head(incr(cons(tail(cons(incr(_x111), active(_x82))), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x111))), _x82)), _x52)))))
mark#(head(incr(cons(cons(mark(_x71), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x62)))))mark#(head(incr(cons(tail(cons(incr(cons(_x131, _x132)), mark(_x112))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(cons(mark(_x131), _x132)))), _x112))), _x52)))))
mark#(head(incr(cons(tail(cons(incr(_x101), mark(_x82))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(incr(mark(_x101)), _x82))), _x62)))))mark#(head(incr(cons(pairs, active(mark(active(_x42))))))) → active#(head(incr(cons(active(pairs), _x42))))
mark#(incr(X)) → active#(incr(mark(X)))mark#(head(incr(cons(tail(cons(incr(_x101), pairs)), mark(_x52))))) → active#(head(active(incr(cons(active(pairs), _x52)))))
mark#(head(incr(cons(s(cons(odds, mark(_x82))), mark(active(_x42)))))) → active#(head(incr(cons(s(active(cons(mark(incr(pairs)), _x82))), _x42))))mark#(head(incr(cons(cons(mark(_x61), active(_x62)), _x62)))) → active#(head(incr(cons(active(cons(_x61, _x62)), _x62))))
mark#(head(incr(incr(tail(tail(_x81)))))) → active#(head(incr(incr(active(tail(active(tail(mark(_x81)))))))))mark#(head(incr(cons(incr(s(_x101)), mark(_x52))))) → active#(head(active(incr(cons(active(incr(active(s(mark(_x101))))), _x52)))))
mark#(head(incr(cons(s(cons(s(_x121), _x92)), mark(active(mark(_x31))))))) → active#(head(mark(cons(s(active(s(active(cons(active(s(mark(_x121))), _x92))))), incr(_x31)))))mark#(head(incr(cons(tail(cons(incr(_x131), mark(active(_x71)))), mark(_x52))))) → active#(head(active(incr(cons(mark(_x71), _x52)))))
mark#(head(incr(cons(cons(_x71, active(_x82)), _x62)))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x82)), _x62)))))mark#(head(incr(cons(s(odds), _x62)))) → active#(head(active(incr(cons(active(s(odds)), _x62)))))
mark#(head(incr(cons(cons(nats, _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(nats), _x72)), _x62)))))mark#(head(s(incr(s(incr(tail(incr(0)))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(0))))))))))))))
mark#(head(s(incr(s(tail(_x101)))))) → active#(head(active(s(incr(active(s(active(tail(mark(_x101))))))))))mark#(head(incr(cons(s(_x71), mark(_x52))))) → active#(head(active(incr(cons(active(s(mark(_x71))), _x52)))))
mark#(head(s(incr(s(tail(s(0))))))) → active#(head(active(s(active(incr(active(s(tail(active(s(active(0))))))))))))mark#(head(s(incr(s(incr(tail(nats))))))) → active#(head(active(s(incr(s(active(incr(tail(active(nats))))))))))
mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(pairs))))))mark#(head(incr(_x51))) → active#(head(active(incr(_x51))))
mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(active(cons(mark(_x61), _x62)))))mark#(head(s(incr(s(incr(incr(tail(_x131)))))))) → active#(head(s(active(incr(active(s(active(incr(active(incr(active(tail(mark(_x131))))))))))))))
mark#(head(incr(0))) → active#(head(incr(active(0))))mark#(head(s(incr(s(tail(odds)))))) → active#(head(active(s(incr(s(active(tail(active(odds)))))))))
mark#(head(s(incr(s(incr(tail(incr(_x141)))))))) → active#(head(active(s(active(incr(s(active(incr(active(tail(active(incr(mark(_x141))))))))))))))mark#(head(incr(cons(tail(cons(incr(_x101), mark(active(_x92)))), mark(mark(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x92))), _x62)))))
mark#(head(incr(cons(s(_x81), mark(active(mark(_x31))))))) → active#(head(mark(cons(s(active(s(mark(_x81)))), incr(_x31)))))mark#(head(incr(incr(tail(cons(incr(_x101), _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(incr(mark(_x101))), _x82))))))))
mark#(head(incr(cons(incr(nats), mark(_x52))))) → active#(head(active(incr(cons(active(incr(active(nats))), _x52)))))mark#(head(incr(cons(tail(cons(incr(_x111), active(_x72))), active(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x111))), _x72)), _x62)))))
mark#(head(incr(cons(tail(cons(incr(_x131), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(_x131)), _x92))), _x52)))))mark#(head(s(incr(s(incr(incr(cons(_x131, _x132)))))))) → active#(head(s(active(incr(active(s(active(incr(active(incr(active(cons(mark(_x131), _x132)))))))))))))
mark#(head(incr(cons(tail(cons(incr(_x101), active(_x82))), _x31)))) → active#(head(mark(cons(s(tail(cons(active(incr(mark(_x101))), _x82))), incr(_x31)))))mark#(head(incr(cons(tail(_x71), active(active(_x72)))))) → active#(head(active(incr(cons(active(tail(mark(_x71))), _x72)))))
mark#(head(incr(cons(tail(cons(_x91, _x61)), mark(_x91))))) → active#(head(active(incr(cons(mark(_x61), _x62)))))mark#(head(incr(cons(incr(_x81), mark(_x52))))) → active#(head(incr(cons(active(incr(mark(_x81))), _x52))))
mark#(head(incr(cons(cons(_x81, active(mark(_x82))), mark(_x52))))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x52)))))mark#(head(incr(cons(tail(cons(incr(tail(_x131)), mark(_x112))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(tail(mark(_x131))))), _x112))), _x52)))))
mark#(head(s(incr(incr(_x81))))) → active#(head(s(active(incr(active(incr(mark(_x81))))))))mark#(head(s(nats))) → active#(head(s(active(nats))))
mark#(head(cons(nats, _x32))) → active#(head(active(cons(active(nats), _x32))))mark#(cons(X1, mark(_x22))) → active#(cons(mark(X1), _x22))
mark#(head(incr(cons(tail(cons(incr(0), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(0))), _x92)), _x62)))))mark#(head(incr(incr(tail(0))))) → active#(head(incr(incr(tail(active(0))))))
mark#(head(s(s(incr(_x81))))) → active#(head(s(active(s(active(incr(mark(_x81))))))))mark#(head(incr(cons(odds, mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(odds), _x52)))))
mark#(head(incr(cons(s(_x81), mark(_x52))))) → active#(head(active(incr(cons(active(s(mark(_x81))), _x52)))))mark#(head(s(incr(s(incr(head(_x121))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(head(mark(_x121)))))))))))))
mark#(head(incr(cons(s(cons(pairs, _x92)), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(pairs), _x92)))), _x52)))))mark#(head(incr(cons(_x51, active(active(_x52)))))) → active#(head(active(incr(cons(_x51, _x52)))))
mark#(head(s(incr(s(incr(tail(cons(_x141, _x142)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(cons(mark(_x141), _x142))))))))))))))mark#(head(incr(cons(tail(cons(incr(head(_x101)), mark(_x72))), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(mark(_x101))))), _x72)), _x62)))))
active#(tail(cons(X, XS))) → mark#(XS)mark#(head(cons(pairs, _x32))) → active#(head(active(cons(active(pairs), _x32))))
mark#(head(incr(cons(cons(active(_x71), _x72), mark(_x52))))) → active#(head(incr(cons(active(cons(_x71, _x72)), _x52))))mark#(head(tail(incr(_x61)))) → active#(head(active(tail(active(incr(mark(_x61)))))))
mark#(head(s(incr(s(incr(incr(odds))))))) → active#(head(s(active(incr(active(s(active(incr(active(incr(active(odds))))))))))))mark#(head(incr(cons(pairs, mark(_x31))))) → active#(head(mark(cons(s(active(pairs)), incr(_x31)))))
mark#(head(incr(cons(s(cons(odds, active(_x112))), mark(active(mark(_x62))))))) → active#(head(active(incr(cons(s(active(cons(active(odds), _x112))), _x62)))))mark#(head(tail(cons(incr(incr(_x111)), _x62)))) → active#(head(active(tail(active(cons(active(incr(active(incr(mark(_x111))))), _x62))))))
mark#(head(incr(cons(tail(cons(incr(_x101), _x61)), active(incr(mark(_x101))))))) → active#(head(active(incr(cons(mark(_x61), _x62)))))mark#(head(incr(incr(cons(_x61, _x62))))) → active#(head(incr(incr(active(cons(mark(_x61), _x62))))))
mark#(head(incr(cons(s(cons(s(s(_x151)), _x92)), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(s(active(s(mark(_x151))))), _x92)))), _x52)))))mark#(head(incr(cons(cons(_x81, _x82), mark(_x52))))) → active#(head(active(incr(cons(active(cons(mark(_x81), _x82)), _x52)))))
mark#(head(incr(cons(s(cons(odds, mark(mark(_x92)))), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(mark(incr(pairs)), _x92)))), _x72))))mark#(head(s(incr(s(s(s(_x121))))))) → active#(head(active(s(active(incr(active(s(active(s(active(s(mark(_x121)))))))))))))
mark#(head(s(incr(s(tail(_x101)))))) → active#(head(s(active(incr(s(active(tail(mark(_x101)))))))))mark#(head(s(s(incr(incr(_x101)))))) → active#(head(active(s(active(s(active(incr(active(incr(mark(_x101)))))))))))
mark#(head(incr(cons(cons(active(mark(active(_x81))), _x82), mark(_x52))))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x52)))))mark#(head(incr(head(cons(_x71, _x72))))) → active#(head(incr(active(head(active(cons(mark(_x71), _x72)))))))
mark#(head(incr(cons(tail(cons(incr(_x131), _x92)), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(_x131)), _x92))), _x52)))))mark#(head(incr(incr(tail(cons(cons(_x91, _x92), _x82)))))) → active#(head(incr(incr(active(tail(cons(active(cons(mark(_x91), _x92)), _x82)))))))
mark#(head(incr(incr(tail(cons(_x71, _x72)))))) → active#(head(incr(incr(tail(active(cons(_x71, _x72)))))))mark#(head(incr(cons(cons(incr(_x91), _x72), _x62)))) → active#(head(incr(cons(active(cons(active(incr(mark(_x91))), _x72)), _x62))))
mark#(cons(_x21, _x22)) → active#(cons(_x21, _x22))mark#(head(s(incr(s(s(cons(_x121, _x122))))))) → active#(head(active(s(active(incr(active(s(active(s(active(cons(mark(_x121), _x122))))))))))))
mark#(head(s(s(incr(_x81))))) → active#(head(active(s(active(s(incr(mark(_x81))))))))mark#(head(s(odds))) → active#(head(active(s(active(odds)))))
mark#(head(incr(cons(pairs, active(mark(_x52)))))) → active#(head(active(incr(cons(pairs, _x52)))))mark#(head(s(incr(s(tail(s(_x111))))))) → active#(head(active(s(active(incr(s(active(tail(active(s(mark(_x111))))))))))))
mark#(head(s(incr(s(tail(incr(tail(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(incr(active(tail(mark(_x141)))))))))))))))mark#(head(incr(incr(s(_x81))))) → active#(head(active(incr(active(incr(active(s(mark(_x81)))))))))
mark#(head(incr(cons(head(_x81), active(active(mark(_x52))))))) → active#(head(active(incr(cons(active(head(mark(_x81))), _x52)))))mark#(head(incr(cons(incr(_x71), mark(active(_x72)))))) → active#(head(active(incr(cons(active(incr(mark(_x71))), _x72)))))
mark#(head(incr(cons(pairs, active(mark(_x52)))))) → active#(head(active(incr(cons(cons(0, incr(odds)), _x52)))))mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(active(active(_x31))))))) → active#(head(mark(cons(s(tail(cons(active(incr(mark(_x111))), _x92))), incr(_x31)))))
mark#(head(tail(cons(_x61, _x62)))) → active#(head(tail(active(cons(mark(_x61), _x62)))))mark#(head(s(s(s(_x81))))) → active#(head(active(s(s(active(s(mark(_x81))))))))
mark#(head(s(incr(s(incr(tail(incr(head(_x151))))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(head(mark(_x151)))))))))))))))mark#(head(s(incr(s(incr(tail(incr(pairs)))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(pairs))))))))))))))
mark#(head(incr(cons(s(pairs), _x62)))) → active#(head(active(incr(cons(active(s(active(pairs))), _x62)))))mark#(head(incr(cons(tail(cons(_x91, _x92)), active(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(mark(_x91), _x92))), _x62)))))
mark#(head(s(s(incr(head(_x91)))))) → active#(head(active(s(s(active(incr(active(head(mark(_x91))))))))))mark#(head(incr(cons(tail(cons(incr(_x101), active(active(_x92)))), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x92))), _x62)))))
mark#(head(s(incr(s(incr(tail(incr(_x141)))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(incr(mark(_x141)))))))))))))mark#(head(s(incr(s(incr(tail(_x91))))))) → active#(head(active(s(active(incr(s(incr(tail(_x91)))))))))
mark#(head(s(s(incr(_x81))))) → active#(head(active(s(s(incr(mark(_x81)))))))mark#(head(s(s(incr(_x81))))) → active#(head(s(s(active(incr(mark(_x81)))))))
mark#(head(incr(cons(tail(cons(incr(head(0)), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(active(0))))), _x92)), _x62)))))mark#(head(s(incr(s(incr(tail(incr(_x141)))))))) → active#(head(s(incr(active(s(active(incr(active(tail(active(incr(mark(_x141)))))))))))))
mark#(head(incr(cons(s(cons(_x91, active(mark(_x122)))), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(mark(_x91), _x122)))), _x52)))))mark#(head(incr(tail(_x61)))) → active#(head(active(incr(active(tail(mark(_x61)))))))
mark#(head(incr(cons(tail(cons(incr(head(s(_x131))), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(active(s(mark(_x131))))))), _x92)), _x62)))))mark#(head(s(s(head(_x81))))) → active#(head(active(s(active(s(active(head(mark(_x81)))))))))
mark#(head(incr(cons(tail(cons(incr(_x121), active(_x82))), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(_x121)), _x82))), _x62)))))mark#(head(incr(cons(tail(cons(incr(_x101), mark(pairs))), mark(active(active(incr(mark(_x101))))))))) → active#(head(active(incr(cons(active(pairs), _x62)))))
mark#(head(s(incr(s(incr(tail(0))))))) → active#(head(active(s(active(incr(s(active(incr(tail(active(0)))))))))))mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(mark(_x52))))))) → active#(head(incr(cons(active(s(active(cons(mark(_x91), _x92)))), _x52))))
mark#(head(incr(cons(tail(cons(incr(_x101), active(_x112))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x112))), _x52)))))mark#(head(incr(cons(s(cons(pairs, _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(active(pairs), _x92))), _x52)))))
mark#(head(s(0))) → active#(head(active(s(active(0)))))mark#(head(incr(cons(s(cons(_x91, active(_x112))), mark(active(mark(active(_x62)))))))) → active#(head(active(incr(cons(active(s(active(cons(mark(_x91), _x112)))), _x62)))))
mark#(head(incr(cons(tail(cons(incr(_x101), active(_x82))), _x31)))) → active#(head(active(cons(mark(s(active(tail(cons(active(incr(mark(_x101))), _x82))))), incr(_x31)))))mark#(head(incr(incr(0)))) → active#(head(incr(incr(active(0)))))
mark#(head(incr(cons(cons(_x81, _x82), active(_x52))))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x52)))))mark#(head(incr(cons(tail(cons(incr(cons(_x121, _x122)), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(cons(mark(_x121), _x122)))), _x92))), _x62)))))
mark#(head(incr(cons(_x61, mark(active(_x31)))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))mark#(head(s(incr(s(_x81))))) → active#(head(active(s(incr(active(s(mark(_x81))))))))
mark#(head(incr(cons(cons(_x81, active(mark(_x82))), _x62)))) → active#(head(incr(cons(active(cons(_x81, _x82)), _x62))))mark#(head(incr(cons(tail(cons(incr(head(_x141)), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(head(mark(_x141))))), _x92))), _x52)))))
mark#(head(incr(cons(s(cons(odds, _x82)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(incr(pairs), _x82)))), _x72))))mark#(head(incr(cons(s(cons(0, active(_x112))), mark(active(mark(active(_x62)))))))) → active#(head(active(incr(cons(active(s(active(cons(active(0), _x112)))), _x62)))))
mark#(head(incr(cons(s(head(_x91)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(head(mark(_x91))))), _x72)))))mark#(head(incr(cons(tail(cons(incr(_x111), _x82)), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(incr(mark(_x111)), _x82)), _x52)))))
mark#(head(s(incr(s(tail(0)))))) → active#(head(active(s(active(incr(s(active(tail(active(0))))))))))mark#(head(incr(cons(s(cons(head(_x111), _x92)), mark(active(active(_x62))))))) → active#(head(active(incr(cons(s(active(cons(active(head(mark(_x111))), _x92))), _x62)))))
mark#(head(incr(cons(pairs, mark(_x52))))) → active#(head(incr(cons(active(pairs), _x52))))mark#(head(incr(cons(cons(mark(_x61), active(_x62)), _x42)))) → active#(head(incr(cons(cons(_x61, _x62), _x42))))
mark#(head(incr(cons(tail(cons(tail(_x101), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(tail(mark(_x101))), _x92))), _x62)))))mark#(head(incr(cons(tail(cons(incr(_x91), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(_x91)), _x92)), _x62)))))
mark#(head(s(cons(pairs, _x62)))) → active#(head(active(s(active(cons(active(pairs), _x62))))))mark#(head(incr(cons(cons(_x81, _x82), _x62)))) → active#(head(active(incr(active(cons(active(cons(mark(_x81), _x82)), _x62))))))
mark#(head(incr(incr(tail(cons(nats, _x82)))))) → active#(head(incr(incr(active(tail(cons(active(nats), _x82)))))))mark#(head(incr(cons(s(cons(odds, _x82)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(odds, _x82)))), _x72))))
mark#(head(incr(cons(s(cons(tail(_x121), _x92)), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(tail(mark(_x121))), _x92)))), _x52)))))mark#(head(incr(cons(s(cons(0, _x92)), mark(active(active(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(0), _x92)))), _x52)))))
mark#(head(s(head(_x61)))) → active#(head(active(s(active(head(mark(_x61)))))))mark#(head(incr(cons(tail(cons(incr(_x111), mark(_x72))), active(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x111))), _x72)), _x62)))))
mark#(head(incr(cons(tail(cons(incr(_x101), _x71)), mark(mark(_x62)))))) → active#(head(active(incr(cons(mark(_x71), _x62)))))mark#(head(s(incr(s(incr(0)))))) → active#(head(active(s(active(incr(active(s(active(incr(active(0)))))))))))
mark#(head(incr(cons(s(cons(head(_x111), active(_x102))), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(active(head(mark(_x111))), _x102))), _x52)))))mark#(head(incr(cons(s(cons(_x91, mark(_x102))), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(mark(_x91), _x102))), _x52)))))
mark#(head(s(s(_x61)))) → active#(head(s(active(s(mark(_x61))))))mark#(head(X)) → mark#(X)
mark#(head(s(incr(s(incr(incr(pairs))))))) → active#(head(active(s(active(incr(s(active(incr(active(incr(active(pairs))))))))))))mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(cons(mark(_x91), _x92))), _x72))))
mark#(head(incr(cons(_x61, active(active(_x72)))))) → active#(head(incr(cons(mark(_x61), _x72))))mark#(head(incr(cons(nats, mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(nats), _x52)))))
mark#(head(incr(cons(tail(cons(incr(cons(_x141, _x142)), _x92)), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(cons(mark(_x141), _x142)))), _x92))), _x52)))))mark#(head(s(incr(s(incr(tail(s(_x101)))))))) → active#(head(active(s(incr(s(active(incr(tail(active(s(mark(_x101))))))))))))
mark#(head(incr(incr(nats)))) → active#(head(active(incr(active(incr(active(nats)))))))mark#(head(incr(cons(tail(cons(incr(cons(_x131, _x132)), active(_x82))), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(cons(mark(_x131), _x132)))), _x82))), _x62)))))
mark#(head(incr(cons(tail(cons(incr(odds), mark(active(_x92)))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(odds))), _x92))), _x52)))))mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(cons(active(odds), _x92)), _x52)))))
mark#(head(incr(cons(s(cons(head(0), _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(active(head(active(0))), _x92))), _x52)))))mark#(head(incr(cons(tail(cons(incr(_x101), mark(_x61))), mark(active(active(incr(mark(_x101))))))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))
mark#(head(s(incr(s(tail(nats)))))) → active#(head(active(s(incr(s(active(tail(active(nats)))))))))mark#(head(s(incr(s(s(_x101)))))) → active#(head(s(active(incr(active(s(active(s(mark(_x101))))))))))
mark#(head(incr(cons(tail(cons(incr(nats), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(nats))), _x92)), _x62)))))mark#(head(s(nats))) → active#(head(active(s(nats))))
mark#(head(incr(cons(cons(active(_x71), _x72), mark(_x62))))) → active#(head(active(incr(cons(cons(_x71, _x72), _x62)))))mark#(head(incr(cons(s(cons(s(_x121), mark(_x112))), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(s(mark(_x121))), _x112)))), _x52)))))
mark#(head(incr(cons(tail(cons(incr(s(_x121)), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(s(mark(_x121))))), _x92))), _x62)))))mark#(head(s(cons(_x61, _x62)))) → active#(head(active(s(cons(mark(_x61), _x62)))))
mark#(head(incr(cons(tail(cons(0, _x102)), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(0, _x102)))), _x62)))))mark#(head(incr(cons(s(cons(_x91, active(_x112))), mark(active(mark(mark(_x62)))))))) → active#(head(active(incr(cons(active(s(active(cons(mark(_x91), _x112)))), _x62)))))
mark#(head(s(s(s(pairs))))) → active#(head(active(s(active(s(active(s(active(pairs)))))))))mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(cons(active(odds), _x92))), _x72))))
mark#(head(s(incr(s(incr(tail(head(_x111)))))))) → active#(head(active(s(active(incr(s(active(incr(tail(active(head(mark(_x111)))))))))))))mark#(head(incr(head(0)))) → active#(head(incr(active(head(active(0))))))
mark#(head(incr(incr(tail(head(odds)))))) → active#(head(incr(incr(active(tail(active(head(active(odds)))))))))mark#(head(incr(cons(tail(cons(incr(pairs), mark(_x112))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(pairs))), _x112))), _x62)))))
mark#(head(incr(cons(s(_x71), mark(active(active(_x52))))))) → active#(head(active(incr(cons(active(s(mark(_x71))), _x52)))))mark#(head(incr(cons(tail(cons(incr(_x101), _x92)), mark(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x101))), _x92)), _x62)))))
mark#(head(incr(cons(tail(cons(incr(incr(_x121)), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(incr(mark(_x121))))), _x92))), _x62)))))mark#(head(incr(cons(tail(cons(incr(_x101), mark(_x92))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(incr(mark(_x101)), _x92))), _x52)))))
mark#(head(incr(incr(incr(_x61))))) → active#(head(incr(incr(active(incr(mark(_x61)))))))mark#(head(incr(cons(incr(_x81), mark(_x31))))) → active#(head(mark(cons(s(active(incr(mark(_x81)))), incr(_x31)))))
mark#(head(incr(cons(0, active(mark(_x72)))))) → active#(head(active(incr(cons(active(0), _x72)))))mark#(head(incr(cons(tail(cons(incr(_x111), _x102)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(incr(mark(_x111)), _x102))), _x52)))))
mark#(head(tail(pairs))) → active#(head(active(tail(active(pairs)))))mark#(head(s(incr(s(incr(tail(incr(nats)))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(mark(cons(0, incr(nats))))))))))))))))
mark#(head(s(cons(0, mark(active(_x62)))))) → active#(head(s(active(cons(active(0), _x62)))))mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(mark(_x42))))))) → active#(head(incr(cons(active(s(active(cons(mark(incr(pairs)), _x92)))), _x42))))
mark#(head(incr(incr(tail(cons(_x91, _x92)))))) → active#(head(incr(active(incr(active(tail(active(cons(mark(_x91), _x92)))))))))mark#(head(s(incr(s(tail(s(0))))))) → active#(head(active(s(active(incr(active(s(active(tail(s(active(0))))))))))))
mark#(head(incr(cons(tail(cons(incr(0), _x92)), active(active(_x31)))))) → active#(head(mark(cons(s(tail(cons(active(incr(active(0))), _x92))), incr(_x31)))))mark#(head(incr(cons(incr(0), mark(active(_x62)))))) → active#(head(active(incr(cons(active(incr(active(0))), _x62)))))
mark#(head(incr(cons(tail(cons(incr(_x101), cons(_x81, _x82))), mark(_x52))))) → active#(head(active(incr(cons(active(cons(mark(_x81), _x82)), _x52)))))mark#(head(incr(cons(s(_x71), mark(active(_x31)))))) → active#(head(mark(cons(s(active(s(mark(_x71)))), incr(_x31)))))
mark#(head(incr(cons(cons(_x71, active(_x72)), _x31)))) → active#(head(mark(cons(s(active(cons(_x71, _x72))), incr(_x31)))))mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(active(odds), _x92)))), _x72)))))
mark#(cons(incr(_x31), X2)) → active#(cons(active(incr(mark(_x31))), X2))mark#(head(incr(cons(cons(_x81, _x82), active(_x52))))) → active#(head(active(incr(cons(active(cons(mark(_x81), _x82)), _x52)))))
mark#(head(0)) → active#(head(active(0)))mark#(head(incr(cons(nats, active(_x72))))) → active#(head(active(incr(active(cons(active(nats), _x72))))))
mark#(head(s(incr(s(incr(_x111)))))) → active#(head(active(s(active(incr(active(s(active(incr(_x111))))))))))mark#(head(incr(cons(incr(tail(_x91)), mark(active(_x62)))))) → active#(head(active(incr(cons(active(incr(active(tail(mark(_x91))))), _x62)))))
mark#(head(s(incr(s(incr(tail(incr(nats)))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(nats)))))))))))))mark#(head(incr(cons(tail(cons(incr(head(_x141)), mark(active(_x92)))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(head(mark(_x141))))), _x92))), _x52)))))
mark#(head(s(incr(s(incr(incr(pairs))))))) → active#(head(active(s(active(incr(active(s(incr(active(incr(active(pairs))))))))))))mark#(head(s(incr(s(tail(incr(pairs))))))) → active#(head(s(active(incr(active(s(active(tail(active(incr(active(pairs))))))))))))
mark#(head(incr(cons(tail(cons(_x101, _x102)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(_x101, _x102))), _x52)))))mark#(head(s(s(s(odds))))) → active#(head(s(active(s(s(odds))))))
mark#(head(incr(cons(s(cons(_x121, active(_x122))), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(_x121, _x122)))), _x52)))))mark#(head(s(incr(s(incr(tail(s(_x101)))))))) → active#(head(active(s(active(incr(s(incr(tail(active(s(mark(_x101))))))))))))
mark#(head(incr(cons(s(cons(_x101, _x102)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(_x101, _x102))), _x52)))))mark#(head(incr(cons(tail(cons(incr(incr(_x141)), mark(active(_x92)))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(incr(mark(_x141))))), _x92))), _x52)))))
mark#(head(incr(incr(tail(odds))))) → active#(head(incr(incr(active(tail(active(odds)))))))mark#(head(incr(cons(cons(_x81, active(mark(_x82))), active(_x52))))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x52)))))
mark#(head(incr(pairs))) → active#(head(incr(mark(cons(0, incr(odds))))))mark#(head(s(incr(s(head(_x101)))))) → active#(head(active(s(active(incr(active(s(active(head(mark(_x101)))))))))))
mark#(head(incr(cons(s(_x71), mark(active(_x52)))))) → active#(head(active(incr(cons(s(mark(_x71)), _x52)))))mark#(head(incr(cons(tail(cons(incr(s(_x121)), mark(_x112))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(s(mark(_x121))))), _x112))), _x62)))))
mark#(head(incr(cons(cons(active(_x81), active(_x82)), _x62)))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x62)))))mark#(head(incr(cons(_x61, mark(active(_x72)))))) → active#(head(incr(cons(mark(_x61), _x72))))
mark#(head(incr(incr(tail(cons(odds, _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(odds), _x82))))))))mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(cons(mark(cons(0, incr(odds))), _x62)))))
mark#(head(incr(cons(s(odds), _x52)))) → active#(head(active(incr(cons(s(active(odds)), _x52)))))mark#(head(s(incr(s(incr(incr(incr(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(incr(mark(_x141)))))))))))))))
mark#(head(s(s(s(incr(_x101)))))) → active#(head(active(s(active(s(active(s(active(incr(mark(_x101)))))))))))mark#(head(incr(cons(s(cons(incr(_x101), _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(incr(mark(_x101))), _x92)))), _x72))))
mark#(head(s(incr(s(incr(tail(incr(head(tail(_x171)))))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(head(active(tail(mark(_x171))))))))))))))))))mark#(head(s(incr(s(tail(incr(_x121))))))) → active#(head(s(active(incr(active(s(tail(active(incr(mark(_x121)))))))))))
mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(_x52)))))) → active#(head(incr(cons(s(active(cons(mark(_x91), _x92))), _x52))))mark#(head(s(incr(s(incr(tail(nats))))))) → active#(head(active(s(active(incr(s(incr(tail(active(nats))))))))))
mark#(head(incr(incr(incr(_x81))))) → active#(head(active(incr(active(incr(active(incr(mark(_x81)))))))))mark#(head(incr(cons(tail(cons(_x91, mark(_x102))), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(mark(_x91), _x102))), _x52)))))
mark#(head(incr(cons(tail(cons(0, active(_x102))), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(active(0), _x102)))), _x62)))))mark#(head(s(incr(s(tail(s(0))))))) → active#(head(active(s(active(incr(s(active(tail(active(s(active(0))))))))))))
mark#(head(s(incr(pairs)))) → active#(head(active(s(active(incr(active(pairs)))))))mark#(head(s(incr(s(incr(tail(nats))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(nats)))))))))))))
mark#(head(s(incr(s(incr(tail(tail(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(tail(mark(_x141)))))))))))))))mark#(head(incr(cons(tail(cons(incr(_x101), mark(tail(_x71)))), mark(active(active(incr(mark(_x101))))))))) → active#(head(active(incr(cons(active(tail(mark(_x71))), _x62)))))
mark#(head(s(s(incr(nats))))) → active#(head(active(s(s(active(incr(nats)))))))mark#(head(cons(cons(_x61, _x62), _x32))) → active#(head(active(cons(active(cons(mark(_x61), _x62)), _x32))))
mark#(head(incr(cons(tail(cons(incr(_x91), _x92)), active(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(_x91)), _x92)), _x62)))))mark#(head(incr(cons(tail(cons(incr(_x101), active(_x82))), mark(_x71))))) → active#(head(mark(cons(s(active(tail(cons(active(incr(mark(_x101))), _x82)))), incr(_x71)))))
mark#(head(incr(incr(_x61)))) → active#(head(incr(active(incr(mark(_x61))))))mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(_x31)))))) → active#(head(mark(cons(s(s(active(cons(active(odds), _x92)))), incr(_x31)))))
mark#(head(incr(cons(s(cons(s(_x121), active(_x112))), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(s(mark(_x121))), _x112)))), _x52)))))mark#(head(incr(incr(tail(cons(head(_x91), _x82)))))) → active#(head(incr(incr(active(tail(cons(active(head(mark(_x91))), _x82)))))))
mark#(head(incr(cons(pairs, mark(active(_x72)))))) → active#(head(active(incr(cons(active(pairs), _x72)))))mark#(head(incr(incr(odds)))) → active#(head(incr(active(incr(active(odds))))))
mark#(head(incr(cons(pairs, _x52)))) → active#(head(active(incr(cons(pairs, _x52)))))mark#(head(incr(cons(odds, _x42)))) → active#(head(incr(cons(incr(pairs), _x42))))
mark#(head(incr(cons(incr(head(_x91)), mark(active(_x62)))))) → active#(head(active(incr(cons(active(incr(active(head(mark(_x91))))), _x62)))))mark#(head(incr(cons(incr(nats), mark(active(_x52)))))) → active#(head(active(incr(cons(incr(active(nats)), _x52)))))
mark#(head(incr(incr(odds)))) → active#(head(incr(incr(active(odds)))))mark#(head(incr(cons(tail(cons(incr(head(_x121)), mark(_x112))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(head(mark(_x121))))), _x112))), _x62)))))
mark#(head(incr(cons(incr(0), mark(active(_x52)))))) → active#(head(active(incr(cons(incr(0), _x52)))))mark#(head(incr(odds))) → active#(head(active(incr(mark(incr(pairs))))))
mark#(head(incr(cons(cons(active(_x71), _x72), active(_x52))))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x52)))))mark#(head(incr(cons(s(_x71), mark(active(_x72)))))) → active#(head(incr(cons(active(s(mark(_x71))), _x72))))
mark#(head(s(s(s(odds))))) → active#(head(active(s(active(s(active(s(odds))))))))mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(mark(mark(_x62)))))))) → active#(head(active(incr(cons(active(s(active(cons(mark(_x91), _x92)))), _x62)))))
mark#(head(s(incr(s(_x81))))) → active#(head(s(active(incr(active(s(mark(_x81))))))))mark#(head(s(incr(s(tail(s(cons(_x141, _x142)))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(active(cons(mark(_x141), _x142))))))))))))))
mark#(head(incr(incr(tail(tail(_x61)))))) → active#(head(incr(incr(tail(active(tail(mark(_x61))))))))mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x111))), _x92))), _x62)))))
mark#(head(incr(cons(tail(_x71), _x62)))) → active#(head(incr(cons(active(tail(mark(_x71))), _x62))))mark#(head(incr(incr(0)))) → active#(head(active(incr(active(incr(active(0)))))))
mark#(head(incr(cons(s(cons(_x91, active(_x82))), mark(active(active(_x42))))))) → active#(head(incr(cons(active(s(active(cons(mark(_x91), _x82)))), _x42))))mark#(head(incr(cons(cons(_x71, _x72), active(active(_x72)))))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x72)), _x72)))))
mark#(head(s(nats))) → active#(head(active(s(mark(cons(0, incr(nats)))))))mark#(head(s(incr(s(s(odds)))))) → active#(head(active(s(active(incr(active(s(active(s(active(odds)))))))))))
mark#(head(incr(cons(_x61, mark(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))mark#(head(incr(cons(head(_x81), mark(active(mark(_x31))))))) → active#(head(mark(cons(s(active(head(mark(_x81)))), incr(_x31)))))
mark#(head(incr(cons(s(cons(cons(_x121, _x122), _x92)), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(cons(mark(_x121), _x122)), _x92)))), _x52)))))mark#(head(s(incr(s(tail(pairs)))))) → active#(head(active(s(active(incr(active(s(active(tail(active(pairs)))))))))))
mark#(head(incr(cons(tail(cons(incr(tail(_x101)), _x92)), active(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(tail(mark(_x101))))), _x92)), _x62)))))mark#(head(incr(cons(tail(cons(incr(head(_x101)), _x92)), active(active(active(_x31))))))) → active#(head(mark(cons(s(tail(cons(active(incr(active(head(mark(_x101))))), _x92))), incr(_x31)))))
mark#(head(incr(cons(tail(cons(incr(_x101), _x92)), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(_x101)), _x92)), _x52)))))mark#(head(incr(cons(tail(cons(_x91, active(_x82))), _x62)))) → active#(head(active(incr(cons(active(tail(cons(mark(_x91), _x82))), _x62)))))
mark#(head(incr(cons(tail(cons(incr(head(_x101)), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(head(mark(_x101)))), _x92)), _x62)))))mark#(odds) → active#(odds)
mark#(head(incr(cons(pairs, mark(_x52))))) → active#(head(active(incr(cons(mark(cons(0, incr(odds))), _x52)))))mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(cons(mark(incr(pairs)), _x92))), _x72))))
mark#(head(incr(incr(_x71)))) → active#(head(active(incr(active(incr(_x71))))))mark#(head(incr(head(nats)))) → active#(head(incr(active(head(mark(cons(0, incr(nats))))))))
mark#(head(s(s(incr(cons(_x91, _x92)))))) → active#(head(active(s(s(active(incr(active(cons(mark(_x91), _x92)))))))))mark#(head(s(s(s(_x91))))) → active#(head(active(s(s(active(s(_x91)))))))
mark#(head(incr(cons(tail(cons(incr(_x101), _x71)), mark(_x52))))) → active#(head(incr(cons(mark(_x71), _x52))))mark#(head(incr(incr(tail(pairs))))) → active#(head(incr(incr(active(tail(active(pairs)))))))
mark#(head(incr(cons(incr(odds), mark(active(_x62)))))) → active#(head(active(incr(cons(active(incr(active(odds))), _x62)))))mark#(head(incr(cons(tail(cons(_x91, _x92)), _x31)))) → active#(head(mark(cons(s(active(tail(active(cons(mark(_x91), _x92))))), incr(_x31)))))
mark#(head(incr(cons(tail(cons(incr(tail(_x121)), mark(_x112))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(tail(mark(_x121))))), _x112))), _x62)))))mark#(head(incr(incr(tail(cons(odds, active(_x72))))))) → active#(head(incr(incr(active(tail(cons(active(odds), _x72)))))))
mark#(head(incr(cons(incr(_x81), mark(active(mark(_x31))))))) → active#(head(mark(cons(s(active(incr(mark(_x81)))), incr(_x31)))))mark#(head(incr(cons(tail(cons(pairs, _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(pairs), _x92))), _x62)))))
mark#(head(s(incr(s(tail(incr(head(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(incr(active(head(mark(_x141)))))))))))))))mark#(head(s(s(s(odds))))) → active#(head(s(active(s(active(s(odds)))))))
mark#(head(incr(cons(tail(cons(incr(_x101), nats)), mark(_x52))))) → active#(head(active(incr(cons(active(nats), _x52)))))mark#(head(incr(cons(tail(cons(incr(tail(_x101)), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(tail(mark(_x101))))), _x92)), _x62)))))
mark#(head(s(incr(_x61)))) → active#(head(active(s(incr(mark(_x61))))))mark#(head(incr(cons(s(cons(0, active(_x112))), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(cons(active(0), _x112))), _x52)))))
mark#(head(incr(cons(s(cons(s(pairs), _x92)), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(s(active(pairs))), _x92)))), _x52)))))mark#(head(s(s(incr(incr(_x91)))))) → active#(head(active(s(s(active(incr(active(incr(mark(_x91))))))))))
mark#(head(incr(cons(_x61, mark(active(mark(active(_x71)))))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x71)))))mark#(head(s(s(s(head(_x101)))))) → active#(head(active(s(active(s(active(s(active(head(mark(_x101)))))))))))
mark#(head(incr(cons(tail(cons(incr(_x101), mark(active(mark(_x92))))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x92))), _x62)))))mark#(head(s(incr(s(incr(incr(pairs))))))) → active#(head(active(s(incr(active(s(active(incr(active(incr(active(pairs))))))))))))
mark#(head(incr(cons(active(_x61), _x62)))) → active#(head(active(incr(cons(_x61, _x62)))))mark#(head(s(incr(s(incr(tail(active(_x121)))))))) → active#(head(active(s(active(incr(active(s(active(incr(tail(_x121)))))))))))
mark#(head(incr(cons(cons(_x71, _x72), active(_x52))))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x72)), _x52)))))mark#(head(incr(incr(tail(cons(_x81, mark(_x72))))))) → active#(head(incr(incr(tail(active(cons(mark(_x81), _x72)))))))
mark#(head(s(incr(s(tail(head(_x121))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(head(mark(_x121)))))))))))))mark#(head(incr(cons(tail(cons(incr(head(nats)), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(active(nats))))), _x92)), _x62)))))
mark#(head(incr(incr(tail(cons(_x81, mark(_x72))))))) → active#(head(incr(incr(active(tail(cons(mark(_x81), _x72)))))))mark#(head(incr(cons(_x61, active(mark(active(_x52))))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))
mark#(head(s(incr(odds)))) → active#(head(active(s(active(incr(active(odds)))))))mark#(head(tail(cons(incr(_x81), active(_x72))))) → active#(head(active(tail(active(cons(active(incr(mark(_x81))), _x72))))))
mark#(head(incr(cons(tail(cons(incr(_x131), mark(active(_x92)))), mark(mark(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(_x131)), _x92))), _x62)))))mark#(head(incr(cons(tail(cons(incr(nats), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(nats))), _x92))), _x62)))))
mark#(head(cons(_x31, _x32))) → active#(head(cons(mark(_x31), _x32)))mark#(head(incr(cons(tail(cons(incr(active(_x121)), mark(active(_x92)))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(_x121)), _x92))), _x52)))))
mark#(head(incr(cons(tail(cons(0, _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(active(cons(active(0), _x92)))), _x52)))))mark#(head(s(incr(s(incr(tail(incr(s(_x161))))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(incr(active(s(mark(_x161)))))))))))))))))
mark#(head(incr(cons(s(cons(odds, mark(_x102))), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(active(odds), _x102))), _x52)))))mark#(head(s(incr(s(tail(odds)))))) → active#(head(active(s(active(incr(active(s(active(tail(active(odds)))))))))))
mark#(head(s(incr(s(incr(tail(incr(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(incr(mark(_x141))))))))))))))mark#(head(s(incr(s(tail(tail(_x91))))))) → active#(head(active(s(active(incr(s(tail(active(tail(mark(_x91)))))))))))
mark#(head(incr(cons(pairs, mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(pairs), _x52)))))mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(active(_x42))))))) → active#(head(incr(cons(active(s(active(cons(active(odds), _x92)))), _x42))))
mark#(head(incr(incr(tail(_x61))))) → active#(head(incr(incr(active(tail(_x61))))))mark#(head(incr(cons(cons(active(_x71), _x72), _x62)))) → active#(head(incr(cons(active(cons(_x71, _x72)), _x62))))
mark#(head(s(s(incr(s(_x101)))))) → active#(head(active(s(active(s(active(incr(active(s(mark(_x101)))))))))))mark#(head(s(incr(s(incr(tail(incr(odds)))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(odds))))))))))))))
active#(incr(cons(X, XS))) → mark#(cons(s(X), incr(XS)))mark#(head(s(s(s(tail(_x101)))))) → active#(head(active(s(active(s(active(s(active(tail(mark(_x101)))))))))))
mark#(head(s(incr(s(incr(tail(_x111))))))) → active#(head(active(s(active(incr(s(active(incr(tail(_x111))))))))))mark#(head(incr(cons(_x61, active(mark(mark(_x52))))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))
mark#(head(incr(cons(tail(_x71), active(_x52))))) → active#(head(active(incr(cons(active(tail(mark(_x71))), _x52)))))mark#(head(incr(cons(tail(nats), _x62)))) → active#(head(active(incr(cons(active(tail(active(nats))), _x62)))))
mark#(head(incr(cons(tail(cons(incr(_x101), mark(odds))), mark(active(active(incr(mark(_x101))))))))) → active#(head(active(incr(cons(active(odds), _x62)))))mark#(head(incr(cons(s(head(_x91)), _x62)))) → active#(head(active(incr(cons(active(s(active(head(mark(_x91))))), _x62)))))
mark#(head(s(s(incr(cons(_x101, _x102)))))) → active#(head(active(s(active(s(active(incr(active(cons(mark(_x101), _x102))))))))))mark#(head(incr(incr(tail(head(_x81)))))) → active#(head(incr(incr(tail(active(head(mark(_x81))))))))
mark#(head(s(incr(s(tail(nats)))))) → active#(head(active(s(active(incr(s(tail(active(nats)))))))))mark#(head(incr(cons(s(cons(head(pairs), _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(active(head(active(pairs))), _x92))), _x52)))))
mark#(head(s(incr(s(tail(head(_x91))))))) → active#(head(active(s(active(incr(s(tail(active(head(mark(_x91)))))))))))mark#(head(incr(cons(s(cons(head(_x111), _x92)), mark(active(_x52)))))) → active#(head(incr(cons(s(active(cons(active(head(mark(_x111))), _x92))), _x52))))
mark#(head(incr(cons(incr(_x81), active(_x52))))) → active#(head(active(incr(cons(active(incr(mark(_x81))), _x52)))))mark#(tail(X)) → mark#(X)
mark#(head(incr(incr(tail(cons(odds, _x82)))))) → active#(head(incr(incr(tail(cons(active(odds), _x82))))))mark#(head(s(s(s(odds))))) → active#(head(s(active(s(s(mark(incr(pairs))))))))
mark#(head(incr(cons(tail(pairs), _x62)))) → active#(head(active(incr(cons(active(tail(active(pairs))), _x62)))))active#(odds) → mark#(incr(pairs))
mark#(head(incr(cons(cons(_x81, active(mark(_x82))), _x31)))) → active#(head(mark(cons(s(active(cons(_x81, _x82))), incr(_x31)))))mark#(head(s(incr(s(incr(incr(s(_x131)))))))) → active#(head(s(active(incr(active(s(active(incr(active(incr(active(s(mark(_x131))))))))))))))
mark#(head(incr(cons(pairs, active(mark(_x31)))))) → active#(head(mark(cons(s(mark(cons(0, incr(odds)))), incr(_x31)))))mark#(head(incr(incr(tail(cons(pairs, _x82)))))) → active#(head(incr(incr(active(tail(cons(active(pairs), _x82)))))))
mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(odds), _x92)))), _x52)))))mark#(head(s(s(incr(nats))))) → active#(head(active(s(active(s(incr(active(nats))))))))
mark#(head(s(incr(s(incr(tail(_x111))))))) → active#(head(active(s(active(incr(active(s(incr(tail(_x111))))))))))mark#(head(incr(cons(incr(incr(_x91)), mark(active(_x52)))))) → active#(head(active(incr(cons(incr(active(incr(mark(_x91)))), _x52)))))
mark#(head(incr(cons(s(cons(_x91, mark(_x82))), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(mark(_x91), _x82)))), _x72))))mark#(head(incr(cons(tail(cons(incr(_x101), mark(incr(_x71)))), mark(active(active(incr(mark(_x101))))))))) → active#(head(active(incr(cons(active(incr(mark(_x71))), _x62)))))
mark#(head(incr(cons(s(cons(odds, active(active(_x102)))), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(odds), _x102)))), _x52)))))mark#(head(incr(cons(head(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(head(mark(_x71))), _x72)))))
mark#(head(incr(cons(incr(head(_x91)), mark(active(_x52)))))) → active#(head(active(incr(cons(incr(active(head(mark(_x91)))), _x52)))))mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(active(_x42))))))) → active#(head(incr(cons(active(s(active(cons(mark(_x91), _x92)))), _x42))))
mark#(head(incr(cons(s(cons(pairs, active(_x112))), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(pairs), _x112)))), _x52)))))mark#(head(s(incr(s(tail(0)))))) → active#(head(active(s(active(incr(active(s(active(tail(active(0)))))))))))
mark#(head(s(incr(incr(odds))))) → active#(head(active(s(active(incr(active(incr(active(odds)))))))))mark#(head(incr(cons(tail(cons(incr(nats), mark(_x112))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(nats))), _x112))), _x52)))))
mark#(head(s(incr(s(incr(_x101)))))) → active#(head(active(s(active(incr(s(active(incr(mark(_x101))))))))))mark#(head(incr(incr(tail(_x71))))) → active#(head(incr(active(incr(tail(mark(_x71)))))))
mark#(head(incr(cons(cons(active(mark(_x91)), _x92), mark(_x62))))) → active#(head(active(incr(cons(cons(_x91, _x92), _x62)))))mark#(head(s(incr(incr(_x81))))) → active#(head(active(s(incr(active(incr(mark(_x81))))))))
mark#(head(s(incr(s(tail(0)))))) → active#(head(active(s(incr(s(active(tail(active(0)))))))))mark#(head(s(incr(s(tail(s(_x121))))))) → active#(head(active(s(active(incr(active(s(active(tail(s(mark(_x121))))))))))))
mark#(head(s(incr(s(incr(tail(head(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(head(mark(_x141)))))))))))))))mark#(head(tail(cons(incr(head(_x111)), _x62)))) → active#(head(active(tail(active(cons(active(incr(active(head(mark(_x111))))), _x62))))))
mark#(head(incr(cons(cons(_x71, active(mark(mark(_x72)))), _x62)))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x62)))))mark#(head(incr(_x41))) → active#(head(incr(_x41)))
mark#(head(incr(incr(head(_x71))))) → active#(head(incr(active(incr(active(head(mark(_x71))))))))mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(mark(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x111))), _x92))), _x62)))))
mark#(head(incr(cons(s(cons(cons(_x101, _x102), _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(cons(mark(_x101), _x102)), _x92)))), _x72))))mark#(head(s(incr(s(_x81))))) → active#(head(active(s(active(incr(s(mark(_x81))))))))
mark#(head(incr(cons(odds, active(active(_x72)))))) → active#(head(active(incr(cons(active(odds), _x72)))))mark#(head(s(s(s(0))))) → active#(head(active(s(active(s(active(s(active(0)))))))))
mark#(head(incr(cons(_x71, mark(active(mark(_x72))))))) → active#(head(active(incr(cons(_x71, _x72)))))mark#(head(s(incr(s(tail(odds)))))) → active#(head(active(s(active(incr(s(tail(active(odds)))))))))
mark#(head(s(incr(s(tail(incr(_x111))))))) → active#(head(s(active(incr(active(s(active(tail(active(incr(_x111)))))))))))mark#(s(X)) → active#(s(mark(X)))
mark#(head(incr(head(_x61)))) → active#(head(active(incr(active(head(mark(_x61)))))))mark#(head(incr(cons(tail(cons(odds, _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(odds), _x92))), _x52)))))
mark#(head(incr(cons(s(cons(odds, mark(_x82))), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(odds), _x82)))), _x72))))mark#(head(incr(cons(s(cons(head(tail(_x141)), _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(active(head(active(tail(mark(_x141))))), _x92))), _x52)))))
mark#(head(incr(cons(incr(cons(_x91, _x92)), mark(active(_x62)))))) → active#(head(active(incr(cons(active(incr(active(cons(mark(_x91), _x92)))), _x62)))))mark#(incr(X)) → mark#(X)
mark#(head(incr(cons(tail(cons(incr(nats), active(_x82))), _x31)))) → active#(head(mark(cons(s(active(tail(cons(active(incr(active(nats))), _x82)))), incr(_x31)))))mark#(head(incr(cons(s(cons(incr(_x131), active(_x112))), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(incr(mark(_x131))), _x112)))), _x52)))))
mark#(head(incr(head(_x51)))) → active#(head(incr(head(mark(_x51)))))mark#(head(incr(incr(tail(head(nats)))))) → active#(head(incr(incr(active(tail(active(head(active(nats)))))))))
mark#(head(incr(cons(cons(_x71, active(_x72)), active(_x42))))) → active#(head(incr(cons(active(cons(_x71, _x72)), _x42))))mark#(head(incr(cons(tail(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(tail(mark(_x71))), _x72)))))
mark#(head(pairs)) → active#(head(active(pairs)))mark#(head(incr(cons(s(s(_x91)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(s(mark(_x91))))), _x72)))))
mark#(head(s(incr(s(incr(tail(tail(_x101)))))))) → active#(head(active(s(active(incr(s(incr(tail(active(tail(mark(_x101))))))))))))mark#(head(s(incr(s(incr(tail(incr(head(incr(_x171)))))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(head(active(incr(mark(_x171))))))))))))))))))
mark#(head(incr(cons(_x71, active(active(mark(_x72))))))) → active#(head(active(incr(cons(_x71, _x72)))))mark#(head(incr(cons(incr(_x81), mark(active(_x31)))))) → active#(head(mark(cons(s(active(incr(mark(_x81)))), incr(_x31)))))
mark#(head(incr(cons(tail(cons(incr(incr(_x131)), mark(_x112))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(incr(mark(_x131))))), _x112))), _x52)))))mark#(head(s(incr(s(tail(pairs)))))) → active#(head(s(active(incr(s(active(tail(active(pairs)))))))))
mark#(head(incr(cons(tail(_x81), mark(active(mark(_x31))))))) → active#(head(mark(cons(s(active(tail(mark(_x81)))), incr(_x31)))))mark#(head(s(incr(s(tail(incr(nats))))))) → active#(head(s(active(incr(active(s(active(tail(incr(active(nats)))))))))))
mark#(head(incr(cons(tail(cons(head(_x101), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(head(mark(_x101))), _x92))), _x62)))))mark#(head(incr(cons(cons(0, _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(0), _x72)), _x62)))))
mark#(head(incr(cons(tail(cons(odds, _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(active(odds), _x92)))), _x62)))))mark#(head(incr(cons(cons(cons(_x91, _x92), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(cons(mark(_x91), _x92)), _x72)), _x62)))))
mark#(head(incr(cons(s(cons(pairs, _x92)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(active(pairs), _x92)))), _x72)))))mark#(head(incr(cons(tail(cons(incr(s(_x121)), _x92)), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(s(mark(_x121))))), _x92)), _x52)))))
mark#(head(incr(cons(tail(cons(incr(mark(_x121)), mark(active(_x92)))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(_x121)), _x92))), _x52)))))mark#(head(cons(0, _x32))) → active#(head(active(cons(active(0), _x32))))
mark#(head(s(incr(s(s(tail(_x121))))))) → active#(head(active(s(active(incr(active(s(active(s(active(tail(mark(_x121)))))))))))))mark#(head(incr(incr(_x41)))) → active#(head(incr(incr(_x41))))
mark#(head(incr(incr(tail(head(s(_x101))))))) → active#(head(incr(incr(active(tail(active(head(active(s(mark(_x101)))))))))))mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(mark(active(_x62)))))))) → active#(head(active(incr(cons(active(s(active(cons(mark(_x91), _x92)))), _x62)))))
mark#(head(incr(incr(tail(cons(_x71, _x72)))))) → active#(head(incr(incr(active(tail(cons(_x71, _x72)))))))mark#(head(tail(cons(incr(odds), _x62)))) → active#(head(active(tail(active(cons(active(incr(active(odds))), _x62))))))
mark#(head(incr(incr(tail(head(pairs)))))) → active#(head(incr(incr(active(tail(active(head(active(pairs)))))))))mark#(head(incr(incr(tail(cons(head(_x91), _x82)))))) → active#(head(incr(incr(tail(active(cons(active(head(mark(_x91))), _x82)))))))
mark#(head(incr(cons(cons(active(mark(mark(_x81))), _x82), mark(_x52))))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x52)))))mark#(head(s(incr(s(incr(tail(pairs))))))) → active#(head(active(s(active(incr(s(incr(tail(active(pairs))))))))))
mark#(head(incr(cons(tail(cons(incr(head(_x101)), _x92)), active(active(active(_x62))))))) → active#(head(incr(cons(tail(cons(active(incr(active(head(mark(_x101))))), _x92)), _x62))))mark#(head(incr(cons(tail(cons(incr(incr(_x121)), _x92)), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(incr(mark(_x121))))), _x92)), _x52)))))
mark#(head(incr(cons(tail(cons(incr(_x131), mark(active(_x92)))), mark(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(_x131)), _x92)), _x62)))))mark#(head(s(s(incr(_x71))))) → active#(head(active(s(s(active(incr(_x71)))))))
mark#(head(incr(incr(tail(head(_x81)))))) → active#(head(incr(incr(active(tail(head(mark(_x81))))))))mark#(head(incr(cons(tail(cons(0, _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(0), _x92))), _x62)))))
mark#(head(incr(cons(tail(cons(incr(_x101), _x92)), mark(_x31))))) → active#(head(mark(cons(s(active(tail(cons(active(incr(mark(_x101))), _x92)))), incr(_x31)))))mark#(head(incr(cons(cons(incr(_x91), _x72), active(_x52))))) → active#(head(active(incr(cons(active(cons(active(incr(mark(_x91))), _x72)), _x52)))))
mark#(head(incr(cons(tail(cons(incr(head(head(_x131))), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(active(head(mark(_x131))))))), _x92)), _x62)))))mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(_x62))))) → active#(head(incr(cons(tail(cons(active(incr(mark(_x111))), _x92)), _x62))))
mark#(head(incr(cons(tail(cons(incr(_x101), mark(_x82))), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x82))), _x62)))))mark#(cons(X1, active(_x22))) → active#(cons(mark(X1), _x22))
mark#(head(incr(cons(tail(cons(odds, _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(odds), _x92))), _x62)))))mark#(head(s(incr(s(incr(tail(_x121))))))) → active#(head(s(incr(s(active(incr(tail(mark(_x121)))))))))
mark#(head(s(incr(s(tail(incr(s(_x131)))))))) → active#(head(s(active(incr(active(s(active(tail(active(incr(active(s(mark(_x131))))))))))))))mark#(head(incr(cons(s(cons(odds, mark(_x82))), mark(active(mark(_x42))))))) → active#(head(incr(cons(active(s(active(cons(mark(incr(pairs)), _x82)))), _x42))))
mark#(head(s(incr(s(tail(pairs)))))) → active#(head(active(s(active(incr(s(active(tail(pairs)))))))))mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(mark(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x111))), _x92)), _x52)))))
mark#(head(incr(cons(incr(s(_x91)), mark(active(_x52)))))) → active#(head(active(incr(cons(incr(active(s(mark(_x91)))), _x52)))))mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(active(active(_x62))))))) → active#(head(incr(cons(tail(cons(active(incr(mark(_x111))), _x92)), _x62))))
mark#(head(incr(cons(tail(_x81), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(tail(mark(_x81))), _x52)))))mark#(head(incr(cons(s(cons(s(incr(_x151)), _x92)), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(s(active(incr(mark(_x151))))), _x92)))), _x52)))))
mark#(head(incr(cons(s(incr(_x91)), _x62)))) → active#(head(active(incr(cons(active(s(active(incr(mark(_x91))))), _x62)))))mark#(head(incr(cons(tail(cons(incr(_x101), active(_x92))), _x62)))) → active#(head(active(incr(cons(active(tail(cons(incr(mark(_x101)), _x92))), _x62)))))
mark#(head(incr(incr(tail(head(tail(_x101))))))) → active#(head(incr(incr(active(tail(active(head(active(tail(mark(_x101)))))))))))mark#(head(incr(incr(tail(odds))))) → active#(head(incr(incr(tail(odds)))))
mark#(head(s(incr(s(tail(cons(_x91, _x92))))))) → active#(head(active(s(incr(s(active(tail(active(cons(mark(_x91), _x92))))))))))mark#(head(incr(cons(tail(cons(incr(cons(_x112, _x111)), mark(active(_x92)))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(mark(cons(s(_x112), incr(_x111))), _x92))), _x52)))))
mark#(head(incr(cons(incr(s(_x91)), mark(active(_x62)))))) → active#(head(active(incr(cons(active(incr(active(s(mark(_x91))))), _x62)))))mark#(head(incr(cons(0, mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(0), _x52)))))
mark#(head(incr(cons(tail(_x71), _x52)))) → active#(head(active(incr(cons(tail(mark(_x71)), _x52)))))mark#(head(incr(incr(nats)))) → active#(head(incr(active(incr(active(nats))))))
mark#(head(incr(cons(s(cons(0, active(_x102))), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(active(0), _x102)))), _x72)))))mark#(head(incr(cons(cons(incr(s(_x121)), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(incr(active(s(mark(_x121))))), _x72)), _x62)))))
mark#(head(incr(cons(cons(_x81, _x82), mark(active(mark(_x31))))))) → active#(head(mark(cons(s(active(cons(mark(_x81), _x82))), incr(_x31)))))mark#(head(s(incr(head(_x81))))) → active#(head(active(s(active(incr(active(head(mark(_x81)))))))))
mark#(head(incr(incr(tail(head(head(_x101))))))) → active#(head(incr(incr(active(tail(active(head(active(head(mark(_x101)))))))))))mark#(head(s(cons(0, active(_x52))))) → active#(head(s(active(cons(active(0), _x52)))))
mark#(head(incr(cons(tail(cons(_x91, _x92)), _x52)))) → active#(head(active(incr(cons(tail(cons(mark(_x91), _x92)), _x52)))))mark#(head(incr(cons(tail(cons(incr(_x101), _x92)), _x52)))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x101))), _x92)), _x52)))))
mark#(head(s(incr(s(tail(incr(nats))))))) → active#(head(s(active(incr(active(s(tail(active(incr(active(nats)))))))))))mark#(head(incr(incr(tail(cons(s(_x101), _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(s(mark(_x101))), _x82))))))))
mark#(head(s(incr(s(tail(cons(_x91, _x92))))))) → active#(head(active(s(active(incr(s(tail(active(cons(mark(_x91), _x92))))))))))mark#(head(s(incr(s(tail(tail(_x91))))))) → active#(head(active(s(incr(s(active(tail(active(tail(mark(_x91)))))))))))
mark#(head(s(incr(s(incr(tail(incr(incr(_x151))))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(incr(mark(_x151))))))))))))))))mark#(head(incr(cons(pairs, _x62)))) → active#(head(active(incr(active(cons(active(pairs), _x62))))))
mark#(head(s(s(s(nats))))) → active#(head(active(s(active(s(active(s(active(nats)))))))))mark#(head(incr(cons(incr(odds), mark(active(_x52)))))) → active#(head(active(incr(cons(incr(active(odds)), _x52)))))
mark#(head(incr(cons(nats, active(mark(_x72)))))) → active#(head(active(incr(cons(active(nats), _x72)))))mark#(head(s(incr(s(incr(_x101)))))) → active#(head(active(s(incr(active(s(active(incr(mark(_x101))))))))))
mark#(cons(pairs, X2)) → active#(cons(active(pairs), X2))mark#(head(s(cons(nats, _x62)))) → active#(head(active(s(active(cons(active(nats), _x62))))))
mark#(head(incr(cons(tail(cons(incr(_x101), mark(_x61))), mark(active(active(incr(mark(_x101))))))))) → active#(head(incr(cons(mark(_x61), _x62))))mark#(head(s(incr(s(tail(incr(_x121))))))) → active#(head(active(s(active(incr(s(active(tail(active(incr(mark(_x121))))))))))))
mark#(head(s(incr(s(incr(incr(_x121))))))) → active#(head(s(active(incr(active(s(incr(active(incr(mark(_x121)))))))))))mark#(head(s(s(incr(nats))))) → active#(head(active(s(s(incr(active(nats)))))))
mark#(head(incr(cons(s(cons(s(_x121), _x92)), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(cons(active(s(mark(_x121))), _x92))), _x52)))))mark#(head(incr(head(nats)))) → active#(head(incr(active(head(nats)))))
mark#(head(incr(cons(incr(pairs), mark(active(_x52)))))) → active#(head(active(incr(cons(incr(active(pairs)), _x52)))))mark#(head(s(cons(_x61, active(_x72))))) → active#(head(active(s(active(cons(mark(_x61), _x72))))))
mark#(head(incr(cons(s(cons(head(nats), _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(active(head(active(nats))), _x92))), _x52)))))mark#(head(incr(incr(s(_x61))))) → active#(head(incr(incr(active(s(mark(_x61)))))))
mark#(head(incr(cons(tail(cons(incr(tail(_x141)), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(tail(mark(_x141))))), _x92))), _x52)))))mark#(head(incr(cons(tail(cons(0, _x92)), _x62)))) → active#(head(incr(cons(active(tail(active(cons(active(0), _x92)))), _x62))))
mark#(head(incr(incr(tail(cons(tail(_x101), _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(tail(mark(_x101))), _x82))))))))mark#(head(incr(cons(incr(pairs), mark(_x52))))) → active#(head(active(incr(cons(active(incr(active(pairs))), _x52)))))
mark#(head(incr(cons(tail(cons(incr(_x101), mark(active(_x112)))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(incr(mark(_x101)), _x112))), _x52)))))mark#(head(incr(cons(tail(_x81), active(active(mark(_x52))))))) → active#(head(active(incr(cons(active(tail(mark(_x81))), _x52)))))
mark#(head(tail(cons(incr(tail(_x111)), _x62)))) → active#(head(active(tail(active(cons(active(incr(active(tail(mark(_x111))))), _x62))))))mark#(head(incr(cons(s(0), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(0))), _x72)))))
mark#(head(s(incr(s(incr(incr(pairs))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(pairs))))))))))))mark#(head(incr(cons(tail(cons(incr(0), active(_x82))), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(0))), _x82)), _x52)))))
mark#(head(incr(cons(tail(cons(incr(_x101), _x71)), mark(active(_x62)))))) → active#(head(active(incr(cons(mark(_x71), _x62)))))mark#(head(incr(cons(s(cons(s(_x121), _x112)), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(s(mark(_x121)), _x112)))), _x52)))))
mark#(head(s(incr(s(s(_x101)))))) → active#(head(active(s(incr(active(s(active(s(mark(_x101))))))))))mark#(head(incr(cons(tail(cons(incr(_x101), mark(head(_x71)))), mark(active(active(incr(mark(_x101))))))))) → active#(head(active(incr(cons(active(head(mark(_x71))), _x62)))))
mark#(head(incr(cons(tail(cons(incr(_x101), active(_x71))), _x31)))) → active#(head(mark(cons(s(mark(_x71)), incr(_x31)))))mark#(head(incr(cons(s(cons(odds, active(mark(_x102)))), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(odds), _x102)))), _x52)))))
mark#(head(incr(cons(0, mark(active(mark(_x31))))))) → active#(head(mark(cons(s(active(0)), incr(_x31)))))mark#(head(incr(cons(cons(_x71, active(_x72)), mark(_x52))))) → active#(head(incr(cons(cons(_x71, _x72), _x52))))
mark#(head(incr(cons(cons(_x71, _x72), mark(active(_x72)))))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x72)), _x72)))))mark#(head(s(incr(s(incr(tail(cons(_x111, _x112)))))))) → active#(head(active(s(active(incr(s(active(incr(tail(active(cons(mark(_x111), _x112))))))))))))
mark#(head(incr(cons(tail(cons(incr(_x101), mark(_x112))), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x112))), _x52)))))mark#(head(incr(cons(incr(0), mark(_x52))))) → active#(head(active(incr(cons(active(incr(active(0))), _x52)))))
mark#(head(incr(cons(tail(cons(incr(_x101), mark(s(_x71)))), mark(active(active(incr(mark(_x101))))))))) → active#(head(active(incr(cons(active(s(mark(_x71))), _x62)))))mark#(head(s(incr(s(tail(0)))))) → active#(head(active(s(active(incr(s(tail(active(0)))))))))
mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(_x52)))))) → active#(head(incr(cons(s(active(cons(active(odds), _x92))), _x52))))mark#(head(incr(cons(s(cons(head(odds), _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(active(head(active(odds))), _x92))), _x52)))))
mark#(head(incr(cons(tail(cons(incr(nats), _x92)), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(nats))), _x92))), _x52)))))mark#(head(incr(cons(tail(cons(incr(_x101), tail(_x81))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(mark(_x81))), _x52)))))
mark#(head(s(incr(incr(cons(_x101, _x102)))))) → active#(head(active(s(active(incr(active(incr(active(cons(mark(_x101), _x102))))))))))mark#(head(incr(cons(_x61, mark(active(active(_x52))))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))
mark#(head(incr(cons(s(cons(_x91, active(_x82))), mark(active(mark(_x42))))))) → active#(head(incr(cons(active(s(active(cons(mark(_x91), _x82)))), _x42))))mark#(head(s(incr(s(s(pairs)))))) → active#(head(active(s(active(incr(active(s(active(s(active(pairs)))))))))))
mark#(head(incr(cons(s(cons(odds, active(_x112))), mark(active(mark(mark(_x62)))))))) → active#(head(active(incr(cons(active(s(active(cons(active(odds), _x112)))), _x62)))))mark#(head(incr(cons(s(cons(odds, active(_x112))), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(cons(active(odds), _x112))), _x52)))))
mark#(head(incr(cons(tail(cons(incr(_x131), mark(active(_x92)))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(_x131)), _x92))), _x62)))))mark#(head(s(incr(s(incr(incr(_x121))))))) → active#(head(active(s(active(incr(active(s(incr(active(incr(mark(_x121))))))))))))
mark#(head(s(incr(tail(_x81))))) → active#(head(active(s(active(incr(active(tail(mark(_x81)))))))))mark#(head(incr(cons(cons(incr(nats), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(incr(active(nats))), _x72)), _x62)))))
mark#(head(incr(cons(incr(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(incr(mark(_x71))), _x72)))))mark#(head(incr(cons(s(cons(odds, mark(active(_x92)))), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(mark(incr(pairs)), _x92)))), _x72))))
mark#(head(s(incr(s(incr(tail(incr(cons(_x151, _x152))))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(cons(mark(_x151), _x152)))))))))))))))mark#(head(incr(cons(tail(cons(incr(incr(_x141)), active(_x82))), _x31)))) → active#(head(mark(cons(s(active(tail(cons(active(incr(active(incr(mark(_x141))))), _x82)))), incr(_x31)))))
mark#(head(s(incr(s(tail(incr(incr(_x131)))))))) → active#(head(s(active(incr(active(s(active(tail(active(incr(active(incr(mark(_x131))))))))))))))mark#(head(incr(incr(_x61)))) → active#(head(active(incr(incr(mark(_x61))))))
mark#(head(s(incr(s(incr(incr(_x111))))))) → active#(head(s(active(incr(active(s(active(incr(active(incr(_x111)))))))))))mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(_x42)))))) → active#(head(incr(cons(s(active(cons(mark(incr(pairs)), _x92))), _x42))))
mark#(head(incr(cons(0, active(active(mark(_x52))))))) → active#(head(active(incr(cons(active(0), _x52)))))mark#(head(incr(cons(s(cons(head(_x111), active(_x82))), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(head(mark(_x111))), _x82)))), _x72))))
mark#(head(s(incr(s(incr(tail(incr(head(_x151))))))))) → active#(head(active(s(incr(active(s(active(incr(tail(active(incr(active(head(mark(_x151)))))))))))))))mark#(head(incr(cons(s(_x71), _x31)))) → active#(head(mark(cons(s(active(s(mark(_x71)))), incr(_x31)))))
mark#(head(incr(cons(odds, active(active(mark(_x52))))))) → active#(head(active(incr(cons(active(odds), _x52)))))mark#(head(incr(cons(tail(cons(incr(_x101), mark(active(_x82)))), mark(active(_x31)))))) → active#(head(mark(cons(s(active(tail(cons(active(incr(mark(_x101))), _x82)))), incr(_x31)))))
mark#(head(incr(cons(cons(_x71, _x72), _x31)))) → active#(head(mark(cons(s(active(cons(mark(_x71), _x72))), incr(_x31)))))mark#(head(s(s(odds)))) → active#(head(active(s(active(s(mark(incr(pairs))))))))
mark#(head(incr(cons(tail(cons(cons(_x111, _x112), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(active(cons(mark(_x111), _x112)), _x92)))), _x62)))))mark#(head(incr(cons(_x51, _x52)))) → active#(head(incr(cons(_x51, _x52))))
mark#(head(s(incr(s(tail(incr(_x121))))))) → active#(head(active(s(active(incr(active(s(tail(active(incr(mark(_x121))))))))))))mark#(head(incr(cons(cons(active(mark(_x91)), _x92), mark(active(_x62)))))) → active#(head(active(incr(cons(active(cons(_x91, _x92)), _x62)))))
mark#(head(incr(cons(tail(odds), _x62)))) → active#(head(active(incr(cons(active(tail(active(odds))), _x62)))))mark#(head(s(incr(s(tail(incr(head(_x131)))))))) → active#(head(s(active(incr(active(s(active(tail(active(incr(active(head(mark(_x131))))))))))))))
mark#(head(s(s(s(_x91))))) → active#(head(active(s(active(s(s(_x91)))))))mark#(head(incr(incr(tail(cons(_x81, mark(_x92))))))) → active#(head(incr(incr(active(tail(active(cons(mark(_x81), _x92))))))))
mark#(head(incr(cons(s(cons(s(_x101), _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(s(mark(_x101))), _x92)))), _x72))))mark#(head(incr(cons(_x61, mark(mark(_x72)))))) → active#(head(active(incr(cons(mark(_x61), _x72)))))
mark#(head(incr(cons(tail(cons(incr(tail(_x141)), active(_x82))), _x31)))) → active#(head(mark(cons(s(active(tail(cons(active(incr(active(tail(mark(_x141))))), _x82)))), incr(_x31)))))mark#(head(incr(cons(tail(cons(incr(head(cons(_x131, _x132))), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(active(cons(mark(_x131), _x132)))))), _x92)), _x62)))))
mark#(head(s(incr(s(tail(s(_x121))))))) → active#(head(active(s(active(incr(s(active(tail(active(s(mark(_x121))))))))))))mark#(head(incr(cons(tail(cons(incr(incr(_x101)), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(incr(mark(_x101))))), _x92)), _x62)))))
mark#(head(incr(cons(_x71, mark(_x72))))) → active#(head(active(incr(cons(_x71, _x72)))))mark#(head(incr(cons(tail(cons(pairs, _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(active(pairs), _x92)))), _x62)))))
mark#(head(incr(cons(s(_x81), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(mark(_x81))), _x52)))))mark#(head(incr(cons(odds, _x52)))) → active#(head(active(incr(cons(odds, _x52)))))
mark#(head(incr(cons(incr(odds), mark(_x52))))) → active#(head(active(incr(cons(active(incr(active(odds))), _x52)))))mark#(head(incr(cons(s(cons(head(head(_x141)), _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(active(head(active(head(mark(_x141))))), _x92))), _x52)))))
mark#(head(incr(cons(s(cons(_x91, active(_x112))), mark(active(mark(_x52))))))) → active#(head(incr(cons(active(s(active(cons(mark(_x91), _x112)))), _x52))))mark#(head(incr(cons(_x61, active(active(mark(mark(_x72)))))))) → active#(head(active(incr(cons(mark(_x61), _x72)))))
mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(active(cons(mark(cons(0, incr(nats))), _x62))))))mark#(head(s(incr(s(s(_x101)))))) → active#(head(active(s(active(incr(s(active(s(mark(_x101))))))))))
mark#(head(s(s(incr(nats))))) → active#(head(s(s(active(incr(active(nats)))))))mark#(head(s(s(incr(head(_x101)))))) → active#(head(active(s(active(s(active(incr(active(head(mark(_x101)))))))))))
mark#(head(incr(cons(s(cons(nats, _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(active(nats), _x92))), _x52)))))mark#(head(incr(cons(s(cons(head(_x111), _x102)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(head(mark(_x111)), _x102))), _x52)))))
mark#(head(s(incr(s(s(_x101)))))) → active#(head(active(s(active(incr(active(s(s(mark(_x101))))))))))mark#(head(incr(cons(head(_x71), _x62)))) → active#(head(active(incr(cons(active(head(mark(_x71))), _x62)))))
mark#(head(incr(cons(_x61, _x62)))) → active#(head(incr(cons(mark(_x61), _x62))))mark#(head(incr(cons(tail(cons(incr(_x101), mark(active(mark(_x112))))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x112))), _x52)))))
mark#(head(s(incr(s(tail(tail(_x121))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(tail(mark(_x121)))))))))))))mark#(head(incr(cons(tail(cons(incr(0), active(_x82))), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(0))), _x82))), _x62)))))
mark#(head(incr(cons(incr(_x71), _x62)))) → active#(head(active(incr(cons(active(incr(mark(_x71))), _x62)))))mark#(head(incr(cons(tail(cons(incr(0), _x92)), active(active(_x52)))))) → active#(head(incr(cons(tail(cons(active(incr(active(0))), _x92)), _x52))))
mark#(head(incr(cons(tail(cons(incr(incr(_x141)), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(incr(mark(_x141))))), _x92))), _x52)))))mark#(head(s(incr(s(tail(cons(_x121, _x122))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(cons(mark(_x121), _x122))))))))))))
mark#(head(s(incr(s(incr(tail(nats))))))) → active#(head(active(s(active(incr(s(active(incr(tail(active(nats)))))))))))mark#(head(s(incr(s(incr(tail(0))))))) → active#(head(active(s(active(incr(active(s(active(incr(tail(active(0))))))))))))
mark#(head(s(s(incr(tail(_x101)))))) → active#(head(active(s(active(s(active(incr(active(tail(mark(_x101)))))))))))mark#(head(s(incr(s(incr(tail(_x121))))))) → active#(head(active(s(incr(s(incr(tail(mark(_x121)))))))))
mark#(head(incr(cons(s(cons(odds, active(_x112))), mark(active(mark(active(_x62)))))))) → active#(head(active(incr(cons(active(s(active(cons(active(odds), _x112)))), _x62)))))mark#(head(incr(cons(tail(cons(0, _x92)), _x52)))) → active#(head(active(incr(cons(tail(active(cons(active(0), _x92))), _x52)))))
mark#(head(incr(cons(tail(cons(incr(nats), mark(active(_x92)))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(nats))), _x92))), _x52)))))mark#(head(incr(cons(s(cons(odds, active(_x82))), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(odds), _x82)))), _x72))))
mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(active(cons(active(odds), _x62))))))mark#(head(s(pairs))) → active#(head(active(s(active(pairs)))))
mark#(head(tail(cons(tail(_x81), _x62)))) → active#(head(active(tail(active(cons(active(tail(mark(_x81))), _x62))))))mark#(head(incr(cons(tail(cons(incr(tail(_x141)), mark(active(_x92)))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(tail(mark(_x141))))), _x92))), _x52)))))
mark#(head(incr(cons(tail(cons(incr(_x101), s(_x81))), mark(_x52))))) → active#(head(active(incr(cons(active(s(mark(_x81))), _x52)))))mark#(head(incr(cons(tail(cons(_x91, _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(active(cons(mark(_x91), _x92)))), _x52)))))
mark#(head(cons(_x31, active(_x52)))) → active#(head(active(cons(mark(_x31), _x52))))mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(_x31)))))) → active#(head(mark(cons(s(s(active(cons(mark(_x91), _x92)))), incr(_x31)))))
mark#(head(incr(cons(s(cons(s(_x111), _x92)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(active(s(mark(_x111))), _x92)))), _x72)))))mark#(head(incr(incr(tail(s(_x81)))))) → active#(head(incr(incr(active(tail(active(s(mark(_x81)))))))))
mark#(head(incr(cons(tail(cons(incr(_x101), _x112)), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(incr(mark(_x101)), _x112))), _x52)))))mark#(head(incr(cons(pairs, active(active(_x72)))))) → active#(head(active(incr(cons(active(pairs), _x72)))))
mark#(head(incr(incr(tail(odds))))) → active#(head(incr(active(incr(active(tail(active(odds))))))))mark#(cons(cons(_x31, _x32), X2)) → active#(cons(active(cons(mark(_x31), _x32)), X2))
mark#(head(incr(cons(s(_x71), active(active(_x72)))))) → active#(head(active(incr(cons(active(s(mark(_x71))), _x72)))))mark#(head(incr(incr(tail(cons(0, _x82)))))) → active#(head(incr(incr(active(tail(cons(active(0), _x82)))))))
mark#(head(incr(cons(tail(cons(s(_x101), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(s(mark(_x101))), _x92))), _x62)))))mark#(head(s(cons(tail(_x81), _x62)))) → active#(head(active(s(active(cons(active(tail(mark(_x81))), _x62))))))
mark#(head(incr(cons(tail(cons(incr(head(_x101)), _x92)), active(active(active(active(_x52)))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(mark(_x101))))), _x92)), _x52)))))mark#(head(s(incr(s(incr(tail(nats))))))) → active#(head(active(s(active(incr(active(s(active(incr(tail(active(nats))))))))))))
mark#(head(incr(cons(head(_x81), active(_x52))))) → active#(head(active(incr(cons(active(head(mark(_x81))), _x52)))))mark#(head(incr(cons(s(pairs), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(pairs))), _x72)))))
mark#(head(incr(cons(s(cons(0, active(_x82))), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(0), _x82)))), _x72))))mark#(head(incr(cons(cons(active(mark(_x91)), _x92), mark(mark(_x62)))))) → active#(head(active(incr(cons(active(cons(_x91, _x92)), _x62)))))
mark#(head(s(incr(s(tail(_x81)))))) → active#(head(active(s(incr(s(active(tail(_x81))))))))mark#(head(incr(cons(pairs, active(mark(_x31)))))) → active#(head(mark(cons(s(active(pairs)), incr(_x31)))))
mark#(head(s(incr(s(tail(s(_x121))))))) → active#(head(active(s(incr(active(s(active(tail(active(s(mark(_x121))))))))))))mark#(head(s(incr(s(incr(tail(incr(head(_x151))))))))) → active#(head(active(s(incr(active(s(incr(active(tail(active(incr(active(head(mark(_x151)))))))))))))))
mark#(head(tail(cons(_x61, _x62)))) → active#(head(active(tail(cons(mark(_x61), _x62)))))mark#(head(incr(cons(nats, mark(active(_x72)))))) → active#(head(active(incr(cons(active(nats), _x72)))))
mark#(head(incr(cons(tail(cons(_x81, _x82)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(_x81, _x82))), _x62)))))mark#(head(s(incr(s(tail(_x101)))))) → active#(head(s(active(incr(active(s(active(tail(mark(_x101))))))))))
mark#(head(s(incr(s(incr(tail(incr(_x141)))))))) → active#(head(active(s(active(incr(active(s(incr(active(tail(active(incr(mark(_x141))))))))))))))mark#(head(s(incr(s(incr(tail(cons(_x131, _x132)))))))) → active#(head(active(s(active(incr(active(s(active(incr(tail(active(cons(mark(_x131), _x132)))))))))))))
mark#(head(incr(cons(incr(_x81), mark(active(_x62)))))) → active#(head(incr(cons(active(incr(mark(_x81))), _x62))))mark#(head(s(incr(s(incr(tail(_x111))))))) → active#(head(active(s(incr(active(s(active(incr(tail(_x111))))))))))
mark#(head(s(incr(s(tail(incr(_x121))))))) → active#(head(s(incr(active(s(active(tail(active(incr(mark(_x121)))))))))))mark#(head(incr(cons(cons(incr(_x91), _x72), _x52)))) → active#(head(active(incr(cons(cons(active(incr(mark(_x91))), _x72), _x52)))))
mark#(head(incr(incr(tail(nats))))) → active#(head(incr(incr(tail(active(nats))))))mark#(head(s(incr(s(tail(s(_x131))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(_x131))))))))))))
mark#(head(incr(cons(tail(_x81), mark(_x52))))) → active#(head(active(incr(cons(active(tail(mark(_x81))), _x52)))))mark#(head(incr(cons(cons(_x81, _x82), _x52)))) → active#(head(active(incr(cons(cons(_x81, _x82), _x52)))))
mark#(head(s(incr(s(incr(incr(pairs))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(mark(cons(0, incr(odds)))))))))))))))mark#(head(s(incr(s(tail(incr(nats))))))) → active#(head(s(active(incr(active(s(active(tail(active(incr(nats)))))))))))
mark#(head(incr(cons(cons(_x81, active(active(_x82))), _x62)))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x62)))))mark#(head(incr(cons(tail(cons(incr(_x131), active(_x82))), _x31)))) → active#(head(mark(cons(s(active(tail(cons(active(incr(_x131)), _x82)))), incr(_x31)))))
mark#(head(s(incr(incr(_x91))))) → active#(head(active(s(active(incr(active(incr(_x91))))))))mark#(head(incr(incr(tail(cons(tail(_x91), _x82)))))) → active#(head(incr(incr(tail(active(cons(active(tail(mark(_x91))), _x82)))))))
mark#(head(s(cons(head(_x81), _x62)))) → active#(head(active(s(active(cons(active(head(mark(_x81))), _x62))))))mark#(head(incr(cons(_x61, _x31)))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))
mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(active(active(active(_x52)))))))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x111))), _x92)), _x52)))))mark#(head(incr(cons(tail(cons(_x91, _x92)), _x31)))) → active#(head(mark(cons(s(active(tail(cons(mark(_x91), _x92)))), incr(_x31)))))
mark#(head(incr(s(_x61)))) → active#(head(active(incr(active(s(mark(_x61)))))))mark#(head(s(incr(s(incr(tail(incr(head(_x161))))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(incr(active(head(mark(_x161)))))))))))))))))
mark#(head(s(incr(s(_x91))))) → active#(head(active(s(active(incr(active(s(_x91))))))))mark#(head(incr(cons(incr(_x81), mark(active(active(_x52))))))) → active#(head(active(incr(cons(active(incr(mark(_x81))), _x52)))))
mark#(head(incr(cons(odds, _x62)))) → active#(head(incr(cons(active(incr(mark(pairs))), _x62))))mark#(head(incr(cons(tail(incr(_x91)), _x62)))) → active#(head(active(incr(cons(active(tail(active(incr(mark(_x91))))), _x62)))))
mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(_x31)))))) → active#(head(mark(cons(s(active(s(active(cons(mark(_x91), _x92))))), incr(_x31)))))mark#(head(incr(cons(tail(cons(incr(_x101), active(_x112))), _x31)))) → active#(head(mark(cons(s(active(tail(cons(incr(mark(_x101)), _x112)))), incr(_x31)))))
mark#(head(s(incr(incr(nats))))) → active#(head(active(s(active(incr(active(incr(active(nats)))))))))mark#(head(incr(incr(pairs)))) → active#(head(incr(active(incr(active(pairs))))))
mark#(head(s(incr(s(incr(tail(head(_x101)))))))) → active#(head(active(s(active(incr(s(incr(tail(active(head(mark(_x101))))))))))))mark#(head(incr(cons(s(cons(0, _x92)), mark(active(_x31)))))) → active#(head(mark(cons(s(active(s(active(cons(active(0), _x92))))), incr(_x31)))))
mark#(head(incr(pairs))) → active#(head(active(incr(mark(cons(0, incr(odds)))))))mark#(head(incr(incr(s(_x71))))) → active#(head(incr(active(incr(active(s(mark(_x71))))))))
mark#(head(incr(cons(s(cons(s(tail(_x151)), _x92)), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(s(active(tail(mark(_x151))))), _x92)))), _x52)))))mark#(head(s(s(s(_x81))))) → active#(head(active(s(active(s(s(mark(_x81))))))))
mark#(head(incr(cons(s(_x71), active(mark(_x72)))))) → active#(head(active(incr(cons(active(s(mark(_x71))), _x72)))))mark#(head(incr(odds))) → active#(head(incr(active(odds))))
mark#(head(incr(cons(s(cons(_x91, mark(_x112))), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(mark(_x91), _x112)))), _x52)))))mark#(head(incr(cons(nats, mark(_x52))))) → active#(head(active(incr(cons(active(nats), _x52)))))
mark#(head(incr(cons(cons(_x81, _x82), mark(_x52))))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x52)))))mark#(head(incr(cons(_x61, active(_x52))))) → active#(head(incr(cons(mark(_x61), _x52))))
mark#(head(incr(cons(s(cons(head(_x111), _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(cons(active(head(mark(_x111))), _x92)), _x52)))))mark#(head(incr(cons(tail(cons(incr(_x101), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x92))), _x52)))))
mark#(head(incr(cons(cons(active(active(_x81)), _x82), _x62)))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x62)))))mark#(head(incr(cons(cons(_x61, active(mark(_x62))), _x62)))) → active#(head(incr(cons(active(cons(_x61, _x62)), _x62))))
mark#(head(s(incr(s(incr(tail(incr(cons(_x161, _x162))))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(incr(active(cons(mark(_x161), _x162))))))))))))))))mark#(head(s(incr(s(incr(tail(incr(nats)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(incr(active(nats)))))))))))))))
mark#(head(incr(cons(cons(active(mark(_x91)), _x92), mark(_x31))))) → active#(head(mark(cons(s(active(cons(_x91, _x92))), incr(_x31)))))mark#(head(s(incr(s(incr(tail(incr(nats)))))))) → active#(head(active(s(incr(active(s(incr(active(tail(active(incr(active(nats)))))))))))))
mark#(head(s(incr(s(tail(incr(_x121))))))) → active#(head(active(s(incr(active(s(active(tail(active(incr(mark(_x121))))))))))))mark#(head(incr(cons(tail(cons(_x91, _x92)), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(mark(_x91), _x92))), _x52)))))
mark#(head(incr(cons(tail(cons(incr(_x101), head(_x81))), mark(_x52))))) → active#(head(active(incr(cons(active(head(mark(_x81))), _x52)))))mark#(head(incr(incr(odds)))) → active#(head(active(incr(active(incr(mark(incr(pairs))))))))
mark#(head(s(incr(s(incr(tail(_x121))))))) → active#(head(s(active(incr(active(s(active(incr(tail(mark(_x121)))))))))))mark#(head(incr(cons(incr(_x81), mark(_x62))))) → active#(head(active(incr(cons(incr(mark(_x81)), _x62)))))
mark#(head(s(incr(s(incr(tail(incr(0)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(incr(active(0)))))))))))))))mark#(head(incr(cons(s(cons(odds, active(_x112))), mark(active(mark(_x31))))))) → active#(head(mark(cons(s(active(s(active(cons(active(odds), _x112))))), incr(_x31)))))
mark#(head(incr(cons(tail(cons(incr(_x131), mark(active(_x92)))), mark(_x52))))) → active#(head(incr(cons(active(tail(cons(active(incr(_x131)), _x92))), _x52))))mark#(head(s(incr(s(tail(incr(odds))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(incr(active(odds)))))))))))))
mark#(head(incr(cons(tail(tail(_x91)), _x62)))) → active#(head(active(incr(cons(active(tail(active(tail(mark(_x91))))), _x62)))))mark#(head(incr(incr(tail(_x81))))) → active#(head(incr(active(incr(active(tail(_x81)))))))
mark#(head(incr(cons(cons(active(_x81), mark(_x82)), _x62)))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x62)))))mark#(head(incr(cons(tail(cons(incr(odds), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(odds))), _x92))), _x62)))))
mark#(head(s(s(tail(_x81))))) → active#(head(active(s(active(s(active(tail(mark(_x81)))))))))mark#(head(incr(cons(tail(cons(_x91, mark(_x82))), _x62)))) → active#(head(active(incr(cons(active(tail(cons(mark(_x91), _x82))), _x62)))))
mark#(head(s(incr(s(incr(incr(cons(_x141, _x142)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(cons(mark(_x141), _x142))))))))))))))mark#(head(tail(cons(incr(s(_x111)), _x62)))) → active#(head(active(tail(active(cons(active(incr(active(s(mark(_x111))))), _x62))))))
mark#(head(incr(cons(s(cons(incr(_x121), _x92)), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(incr(mark(_x121))), _x92)))), _x52)))))mark#(head(s(incr(s(incr(tail(_x121))))))) → active#(head(active(s(active(incr(active(s(incr(tail(mark(_x121)))))))))))
mark#(head(incr(cons(s(cons(nats, _x92)), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(nats), _x92)))), _x52)))))mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(active(mark(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x111))), _x92)), _x62)))))
mark#(pairs) → active#(pairs)active#(pairs) → mark#(cons(0, incr(odds)))
mark#(head(incr(cons(tail(cons(incr(head(odds)), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(active(odds))))), _x92)), _x62)))))mark#(head(incr(cons(tail(cons(_x91, _x92)), active(_x31))))) → active#(head(mark(cons(s(active(tail(cons(mark(_x91), _x92)))), incr(_x31)))))
mark#(head(incr(cons(tail(cons(incr(pairs), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(pairs))), _x92))), _x52)))))mark#(head(head(_x31))) → active#(head(active(head(mark(_x31)))))
mark#(head(s(incr(s(incr(s(_x121))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(s(mark(_x121)))))))))))))mark#(head(incr(cons(tail(cons(incr(odds), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(odds))), _x92)), _x62)))))
mark#(head(s(s(incr(pairs))))) → active#(head(active(s(active(s(active(incr(active(pairs)))))))))mark#(head(incr(cons(s(cons(nats, active(_x82))), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(nats), _x82)))), _x72))))
mark#(head(s(incr(s(incr(incr(head(_x131)))))))) → active#(head(s(active(incr(active(s(active(incr(active(incr(active(head(mark(_x131))))))))))))))mark#(head(incr(cons(s(cons(s(0), _x92)), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(s(active(0))), _x92)))), _x52)))))
mark#(head(incr(cons(pairs, mark(active(_x62)))))) → active#(head(active(incr(cons(active(pairs), _x62)))))mark#(head(incr(incr(tail(nats))))) → active#(head(incr(active(incr(active(tail(active(nats))))))))
mark#(head(s(cons(_x71, _x72)))) → active#(head(active(s(active(cons(_x71, _x72))))))mark#(head(s(s(pairs)))) → active#(head(active(s(active(s(mark(cons(0, incr(odds)))))))))
mark#(head(tail(0))) → active#(head(active(tail(active(0)))))mark#(head(incr(cons(odds, mark(active(_x72)))))) → active#(head(active(incr(cons(active(odds), _x72)))))
mark#(head(s(incr(incr(0))))) → active#(head(active(s(active(incr(active(incr(active(0)))))))))mark#(head(s(s(s(odds))))) → active#(head(s(s(s(active(odds))))))
mark#(head(incr(cons(nats, active(active(_x72)))))) → active#(head(incr(cons(active(nats), _x72))))mark#(head(incr(cons(head(_x81), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(head(mark(_x81))), _x52)))))
mark#(head(incr(incr(0)))) → active#(head(incr(active(incr(active(0))))))mark#(head(incr(cons(tail(cons(incr(_x101), mark(active(_x82)))), mark(active(_x62)))))) → active#(head(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x82))), _x62))))
mark#(head(s(incr(s(incr(tail(incr(head(_x151))))))))) → active#(head(active(s(incr(s(active(incr(active(tail(active(incr(active(head(mark(_x151)))))))))))))))mark#(head(incr(cons(_x61, active(active(active(_x52))))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))
mark#(head(tail(cons(odds, _x62)))) → active#(head(active(tail(active(cons(active(odds), _x62))))))mark#(head(incr(cons(cons(odds, _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(odds), _x72)), _x62)))))
mark#(head(incr(cons(tail(cons(_x91, active(_x102))), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(mark(_x91), _x102))), _x52)))))mark#(head(incr(incr(tail(cons(_x81, active(_x72))))))) → active#(head(incr(incr(tail(active(cons(mark(_x81), _x72)))))))
mark#(head(incr(pairs))) → active#(head(active(incr(pairs))))mark#(head(incr(cons(incr(incr(_x91)), mark(active(_x62)))))) → active#(head(active(incr(cons(active(incr(active(incr(mark(_x91))))), _x62)))))
mark#(head(s(incr(s(incr(tail(_x121))))))) → active#(head(s(active(incr(s(incr(tail(mark(_x121)))))))))mark#(head(incr(cons(s(cons(s(_x141), _x92)), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(s(_x141)), _x92)))), _x52)))))
mark#(head(incr(cons(cons(mark(_x71), active(mark(_x72))), _x62)))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x62)))))mark#(head(incr(cons(tail(cons(incr(_x101), active(mark(_x112)))), _x31)))) → active#(head(mark(cons(s(active(tail(cons(active(incr(mark(_x101))), _x112)))), incr(_x31)))))
mark#(head(incr(cons(tail(cons(incr(_x101), mark(_x61))), mark(active(active(incr(mark(_x101))))))))) → active#(head(active(incr(cons(mark(_x61), _x52)))))mark#(head(incr(cons(nats, _x72)))) → active#(head(active(incr(active(cons(nats, _x72))))))
mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(mark(_x62))))))) → active#(head(active(incr(cons(s(active(cons(mark(_x91), _x92))), _x62)))))mark#(head(s(tail(_x61)))) → active#(head(active(s(active(tail(mark(_x61)))))))
mark#(head(tail(cons(nats, _x62)))) → active#(head(active(tail(active(cons(active(nats), _x62))))))mark#(head(s(incr(s(incr(tail(incr(_x101)))))))) → active#(head(active(s(incr(s(active(incr(tail(active(incr(mark(_x101))))))))))))
mark#(head(incr(cons(tail(cons(_x91, _x92)), mark(_x52))))) → active#(head(active(incr(cons(active(tail(active(cons(mark(_x91), _x92)))), _x52)))))mark#(head(incr(cons(tail(cons(incr(pairs), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(pairs))), _x92))), _x62)))))
mark#(head(s(incr(cons(_x81, _x82))))) → active#(head(active(s(active(incr(active(cons(mark(_x81), _x82))))))))mark#(head(tail(_x31))) → active#(head(tail(mark(_x31))))
mark#(head(s(cons(_x61, _x62)))) → active#(head(s(active(cons(mark(_x61), _x62)))))mark#(head(incr(cons(tail(cons(incr(0), mark(_x112))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(0))), _x112))), _x52)))))
mark#(head(s(incr(s(incr(cons(_x121, _x122))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(cons(mark(_x121), _x122))))))))))))mark#(head(incr(cons(cons(active(_x71), _x72), mark(active(_x62)))))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x62)))))
mark#(head(incr(cons(tail(cons(incr(odds), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(odds))), _x92))), _x52)))))mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(mark(_x42))))))) → active#(head(incr(cons(active(s(active(cons(mark(_x91), _x92)))), _x42))))
mark#(head(incr(cons(tail(cons(incr(_x101), mark(_x71))), mark(_x52))))) → active#(head(active(incr(cons(mark(_x71), _x52)))))mark#(head(incr(cons(incr(incr(_x101)), mark(_x52))))) → active#(head(active(incr(cons(active(incr(active(incr(mark(_x101))))), _x52)))))
mark#(head(s(incr(s(tail(pairs)))))) → active#(head(active(s(active(incr(s(tail(active(pairs)))))))))mark#(head(incr(incr(tail(head(_x61)))))) → active#(head(incr(incr(tail(active(head(mark(_x61))))))))
mark#(head(s(incr(s(incr(tail(odds))))))) → active#(head(active(s(active(incr(s(active(incr(tail(active(odds)))))))))))mark#(head(incr(cons(s(cons(0, active(_x112))), mark(active(mark(_x52))))))) → active#(head(incr(cons(active(s(active(cons(active(0), _x112)))), _x52))))
mark#(head(s(incr(s(tail(incr(s(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(incr(active(s(mark(_x141)))))))))))))))mark#(head(incr(cons(s(cons(0, _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(active(0), _x92))), _x52)))))
mark#(head(incr(cons(cons(_x71, _x72), active(mark(_x72)))))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x72)), _x72)))))mark#(head(incr(cons(s(cons(s(_x121), _x92)), mark(active(mark(_x52))))))) → active#(head(incr(cons(active(s(active(cons(active(s(mark(_x121))), _x92)))), _x52))))
mark#(head(incr(cons(_x61, mark(active(mark(mark(_x72)))))))) → active#(head(active(incr(cons(mark(_x61), _x72)))))mark#(head(incr(cons(tail(cons(incr(nats), mark(active(_x82)))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(nats))), _x82))), _x62)))))
mark#(head(incr(cons(s(cons(_x91, mark(_x102))), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(mark(_x91), _x102)))), _x72)))))mark#(head(incr(incr(tail(0))))) → active#(head(incr(incr(active(tail(active(0)))))))
mark#(head(incr(cons(nats, active(active(active(_x52))))))) → active#(head(active(incr(cons(active(nats), _x52)))))mark#(head(s(incr(s(tail(s(0))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(0))))))))))))
mark#(head(incr(cons(s(cons(nats, active(_x112))), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(nats), _x112)))), _x52)))))mark#(head(incr(cons(s(cons(s(_x121), _x92)), mark(active(mark(_x62))))))) → active#(head(active(incr(cons(s(active(cons(active(s(mark(_x121))), _x92))), _x62)))))
mark#(head(s(incr(s(tail(head(_x91))))))) → active#(head(active(s(incr(s(active(tail(active(head(mark(_x91)))))))))))mark#(head(s(incr(s(cons(_x101, _x102)))))) → active#(head(active(s(active(incr(active(s(active(cons(mark(_x101), _x102))))))))))
mark#(head(incr(cons(tail(cons(incr(_x101), active(_x82))), _x52)))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x101))), _x82)), _x52)))))mark#(head(s(incr(s(tail(s(odds))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(active(odds)))))))))))))
mark#(head(incr(cons(tail(cons(incr(_x101), active(_x82))), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x82))), _x52)))))mark#(head(s(cons(0, mark(_x62))))) → active#(head(s(active(cons(0, _x62)))))
mark#(head(s(incr(s(incr(incr(pairs))))))) → active#(head(active(s(active(incr(active(s(active(incr(incr(active(pairs))))))))))))mark#(head(incr(cons(tail(cons(incr(tail(_x131)), active(_x82))), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(tail(mark(_x131))))), _x82))), _x62)))))
mark#(head(s(incr(incr(tail(_x101)))))) → active#(head(active(s(active(incr(active(incr(active(tail(mark(_x101)))))))))))mark#(head(incr(cons(s(odds), _x62)))) → active#(head(incr(cons(active(s(active(odds))), _x62))))
mark#(head(s(cons(cons(_x81, _x82), _x62)))) → active#(head(active(s(active(cons(active(cons(mark(_x81), _x82)), _x62))))))mark#(head(incr(cons(_x51, _x52)))) → active#(head(incr(active(cons(mark(_x51), _x52)))))
mark#(head(incr(cons(tail(cons(0, mark(_x102))), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(active(0), _x102)))), _x62)))))mark#(head(s(incr(s(tail(incr(_x111))))))) → active#(head(active(s(active(incr(s(active(tail(active(incr(mark(_x111))))))))))))
mark#(head(s(incr(s(incr(tail(incr(nats)))))))) → active#(head(s(incr(active(s(active(incr(active(tail(active(incr(active(nats)))))))))))))mark#(head(incr(incr(cons(_x71, _x72))))) → active#(head(incr(active(incr(active(cons(mark(_x71), _x72)))))))
mark#(head(incr(cons(tail(cons(incr(_x131), mark(active(active(_x102))))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(_x131)), _x102))), _x52)))))mark#(head(incr(cons(s(_x71), _x62)))) → active#(head(incr(cons(active(s(mark(_x71))), _x62))))
mark#(head(incr(cons(_x61, active(mark(_x31)))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))mark#(head(incr(cons(tail(cons(incr(_x101), _x82)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(incr(mark(_x101)), _x82))), _x62)))))
mark#(head(s(incr(s(tail(incr(cons(_x131, _x132)))))))) → active#(head(s(active(incr(active(s(active(tail(active(incr(active(cons(mark(_x131), _x132)))))))))))))mark#(head(incr(cons(tail(cons(incr(_x101), mark(active(_x71)))), mark(_x52))))) → active#(head(active(incr(cons(mark(_x71), _x52)))))
mark#(head(incr(cons(tail(cons(incr(_x101), 0)), mark(_x52))))) → active#(head(active(incr(cons(active(0), _x52)))))mark#(head(incr(cons(tail(cons(incr(cons(_x101, _x102)), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(cons(mark(_x101), _x102)))), _x92)), _x62)))))
mark#(head(incr(cons(_x51, mark(active(_x52)))))) → active#(head(active(incr(cons(_x51, _x52)))))mark#(head(incr(cons(incr(nats), mark(active(_x62)))))) → active#(head(active(incr(cons(active(incr(active(nats))), _x62)))))
mark#(head(incr(cons(tail(cons(incr(odds), mark(_x112))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(odds))), _x112))), _x52)))))mark#(head(incr(incr(tail(head(incr(_x101))))))) → active#(head(incr(incr(active(tail(active(head(active(incr(mark(_x101)))))))))))
mark#(head(incr(cons(incr(_x81), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(incr(mark(_x81))), _x52)))))mark#(head(incr(cons(cons(active(_x61), active(_x62)), _x42)))) → active#(head(incr(cons(cons(_x61, _x62), _x42))))
mark#(head(incr(cons(tail(cons(incr(cons(_x141, _x142)), mark(active(_x92)))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(cons(mark(_x141), _x142)))), _x92))), _x52)))))mark#(head(incr(cons(tail(cons(incr(head(tail(_x131))), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(active(tail(mark(_x131))))))), _x92)), _x62)))))
mark#(head(s(incr(s(incr(tail(0))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(0)))))))))))))mark#(head(incr(cons(tail(cons(incr(_x101), mark(active(_x92)))), mark(_x52))))) → active#(head(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x92))), _x52))))
mark#(head(incr(cons(tail(cons(incr(pairs), mark(_x112))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(pairs))), _x112))), _x52)))))mark#(head(incr(odds))) → active#(head(active(incr(odds))))
mark#(head(incr(incr(head(_x81))))) → active#(head(active(incr(active(incr(active(head(mark(_x81)))))))))mark#(head(incr(cons(tail(cons(incr(odds), _x92)), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(odds))), _x92)), _x52)))))
mark#(head(incr(cons(tail(cons(_x91, _x92)), active(_x52))))) → active#(head(incr(cons(active(tail(cons(mark(_x91), _x92))), _x52))))mark#(head(incr(cons(tail(cons(incr(cons(_x101, _x102)), _x92)), active(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(cons(mark(_x101), _x102)))), _x92)), _x62)))))
mark#(head(incr(cons(incr(_x71), mark(active(_x52)))))) → active#(head(active(incr(cons(incr(_x71), _x52)))))mark#(head(incr(cons(pairs, active(mark(mark(_x52))))))) → active#(head(active(incr(cons(active(pairs), _x52)))))
mark#(head(s(incr(s(tail(s(_x91))))))) → active#(head(active(s(active(incr(s(tail(active(s(mark(_x91)))))))))))mark#(head(incr(cons(tail(cons(incr(_x101), mark(active(_x92)))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(incr(mark(_x101)), _x92))), _x62)))))
mark#(head(s(incr(s(incr(tail(incr(head(_x161))))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(head(_x161)))))))))))))))mark#(head(incr(cons(s(cons(tail(_x111), _x92)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(active(tail(mark(_x111))), _x92)))), _x72)))))
mark#(head(s(incr(_x71)))) → active#(head(active(s(active(incr(_x71))))))mark#(head(s(incr(s(tail(s(pairs))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(active(pairs)))))))))))))
mark#(head(incr(incr(tail(head(0)))))) → active#(head(incr(incr(active(tail(active(head(active(0)))))))))mark#(head(incr(cons(s(cons(head(incr(_x141)), _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(active(head(active(incr(mark(_x141))))), _x92))), _x52)))))
mark#(head(incr(cons(odds, active(_x42))))) → active#(head(incr(cons(mark(incr(pairs)), _x42))))mark#(head(_x21)) → active#(head(_x21))
mark#(head(incr(cons(tail(cons(incr(odds), mark(_x112))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(odds))), _x112))), _x62)))))mark#(head(incr(cons(tail(cons(incr(_x131), mark(active(mark(_x102))))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(_x131)), _x102))), _x52)))))
mark#(head(incr(cons(incr(_x81), active(active(mark(_x52))))))) → active#(head(active(incr(cons(active(incr(mark(_x81))), _x52)))))mark#(head(incr(incr(odds)))) → active#(head(active(incr(active(incr(odds))))))
mark#(head(incr(cons(tail(cons(incr(_x101), mark(active(_x92)))), mark(_x31))))) → active#(head(mark(cons(s(active(tail(cons(active(incr(mark(_x101))), _x92)))), incr(_x31)))))mark#(head(incr(cons(s(_x81), _x62)))) → active#(head(active(incr(cons(active(s(_x81)), _x62)))))
mark#(head(incr(cons(s(cons(head(s(_x141)), _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(active(head(active(s(mark(_x141))))), _x92))), _x52)))))mark#(head(incr(cons(tail(cons(incr(head(_x101)), active(_x72))), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(mark(_x101))))), _x72)), _x62)))))
mark#(cons(s(_x31), X2)) → active#(cons(active(s(mark(_x31))), X2))mark#(head(s(incr(incr(s(_x101)))))) → active#(head(active(s(active(incr(active(incr(active(s(mark(_x101)))))))))))
mark#(head(s(s(odds)))) → active#(head(active(s(active(s(odds))))))mark#(head(cons(odds, _x32))) → active#(head(active(cons(active(odds), _x32))))
mark#(head(s(incr(s(tail(tail(_x111))))))) → active#(head(active(s(active(incr(s(active(tail(active(tail(mark(_x111))))))))))))mark#(head(incr(cons(tail(cons(incr(_x101), mark(_x112))), mark(active(active(_x52))))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x112))), _x52)))))
mark#(head(incr(cons(s(cons(_x101, _x102)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(_x101, _x102)))), _x72)))))mark#(head(incr(cons(tail(cons(incr(nats), mark(_x112))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(nats))), _x112))), _x62)))))
mark#(head(incr(cons(nats, active(_x52))))) → active#(head(active(incr(cons(active(nats), _x52)))))mark#(head(incr(cons(s(_x71), _x52)))) → active#(head(active(incr(cons(s(mark(_x71)), _x52)))))
mark#(head(incr(cons(tail(cons(nats, _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(active(nats), _x92)))), _x62)))))mark#(head(incr(cons(0, active(_x52))))) → active#(head(active(incr(cons(active(0), _x52)))))
mark#(head(incr(cons(tail(cons(incr(_x101), active(mark(_x92)))), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x92))), _x62)))))mark#(head(tail(cons(incr(cons(_x111, _x112)), _x62)))) → active#(head(active(tail(active(cons(active(incr(active(cons(mark(_x111), _x112)))), _x62))))))
mark#(head(incr(cons(tail(cons(incr(_x131), mark(active(_x102)))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(incr(_x131), _x102))), _x52)))))mark#(head(incr(cons(s(cons(0, active(_x112))), mark(active(mark(_x31))))))) → active#(head(mark(cons(s(active(s(active(cons(active(0), _x112))))), incr(_x31)))))
mark#(head(tail(cons(0, _x62)))) → active#(head(active(tail(active(cons(active(0), _x62))))))mark#(head(incr(cons(tail(cons(incr(s(_x141)), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(s(mark(_x141))))), _x92))), _x52)))))
mark#(head(incr(cons(tail(cons(incr(_x111), _x72)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(incr(mark(_x111)), _x72)), _x62)))))mark#(head(s(incr(s(tail(s(tail(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(active(tail(mark(_x141)))))))))))))))
mark#(head(incr(cons(nats, mark(_x72))))) → active#(head(active(incr(active(cons(active(nats), _x72))))))mark#(head(s(s(incr(s(_x91)))))) → active#(head(active(s(s(active(incr(active(s(mark(_x91))))))))))
mark#(head(incr(cons(tail(cons(incr(head(_x121)), _x92)), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(mark(_x121))))), _x92)), _x52)))))mark#(head(s(incr(s(incr(tail(0))))))) → active#(head(active(s(incr(s(active(incr(tail(active(0))))))))))
mark#(head(incr(cons(tail(cons(incr(_x101), _x71)), mark(_x31))))) → active#(head(mark(cons(s(mark(_x71)), incr(_x31)))))mark#(head(s(s(pairs)))) → active#(head(active(s(s(active(pairs))))))
mark#(head(tail(s(_x61)))) → active#(head(active(tail(active(s(mark(_x61)))))))mark#(head(incr(cons(pairs, active(mark(_x72)))))) → active#(head(incr(cons(mark(cons(0, incr(odds))), _x72))))
mark#(head(s(incr(s(incr(_x101)))))) → active#(head(s(active(incr(active(s(active(incr(mark(_x101))))))))))mark#(cons(tail(_x31), X2)) → active#(cons(active(tail(mark(_x31))), X2))
mark#(head(incr(cons(tail(cons(incr(head(_x101)), _x92)), active(active(active(mark(_x52)))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(mark(_x101))))), _x92)), _x52)))))mark#(head(s(incr(s(incr(tail(incr(odds)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(incr(active(odds)))))))))))))))
mark#(head(s(incr(s(tail(s(s(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(active(s(mark(_x141)))))))))))))))mark#(head(s(s(incr(nats))))) → active#(head(active(s(active(s(active(incr(nats))))))))
mark#(head(s(incr(s(tail(incr(nats))))))) → active#(head(s(active(incr(s(active(tail(active(incr(active(nats)))))))))))mark#(head(s(s(s(odds))))) → active#(head(s(s(active(s(active(odds)))))))
mark#(head(s(s(s(_x91))))) → active#(head(s(active(s(active(s(_x91)))))))mark#(head(incr(cons(pairs, active(mark(mark(_x42))))))) → active#(head(incr(cons(active(pairs), _x42))))
mark#(head(incr(cons(s(cons(head(_x111), _x92)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(active(head(mark(_x111))), _x92)))), _x72)))))mark#(head(s(incr(s(pairs))))) → active#(head(active(s(active(incr(active(s(active(pairs)))))))))
mark#(head(incr(cons(tail(cons(incr(_x101), mark(mark(_x82)))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x82))), _x62)))))mark#(head(incr(cons(incr(_x81), mark(active(active(_x62))))))) → active#(head(active(incr(cons(incr(mark(_x81)), _x62)))))
mark#(head(incr(cons(nats, active(active(_x52)))))) → active#(head(active(incr(cons(nats, _x52)))))mark#(head(tail(cons(incr(nats), _x62)))) → active#(head(active(tail(active(cons(active(incr(active(nats))), _x62))))))
mark#(head(s(incr(s(tail(incr(nats))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(incr(active(nats)))))))))))))mark#(head(incr(incr(nats)))) → active#(head(incr(incr(active(nats)))))
mark#(head(incr(0))) → active#(head(active(incr(active(0)))))mark#(head(s(incr(s(tail(incr(0))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(incr(active(0)))))))))))))
mark#(head(incr(cons(odds, active(mark(_x72)))))) → active#(head(active(incr(cons(active(odds), _x72)))))mark#(head(incr(incr(tail(cons(odds, _x72)))))) → active#(head(incr(incr(active(tail(cons(odds, _x72)))))))
mark#(head(incr(cons(s(tail(_x91)), _x62)))) → active#(head(active(incr(cons(active(s(active(tail(mark(_x91))))), _x62)))))mark#(head(cons(_x31, mark(_x52)))) → active#(head(active(cons(mark(_x31), _x52))))
mark#(head(tail(cons(_x61, active(_x72))))) → active#(head(active(tail(active(cons(mark(_x61), _x72))))))mark#(head(s(incr(s(odds))))) → active#(head(active(s(active(incr(active(s(active(odds)))))))))
mark#(head(s(incr(s(incr(tail(_x131))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(_x131))))))))))))mark#(head(incr(cons(tail(cons(pairs, _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(pairs), _x92))), _x52)))))
mark#(head(incr(cons(tail(cons(incr(odds), _x92)), active(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(odds))), _x92)), _x62)))))mark#(head(incr(cons(tail(cons(incr(_x101), _x92)), mark(_x52))))) → active#(head(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x92))), _x52))))
mark#(head(incr(cons(tail(_x71), _x31)))) → active#(head(mark(cons(s(active(tail(mark(_x71)))), incr(_x31)))))mark#(head(s(s(0)))) → active#(head(active(s(active(s(active(0)))))))
mark#(head(incr(cons(s(_x81), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(_x81)), _x72)))))mark#(head(s(incr(s(s(0)))))) → active#(head(active(s(active(incr(active(s(active(s(active(0)))))))))))
mark#(head(incr(cons(nats, active(active(mark(_x52))))))) → active#(head(active(incr(cons(active(nats), _x52)))))mark#(head(incr(cons(tail(cons(incr(_x101), active(_x82))), _x31)))) → active#(head(cons(s(active(tail(cons(active(incr(mark(_x101))), _x82)))), incr(_x31))))
mark#(head(incr(cons(tail(cons(incr(odds), active(_x82))), _x31)))) → active#(head(mark(cons(s(active(tail(cons(active(incr(active(odds))), _x82)))), incr(_x31)))))mark#(head(s(incr(s(incr(incr(0))))))) → active#(head(s(active(incr(active(s(active(incr(active(incr(active(0))))))))))))
mark#(head(incr(cons(s(cons(_x91, active(_x112))), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(cons(mark(_x91), _x112))), _x52)))))mark#(head(incr(cons(tail(cons(incr(_x111), active(_x72))), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x111))), _x72)), _x62)))))
mark#(head(incr(head(odds)))) → active#(head(incr(active(head(active(odds))))))mark#(head(incr(cons(cons(_x71, active(mark(active(_x72)))), _x62)))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x62)))))
mark#(head(incr(cons(incr(tail(_x101)), mark(_x52))))) → active#(head(active(incr(cons(active(incr(active(tail(mark(_x101))))), _x52)))))mark#(head(incr(cons(s(odds), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(odds))), _x72)))))
mark#(head(s(incr(s(incr(tail(odds))))))) → active#(head(active(s(active(incr(s(incr(tail(active(odds))))))))))mark#(head(incr(cons(tail(cons(incr(_x101), active(_x82))), active(_x71))))) → active#(head(mark(cons(s(active(tail(cons(active(incr(mark(_x101))), _x82)))), incr(_x71)))))
mark#(head(incr(incr(tail(cons(_x91, _x92)))))) → active#(head(incr(incr(active(tail(active(cons(_x91, _x92))))))))mark#(head(s(incr(s(incr(tail(incr(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(tail(active(incr(mark(_x141))))))))))))))
mark#(head(incr(cons(tail(cons(incr(tail(_x121)), _x92)), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(tail(mark(_x121))))), _x92)), _x52)))))mark#(head(s(s(s(_x81))))) → active#(head(s(active(s(active(s(mark(_x81))))))))
mark#(head(s(incr(s(incr(tail(incr(pairs)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(incr(active(pairs)))))))))))))))mark#(head(incr(incr(pairs)))) → active#(head(active(incr(active(incr(active(pairs)))))))
mark#(head(incr(cons(s(s(_x91)), _x62)))) → active#(head(active(incr(cons(active(s(active(s(mark(_x91))))), _x62)))))mark#(head(s(incr(s(incr(tail(pairs))))))) → active#(head(active(s(active(incr(s(active(incr(tail(active(pairs)))))))))))
mark#(head(s(incr(s(s(nats)))))) → active#(head(active(s(active(incr(active(s(active(s(active(nats)))))))))))mark#(head(incr(incr(tail(head(cons(_x101, _x102))))))) → active#(head(incr(incr(active(tail(active(head(active(cons(mark(_x101), _x102))))))))))
mark#(head(incr(cons(tail(cons(incr(_x101), mark(_x112))), mark(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x101))), _x112)), _x52)))))mark#(head(incr(cons(s(_x71), active(_x52))))) → active#(head(active(incr(cons(active(s(mark(_x71))), _x52)))))
mark#(head(incr(cons(s(cons(_x91, active(_x82))), mark(active(_x42)))))) → active#(head(incr(cons(s(active(cons(mark(_x91), _x82))), _x42))))mark#(head(incr(cons(s(cons(_x91, active(mark(_x102)))), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(mark(_x91), _x102)))), _x72))))
mark#(head(incr(cons(s(cons(cons(_x111, _x112), _x92)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(active(cons(mark(_x111), _x112)), _x92)))), _x72)))))mark#(head(incr(cons(tail(cons(incr(cons(_x121, _x122)), _x92)), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(cons(mark(_x121), _x122)))), _x92)), _x52)))))
mark#(head(incr(incr(tail(cons(odds, _x51)))))) → active#(head(incr(incr(mark(_x51)))))mark#(head(incr(cons(cons(active(_x71), _x72), _x31)))) → active#(head(mark(cons(s(active(cons(_x71, _x72))), incr(_x31)))))
mark#(head(s(incr(s(tail(incr(0))))))) → active#(head(s(active(incr(active(s(active(tail(active(incr(active(0))))))))))))mark#(head(incr(incr(_x61)))) → active#(head(incr(active(incr(_x61)))))
mark#(head(incr(incr(tail(incr(_x91)))))) → active#(head(incr(active(incr(active(tail(active(incr(mark(_x91))))))))))mark#(head(incr(incr(tail(cons(odds, mark(_x72))))))) → active#(head(incr(incr(active(tail(cons(active(odds), _x72)))))))
mark#(head(incr(cons(odds, mark(active(mark(_x31))))))) → active#(head(mark(cons(s(active(odds)), incr(_x31)))))mark#(head(s(s(cons(_x81, _x82))))) → active#(head(active(s(active(s(active(cons(mark(_x81), _x82))))))))
mark#(head(incr(head(pairs)))) → active#(head(incr(active(head(active(pairs))))))mark#(head(incr(cons(tail(cons(incr(_x101), _x92)), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x92))), _x62)))))
mark#(head(s(incr(s(incr(tail(incr(head(cons(_x171, _x172)))))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(head(active(cons(mark(_x171), _x172)))))))))))))))))mark#(cons(0, X2)) → active#(cons(active(0), X2))
mark#(head(incr(cons(tail(cons(incr(_x101), mark(_x112))), mark(_x31))))) → active#(head(mark(cons(s(active(tail(cons(active(incr(mark(_x101))), _x112)))), incr(_x31)))))mark#(head(s(incr(s(tail(s(head(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(active(head(mark(_x141)))))))))))))))
mark#(head(incr(cons(cons(_x71, active(_x72)), mark(_x42))))) → active#(head(incr(cons(active(cons(_x71, _x72)), _x42))))mark#(head(incr(cons(0, mark(active(_x72)))))) → active#(head(active(incr(cons(active(0), _x72)))))
mark#(head(s(incr(incr(head(_x101)))))) → active#(head(active(s(active(incr(active(incr(active(head(mark(_x101)))))))))))mark#(head(incr(cons(odds, mark(_x42))))) → active#(head(incr(cons(mark(incr(pairs)), _x42))))
mark#(head(s(incr(s(incr(tail(incr(tail(_x151))))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(tail(mark(_x151))))))))))))))))mark#(head(s(s(s(odds))))) → active#(head(active(s(s(active(s(active(odds))))))))
mark#(head(incr(incr(tail(cons(s(_x91), _x82)))))) → active#(head(incr(incr(active(tail(cons(active(s(mark(_x91))), _x82)))))))mark#(head(s(incr(s(incr(incr(_x121))))))) → active#(head(s(active(incr(active(s(active(incr(incr(mark(_x121)))))))))))
mark#(head(incr(cons(tail(cons(incr(head(_x101)), _x92)), active(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(mark(_x101))))), _x92)), _x62)))))mark#(head(incr(cons(tail(cons(incr(0), mark(_x112))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(0))), _x112))), _x62)))))
mark#(head(incr(incr(tail(cons(_x81, _x82)))))) → active#(head(incr(incr(tail(cons(mark(_x81), _x82))))))mark#(head(incr(cons(tail(cons(0, _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(0), _x92))), _x52)))))
mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(_x31))))) → active#(head(mark(cons(s(active(tail(cons(active(incr(mark(_x111))), _x92)))), incr(_x31)))))mark#(head(incr(cons(tail(cons(s(_x111), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(s(mark(_x111))), _x92))), _x52)))))
mark#(head(incr(cons(s(cons(pairs, _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(pairs), _x92)))), _x72))))mark#(head(incr(cons(tail(cons(_x91, _x92)), _x62)))) → active#(head(incr(cons(active(tail(cons(mark(_x91), _x92))), _x62))))
mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(active(_x52)))))) → active#(head(incr(cons(tail(cons(active(incr(mark(_x111))), _x92)), _x52))))mark#(head(s(incr(s(tail(incr(pairs))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(incr(active(pairs)))))))))))))
mark#(head(incr(cons(incr(cons(_x101, _x102)), mark(_x52))))) → active#(head(active(incr(cons(active(incr(active(cons(mark(_x101), _x102)))), _x52)))))mark#(head(incr(incr(tail(pairs))))) → active#(head(incr(incr(tail(active(pairs))))))
mark#(head(incr(cons(tail(cons(incr(_x121), mark(active(_x82)))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(_x121)), _x82))), _x62)))))mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(_x111)), _x92))), _x62)))))
mark#(head(s(cons(0, active(_x72))))) → active#(head(active(s(active(cons(active(0), _x72))))))mark#(head(s(incr(s(incr(tail(incr(head(nats))))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(head(active(nats))))))))))))))))
mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(mark(_x42))))))) → active#(head(incr(cons(active(s(active(cons(active(odds), _x92)))), _x42))))mark#(head(s(incr(s(incr(tail(incr(head(head(_x171)))))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(head(active(head(mark(_x171))))))))))))))))))
mark#(head(tail(nats))) → active#(head(active(tail(active(nats)))))mark#(head(incr(cons(pairs, _x62)))) → active#(head(incr(cons(active(pairs), _x62))))
mark#(head(incr(cons(cons(_x71, mark(_x72)), _x62)))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x62)))))mark#(head(incr(cons(cons(_x61, active(active(_x62))), _x42)))) → active#(head(incr(cons(cons(_x61, _x62), _x42))))
mark#(head(incr(cons(pairs, mark(mark(_x62)))))) → active#(head(active(incr(cons(active(pairs), _x62)))))mark#(head(s(incr(s(tail(incr(incr(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(incr(active(incr(mark(_x141)))))))))))))))
mark#(head(incr(cons(odds, _x42)))) → active#(head(incr(cons(odds, _x42))))mark#(nats) → active#(nats)
mark#(head(s(s(pairs)))) → active#(head(s(active(s(active(pairs))))))mark#(head(incr(cons(tail(head(_x91)), _x62)))) → active#(head(active(incr(cons(active(tail(active(head(mark(_x91))))), _x62)))))
mark#(head(incr(cons(cons(_x71, active(_x72)), mark(_x52))))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x52)))))mark#(head(incr(cons(tail(_x71), mark(_x52))))) → active#(head(active(incr(cons(active(tail(mark(_x71))), _x52)))))
mark#(head(incr(cons(_x61, mark(_x52))))) → active#(head(incr(cons(mark(_x61), _x52))))mark#(head(incr(cons(s(cons(head(_x131), _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(active(head(_x131)), _x92))), _x52)))))
mark#(head(s(incr(s(incr(tail(incr(_x111)))))))) → active#(head(active(s(active(incr(s(active(incr(tail(active(incr(mark(_x111)))))))))))))mark#(head(incr(cons(nats, active(active(_x31)))))) → active#(head(mark(cons(s(active(nats)), incr(_x31)))))
mark#(head(incr(cons(tail(cons(incr(nats), _x92)), active(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(nats))), _x92)), _x62)))))mark#(head(s(incr(incr(incr(_x101)))))) → active#(head(active(s(active(incr(active(incr(active(incr(mark(_x101)))))))))))
mark#(head(incr(cons(_x61, mark(_x31))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))mark#(head(incr(cons(tail(cons(incr(_x101), mark(_x112))), mark(mark(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x112))), _x62)))))
mark#(head(incr(cons(tail(cons(incr(_x101), mark(active(active(_x112))))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x112))), _x52)))))mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(active(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(mark(_x91), _x92)))), _x52)))))
active#(head(cons(X, XS))) → mark#(X)mark#(head(incr(cons(tail(cons(incr(0), _x92)), active(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(0))), _x92)), _x62)))))
mark#(head(incr(incr(tail(s(_x61)))))) → active#(head(incr(incr(tail(active(s(mark(_x61))))))))mark#(head(incr(cons(tail(cons(incr(_x101), odds)), mark(_x52))))) → active#(head(active(incr(cons(active(odds), _x52)))))
mark#(head(incr(cons(tail(cons(incr(incr(_x131)), active(_x82))), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(incr(mark(_x131))))), _x82))), _x62)))))mark#(head(s(incr(s(incr(tail(incr(_x131)))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(_x131)))))))))))))
mark#(head(incr(cons(s(incr(_x91)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(incr(mark(_x91))))), _x72)))))mark#(head(incr(cons(s(cons(tail(_x111), active(_x82))), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(tail(mark(_x111))), _x82)))), _x72))))
mark#(head(incr(cons(cons(_x81, _x82), _x62)))) → active#(head(incr(cons(active(cons(_x81, _x82)), _x62))))mark#(head(incr(cons(_x61, active(mark(_x72)))))) → active#(head(incr(cons(mark(_x61), _x72))))
mark#(head(incr(cons(cons(active(_x71), _x72), mark(_x31))))) → active#(head(mark(cons(s(active(cons(_x71, _x72))), incr(_x31)))))mark#(head(incr(incr(tail(_x81))))) → active#(head(active(incr(active(incr(active(tail(mark(_x81)))))))))
mark#(head(incr(cons(tail(cons(0, _x92)), mark(_x52))))) → active#(head(active(incr(cons(active(tail(active(cons(active(0), _x92)))), _x52)))))mark#(head(incr(cons(tail(cons(incr(0), mark(active(_x92)))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(0))), _x92))), _x52)))))
mark#(head(incr(cons(tail(cons(incr(_x101), mark(active(_x92)))), mark(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x101))), _x92)), _x62)))))mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(active(_x62))))))) → active#(head(active(incr(cons(s(active(cons(mark(_x91), _x92))), _x62)))))
mark#(head(incr(cons(s(cons(0, active(_x102))), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(0, _x102)))), _x52)))))mark#(head(cons(_x51, _x52))) → active#(head(active(cons(_x51, _x52))))
mark#(head(s(_x51))) → active#(head(active(s(_x51))))mark#(head(s(incr(s(incr(tail(incr(nats)))))))) → active#(head(active(s(incr(active(s(active(incr(tail(active(incr(active(nats)))))))))))))
mark#(head(incr(head(_x61)))) → active#(head(incr(active(head(_x61)))))mark#(head(incr(cons(cons(active(_x71), _x72), _x52)))) → active#(head(active(incr(cons(cons(_x71, _x72), _x52)))))
mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(_x42)))))) → active#(head(incr(cons(s(active(cons(active(odds), _x92))), _x42))))mark#(head(s(s(s(odds))))) → active#(head(active(s(active(s(s(active(odds))))))))
mark#(head(incr(cons(tail(cons(incr(0), mark(active(_x82)))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(0))), _x82))), _x62)))))mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(cons(mark(_x91), _x92))), _x52)))))
mark#(head(s(incr(s(incr(incr(head(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(head(mark(_x141)))))))))))))))mark#(head(incr(cons(tail(cons(incr(0), _x92)), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(0))), _x92))), _x52)))))
mark#(head(incr(cons(odds, mark(_x42))))) → active#(head(incr(cons(active(odds), _x42))))mark#(head(incr(cons(_x61, mark(_x62))))) → active#(head(active(incr(cons(_x61, _x62)))))
mark#(head(s(s(incr(0))))) → active#(head(active(s(active(s(active(incr(active(0)))))))))mark#(head(incr(cons(incr(0), mark(active(_x31)))))) → active#(head(mark(cons(s(incr(active(0))), incr(_x31)))))
mark#(head(tail(cons(incr(_x81), mark(_x72))))) → active#(head(active(tail(active(cons(active(incr(mark(_x81))), _x72))))))mark#(head(s(incr(s(incr(tail(incr(_x141)))))))) → active#(head(active(s(incr(active(s(active(incr(tail(active(incr(mark(_x141)))))))))))))
mark#(head(incr(cons(s(odds), mark(_x52))))) → active#(head(active(incr(cons(active(s(active(odds))), _x52)))))mark#(head(incr(cons(tail(cons(incr(s(_x101)), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(s(mark(_x101))))), _x92)), _x62)))))
mark#(cons(odds, X2)) → active#(cons(active(odds), X2))mark#(head(s(incr(s(incr(nats)))))) → active#(head(active(s(active(incr(active(s(active(incr(active(nats)))))))))))
mark#(head(incr(cons(s(cons(s(cons(_x151, _x152)), _x92)), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(s(active(cons(mark(_x151), _x152)))), _x92)))), _x52)))))mark#(head(incr(cons(tail(cons(incr(_x101), _x61)), mark(_x62))))) → active#(head(active(incr(cons(_x61, _x62)))))
mark#(head(incr(cons(_x61, active(_x72))))) → active#(head(active(incr(active(cons(mark(_x61), _x72))))))mark#(head(incr(cons(odds, _x62)))) → active#(head(active(incr(cons(mark(incr(pairs)), _x62)))))
mark#(head(incr(cons(incr(0), mark(active(active(_x62))))))) → active#(head(active(incr(cons(incr(active(0)), _x62)))))mark#(head(incr(cons(tail(cons(incr(0), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(0))), _x92))), _x52)))))
mark#(head(s(incr(s(tail(s(0))))))) → active#(head(s(active(incr(active(s(active(tail(active(s(active(0))))))))))))mark#(head(incr(cons(incr(_x81), mark(mark(_x62)))))) → active#(head(active(incr(cons(active(incr(mark(_x81))), _x62)))))
mark#(head(incr(cons(odds, active(_x52))))) → active#(head(active(incr(cons(active(odds), _x52)))))mark#(head(s(incr(s(tail(nats)))))) → active#(head(active(s(active(incr(s(active(tail(active(nats))))))))))
mark#(head(incr(cons(tail(_x81), _x62)))) → active#(head(active(incr(cons(active(tail(_x81)), _x62)))))mark#(head(incr(cons(cons(incr(0), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(incr(active(0))), _x72)), _x62)))))
mark#(head(incr(cons(s(cons(head(_x121), _x92)), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(head(mark(_x121))), _x92)))), _x52)))))mark#(cons(head(_x31), X2)) → active#(cons(active(head(mark(_x31))), X2))
mark#(head(incr(incr(tail(tail(_x91)))))) → active#(head(incr(active(incr(active(tail(active(tail(mark(_x91))))))))))mark#(head(incr(cons(cons(incr(_x91), active(_x82)), _x62)))) → active#(head(active(incr(cons(active(cons(active(incr(mark(_x91))), _x82)), _x62)))))
mark#(head(incr(incr(tail(_x51))))) → active#(head(incr(incr(tail(_x51)))))mark#(head(incr(cons(s(cons(head(cons(_x141, _x142)), _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(active(head(active(cons(mark(_x141), _x142)))), _x92))), _x52)))))
mark#(head(s(incr(s(incr(tail(incr(nats)))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(incr(active(nats)))))))))))))mark#(head(s(incr(s(incr(tail(head(_x101)))))))) → active#(head(active(s(incr(s(active(incr(tail(active(head(mark(_x101))))))))))))
mark#(head(incr(incr(head(_x61))))) → active#(head(incr(incr(active(head(mark(_x61)))))))mark#(head(s(incr(s(tail(s(nats))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(active(nats)))))))))))))
mark#(head(s(incr(s(incr(tail(s(_x131)))))))) → active#(head(active(s(active(incr(active(s(active(incr(tail(active(s(mark(_x131))))))))))))))mark#(head(s(incr(s(incr(tail(incr(s(_x151))))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(s(mark(_x151))))))))))))))))
mark#(head(incr(cons(tail(cons(incr(odds), mark(active(_x82)))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(odds))), _x82))), _x62)))))mark#(head(incr(incr(tail(cons(_x61, _x62)))))) → active#(head(incr(incr(tail(active(cons(mark(_x61), _x62)))))))
mark#(head(incr(cons(s(cons(s(_x111), _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(active(s(mark(_x111))), _x92))), _x52)))))mark#(head(incr(cons(s(cons(s(head(_x151)), _x92)), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(s(active(head(mark(_x151))))), _x92)))), _x52)))))
mark#(head(incr(cons(s(cons(s(_x121), _x92)), mark(active(mark(mark(_x62)))))))) → active#(head(active(incr(cons(active(s(active(cons(active(s(mark(_x121))), _x92)))), _x62)))))mark#(head(incr(cons(incr(cons(_x91, _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(incr(active(cons(mark(_x91), _x92))), _x52)))))
mark#(head(incr(cons(tail(cons(incr(head(pairs)), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(head(active(pairs))))), _x92)), _x62)))))mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(mark(_x31))))))) → active#(head(mark(cons(s(active(s(active(cons(mark(_x91), _x92))))), incr(_x31)))))
mark#(head(incr(cons(incr(0), mark(active(_x52)))))) → active#(head(incr(cons(incr(active(0)), _x52))))mark#(head(s(incr(s(tail(incr(cons(_x141, _x142)))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(incr(active(cons(mark(_x141), _x142))))))))))))))
mark#(head(s(incr(s(tail(incr(_x91))))))) → active#(head(active(s(incr(s(active(tail(active(incr(mark(_x91)))))))))))mark#(head(tail(cons(incr(_x81), _x62)))) → active#(head(active(tail(cons(active(incr(mark(_x81))), _x62)))))
mark#(head(s(incr(s(incr(tail(odds))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(odds)))))))))))))mark#(head(incr(cons(incr(_x81), mark(active(_x52)))))) → active#(head(incr(cons(incr(mark(_x81)), _x52))))
mark#(head(s(s(incr(odds))))) → active#(head(active(s(active(s(active(incr(active(odds)))))))))mark#(head(incr(incr(tail(s(_x91)))))) → active#(head(incr(active(incr(active(tail(active(s(mark(_x91))))))))))
mark#(head(incr(cons(s(cons(0, active(_x112))), mark(active(mark(_x62))))))) → active#(head(active(incr(cons(s(active(cons(active(0), _x112))), _x62)))))mark#(head(incr(incr(tail(cons(_x81, _x51)))))) → active#(head(incr(incr(mark(_x51)))))
mark#(head(cons(s(_x61), _x32))) → active#(head(active(cons(active(s(mark(_x61))), _x32))))mark#(head(incr(head(nats)))) → active#(head(incr(head(active(nats)))))
mark#(head(incr(cons(tail(cons(incr(head(_x141)), active(_x82))), _x31)))) → active#(head(mark(cons(s(active(tail(cons(active(incr(active(head(mark(_x141))))), _x82)))), incr(_x31)))))mark#(head(s(incr(s(incr(tail(incr(head(_x151))))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(incr(active(head(mark(_x151)))))))))))))))
mark#(head(incr(cons(tail(cons(incr(incr(_x101)), _x92)), active(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(incr(mark(_x101))))), _x92)), _x62)))))mark#(head(incr(cons(s(cons(head(_x101), _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(head(mark(_x101))), _x92)))), _x72))))
mark#(head(incr(cons(tail(cons(nats, _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(nats), _x92))), _x52)))))mark#(head(s(s(_x71)))) → active#(head(active(s(active(s(_x71))))))
mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(active(_x42))))))) → active#(head(incr(cons(active(s(active(cons(mark(incr(pairs)), _x92)))), _x42))))mark#(head(incr(cons(s(cons(odds, mark(_x82))), mark(active(_x72)))))) → active#(head(incr(cons(active(s(cons(mark(incr(pairs)), _x82))), _x72))))
mark#(head(s(incr(s(incr(tail(tail(_x131)))))))) → active#(head(active(s(active(incr(active(s(active(incr(tail(active(tail(mark(_x131))))))))))))))mark#(head(incr(incr(tail(_x61))))) → active#(head(incr(incr(active(tail(mark(_x61)))))))
mark#(head(s(incr(s(incr(tail(tail(_x101)))))))) → active#(head(active(s(incr(s(active(incr(tail(active(tail(mark(_x101))))))))))))mark#(head(incr(cons(tail(cons(incr(tail(_x141)), _x92)), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(tail(mark(_x141))))), _x92))), _x52)))))
mark#(head(incr(cons(tail(s(_x91)), _x62)))) → active#(head(active(incr(cons(active(tail(active(s(mark(_x91))))), _x62)))))mark#(head(incr(incr(tail(cons(0, _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(0), _x82))))))))
mark#(head(s(s(incr(_x91))))) → active#(head(active(s(active(s(active(incr(_x91))))))))mark#(head(s(incr(s(tail(s(0))))))) → active#(head(active(s(incr(active(s(active(tail(active(s(active(0))))))))))))
mark#(head(incr(nats))) → active#(head(incr(active(nats))))mark#(head(incr(incr(tail(cons(cons(_x101, _x102), _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(cons(mark(_x101), _x102)), _x82))))))))
mark#(head(incr(cons(tail(cons(incr(incr(_x141)), _x92)), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(incr(mark(_x141))))), _x92))), _x52)))))mark#(head(incr(cons(s(cons(odds, _x102)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(odds, _x102))), _x52)))))
mark#(head(s(incr(s(incr(incr(tail(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(tail(mark(_x141)))))))))))))))mark#(head(s(_x31))) → active#(head(s(mark(_x31))))
mark#(head(incr(incr(tail(head(_x91)))))) → active#(head(incr(active(incr(active(tail(active(head(mark(_x91))))))))))mark#(head(incr(cons(incr(pairs), mark(active(_x62)))))) → active#(head(active(incr(cons(active(incr(active(pairs))), _x62)))))
mark#(head(s(incr(_x61)))) → active#(head(s(active(incr(mark(_x61))))))mark#(head(incr(incr(tail(cons(odds, _x82)))))) → active#(head(incr(incr(active(tail(cons(mark(incr(pairs)), _x82)))))))
mark#(head(odds)) → active#(head(active(odds)))mark#(head(s(cons(_x61, mark(_x72))))) → active#(head(active(s(active(cons(mark(_x61), _x72))))))
mark#(head(incr(cons(0, active(active(_x72)))))) → active#(head(active(incr(cons(active(0), _x72)))))mark#(head(s(incr(s(tail(s(_x91))))))) → active#(head(active(s(incr(s(active(tail(active(s(mark(_x91)))))))))))
mark#(head(incr(cons(tail(cons(incr(0), mark(_x82))), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(0))), _x82)), _x52)))))mark#(head(incr(cons(cons(_x71, active(_x72)), active(_x52))))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x52)))))
mark#(head(s(incr(s(incr(incr(0))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(0)))))))))))))mark#(head(incr(cons(tail(cons(incr(_x111), active(_x102))), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x111))), _x102))), _x52)))))
mark#(head(s(incr(s(incr(incr(_x121))))))) → active#(head(s(incr(active(s(active(incr(active(incr(mark(_x121)))))))))))mark#(head(incr(cons(pairs, active(mark(_x42)))))) → active#(head(incr(cons(pairs, _x42))))
mark#(head(tail(cons(_x71, _x72)))) → active#(head(active(tail(active(cons(_x71, _x72))))))mark#(head(s(incr(incr(pairs))))) → active#(head(active(s(active(incr(active(incr(active(pairs)))))))))
mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(active(_x31)))))) → active#(head(mark(cons(s(tail(cons(active(incr(mark(_x111))), _x92))), incr(_x31)))))mark#(head(incr(cons(tail(cons(incr(cons(_x131, _x132)), mark(active(_x82)))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(cons(mark(_x131), _x132)))), _x82))), _x62)))))
mark#(head(incr(cons(tail(cons(incr(cons(_x141, _x142)), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(cons(mark(_x141), _x142)))), _x92))), _x52)))))mark#(head(incr(cons(cons(incr(_x111), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(incr(_x111)), _x72)), _x62)))))
mark#(head(incr(cons(s(cons(0, active(_x112))), mark(active(mark(mark(_x62)))))))) → active#(head(active(incr(cons(active(s(active(cons(active(0), _x112)))), _x62)))))mark#(head(s(incr(s(incr(tail(s(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(s(mark(_x141)))))))))))))))
mark#(head(s(incr(s(tail(_x101)))))) → active#(head(active(s(incr(s(tail(mark(_x101))))))))mark#(head(incr(cons(mark(_x61), _x62)))) → active#(head(active(incr(cons(_x61, _x62)))))
mark#(head(incr(cons(s(cons(tail(_x101), _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(tail(mark(_x101))), _x92)))), _x72))))mark#(head(s(cons(s(_x81), _x62)))) → active#(head(active(s(active(cons(active(s(mark(_x81))), _x62))))))
mark#(head(s(incr(s(tail(s(incr(_x141)))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(s(active(incr(mark(_x141)))))))))))))))mark#(head(incr(cons(cons(_x71, mark(_x82)), _x62)))) → active#(head(active(incr(cons(active(cons(mark(_x71), _x82)), _x62)))))
mark#(head(incr(cons(cons(_x61, active(active(_x62))), _x62)))) → active#(head(incr(cons(active(cons(_x61, _x62)), _x62))))mark#(head(s(incr(s(incr(incr(nats))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(incr(active(nats)))))))))))))
mark#(head(incr(cons(tail(cons(incr(_x101), mark(_x112))), mark(_x52))))) → active#(head(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x112))), _x52))))mark#(head(incr(cons(tail(cons(incr(_x111), _x72)), active(_x62))))) → active#(head(active(incr(cons(tail(cons(incr(mark(_x111)), _x72)), _x62)))))
mark#(head(incr(cons(tail(cons(_x91, mark(_x102))), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(mark(_x91), _x102)))), _x62)))))mark#(head(incr(cons(tail(cons(incr(s(_x141)), active(_x82))), _x31)))) → active#(head(mark(cons(s(active(tail(cons(active(incr(active(s(mark(_x141))))), _x82)))), incr(_x31)))))
mark#(head(s(incr(s(incr(incr(_x121))))))) → active#(head(active(s(active(incr(s(active(incr(active(incr(mark(_x121))))))))))))mark#(head(s(incr(s(incr(tail(incr(_x141)))))))) → active#(head(s(active(incr(active(s(active(incr(active(tail(active(incr(mark(_x141))))))))))))))
mark#(head(incr(cons(incr(_x71), active(active(_x72)))))) → active#(head(active(incr(cons(active(incr(mark(_x71))), _x72)))))mark#(head(s(incr(s(incr(tail(tail(_x111)))))))) → active#(head(active(s(active(incr(s(active(incr(tail(active(tail(mark(_x111)))))))))))))
mark#(head(incr(cons(s(cons(s(_x121), _x92)), mark(active(mark(active(_x62)))))))) → active#(head(active(incr(cons(active(s(active(cons(active(s(mark(_x121))), _x92)))), _x62)))))mark#(head(s(incr(s(incr(tail(s(_x111)))))))) → active#(head(active(s(active(incr(s(active(incr(tail(active(s(mark(_x111)))))))))))))
mark#(head(incr(cons(odds, _x31)))) → active#(head(mark(cons(s(active(odds)), incr(_x31)))))mark#(head(incr(cons(odds, mark(_x52))))) → active#(head(active(incr(cons(active(odds), _x52)))))
mark#(head(incr(cons(tail(cons(incr(pairs), _x92)), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(pairs))), _x92)), _x52)))))mark#(head(incr(head(incr(_x71))))) → active#(head(incr(active(head(active(incr(mark(_x71))))))))
mark#(head(incr(cons(tail(cons(incr(cons(_x141, _x142)), active(_x82))), _x31)))) → active#(head(mark(cons(s(active(tail(cons(active(incr(active(cons(mark(_x141), _x142)))), _x82)))), incr(_x31)))))mark#(head(incr(cons(tail(_x81), active(_x52))))) → active#(head(active(incr(cons(active(tail(mark(_x81))), _x52)))))
mark#(head(s(incr(s(tail(incr(odds))))))) → active#(head(s(active(incr(active(s(active(tail(active(incr(active(odds))))))))))))mark#(head(s(s(s(active(_x81)))))) → active#(head(active(s(active(s(active(s(_x81))))))))
mark#(head(incr(cons(s(cons(s(_x111), active(_x82))), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(s(mark(_x111))), _x82)))), _x72))))mark#(head(incr(cons(cons(_x81, _x82), active(active(mark(_x52))))))) → active#(head(active(incr(cons(active(cons(mark(_x81), _x82)), _x52)))))
mark#(head(incr(cons(tail(cons(incr(nats), _x92)), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(nats))), _x92)), _x52)))))mark#(head(s(incr(s(incr(tail(incr(head(odds))))))))) → active#(head(active(s(incr(active(s(active(incr(active(tail(active(incr(active(head(active(odds))))))))))))))))
mark#(head(incr(cons(tail(cons(s(_x111), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(active(s(mark(_x111))), _x92)))), _x62)))))mark#(head(incr(pairs))) → active#(head(incr(pairs)))
mark#(head(incr(cons(tail(cons(incr(_x111), mark(_x72))), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x111))), _x72)), _x62)))))mark#(head(incr(cons(head(_x71), active(active(_x72)))))) → active#(head(active(incr(cons(active(head(mark(_x71))), _x72)))))
mark#(head(s(incr(s(incr(incr(incr(_x131)))))))) → active#(head(s(active(incr(active(s(active(incr(active(incr(active(incr(mark(_x131))))))))))))))mark#(head(incr(cons(tail(cons(incr(0), active(_x82))), _x31)))) → active#(head(mark(cons(s(active(tail(cons(active(incr(active(0))), _x82)))), incr(_x31)))))
mark#(head(incr(cons(cons(active(_x71), active(mark(_x72))), _x62)))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x62)))))mark#(head(incr(cons(s(cons(incr(_x111), active(_x82))), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(incr(mark(_x111))), _x82)))), _x72))))
mark#(head(incr(cons(tail(cons(incr(_x101), mark(mark(_x92)))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x92))), _x52)))))mark#(head(tail(cons(head(_x81), _x62)))) → active#(head(active(tail(active(cons(active(head(mark(_x81))), _x62))))))
mark#(head(s(s(_x61)))) → active#(head(active(s(s(mark(_x61))))))mark#(head(incr(cons(tail(cons(incr(nats), active(_x82))), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(nats))), _x82))), _x62)))))
mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(incr(mark(pairs))), _x92)))), _x72))))mark#(head(s(s(incr(nats))))) → active#(head(active(s(s(active(incr(mark(cons(0, incr(nats))))))))))
mark#(head(incr(cons(head(_x71), mark(active(_x72)))))) → active#(head(active(incr(cons(active(head(mark(_x71))), _x72)))))mark#(head(incr(cons(cons(incr(tail(_x121)), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(incr(active(tail(mark(_x121))))), _x72)), _x62)))))
mark#(head(s(s(incr(tail(_x91)))))) → active#(head(active(s(s(active(incr(active(tail(mark(_x91))))))))))mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(cons(active(0), _x62)))))
mark#(head(s(cons(0, _x52)))) → active#(head(s(active(cons(0, _x52)))))mark#(head(s(incr(s(s(_x111)))))) → active#(head(active(s(active(incr(active(s(active(s(_x111))))))))))
mark#(head(incr(cons(_x71, active(_x72))))) → active#(head(active(incr(cons(_x71, _x72)))))mark#(head(s(cons(0, _x72)))) → active#(head(active(s(active(cons(0, _x72))))))
mark#(head(incr(cons(incr(_x91), mark(_x52))))) → active#(head(active(incr(cons(active(incr(_x91)), _x52)))))mark#(head(incr(cons(cons(incr(head(_x121)), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(incr(active(head(mark(_x121))))), _x72)), _x62)))))
mark#(head(incr(cons(s(_x81), _x62)))) → active#(head(active(incr(active(cons(active(s(mark(_x81))), _x62))))))mark#(head(incr(incr(tail(cons(head(_x101), _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(head(mark(_x101))), _x82))))))))
mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(_x52))))) → active#(head(incr(cons(active(tail(cons(active(incr(mark(_x111))), _x92))), _x52))))mark#(head(incr(cons(tail(cons(incr(_x101), _x92)), _x62)))) → active#(head(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x92))), _x62))))
mark#(head(incr(cons(tail(cons(incr(odds), active(_x82))), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(odds))), _x82))), _x62)))))mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(active(_x62))))))) → active#(head(active(incr(cons(s(active(cons(active(odds), _x92))), _x62)))))
mark#(head(incr(cons(tail(cons(incr(pairs), _x92)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(active(incr(active(pairs))), _x92)), _x62)))))mark#(head(incr(incr(tail(cons(0, _x82)))))) → active#(head(incr(incr(tail(active(cons(active(0), _x82)))))))
mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(cons(mark(_x91), _x92)), _x52)))))mark#(head(incr(cons(tail(cons(incr(_x111), mark(_x82))), active(active(_x52)))))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x111))), _x82)), _x52)))))
mark#(head(incr(cons(tail(cons(incr(_x101), _x92)), _x31)))) → active#(head(mark(cons(s(active(tail(cons(active(incr(mark(_x101))), _x92)))), incr(_x31)))))mark#(head(incr(cons(s(cons(s(nats), _x92)), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(s(active(nats))), _x92)))), _x52)))))
mark#(head(s(incr(s(incr(tail(cons(_x101, _x102)))))))) → active#(head(active(s(incr(s(active(incr(tail(active(cons(mark(_x101), _x102)))))))))))mark#(head(incr(cons(odds, active(_x42))))) → active#(head(incr(cons(active(odds), _x42))))
mark#(head(s(s(incr(odds))))) → active#(head(active(s(s(active(incr(active(odds))))))))mark#(head(incr(cons(_x61, active(_x31))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))
mark#(head(incr(cons(cons(incr(_x91), _x82), _x62)))) → active#(head(active(incr(cons(active(cons(incr(mark(_x91)), _x82)), _x62)))))mark#(head(s(incr(nats)))) → active#(head(active(s(active(incr(active(nats)))))))
mark#(head(s(incr(incr(_x81))))) → active#(head(active(s(active(incr(incr(mark(_x81))))))))mark#(head(incr(cons(tail(cons(incr(pairs), active(_x82))), _x31)))) → active#(head(mark(cons(s(active(tail(cons(active(incr(active(pairs))), _x82)))), incr(_x31)))))
mark#(head(incr(cons(tail(0), _x62)))) → active#(head(active(incr(cons(active(tail(active(0))), _x62)))))mark#(head(incr(cons(tail(cons(incr(_x121), mark(_x112))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(_x121)), _x112))), _x52)))))
mark#(head(incr(cons(s(odds), active(_x52))))) → active#(head(active(incr(cons(active(s(active(odds))), _x52)))))mark#(head(incr(cons(s(cons(tail(_x131), active(_x112))), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(tail(mark(_x131))), _x112)))), _x52)))))
mark#(head(incr(cons(0, _x62)))) → active#(head(active(incr(active(cons(active(0), _x62))))))mark#(head(s(incr(s(incr(tail(incr(tail(_x161))))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(incr(active(tail(mark(_x161)))))))))))))))))
mark#(head(tail(cons(cons(_x81, _x82), _x62)))) → active#(head(active(tail(active(cons(active(cons(mark(_x81), _x82)), _x62))))))mark#(head(s(incr(s(incr(tail(pairs))))))) → active#(head(active(s(active(incr(active(s(active(incr(tail(active(pairs))))))))))))
mark#(head(incr(incr(tail(cons(pairs, _x82)))))) → active#(head(incr(incr(tail(active(cons(active(pairs), _x82)))))))mark#(head(incr(cons(_x61, active(active(mark(_x31))))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))
mark#(head(incr(cons(s(cons(odds, mark(_x92))), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(incr(pairs), _x92)))), _x72))))mark#(head(s(incr(s(tail(incr(_x121))))))) → active#(head(active(s(active(incr(active(s(active(tail(incr(mark(_x121))))))))))))
mark#(head(s(incr(s(tail(incr(nats))))))) → active#(head(s(incr(active(s(active(tail(active(incr(active(nats)))))))))))mark#(head(incr(incr(tail(nats))))) → active#(head(incr(incr(active(tail(active(nats)))))))
mark#(head(s(incr(s(incr(incr(_x121))))))) → active#(head(s(active(incr(s(active(incr(active(incr(mark(_x121)))))))))))mark#(head(tail(cons(incr(_x81), _x62)))) → active#(head(tail(active(cons(active(incr(mark(_x81))), _x62)))))
mark#(head(incr(incr(tail(cons(nats, _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(nats), _x82))))))))mark#(head(incr(cons(cons(incr(_x91), _x72), _x31)))) → active#(head(mark(cons(s(active(cons(active(incr(mark(_x91))), _x72))), incr(_x31)))))
mark#(head(s(incr(s(tail(pairs)))))) → active#(head(active(s(incr(s(active(tail(active(pairs)))))))))mark#(head(incr(cons(_x61, active(active(mark(_x52))))))) → active#(head(incr(cons(mark(_x61), _x52))))
mark#(head(s(incr(s(tail(_x101)))))) → active#(head(s(active(incr(s(tail(mark(_x101))))))))mark#(head(incr(cons(tail(cons(cons(_x111, _x112), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(cons(mark(_x111), _x112)), _x92))), _x52)))))
mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(cons(mark(_x91), _x92))), _x72)))))mark#(head(incr(cons(tail(cons(incr(_x101), mark(active(active(_x92))))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x92))), _x62)))))
mark#(head(s(cons(0, _x62)))) → active#(head(s(cons(active(0), _x62))))mark#(head(incr(cons(tail(cons(head(_x111), _x92)), _x62)))) → active#(head(active(incr(cons(active(tail(active(cons(active(head(mark(_x111))), _x92)))), _x62)))))
mark#(head(incr(cons(cons(active(_x71), _x72), mark(mark(_x62)))))) → active#(head(active(incr(cons(active(cons(_x71, _x72)), _x62)))))mark#(head(incr(cons(s(0), _x62)))) → active#(head(active(incr(cons(active(s(active(0))), _x62)))))
mark#(head(incr(cons(incr(0), mark(active(mark(_x62))))))) → active#(head(active(incr(cons(incr(active(0)), _x62)))))mark#(head(incr(cons(cons(active(active(_x91)), _x92), mark(_x52))))) → active#(head(active(incr(cons(active(cons(_x91, _x92)), _x52)))))
mark#(head(incr(cons(cons(_x81, _x82), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(cons(mark(_x81), _x82)), _x52)))))mark#(head(s(s(odds)))) → active#(head(s(active(s(active(odds))))))
mark#(head(tail(_x51))) → active#(head(active(tail(_x51))))mark#(head(incr(cons(tail(cons(incr(_x131), mark(active(_x92)))), mark(_x31))))) → active#(head(mark(cons(s(active(tail(cons(active(incr(_x131)), _x92)))), incr(_x31)))))
mark#(head(incr(cons(nats, mark(active(mark(_x31))))))) → active#(head(mark(cons(s(active(nats)), incr(_x31)))))mark#(head(incr(cons(tail(cons(incr(_x111), mark(_x102))), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x111))), _x102))), _x52)))))
mark#(head(incr(cons(tail(cons(incr(_x101), mark(_x112))), mark(active(_x62)))))) → active#(head(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x112))), _x62))))mark#(head(incr(cons(s(cons(0, active(mark(_x102)))), mark(active(mark(_x52))))))) → active#(head(active(incr(cons(active(s(active(cons(active(0), _x102)))), _x52)))))
mark#(head(incr(cons(incr(head(_x101)), mark(_x52))))) → active#(head(active(incr(cons(active(incr(active(head(mark(_x101))))), _x52)))))mark#(head(incr(s(_x51)))) → active#(head(incr(active(s(mark(_x51))))))
mark#(head(incr(cons(s(cons(pairs, active(_x82))), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(pairs), _x82)))), _x72))))mark#(head(s(incr(s(incr(tail(cons(_x101, _x102)))))))) → active#(head(active(s(active(incr(s(incr(tail(active(cons(mark(_x101), _x102)))))))))))
mark#(head(incr(head(s(_x71))))) → active#(head(incr(active(head(active(s(mark(_x71))))))))mark#(head(s(cons(0, mark(_x72))))) → active#(head(active(s(active(cons(active(0), _x72))))))
mark#(head(s(incr(s(incr(tail(pairs))))))) → active#(head(active(s(active(incr(active(s(active(incr(active(tail(active(pairs)))))))))))))mark#(head(incr(cons(s(cons(odds, active(_x102))), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(active(odds), _x102))), _x52)))))
mark#(head(s(incr(s(incr(incr(_x121))))))) → active#(head(active(s(incr(active(s(active(incr(active(incr(mark(_x121))))))))))))mark#(head(s(incr(s(incr(tail(_x121))))))) → active#(head(active(s(active(incr(active(s(incr(active(tail(mark(_x121))))))))))))
mark#(head(s(incr(s(tail(_x101)))))) → active#(head(active(s(active(incr(active(s(tail(mark(_x101))))))))))mark#(head(incr(cons(tail(cons(incr(_x111), _x92)), active(_x31))))) → active#(head(mark(cons(s(tail(cons(active(incr(mark(_x111))), _x92))), incr(_x31)))))
mark#(head(incr(cons(tail(_x81), _x62)))) → active#(head(active(incr(active(cons(active(tail(mark(_x81))), _x62))))))mark#(head(s(s(s(mark(_x81)))))) → active#(head(active(s(active(s(active(s(_x81))))))))
mark#(head(incr(cons(tail(cons(incr(pairs), active(_x82))), _x62)))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(pairs))), _x82))), _x62)))))mark#(head(incr(cons(s(cons(_x91, active(_x82))), mark(active(_x72)))))) → active#(head(incr(cons(active(s(cons(mark(_x91), _x82))), _x72))))
mark#(head(incr(incr(cons(_x81, _x82))))) → active#(head(active(incr(active(incr(active(cons(mark(_x81), _x82))))))))mark#(head(s(incr(s(incr(tail(_x111))))))) → active#(head(s(active(incr(active(s(active(incr(tail(_x111))))))))))
mark#(head(incr(cons(_x71, _x72)))) → active#(head(active(incr(active(cons(_x71, _x72))))))mark#(head(incr(incr(tail(cons(pairs, _x82)))))) → active#(head(incr(incr(active(tail(active(cons(active(pairs), _x82))))))))
mark#(head(incr(cons(s(cons(0, _x92)), mark(active(_x72)))))) → active#(head(incr(cons(active(s(active(cons(active(0), _x92)))), _x72))))mark#(head(s(incr(s(tail(incr(_x91))))))) → active#(head(active(s(active(incr(s(tail(active(incr(mark(_x91)))))))))))
mark#(head(s(incr(s(incr(incr(_x121))))))) → active#(head(active(s(active(incr(active(s(active(incr(incr(mark(_x121))))))))))))mark#(head(incr(cons(s(odds), _x31)))) → active#(head(mark(cons(s(active(s(active(odds)))), incr(_x31)))))
mark#(head(incr(cons(cons(incr(_x91), mark(_x82)), _x62)))) → active#(head(active(incr(cons(active(cons(active(incr(mark(_x91))), _x82)), _x62)))))mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(mark(_x62))))))) → active#(head(active(incr(cons(s(active(cons(active(odds), _x92))), _x62)))))
mark#(head(incr(cons(_x61, mark(active(mark(mark(_x71)))))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x71)))))mark#(head(s(incr(s(incr(tail(0))))))) → active#(head(active(s(active(incr(s(incr(tail(active(0))))))))))
mark#(head(s(incr(s(incr(tail(incr(_x101)))))))) → active#(head(active(s(active(incr(s(incr(tail(active(incr(mark(_x101))))))))))))mark#(head(s(incr(s(tail(incr(_x131))))))) → active#(head(active(s(active(incr(active(s(active(tail(active(incr(_x131))))))))))))
mark#(head(incr(cons(cons(incr(cons(_x121, _x122)), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(incr(active(cons(mark(_x121), _x122)))), _x72)), _x62)))))mark#(head(tail(head(_x61)))) → active#(head(active(tail(active(head(mark(_x61)))))))
mark#(head(incr(cons(pairs, active(mark(active(_x52))))))) → active#(head(active(incr(cons(active(pairs), _x52)))))mark#(head(incr(cons(tail(cons(incr(head(_x131)), mark(_x112))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(head(mark(_x131))))), _x112))), _x52)))))
mark#(head(incr(incr(pairs)))) → active#(head(incr(incr(active(pairs)))))mark#(head(incr(cons(s(cons(incr(_x111), _x92)), mark(active(_x72)))))) → active#(head(active(incr(cons(active(s(active(cons(active(incr(mark(_x111))), _x92)))), _x72)))))
mark#(head(incr(cons(_x61, active(active(_x31)))))) → active#(head(mark(cons(s(mark(_x61)), incr(_x31)))))mark#(head(incr(cons(_x32, _x31)))) → active#(head(mark(cons(s(_x32), incr(_x31)))))
mark#(head(incr(incr(tail(odds))))) → active#(head(incr(incr(tail(mark(incr(pairs)))))))mark#(head(incr(cons(tail(cons(incr(_x101), mark(_x112))), mark(_x62))))) → active#(head(active(incr(cons(tail(cons(active(incr(mark(_x101))), _x112)), _x62)))))
mark#(head(s(incr(s(tail(odds)))))) → active#(head(active(s(active(incr(s(active(tail(active(odds))))))))))mark#(head(incr(cons(pairs, active(_x52))))) → active#(head(active(incr(cons(active(pairs), _x52)))))
mark#(head(incr(cons(_x61, mark(active(mark(active(_x72)))))))) → active#(head(active(incr(cons(mark(_x61), _x72)))))mark#(head(incr(cons(tail(cons(_x91, _x92)), active(_x62))))) → active#(head(active(incr(cons(tail(cons(mark(_x91), _x92)), _x62)))))
mark#(head(incr(cons(s(cons(head(_x111), mark(_x102))), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(active(head(mark(_x111))), _x102))), _x52)))))mark#(head(tail(cons(incr(_x101), _x62)))) → active#(head(active(tail(active(cons(active(incr(_x101)), _x62))))))
mark#(head(incr(cons(tail(cons(incr(nats), _x92)), active(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(nats))), _x92))), _x52)))))mark#(head(incr(cons(tail(cons(incr(head(_x101)), _x72)), active(active(active(_x62))))))) → active#(head(active(incr(cons(tail(cons(incr(active(head(mark(_x101)))), _x72)), _x62)))))
mark#(head(s(incr(s(incr(tail(head(_x131)))))))) → active#(head(active(s(active(incr(active(s(active(incr(tail(active(head(mark(_x131))))))))))))))mark#(head(incr(cons(pairs, _x31)))) → active#(head(mark(cons(s(active(pairs)), incr(_x31)))))
mark#(head(incr(cons(cons(incr(_x91), _x72), mark(_x52))))) → active#(head(active(incr(cons(active(cons(active(incr(mark(_x91))), _x72)), _x52)))))mark#(head(incr(cons(s(nats), _x62)))) → active#(head(active(incr(cons(active(s(active(nats))), _x62)))))
mark#(head(incr(cons(pairs, active(mark(_x72)))))) → active#(head(active(incr(cons(active(cons(mark(0), incr(odds))), _x72)))))mark#(head(incr(cons(tail(cons(incr(_x101), active(_x82))), mark(_x52))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(mark(_x101))), _x82))), _x52)))))
mark#(head(incr(cons(cons(active(mark(_x81)), _x82), _x62)))) → active#(head(active(incr(cons(active(cons(_x81, _x82)), _x62)))))mark#(head(s(s(incr(nats))))) → active#(head(active(s(active(s(active(incr(mark(cons(0, incr(nats)))))))))))
mark#(head(incr(cons(cons(_x71, _x72), _x62)))) → active#(head(incr(cons(active(cons(mark(_x71), _x72)), _x62))))mark#(head(s(incr(s(tail(nats)))))) → active#(head(active(s(active(incr(active(s(active(tail(active(nats)))))))))))
mark#(head(incr(cons(tail(cons(_x91, _x92)), active(mark(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(mark(_x91), _x92))), _x62)))))mark#(head(incr(cons(s(cons(_x91, active(_x102))), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(mark(_x91), _x102))), _x52)))))
mark#(head(incr(cons(s(cons(_x91, _x92)), mark(active(_x42)))))) → active#(head(incr(cons(s(active(cons(mark(_x91), _x92))), _x42))))mark#(head(s(s(incr(pairs))))) → active#(head(active(s(s(active(incr(active(pairs))))))))
mark#(head(s(incr(s(tail(incr(tail(_x131)))))))) → active#(head(s(active(incr(active(s(active(tail(active(incr(active(tail(mark(_x131))))))))))))))mark#(head(incr(cons(cons(_x81, _x82), _x31)))) → active#(head(mark(cons(s(active(cons(_x81, _x82))), incr(_x31)))))
mark#(head(incr(cons(s(odds), _x62)))) → active#(head(active(incr(cons(active(s(mark(incr(pairs)))), _x62)))))mark#(head(incr(cons(cons(active(mark(_x91)), _x92), mark(_x52))))) → active#(head(incr(cons(active(cons(_x91, _x92)), _x52))))
mark#(head(incr(cons(cons(tail(_x91), _x72), _x62)))) → active#(head(active(incr(cons(active(cons(active(tail(mark(_x91))), _x72)), _x62)))))mark#(head(incr(cons(tail(cons(incr(incr(_x131)), mark(active(_x82)))), mark(active(_x62)))))) → active#(head(active(incr(cons(active(tail(cons(active(incr(active(incr(mark(_x131))))), _x82))), _x62)))))
mark#(head(s(incr(s(incr(tail(incr(head(_x151))))))))) → active#(head(s(incr(active(s(active(incr(active(tail(active(incr(active(head(mark(_x151)))))))))))))))mark#(head(s(incr(s(tail(s(_x121))))))) → active#(head(active(s(active(incr(active(s(tail(active(s(mark(_x121))))))))))))
mark#(head(s(cons(incr(_x81), _x62)))) → active#(head(active(s(active(cons(active(incr(mark(_x81))), _x62))))))mark#(head(s(incr(s(tail(_x111)))))) → active#(head(active(s(active(incr(active(s(active(tail(_x111))))))))))
mark#(head(incr(cons(nats, _x62)))) → active#(head(active(incr(cons(active(nats), _x62)))))mark#(head(incr(cons(cons(_x71, active(_x72)), active(_x52))))) → active#(head(incr(cons(cons(_x71, _x72), _x52))))
mark#(head(tail(cons(incr(_x81), _x72)))) → active#(head(active(tail(active(cons(incr(mark(_x81)), _x72))))))mark#(head(s(incr(s(nats))))) → active#(head(active(s(active(incr(active(s(active(nats)))))))))
mark#(head(tail(cons(pairs, _x62)))) → active#(head(active(tail(active(cons(active(pairs), _x62))))))mark#(head(incr(cons(s(cons(incr(_x111), _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(active(incr(mark(_x111))), _x92))), _x52)))))
mark#(head(incr(incr(tail(cons(nats, _x82)))))) → active#(head(incr(incr(tail(active(cons(active(nats), _x82)))))))

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, pairs, s, active, mark, incr, head, odds, tail, cons

Strategy

The right-hand side of the rule mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(mark(incr(pairs)), _x92))), _x52))))) 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
active#(head(incr(cons(s(active(cons(mark(incr(pairs)), _x92))), _x52)))) 
active#(head(active(incr(cons(s(active(cons(active(incr(mark(pairs))), _x92))), _x52))))) 
active#(head(active(incr(cons(s(active(cons(mark(incr(pairs)), _x92))), _x62))))) 
active#(head(mark(cons(s(s(active(cons(mark(incr(pairs)), _x92)))), incr(_x31))))) 
active#(head(active(incr(cons(s(cons(mark(incr(pairs)), _x92)), _x52))))) 
active#(head(active(incr(cons(s(active(cons(incr(pairs), _x102))), _x52))))) 
active#(head(active(incr(cons(s(active(cons(mark(incr(pairs)), _x102))), _x52))))) 
Thus, the rule mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(mark(incr(pairs)), _x92))), _x52))))) is replaced by the following rules:
mark#(head(incr(cons(s(cons(odds, active(_x102))), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(mark(incr(pairs)), _x102))), _x52)))))mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(mark(_x62))))))) → active#(head(active(incr(cons(s(active(cons(mark(incr(pairs)), _x92))), _x62)))))
mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(_x52)))))) → active#(head(incr(cons(s(active(cons(mark(incr(pairs)), _x92))), _x52))))mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(cons(mark(incr(pairs)), _x92)), _x52)))))
mark#(head(incr(cons(s(cons(odds, _x102)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(incr(pairs), _x102))), _x52)))))mark#(head(incr(cons(s(cons(odds, mark(_x102))), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(mark(incr(pairs)), _x102))), _x52)))))
mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(_x52)))))) → active#(head(active(incr(cons(s(active(cons(active(incr(mark(pairs))), _x92))), _x52)))))mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(active(_x62))))))) → active#(head(active(incr(cons(s(active(cons(mark(incr(pairs)), _x92))), _x62)))))
mark#(head(incr(cons(s(cons(odds, _x92)), mark(active(_x31)))))) → active#(head(mark(cons(s(s(active(cons(mark(incr(pairs)), _x92)))), incr(_x31)))))

Problem 4: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

head#(mark(X)) → head#(X)head#(active(X)) → head#(X)

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, pairs, s, active, mark, incr, head, odds, tail, cons

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

head#(mark(X)) → head#(X)head#(active(X)) → head#(X)

Problem 5: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

s#(mark(X)) → s#(X)s#(active(X)) → s#(X)

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, pairs, s, active, mark, incr, head, odds, tail, cons

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

s#(mark(X)) → s#(X)s#(active(X)) → s#(X)

Problem 6: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

cons#(X1, active(X2)) → cons#(X1, X2)cons#(mark(X1), X2) → cons#(X1, X2)
cons#(X1, mark(X2)) → cons#(X1, X2)cons#(active(X1), X2) → cons#(X1, X2)

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, pairs, s, active, mark, incr, head, odds, tail, cons

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

cons#(mark(X1), X2) → cons#(X1, X2)cons#(active(X1), X2) → cons#(X1, X2)

Problem 8: ReductionPairSAT

Dependency Pair Problem

Dependency Pairs

cons#(X1, active(X2)) → cons#(X1, X2)cons#(X1, mark(X2)) → cons#(X1, X2)

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, s, pairs, active, mark, incr, head, tail, odds, cons

Strategy

Function Precedence

mark < cons# = nats = 0 = s = pairs = active = incr = head = odds = tail = cons

Argument Filtering

cons#: collapses to 2
nats: all arguments are removed from nats
0: all arguments are removed from 0
s: all arguments are removed from s
pairs: all arguments are removed from pairs
active: collapses to 1
mark: 1
incr: all arguments are removed from incr
head: collapses to 1
odds: all arguments are removed from odds
tail: all arguments are removed from tail
cons: 1 2

Status

nats: multiset
0: multiset
s: multiset
pairs: multiset
mark: multiset
incr: multiset
odds: multiset
tail: multiset
cons: lexicographic with permutation 1 → 1 2 → 2

Usable Rules

There are no usable rules.

The dependency pairs and usable rules are stronlgy conservative!

Eliminated dependency pairs

The following dependency pairs (at least) can be eliminated according to the given precedence.

cons#(X1, mark(X2)) → cons#(X1, X2)

Problem 9: ReductionPairSAT

Dependency Pair Problem

Dependency Pairs

cons#(X1, active(X2)) → cons#(X1, X2)

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, pairs, s, active, mark, incr, head, odds, tail, cons

Strategy

Function Precedence

cons# = nats = 0 = s = pairs = active = mark = incr = head = odds = tail = cons

Argument Filtering

cons#: collapses to 2
nats: all arguments are removed from nats
0: all arguments are removed from 0
s: all arguments are removed from s
pairs: all arguments are removed from pairs
active: 1
mark: all arguments are removed from mark
incr: 1
head: 1
odds: all arguments are removed from odds
tail: all arguments are removed from tail
cons: 1 2

Status

nats: multiset
0: multiset
s: multiset
pairs: multiset
active: multiset
mark: multiset
incr: lexicographic with permutation 1 → 1
head: lexicographic with permutation 1 → 1
odds: multiset
tail: multiset
cons: lexicographic with permutation 1 → 1 2 → 2

Usable Rules

There are no usable rules.

The dependency pairs and usable rules are stronlgy conservative!

Eliminated dependency pairs

The following dependency pairs (at least) can be eliminated according to the given precedence.

cons#(X1, active(X2)) → cons#(X1, X2)

Problem 7: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

incr#(active(X)) → incr#(X)incr#(mark(X)) → incr#(X)

Rewrite Rules

active(nats) → mark(cons(0, incr(nats)))active(pairs) → mark(cons(0, incr(odds)))
active(odds) → mark(incr(pairs))active(incr(cons(X, XS))) → mark(cons(s(X), incr(XS)))
active(head(cons(X, XS))) → mark(X)active(tail(cons(X, XS))) → mark(XS)
mark(nats) → active(nats)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)mark(incr(X)) → active(incr(mark(X)))
mark(pairs) → active(pairs)mark(odds) → active(odds)
mark(s(X)) → active(s(mark(X)))mark(head(X)) → active(head(mark(X)))
mark(tail(X)) → active(tail(mark(X)))cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)incr(mark(X)) → incr(X)
incr(active(X)) → incr(X)s(mark(X)) → s(X)
s(active(X)) → s(X)head(mark(X)) → head(X)
head(active(X)) → head(X)tail(mark(X)) → tail(X)
tail(active(X)) → tail(X)

Original Signature

Termination of terms over the following signature is verified: nats, 0, pairs, s, active, mark, incr, head, odds, tail, cons

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

incr#(active(X)) → incr#(X)incr#(mark(X)) → incr#(X)