TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60005 ms.

The following DP Processors were used


Problem 1 was processed with processor DependencyGraph (105ms).
 | – Problem 2 was processed with processor PolynomialLinearRange4iUR (1431ms).
 |    | – Problem 3 was processed with processor PolynomialLinearRange4iUR (950ms).
 |    |    | – Problem 4 was processed with processor DependencyGraph (25ms).
 |    |    |    | – Problem 5 was processed with processor PolynomialLinearRange4iUR (832ms).
 |    |    |    |    | – Problem 6 was processed with processor DependencyGraph (14ms).
 |    |    |    |    |    | – Problem 7 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    | – Problem 8 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    | – Problem 9 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    |    | – Problem 10 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    | – Problem 11 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    |    |    |    |    | – Problem 12 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    |    |    |    |    |    | – Problem 13 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 14 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 15 was processed with processor ForwardNarrowing (48ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 16 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 17 was processed with processor ForwardNarrowing (7ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 18 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 19 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 20 was processed with processor ForwardNarrowing (7ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 21 was processed with processor ForwardNarrowing (35ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 22 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 23 was processed with processor ForwardNarrowing (8ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 24 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 25 was processed with processor ForwardNarrowing (8ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 26 was processed with processor ForwardNarrowing (14ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 27 was processed with processor ForwardNarrowing (10ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 28 was processed with processor ForwardNarrowing (18ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 29 was processed with processor ForwardNarrowing (50ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 30 was processed with processor ForwardNarrowing (129ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 31 was processed with processor ForwardNarrowing (217ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 32 was processed with processor ForwardNarrowing (488ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 33 remains open; application of the following processors failed [ForwardNarrowing (132ms), ForwardNarrowing (129ms), ForwardNarrowing (117ms), ForwardNarrowing (123ms), ForwardNarrowing (306ms), ForwardNarrowing (111ms), ForwardNarrowing (308ms), ForwardNarrowing (152ms), ForwardNarrowing (341ms), ForwardNarrowing (142ms), ForwardNarrowing (313ms), ForwardNarrowing (117ms), ForwardNarrowing (360ms), ForwardNarrowing (155ms), ForwardNarrowing (338ms), ForwardNarrowing (157ms), ForwardNarrowing (314ms), ForwardNarrowing (105ms), ForwardNarrowing (307ms), ForwardNarrowing (193ms), ForwardNarrowing (309ms), ForwardNarrowing (189ms), ForwardNarrowing (308ms), ForwardNarrowing (105ms), ForwardNarrowing (314ms), ForwardNarrowing (209ms), ForwardNarrowing (101ms), ForwardNarrowing (104ms), ForwardNarrowing (104ms), ForwardNarrowing (110ms), ForwardNarrowing (122ms), ForwardNarrowing (293ms), ForwardNarrowing (124ms), ForwardNarrowing (210ms), ForwardNarrowing (194ms), ForwardNarrowing (195ms), ForwardNarrowing (timeout)].

The following open problems remain:

Open Dependency Pair Problem 7

Dependency Pairs

mark#(incr(X)) → a__incr#(mark(X))mark#(cons(X1, X2)) → mark#(X1)
a__incr#(cons(X, XS)) → mark#(X)mark#(s(X)) → mark#(X)
mark#(incr(X)) → mark#(X)

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, a__head, head, cons, nil

Problem 1: DependencyGraph

Dependency Pair Problem

Dependency Pairs

a__tail#(cons(X, XS)) → mark#(XS)a__odds# → a__pairs#
mark#(pairs) → a__pairs#mark#(incr(X)) → a__incr#(mark(X))
a__odds# → a__incr#(a__pairs)mark#(cons(X1, X2)) → mark#(X1)
mark#(nats) → a__nats#mark#(incr(X)) → mark#(X)
mark#(odds) → a__odds#mark#(head(X)) → mark#(X)
mark#(tail(X)) → mark#(X)mark#(head(X)) → a__head#(mark(X))
a__incr#(cons(X, XS)) → mark#(X)mark#(tail(X)) → a__tail#(mark(X))
mark#(s(X)) → mark#(X)a__head#(cons(X, XS)) → mark#(X)

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, a__head, head, cons, nil

Strategy

The following SCCs where found

a__tail#(cons(X, XS)) → mark#(XS)mark#(incr(X)) → a__incr#(mark(X))
a__odds# → a__incr#(a__pairs)mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(X)) → mark#(X)mark#(odds) → a__odds#
mark#(head(X)) → mark#(X)mark#(tail(X)) → mark#(X)
mark#(head(X)) → a__head#(mark(X))a__incr#(cons(X, XS)) → mark#(X)
mark#(tail(X)) → a__tail#(mark(X))mark#(s(X)) → mark#(X)
a__head#(cons(X, XS)) → mark#(X)

Problem 2: PolynomialLinearRange4iUR

Dependency Pair Problem

Dependency Pairs

a__tail#(cons(X, XS)) → mark#(XS)mark#(incr(X)) → a__incr#(mark(X))
a__odds# → a__incr#(a__pairs)mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(X)) → mark#(X)mark#(head(X)) → mark#(X)
mark#(odds) → a__odds#mark#(tail(X)) → mark#(X)
mark#(head(X)) → a__head#(mark(X))a__incr#(cons(X, XS)) → mark#(X)
mark#(s(X)) → mark#(X)mark#(tail(X)) → a__tail#(mark(X))
a__head#(cons(X, XS)) → mark#(X)

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, a__head, head, cons, nil

Strategy

Polynomial Interpretation

Improved Usable rules

a__head(X) → head(X)mark(cons(X1, X2)) → cons(mark(X1), X2)
a__odds → oddsa__nats → cons(0, incr(nats))
mark(0) → 0mark(head(X)) → a__head(mark(X))
a__odds → a__incr(a__pairs)a__tail(X) → tail(X)
mark(tail(X)) → a__tail(mark(X))mark(pairs) → a__pairs
a__pairs → pairsmark(nats) → a__nats
a__tail(cons(X, XS)) → mark(XS)a__head(cons(X, XS)) → mark(X)
mark(incr(X)) → a__incr(mark(X))a__nats → nats
mark(s(X)) → s(mark(X))mark(odds) → a__odds
a__incr(X) → incr(X)mark(nil) → nil
a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))a__pairs → cons(0, incr(odds))

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

a__tail#(cons(X, XS)) → mark#(XS)mark#(tail(X)) → mark#(X)
mark#(tail(X)) → a__tail#(mark(X))

Problem 3: PolynomialLinearRange4iUR

Dependency Pair Problem

Dependency Pairs

mark#(odds) → a__odds#mark#(head(X)) → mark#(X)
mark#(incr(X)) → a__incr#(mark(X))a__odds# → a__incr#(a__pairs)
mark#(head(X)) → a__head#(mark(X))mark#(cons(X1, X2)) → mark#(X1)
a__incr#(cons(X, XS)) → mark#(X)mark#(s(X)) → mark#(X)
mark#(incr(X)) → mark#(X)a__head#(cons(X, XS)) → mark#(X)

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, head, a__head, nil, cons

Strategy

Polynomial Interpretation

Improved Usable rules

a__head(X) → head(X)mark(cons(X1, X2)) → cons(mark(X1), X2)
a__odds → oddsa__nats → cons(0, incr(nats))
mark(0) → 0mark(head(X)) → a__head(mark(X))
a__odds → a__incr(a__pairs)a__tail(X) → tail(X)
mark(tail(X)) → a__tail(mark(X))mark(pairs) → a__pairs
a__pairs → pairsmark(nats) → a__nats
a__tail(cons(X, XS)) → mark(XS)a__head(cons(X, XS)) → mark(X)
mark(incr(X)) → a__incr(mark(X))a__nats → nats
mark(s(X)) → s(mark(X))mark(odds) → a__odds
a__incr(X) → incr(X)mark(nil) → nil
a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))a__pairs → cons(0, incr(odds))

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

mark#(odds) → a__odds#

Problem 4: DependencyGraph

Dependency Pair Problem

Dependency Pairs

mark#(head(X)) → mark#(X)mark#(incr(X)) → a__incr#(mark(X))
a__odds# → a__incr#(a__pairs)mark#(cons(X1, X2)) → mark#(X1)
mark#(head(X)) → a__head#(mark(X))a__incr#(cons(X, XS)) → mark#(X)
mark#(s(X)) → mark#(X)mark#(incr(X)) → mark#(X)
a__head#(cons(X, XS)) → mark#(X)

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, a__head, head, cons, nil

Strategy

The following SCCs where found

mark#(head(X)) → mark#(X)mark#(incr(X)) → a__incr#(mark(X))
mark#(head(X)) → a__head#(mark(X))mark#(cons(X1, X2)) → mark#(X1)
a__incr#(cons(X, XS)) → mark#(X)mark#(s(X)) → mark#(X)
mark#(incr(X)) → mark#(X)a__head#(cons(X, XS)) → mark#(X)

Problem 5: PolynomialLinearRange4iUR

Dependency Pair Problem

Dependency Pairs

mark#(head(X)) → mark#(X)mark#(incr(X)) → a__incr#(mark(X))
mark#(head(X)) → a__head#(mark(X))mark#(cons(X1, X2)) → mark#(X1)
a__incr#(cons(X, XS)) → mark#(X)mark#(s(X)) → mark#(X)
mark#(incr(X)) → mark#(X)a__head#(cons(X, XS)) → mark#(X)

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, a__head, head, cons, nil

Strategy

Polynomial Interpretation

Improved Usable rules

a__head(X) → head(X)mark(cons(X1, X2)) → cons(mark(X1), X2)
a__odds → oddsa__nats → cons(0, incr(nats))
mark(0) → 0mark(head(X)) → a__head(mark(X))
a__odds → a__incr(a__pairs)a__tail(X) → tail(X)
mark(tail(X)) → a__tail(mark(X))mark(pairs) → a__pairs
a__pairs → pairsmark(nats) → a__nats
a__tail(cons(X, XS)) → mark(XS)a__head(cons(X, XS)) → mark(X)
mark(incr(X)) → a__incr(mark(X))a__nats → nats
mark(s(X)) → s(mark(X))mark(odds) → a__odds
a__incr(X) → incr(X)mark(nil) → nil
a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))a__pairs → cons(0, incr(odds))

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

mark#(head(X)) → mark#(X)mark#(head(X)) → a__head#(mark(X))

Problem 6: DependencyGraph

Dependency Pair Problem

Dependency Pairs

mark#(incr(X)) → a__incr#(mark(X))mark#(cons(X1, X2)) → mark#(X1)
a__incr#(cons(X, XS)) → mark#(X)mark#(s(X)) → mark#(X)
mark#(incr(X)) → mark#(X)a__head#(cons(X, XS)) → mark#(X)

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, head, a__head, nil, cons

Strategy

The following SCCs where found

mark#(incr(X)) → a__incr#(mark(X))mark#(cons(X1, X2)) → mark#(X1)
a__incr#(cons(X, XS)) → mark#(X)mark#(s(X)) → mark#(X)
mark#(incr(X)) → mark#(X)

Problem 7: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(X)) → a__incr#(mark(X))mark#(cons(X1, X2)) → mark#(X1)
a__incr#(cons(X, XS)) → mark#(X)mark#(s(X)) → mark#(X)
mark#(incr(X)) → mark#(X)

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, head, a__head, nil, cons

Strategy

The right-hand side of the rule mark#(incr(X)) → a__incr#(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
a__incr#(a__head(mark(_x21))) 
a__incr#(a__nats) 
a__incr#(nil) 
a__incr#(s(mark(_x21))) 
a__incr#(0) 
a__incr#(a__incr(mark(_x21))) 
a__incr#(cons(mark(_x21), _x22)) 
a__incr#(a__tail(mark(_x21))) 
a__incr#(a__odds) 
a__incr#(a__pairs) 
Thus, the rule mark#(incr(X)) → a__incr#(mark(X)) is replaced by the following rules:
mark#(incr(0)) → a__incr#(0)mark#(incr(odds)) → a__incr#(a__odds)
mark#(incr(head(_x21))) → a__incr#(a__head(mark(_x21)))mark#(incr(incr(_x21))) → a__incr#(a__incr(mark(_x21)))
mark#(incr(pairs)) → a__incr#(a__pairs)mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))
mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
mark#(incr(nats)) → a__incr#(a__nats)mark#(incr(nil)) → a__incr#(nil)

Problem 8: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(0)) → a__incr#(0)mark#(incr(odds)) → a__incr#(a__odds)
mark#(incr(head(_x21))) → a__incr#(a__head(mark(_x21)))mark#(incr(incr(_x21))) → a__incr#(a__incr(mark(_x21)))
mark#(cons(X1, X2)) → mark#(X1)mark#(incr(X)) → mark#(X)
mark#(incr(pairs)) → a__incr#(a__pairs)mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))
mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))a__incr#(cons(X, XS)) → mark#(X)
mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))mark#(s(X)) → mark#(X)
mark#(incr(nats)) → a__incr#(a__nats)mark#(incr(nil)) → a__incr#(nil)

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, a__head, head, cons, nil

Strategy

The right-hand side of the rule mark#(incr(0)) → a__incr#(0) 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
Thus, the rule mark#(incr(0)) → a__incr#(0) is deleted.

Problem 9: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(odds)) → a__incr#(a__odds)mark#(incr(head(_x21))) → a__incr#(a__head(mark(_x21)))
mark#(incr(incr(_x21))) → a__incr#(a__incr(mark(_x21)))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(X)) → mark#(X)mark#(incr(pairs)) → a__incr#(a__pairs)
mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))
a__incr#(cons(X, XS)) → mark#(X)mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
mark#(s(X)) → mark#(X)mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(nil)) → a__incr#(nil)

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, head, a__head, nil, cons

Strategy

The right-hand side of the rule mark#(incr(odds)) → a__incr#(a__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
a__incr#(odds) 
a__incr#(a__incr(a__pairs)) 
Thus, the rule mark#(incr(odds)) → a__incr#(a__odds) is replaced by the following rules:
mark#(incr(odds)) → a__incr#(odds)mark#(incr(odds)) → a__incr#(a__incr(a__pairs))

Problem 10: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(_x21))) → a__incr#(a__head(mark(_x21)))mark#(incr(incr(_x21))) → a__incr#(a__incr(mark(_x21)))
mark#(cons(X1, X2)) → mark#(X1)mark#(incr(odds)) → a__incr#(a__incr(a__pairs))
mark#(incr(X)) → mark#(X)mark#(incr(odds)) → a__incr#(odds)
mark#(incr(pairs)) → a__incr#(a__pairs)mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))
mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))a__incr#(cons(X, XS)) → mark#(X)
mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))mark#(s(X)) → mark#(X)
mark#(incr(nats)) → a__incr#(a__nats)mark#(incr(nil)) → a__incr#(nil)

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, a__head, head, cons, nil

Strategy

The right-hand side of the rule mark#(incr(head(_x21))) → a__incr#(a__head(mark(_x21))) 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
a__incr#(a__head(0)) 
a__incr#(a__head(a__odds)) 
a__incr#(a__head(a__incr(mark(_x41)))) 
a__incr#(a__head(a__nats)) 
a__incr#(a__head(s(mark(_x41)))) 
a__incr#(a__head(a__head(mark(_x41)))) 
a__incr#(a__head(a__pairs)) 
a__incr#(head(mark(_x21))) 
a__incr#(a__head(a__tail(mark(_x41)))) 
a__incr#(a__head(nil)) 
a__incr#(a__head(cons(mark(_x41), _x42))) 
Thus, the rule mark#(incr(head(_x21))) → a__incr#(a__head(mark(_x21))) is replaced by the following rules:
mark#(incr(head(nil))) → a__incr#(a__head(nil))mark#(incr(head(s(_x41)))) → a__incr#(a__head(s(mark(_x41))))
mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(head(pairs))) → a__incr#(a__head(a__pairs))mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(head(odds))) → a__incr#(a__head(a__odds))
mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))mark#(incr(head(nats))) → a__incr#(a__head(a__nats))
mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))

Problem 11: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(s(_x41)))) → a__incr#(a__head(s(mark(_x41))))mark#(incr(head(nil))) → a__incr#(a__head(nil))
mark#(incr(incr(_x21))) → a__incr#(a__incr(mark(_x21)))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(head(odds))) → a__incr#(a__head(a__odds))mark#(incr(odds)) → a__incr#(a__incr(a__pairs))
mark#(incr(X)) → mark#(X)mark#(incr(odds)) → a__incr#(odds)
mark#(incr(pairs)) → a__incr#(a__pairs)mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))
mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(incr(head(pairs))) → a__incr#(a__head(a__pairs))
mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))
mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))a__incr#(cons(X, XS)) → mark#(X)
mark#(incr(nats)) → a__incr#(a__nats)mark#(s(X)) → mark#(X)
mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))mark#(incr(head(nats))) → a__incr#(a__head(a__nats))
mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))mark#(incr(nil)) → a__incr#(nil)

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, head, a__head, nil, cons

Strategy

The right-hand side of the rule mark#(incr(head(s(_x41)))) → a__incr#(a__head(s(mark(_x41)))) 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
a__incr#(a__head(s(a__tail(mark(_x51))))) 
a__incr#(a__head(s(0))) 
a__incr#(a__head(s(s(mark(_x51))))) 
a__incr#(a__head(s(a__head(mark(_x51))))) 
a__incr#(a__head(s(nil))) 
a__incr#(a__head(s(a__nats))) 
a__incr#(a__head(s(a__incr(mark(_x51))))) 
a__incr#(a__head(s(cons(mark(_x51), _x52)))) 
a__incr#(a__head(s(a__odds))) 
a__incr#(head(s(mark(_x41)))) 
a__incr#(a__head(s(a__pairs))) 
Thus, the rule mark#(incr(head(s(_x41)))) → a__incr#(a__head(s(mark(_x41)))) is replaced by the following rules:
mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))
mark#(incr(head(s(pairs)))) → a__incr#(a__head(s(a__pairs)))mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(incr(head(s(odds)))) → a__incr#(a__head(s(a__odds)))
mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))
mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(a__head(mark(_x51)))))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(head(s(nil)))) → a__incr#(a__head(s(nil)))

Problem 12: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(nil))) → a__incr#(a__head(nil))mark#(incr(incr(_x21))) → a__incr#(a__incr(mark(_x21)))
mark#(incr(head(s(pairs)))) → a__incr#(a__head(s(a__pairs)))mark#(incr(odds)) → a__incr#(a__incr(a__pairs))
mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(a__head(mark(_x51)))))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(head(s(nil)))) → a__incr#(a__head(s(nil)))mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))
mark#(incr(odds)) → a__incr#(odds)mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))
mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))
a__incr#(cons(X, XS)) → mark#(X)mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
mark#(s(X)) → mark#(X)mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))
mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))mark#(incr(nil)) → a__incr#(nil)
mark#(incr(head(s(odds)))) → a__incr#(a__head(s(a__odds)))mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))
mark#(cons(X1, X2)) → mark#(X1)mark#(incr(head(odds))) → a__incr#(a__head(a__odds))
mark#(incr(X)) → mark#(X)mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))
mark#(incr(pairs)) → a__incr#(a__pairs)mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))
mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(head(pairs))) → a__incr#(a__head(a__pairs))mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))
mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))mark#(incr(head(nats))) → a__incr#(a__head(a__nats))

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, a__head, head, cons, nil

Strategy

The right-hand side of the rule mark#(incr(incr(_x21))) → a__incr#(a__incr(mark(_x21))) 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
a__incr#(a__incr(a__nats)) 
a__incr#(a__incr(a__odds)) 
a__incr#(a__incr(nil)) 
a__incr#(incr(mark(_x21))) 
a__incr#(a__incr(0)) 
a__incr#(a__incr(a__tail(mark(_x41)))) 
a__incr#(a__incr(a__head(mark(_x41)))) 
a__incr#(a__incr(s(mark(_x41)))) 
a__incr#(a__incr(a__pairs)) 
a__incr#(a__incr(a__incr(mark(_x41)))) 
a__incr#(a__incr(cons(mark(_x41), _x42))) 
Thus, the rule mark#(incr(incr(_x21))) → a__incr#(a__incr(mark(_x21))) is replaced by the following rules:
mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))
mark#(incr(incr(0))) → a__incr#(a__incr(0))mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))
mark#(incr(incr(pairs))) → a__incr#(a__incr(a__pairs))mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(a__incr(mark(_x41))))
mark#(incr(incr(nil))) → a__incr#(a__incr(nil))mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))
mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))
mark#(incr(incr(odds))) → a__incr#(a__incr(a__odds))

Problem 13: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(nil))) → a__incr#(a__head(nil))mark#(incr(head(s(pairs)))) → a__incr#(a__head(s(a__pairs)))
mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(a__incr(mark(_x41))))mark#(incr(odds)) → a__incr#(a__incr(a__pairs))
mark#(incr(incr(nil))) → a__incr#(a__incr(nil))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(a__head(mark(_x51)))))mark#(incr(head(s(nil)))) → a__incr#(a__head(s(nil)))
mark#(incr(odds)) → a__incr#(odds)mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))
mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))
mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))
a__incr#(cons(X, XS)) → mark#(X)mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
mark#(s(X)) → mark#(X)mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))
mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))mark#(incr(nil)) → a__incr#(nil)
mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(incr(incr(0))) → a__incr#(a__incr(0))
mark#(incr(head(s(odds)))) → a__incr#(a__head(s(a__odds)))mark#(incr(head(odds))) → a__incr#(a__head(a__odds))
mark#(incr(X)) → mark#(X)mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))
mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))mark#(incr(incr(odds))) → a__incr#(a__incr(a__odds))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(pairs)) → a__incr#(a__pairs)
mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))
mark#(incr(head(0))) → a__incr#(a__head(0))mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))
mark#(incr(head(pairs))) → a__incr#(a__head(a__pairs))mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(incr(pairs))) → a__incr#(a__incr(a__pairs))
mark#(incr(head(nats))) → a__incr#(a__head(a__nats))mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, head, a__head, nil, cons

Strategy

The right-hand side of the rule mark#(incr(head(nil))) → a__incr#(a__head(nil)) 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
a__incr#(head(nil)) 
Thus, the rule mark#(incr(head(nil))) → a__incr#(a__head(nil)) is replaced by the following rules:
mark#(incr(head(nil))) → a__incr#(head(nil))

Problem 14: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(s(pairs)))) → a__incr#(a__head(s(a__pairs)))mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(a__incr(mark(_x41))))
mark#(incr(incr(nil))) → a__incr#(a__incr(nil))mark#(incr(odds)) → a__incr#(a__incr(a__pairs))
mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(a__head(mark(_x51)))))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(head(s(nil)))) → a__incr#(a__head(s(nil)))mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))
mark#(incr(odds)) → a__incr#(odds)mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))
mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))
mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))a__incr#(cons(X, XS)) → mark#(X)
mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))mark#(s(X)) → mark#(X)
mark#(incr(nats)) → a__incr#(a__nats)mark#(incr(head(nil))) → a__incr#(head(nil))
mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))
mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))mark#(incr(nil)) → a__incr#(nil)
mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))mark#(incr(head(s(odds)))) → a__incr#(a__head(s(a__odds)))
mark#(incr(incr(0))) → a__incr#(a__incr(0))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(incr(head(odds))) → a__incr#(a__head(a__odds))
mark#(incr(X)) → mark#(X)mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))
mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))mark#(incr(incr(odds))) → a__incr#(a__incr(a__odds))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(pairs)) → a__incr#(a__pairs)
mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))
mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(head(pairs))) → a__incr#(a__head(a__pairs))mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))
mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))mark#(incr(incr(pairs))) → a__incr#(a__incr(a__pairs))
mark#(incr(head(nats))) → a__incr#(a__head(a__nats))mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, a__head, head, cons, nil

Strategy

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

Problem 15: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(s(pairs)))) → a__incr#(head(s(a__pairs)))mark#(incr(head(s(pairs)))) → a__incr#(a__head(s(cons(0, incr(odds)))))
mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(a__incr(mark(_x41))))mark#(incr(odds)) → a__incr#(a__incr(a__pairs))
mark#(incr(incr(nil))) → a__incr#(a__incr(nil))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(a__head(mark(_x51)))))mark#(incr(head(s(nil)))) → a__incr#(a__head(s(nil)))
mark#(incr(odds)) → a__incr#(odds)mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))
mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))mark#(incr(head(s(pairs)))) → a__incr#(a__head(s(pairs)))
mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))
mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))a__incr#(cons(X, XS)) → mark#(X)
mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))mark#(s(X)) → mark#(X)
mark#(incr(nats)) → a__incr#(a__nats)mark#(incr(head(nil))) → a__incr#(head(nil))
mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))
mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))mark#(incr(nil)) → a__incr#(nil)
mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))
mark#(cons(X1, X2)) → mark#(X1)mark#(incr(incr(0))) → a__incr#(a__incr(0))
mark#(incr(head(s(odds)))) → a__incr#(a__head(s(a__odds)))mark#(incr(head(odds))) → a__incr#(a__head(a__odds))
mark#(incr(X)) → mark#(X)mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))
mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))mark#(incr(incr(odds))) → a__incr#(a__incr(a__odds))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(pairs)) → a__incr#(a__pairs)
mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))
mark#(incr(head(0))) → a__incr#(a__head(0))mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))
mark#(incr(head(pairs))) → a__incr#(a__head(a__pairs))mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(incr(pairs))) → a__incr#(a__incr(a__pairs))
mark#(incr(head(nats))) → a__incr#(a__head(a__nats))mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, head, a__head, nil, cons

Strategy

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

Problem 16: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(s(pairs)))) → a__incr#(a__head(s(cons(0, incr(odds)))))mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(a__incr(mark(_x41))))
mark#(incr(incr(nil))) → a__incr#(a__incr(nil))mark#(incr(odds)) → a__incr#(a__incr(a__pairs))
mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(a__head(mark(_x51)))))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(head(s(pairs)))) → a__incr#(head(s(pairs)))mark#(incr(head(s(nil)))) → a__incr#(a__head(s(nil)))
mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))mark#(incr(odds)) → a__incr#(odds)
mark#(incr(head(s(pairs)))) → a__incr#(a__head(s(pairs)))mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))
mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))
mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))a__incr#(cons(X, XS)) → mark#(X)
mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))mark#(s(X)) → mark#(X)
mark#(incr(nats)) → a__incr#(a__nats)mark#(incr(head(nil))) → a__incr#(head(nil))
mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))
mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))mark#(incr(nil)) → a__incr#(nil)
mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))mark#(incr(head(s(odds)))) → a__incr#(a__head(s(a__odds)))
mark#(incr(incr(0))) → a__incr#(a__incr(0))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(incr(head(odds))) → a__incr#(a__head(a__odds))
mark#(incr(X)) → mark#(X)mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))
mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))mark#(incr(incr(odds))) → a__incr#(a__incr(a__odds))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(pairs)) → a__incr#(a__pairs)
mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))
mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(head(pairs))) → a__incr#(a__head(a__pairs))mark#(incr(head(s(pairs)))) → a__incr#(head(s(cons(0, incr(odds)))))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))
mark#(incr(incr(pairs))) → a__incr#(a__incr(a__pairs))mark#(incr(head(nats))) → a__incr#(a__head(a__nats))
mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, a__head, head, cons, nil

Strategy

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

Problem 17: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(a__incr(mark(_x41))))mark#(incr(odds)) → a__incr#(a__incr(a__pairs))
mark#(incr(incr(nil))) → a__incr#(a__incr(nil))mark#(incr(head(s(pairs)))) → a__incr#(head(s(pairs)))
mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(a__head(mark(_x51)))))
mark#(incr(head(s(nil)))) → a__incr#(a__head(s(nil)))mark#(incr(odds)) → a__incr#(odds)
mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))
mark#(incr(head(s(pairs)))) → a__incr#(a__head(s(pairs)))mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))
mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))
a__incr#(cons(X, XS)) → mark#(X)mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
mark#(s(X)) → mark#(X)mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(head(nil))) → a__incr#(head(nil))mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))
mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))
mark#(incr(nil)) → a__incr#(nil)mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(incr(0))) → a__incr#(a__incr(0))mark#(incr(head(s(odds)))) → a__incr#(a__head(s(a__odds)))
mark#(incr(head(odds))) → a__incr#(a__head(a__odds))mark#(incr(X)) → mark#(X)
mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))
mark#(incr(incr(odds))) → a__incr#(a__incr(a__odds))mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))
mark#(incr(pairs)) → a__incr#(a__pairs)mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))
mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))mark#(incr(head(s(pairs)))) → a__incr#(head(s(cons(0, incr(odds)))))
mark#(incr(head(pairs))) → a__incr#(a__head(a__pairs))mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(incr(pairs))) → a__incr#(a__incr(a__pairs))
mark#(incr(head(nats))) → a__incr#(a__head(a__nats))mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, head, a__head, nil, cons

Strategy

The right-hand side of the rule mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(a__incr(mark(_x41)))) 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
a__incr#(a__incr(a__incr(a__tail(mark(_x51))))) 
a__incr#(incr(a__incr(mark(_x41)))) 
a__incr#(a__incr(a__incr(cons(mark(_x51), _x52)))) 
a__incr#(a__incr(a__incr(a__odds))) 
a__incr#(a__incr(a__incr(a__nats))) 
a__incr#(a__incr(a__incr(s(mark(_x51))))) 
a__incr#(a__incr(a__incr(nil))) 
a__incr#(a__incr(incr(mark(_x41)))) 
a__incr#(a__incr(a__incr(a__pairs))) 
a__incr#(a__incr(a__incr(a__incr(mark(_x51))))) 
a__incr#(a__incr(a__incr(a__head(mark(_x51))))) 
a__incr#(a__incr(a__incr(0))) 
Thus, the rule mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(a__incr(mark(_x41)))) is replaced by the following rules:
mark#(incr(incr(incr(odds)))) → a__incr#(a__incr(a__incr(a__odds)))mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))
mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))
mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))
mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(a__tail(mark(_x51)))))mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))
mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))
mark#(incr(incr(incr(pairs)))) → a__incr#(a__incr(a__incr(a__pairs)))mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))

Problem 18: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(incr(nil))) → a__incr#(a__incr(nil))mark#(incr(odds)) → a__incr#(a__incr(a__pairs))
mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(a__head(mark(_x51)))))mark#(incr(head(s(nil)))) → a__incr#(a__head(s(nil)))
mark#(incr(odds)) → a__incr#(odds)mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))
mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
a__incr#(cons(X, XS)) → mark#(X)mark#(s(X)) → mark#(X)
mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))
mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))
mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))
mark#(cons(X1, X2)) → mark#(X1)mark#(incr(head(s(odds)))) → a__incr#(a__head(s(a__odds)))
mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(a__tail(mark(_x51)))))mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))
mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))mark#(incr(incr(odds))) → a__incr#(a__incr(a__odds))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(pairs)) → a__incr#(a__pairs)
mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))
mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))mark#(incr(head(pairs))) → a__incr#(a__head(a__pairs))
mark#(incr(head(s(pairs)))) → a__incr#(head(s(cons(0, incr(odds)))))mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))
mark#(incr(head(nats))) → a__incr#(a__head(a__nats))mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))
mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(head(s(pairs)))) → a__incr#(head(s(pairs)))mark#(incr(incr(incr(pairs)))) → a__incr#(a__incr(a__incr(a__pairs)))
mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))
mark#(incr(head(s(pairs)))) → a__incr#(a__head(s(pairs)))mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))
mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(head(nil))) → a__incr#(head(nil))mark#(incr(nil)) → a__incr#(nil)
mark#(incr(incr(incr(odds)))) → a__incr#(a__incr(a__incr(a__odds)))mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))
mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))mark#(incr(incr(0))) → a__incr#(a__incr(0))
mark#(incr(head(odds))) → a__incr#(a__head(a__odds))mark#(incr(X)) → mark#(X)
mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))
mark#(incr(incr(pairs))) → a__incr#(a__incr(a__pairs))mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))
mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, a__head, head, cons, nil

Strategy

The right-hand side of the rule mark#(incr(incr(nil))) → a__incr#(a__incr(nil)) 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
a__incr#(incr(nil)) 
Thus, the rule mark#(incr(incr(nil))) → a__incr#(a__incr(nil)) is replaced by the following rules:
mark#(incr(incr(nil))) → a__incr#(incr(nil))

Problem 19: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(odds)) → a__incr#(a__incr(a__pairs))mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(a__head(mark(_x51)))))
mark#(incr(head(s(nil)))) → a__incr#(a__head(s(nil)))mark#(incr(odds)) → a__incr#(odds)
mark#(incr(incr(nil))) → a__incr#(incr(nil))mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))
mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
a__incr#(cons(X, XS)) → mark#(X)mark#(s(X)) → mark#(X)
mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))
mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))
mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))mark#(incr(head(s(odds)))) → a__incr#(a__head(s(a__odds)))
mark#(cons(X1, X2)) → mark#(X1)mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))
mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(a__tail(mark(_x51)))))mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))
mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))mark#(incr(incr(odds))) → a__incr#(a__incr(a__odds))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(pairs)) → a__incr#(a__pairs)
mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))
mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))mark#(incr(head(pairs))) → a__incr#(a__head(a__pairs))
mark#(incr(head(s(pairs)))) → a__incr#(head(s(cons(0, incr(odds)))))mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))
mark#(incr(head(nats))) → a__incr#(a__head(a__nats))mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))
mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(head(s(pairs)))) → a__incr#(head(s(pairs)))mark#(incr(incr(incr(pairs)))) → a__incr#(a__incr(a__incr(a__pairs)))
mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))
mark#(incr(head(s(pairs)))) → a__incr#(a__head(s(pairs)))mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))
mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(head(nil))) → a__incr#(head(nil))mark#(incr(nil)) → a__incr#(nil)
mark#(incr(incr(incr(odds)))) → a__incr#(a__incr(a__incr(a__odds)))mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))
mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))mark#(incr(incr(0))) → a__incr#(a__incr(0))
mark#(incr(head(odds))) → a__incr#(a__head(a__odds))mark#(incr(X)) → mark#(X)
mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))
mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))mark#(incr(incr(pairs))) → a__incr#(a__incr(a__pairs))
mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, head, a__head, nil, cons

Strategy

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

Problem 20: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(a__head(mark(_x51)))))mark#(incr(head(s(nil)))) → a__incr#(a__head(s(nil)))
mark#(incr(odds)) → a__incr#(odds)mark#(incr(incr(nil))) → a__incr#(incr(nil))
mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))
mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))a__incr#(cons(X, XS)) → mark#(X)
mark#(s(X)) → mark#(X)mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))
mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))mark#(incr(odds)) → a__incr#(a__incr(cons(0, incr(odds))))
mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))
mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))
mark#(cons(X1, X2)) → mark#(X1)mark#(incr(head(s(odds)))) → a__incr#(a__head(s(a__odds)))
mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(a__tail(mark(_x51)))))mark#(incr(odds)) → a__incr#(incr(a__pairs))
mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))
mark#(incr(incr(odds))) → a__incr#(a__incr(a__odds))mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))
mark#(incr(pairs)) → a__incr#(a__pairs)mark#(incr(odds)) → a__incr#(a__incr(pairs))
mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))
mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))mark#(incr(head(pairs))) → a__incr#(a__head(a__pairs))
mark#(incr(head(s(pairs)))) → a__incr#(head(s(cons(0, incr(odds)))))mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))
mark#(incr(head(nats))) → a__incr#(a__head(a__nats))mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))
mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(head(s(pairs)))) → a__incr#(head(s(pairs)))mark#(incr(incr(incr(pairs)))) → a__incr#(a__incr(a__incr(a__pairs)))
mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))
mark#(incr(head(s(pairs)))) → a__incr#(a__head(s(pairs)))mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))
mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(head(nil))) → a__incr#(head(nil))mark#(incr(nil)) → a__incr#(nil)
mark#(incr(incr(incr(odds)))) → a__incr#(a__incr(a__incr(a__odds)))mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))
mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))mark#(incr(incr(0))) → a__incr#(a__incr(0))
mark#(incr(head(odds))) → a__incr#(a__head(a__odds))mark#(incr(X)) → mark#(X)
mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))
mark#(incr(incr(pairs))) → a__incr#(a__incr(a__pairs))mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))
mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, a__head, head, cons, nil

Strategy

The right-hand side of the rule mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(a__head(mark(_x51))))) 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
a__incr#(a__head(s(a__head(a__odds)))) 
a__incr#(a__head(s(a__head(s(mark(_x61)))))) 
a__incr#(a__head(s(a__head(nil)))) 
a__incr#(a__head(s(a__head(a__head(mark(_x61)))))) 
a__incr#(a__head(s(a__head(cons(mark(_x61), _x62))))) 
a__incr#(a__head(s(a__head(a__tail(mark(_x61)))))) 
a__incr#(a__head(s(a__head(a__pairs)))) 
a__incr#(a__head(s(a__head(a__nats)))) 
a__incr#(a__head(s(a__head(a__incr(mark(_x61)))))) 
a__incr#(a__head(s(head(mark(_x51))))) 
a__incr#(head(s(a__head(mark(_x51))))) 
a__incr#(a__head(s(a__head(0)))) 
Thus, the rule mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(a__head(mark(_x51))))) is replaced by the following rules:
mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))mark#(incr(head(s(head(pairs))))) → a__incr#(a__head(s(a__head(a__pairs))))
mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(a__head(0))))mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))
mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))
mark#(incr(head(s(head(odds))))) → a__incr#(a__head(s(a__head(a__odds))))mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(a__head(s(mark(_x61))))))
mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))
mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(a__head(mark(_x51)))))

Problem 21: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(s(nil)))) → a__incr#(a__head(s(nil)))mark#(incr(odds)) → a__incr#(odds)
mark#(incr(incr(nil))) → a__incr#(incr(nil))mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(a__head(0))))
mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))
mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))a__incr#(cons(X, XS)) → mark#(X)
mark#(s(X)) → mark#(X)mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))
mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))
mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))mark#(incr(odds)) → a__incr#(a__incr(cons(0, incr(odds))))
mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))
mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))
mark#(incr(head(s(odds)))) → a__incr#(a__head(s(a__odds)))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))
mark#(incr(odds)) → a__incr#(incr(a__pairs))mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(a__tail(mark(_x51)))))
mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))
mark#(incr(incr(odds))) → a__incr#(a__incr(a__odds))mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))
mark#(incr(pairs)) → a__incr#(a__pairs)mark#(incr(odds)) → a__incr#(a__incr(pairs))
mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))
mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))mark#(incr(head(pairs))) → a__incr#(a__head(a__pairs))
mark#(incr(head(s(pairs)))) → a__incr#(head(s(cons(0, incr(odds)))))mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(a__head(s(mark(_x61))))))
mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))mark#(incr(head(nats))) → a__incr#(a__head(a__nats))
mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(a__head(mark(_x51)))))mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))
mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(head(s(pairs)))) → a__incr#(head(s(pairs)))mark#(incr(incr(incr(pairs)))) → a__incr#(a__incr(a__incr(a__pairs)))
mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))
mark#(incr(head(s(head(pairs))))) → a__incr#(a__head(s(a__head(a__pairs))))mark#(incr(head(s(pairs)))) → a__incr#(a__head(s(pairs)))
mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))
mark#(incr(nats)) → a__incr#(a__nats)mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))
mark#(incr(head(nil))) → a__incr#(head(nil))mark#(incr(nil)) → a__incr#(nil)
mark#(incr(incr(incr(odds)))) → a__incr#(a__incr(a__incr(a__odds)))mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))
mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))
mark#(incr(incr(0))) → a__incr#(a__incr(0))mark#(incr(head(odds))) → a__incr#(a__head(a__odds))
mark#(incr(X)) → mark#(X)mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))
mark#(incr(head(0))) → a__incr#(a__head(0))mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))
mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))mark#(incr(head(s(head(odds))))) → a__incr#(a__head(s(a__head(a__odds))))
mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))mark#(incr(incr(pairs))) → a__incr#(a__incr(a__pairs))
mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, head, a__head, nil, cons

Strategy

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

Problem 22: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(odds)) → a__incr#(odds)mark#(incr(incr(nil))) → a__incr#(incr(nil))
mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(a__head(0))))mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))
mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
a__incr#(cons(X, XS)) → mark#(X)mark#(s(X)) → mark#(X)
mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))
mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))
mark#(incr(odds)) → a__incr#(a__incr(cons(0, incr(odds))))mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))
mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))
mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(head(s(odds)))) → a__incr#(a__head(s(a__odds)))mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(a__tail(mark(_x51)))))
mark#(incr(odds)) → a__incr#(incr(a__pairs))mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))
mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))mark#(incr(incr(odds))) → a__incr#(a__incr(a__odds))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(pairs)) → a__incr#(a__pairs)
mark#(incr(odds)) → a__incr#(a__incr(pairs))mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))
mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))mark#(incr(head(s(nil)))) → a__incr#(head(s(nil)))
mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))mark#(incr(head(pairs))) → a__incr#(a__head(a__pairs))
mark#(incr(head(s(pairs)))) → a__incr#(head(s(cons(0, incr(odds)))))mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(a__head(s(mark(_x61))))))
mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))mark#(incr(head(nats))) → a__incr#(a__head(a__nats))
mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(a__head(mark(_x51)))))mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))
mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(head(s(pairs)))) → a__incr#(head(s(pairs)))mark#(incr(incr(incr(pairs)))) → a__incr#(a__incr(a__incr(a__pairs)))
mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))
mark#(incr(head(s(head(pairs))))) → a__incr#(a__head(s(a__head(a__pairs))))mark#(incr(head(s(pairs)))) → a__incr#(a__head(s(pairs)))
mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))
mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(head(nil))) → a__incr#(head(nil))mark#(incr(nil)) → a__incr#(nil)
mark#(incr(incr(incr(odds)))) → a__incr#(a__incr(a__incr(a__odds)))mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))
mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))
mark#(incr(incr(0))) → a__incr#(a__incr(0))mark#(incr(head(odds))) → a__incr#(a__head(a__odds))
mark#(incr(X)) → mark#(X)mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))
mark#(incr(head(0))) → a__incr#(a__head(0))mark#(incr(head(s(head(odds))))) → a__incr#(a__head(s(a__head(a__odds))))
mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))
mark#(incr(incr(pairs))) → a__incr#(a__incr(a__pairs))mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))
mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, a__head, head, cons, nil

Strategy

The right-hand side of the rule mark#(incr(odds)) → a__incr#(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
Thus, the rule mark#(incr(odds)) → a__incr#(odds) is deleted.

Problem 23: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(incr(nil))) → a__incr#(incr(nil))mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(a__head(0))))
mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))
mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))a__incr#(cons(X, XS)) → mark#(X)
mark#(s(X)) → mark#(X)mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))
mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))
mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))mark#(incr(odds)) → a__incr#(a__incr(cons(0, incr(odds))))
mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))
mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))
mark#(incr(head(s(odds)))) → a__incr#(a__head(s(a__odds)))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))
mark#(incr(odds)) → a__incr#(incr(a__pairs))mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(a__tail(mark(_x51)))))
mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))
mark#(incr(incr(odds))) → a__incr#(a__incr(a__odds))mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))
mark#(incr(pairs)) → a__incr#(a__pairs)mark#(incr(odds)) → a__incr#(a__incr(pairs))
mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))
mark#(incr(head(s(nil)))) → a__incr#(head(s(nil)))mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))
mark#(incr(head(pairs))) → a__incr#(a__head(a__pairs))mark#(incr(head(s(pairs)))) → a__incr#(head(s(cons(0, incr(odds)))))
mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(a__head(s(mark(_x61))))))mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))
mark#(incr(head(nats))) → a__incr#(a__head(a__nats))mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(a__head(mark(_x51)))))
mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))
mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))mark#(incr(head(s(pairs)))) → a__incr#(head(s(pairs)))
mark#(incr(incr(incr(pairs)))) → a__incr#(a__incr(a__incr(a__pairs)))mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))
mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))mark#(incr(head(s(head(pairs))))) → a__incr#(a__head(s(a__head(a__pairs))))
mark#(incr(head(s(pairs)))) → a__incr#(a__head(s(pairs)))mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))
mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))mark#(incr(head(nil))) → a__incr#(head(nil))
mark#(incr(nil)) → a__incr#(nil)mark#(incr(incr(incr(odds)))) → a__incr#(a__incr(a__incr(a__odds)))
mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))
mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))mark#(incr(incr(0))) → a__incr#(a__incr(0))
mark#(incr(head(odds))) → a__incr#(a__head(a__odds))mark#(incr(X)) → mark#(X)
mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))
mark#(incr(head(s(head(odds))))) → a__incr#(a__head(s(a__head(a__odds))))mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))
mark#(incr(incr(pairs))) → a__incr#(a__incr(a__pairs))mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))
mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, head, a__head, nil, cons

Strategy

The right-hand side of the rule mark#(incr(incr(nil))) → a__incr#(incr(nil)) 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
Thus, the rule mark#(incr(incr(nil))) → a__incr#(incr(nil)) is deleted.

Problem 24: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(a__head(0))))mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))
mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
a__incr#(cons(X, XS)) → mark#(X)mark#(s(X)) → mark#(X)
mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))
mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))
mark#(incr(odds)) → a__incr#(a__incr(cons(0, incr(odds))))mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))
mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))
mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(head(s(odds)))) → a__incr#(a__head(s(a__odds)))mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(a__tail(mark(_x51)))))
mark#(incr(odds)) → a__incr#(incr(a__pairs))mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))
mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))mark#(incr(incr(odds))) → a__incr#(a__incr(a__odds))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(pairs)) → a__incr#(a__pairs)
mark#(incr(odds)) → a__incr#(a__incr(pairs))mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))
mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))mark#(incr(head(s(nil)))) → a__incr#(head(s(nil)))
mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))mark#(incr(head(pairs))) → a__incr#(a__head(a__pairs))
mark#(incr(head(s(pairs)))) → a__incr#(head(s(cons(0, incr(odds)))))mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(a__head(s(mark(_x61))))))
mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))mark#(incr(head(nats))) → a__incr#(a__head(a__nats))
mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(a__head(mark(_x51)))))mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))
mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(head(s(pairs)))) → a__incr#(head(s(pairs)))mark#(incr(incr(incr(pairs)))) → a__incr#(a__incr(a__incr(a__pairs)))
mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))
mark#(incr(head(s(head(pairs))))) → a__incr#(a__head(s(a__head(a__pairs))))mark#(incr(head(s(pairs)))) → a__incr#(a__head(s(pairs)))
mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))
mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(head(nil))) → a__incr#(head(nil))mark#(incr(nil)) → a__incr#(nil)
mark#(incr(incr(incr(odds)))) → a__incr#(a__incr(a__incr(a__odds)))mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))
mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))
mark#(incr(incr(0))) → a__incr#(a__incr(0))mark#(incr(head(odds))) → a__incr#(a__head(a__odds))
mark#(incr(X)) → mark#(X)mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))
mark#(incr(head(0))) → a__incr#(a__head(0))mark#(incr(head(s(head(odds))))) → a__incr#(a__head(s(a__head(a__odds))))
mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))
mark#(incr(incr(pairs))) → a__incr#(a__incr(a__pairs))mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))
mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, a__head, head, cons, nil

Strategy

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

Problem 25: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))
mark#(incr(head(s(head(0))))) → a__incr#(head(s(a__head(0))))mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
a__incr#(cons(X, XS)) → mark#(X)mark#(s(X)) → mark#(X)
mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))
mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))
mark#(incr(odds)) → a__incr#(a__incr(cons(0, incr(odds))))mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))
mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))
mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))mark#(incr(head(s(odds)))) → a__incr#(a__head(s(a__odds)))
mark#(cons(X1, X2)) → mark#(X1)mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))
mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))mark#(incr(odds)) → a__incr#(incr(a__pairs))
mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(a__tail(mark(_x51)))))mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))
mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))mark#(incr(incr(odds))) → a__incr#(a__incr(a__odds))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(pairs)) → a__incr#(a__pairs)
mark#(incr(odds)) → a__incr#(a__incr(pairs))mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))
mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(head(0))))mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))
mark#(incr(head(s(nil)))) → a__incr#(head(s(nil)))mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))
mark#(incr(head(pairs))) → a__incr#(a__head(a__pairs))mark#(incr(head(s(pairs)))) → a__incr#(head(s(cons(0, incr(odds)))))
mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(a__head(s(mark(_x61))))))mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))
mark#(incr(head(nats))) → a__incr#(a__head(a__nats))mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(a__head(mark(_x51)))))
mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))
mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))mark#(incr(head(s(pairs)))) → a__incr#(head(s(pairs)))
mark#(incr(incr(incr(pairs)))) → a__incr#(a__incr(a__incr(a__pairs)))mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))
mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))mark#(incr(head(s(head(pairs))))) → a__incr#(a__head(s(a__head(a__pairs))))
mark#(incr(head(s(pairs)))) → a__incr#(a__head(s(pairs)))mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))
mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))mark#(incr(head(nil))) → a__incr#(head(nil))
mark#(incr(nil)) → a__incr#(nil)mark#(incr(incr(incr(odds)))) → a__incr#(a__incr(a__incr(a__odds)))
mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))
mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))mark#(incr(incr(0))) → a__incr#(a__incr(0))
mark#(incr(head(odds))) → a__incr#(a__head(a__odds))mark#(incr(X)) → mark#(X)
mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))
mark#(incr(head(s(head(odds))))) → a__incr#(a__head(s(a__head(a__odds))))mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))
mark#(incr(incr(pairs))) → a__incr#(a__incr(a__pairs))mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))
mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, head, a__head, nil, cons

Strategy

The right-hand side of the rule mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51))))) 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
a__incr#(a__head(s(a__tail(a__pairs)))) 
a__incr#(a__head(s(a__tail(a__incr(mark(_x61)))))) 
a__incr#(a__head(s(a__tail(a__odds)))) 
a__incr#(a__head(s(a__tail(a__head(mark(_x61)))))) 
a__incr#(a__head(s(a__tail(s(mark(_x61)))))) 
a__incr#(a__head(s(a__tail(nil)))) 
a__incr#(a__head(s(a__tail(0)))) 
a__incr#(a__head(s(a__tail(cons(mark(_x61), _x62))))) 
a__incr#(a__head(s(a__tail(a__nats)))) 
a__incr#(a__head(s(tail(mark(_x51))))) 
a__incr#(head(s(a__tail(mark(_x51))))) 
a__incr#(a__head(s(a__tail(a__tail(mark(_x61)))))) 
Thus, the rule mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51))))) is replaced by the following rules:
mark#(incr(head(s(tail(0))))) → a__incr#(a__head(s(a__tail(0))))mark#(incr(head(s(tail(pairs))))) → a__incr#(a__head(s(a__tail(a__pairs))))
mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(tail(mark(_x51)))))mark#(incr(head(s(tail(tail(_x61)))))) → a__incr#(a__head(s(a__tail(a__tail(mark(_x61))))))
mark#(incr(head(s(tail(nats))))) → a__incr#(a__head(s(a__tail(a__nats))))mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(a__head(s(a__tail(a__incr(mark(_x61))))))
mark#(incr(head(s(tail(s(_x61)))))) → a__incr#(a__head(s(a__tail(s(mark(_x61))))))mark#(incr(head(s(tail(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__tail(cons(mark(_x61), _x62)))))
mark#(incr(head(s(tail(_x51))))) → a__incr#(head(s(a__tail(mark(_x51)))))mark#(incr(head(s(tail(head(_x61)))))) → a__incr#(a__head(s(a__tail(a__head(mark(_x61))))))
mark#(incr(head(s(tail(nil))))) → a__incr#(a__head(s(a__tail(nil))))mark#(incr(head(s(tail(odds))))) → a__incr#(a__head(s(a__tail(a__odds))))

Problem 26: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(s(tail(_x51))))) → a__incr#(head(s(a__tail(mark(_x51)))))mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(tail(mark(_x51)))))
mark#(incr(head(s(tail(nats))))) → a__incr#(a__head(s(a__tail(a__nats))))mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))
mark#(incr(head(s(head(0))))) → a__incr#(head(s(a__head(0))))mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
a__incr#(cons(X, XS)) → mark#(X)mark#(s(X)) → mark#(X)
mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))
mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))
mark#(incr(odds)) → a__incr#(a__incr(cons(0, incr(odds))))mark#(incr(head(s(tail(odds))))) → a__incr#(a__head(s(a__tail(a__odds))))
mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))mark#(incr(head(s(tail(pairs))))) → a__incr#(a__head(s(a__tail(a__pairs))))
mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))
mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(head(s(odds)))) → a__incr#(a__head(s(a__odds)))mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(a__tail(mark(_x51)))))
mark#(incr(odds)) → a__incr#(incr(a__pairs))mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))
mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))mark#(incr(incr(odds))) → a__incr#(a__incr(a__odds))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(pairs)) → a__incr#(a__pairs)
mark#(incr(odds)) → a__incr#(a__incr(pairs))mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))
mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(head(0))))mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))
mark#(incr(head(s(nil)))) → a__incr#(head(s(nil)))mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))
mark#(incr(head(pairs))) → a__incr#(a__head(a__pairs))mark#(incr(head(s(pairs)))) → a__incr#(head(s(cons(0, incr(odds)))))
mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(a__head(s(mark(_x61))))))mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))
mark#(incr(head(nats))) → a__incr#(a__head(a__nats))mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(a__head(mark(_x51)))))
mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))mark#(incr(head(s(tail(nil))))) → a__incr#(a__head(s(a__tail(nil))))
mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(a__head(s(a__tail(a__incr(mark(_x61))))))mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))
mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))mark#(incr(head(s(pairs)))) → a__incr#(head(s(pairs)))
mark#(incr(incr(incr(pairs)))) → a__incr#(a__incr(a__incr(a__pairs)))mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))
mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))mark#(incr(head(s(head(pairs))))) → a__incr#(a__head(s(a__head(a__pairs))))
mark#(incr(head(s(pairs)))) → a__incr#(a__head(s(pairs)))mark#(incr(head(s(tail(tail(_x61)))))) → a__incr#(a__head(s(a__tail(a__tail(mark(_x61))))))
mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))
mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(head(nil))) → a__incr#(head(nil))mark#(incr(head(s(tail(head(_x61)))))) → a__incr#(a__head(s(a__tail(a__head(mark(_x61))))))
mark#(incr(nil)) → a__incr#(nil)mark#(incr(incr(incr(odds)))) → a__incr#(a__incr(a__incr(a__odds)))
mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))
mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))mark#(incr(incr(0))) → a__incr#(a__incr(0))
mark#(incr(head(s(tail(s(_x61)))))) → a__incr#(a__head(s(a__tail(s(mark(_x61))))))mark#(incr(head(odds))) → a__incr#(a__head(a__odds))
mark#(incr(head(s(tail(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__tail(cons(mark(_x61), _x62)))))mark#(incr(X)) → mark#(X)
mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))mark#(incr(head(s(tail(0))))) → a__incr#(a__head(s(a__tail(0))))
mark#(incr(head(0))) → a__incr#(a__head(0))mark#(incr(head(s(head(odds))))) → a__incr#(a__head(s(a__head(a__odds))))
mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))
mark#(incr(incr(pairs))) → a__incr#(a__incr(a__pairs))mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))
mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, a__head, head, cons, nil

Strategy

The right-hand side of the rule mark#(incr(head(s(tail(_x51))))) → a__incr#(head(s(a__tail(mark(_x51))))) 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
a__incr#(head(s(a__tail(a__pairs)))) 
a__incr#(head(s(a__tail(a__nats)))) 
a__incr#(head(s(a__tail(a__odds)))) 
a__incr#(head(s(a__tail(cons(mark(_x61), _x62))))) 
a__incr#(head(s(a__tail(a__tail(mark(_x61)))))) 
a__incr#(head(s(a__tail(s(mark(_x61)))))) 
a__incr#(head(s(tail(mark(_x51))))) 
a__incr#(head(s(a__tail(a__head(mark(_x61)))))) 
a__incr#(head(s(a__tail(0)))) 
a__incr#(head(s(a__tail(a__incr(mark(_x61)))))) 
a__incr#(head(s(a__tail(nil)))) 
Thus, the rule mark#(incr(head(s(tail(_x51))))) → a__incr#(head(s(a__tail(mark(_x51))))) is replaced by the following rules:
mark#(incr(head(s(tail(s(_x61)))))) → a__incr#(head(s(a__tail(s(mark(_x61))))))mark#(incr(head(s(tail(nats))))) → a__incr#(head(s(a__tail(a__nats))))
mark#(incr(head(s(tail(0))))) → a__incr#(head(s(a__tail(0))))mark#(incr(head(s(tail(_x51))))) → a__incr#(head(s(tail(mark(_x51)))))
mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(head(s(a__tail(a__incr(mark(_x61))))))mark#(incr(head(s(tail(pairs))))) → a__incr#(head(s(a__tail(a__pairs))))
mark#(incr(head(s(tail(tail(_x61)))))) → a__incr#(head(s(a__tail(a__tail(mark(_x61))))))mark#(incr(head(s(tail(odds))))) → a__incr#(head(s(a__tail(a__odds))))
mark#(incr(head(s(tail(nil))))) → a__incr#(head(s(a__tail(nil))))mark#(incr(head(s(tail(head(_x61)))))) → a__incr#(head(s(a__tail(a__head(mark(_x61))))))
mark#(incr(head(s(tail(cons(_x61, _x62)))))) → a__incr#(head(s(a__tail(cons(mark(_x61), _x62)))))

Problem 27: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(s(X)) → mark#(X)
mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(a__head(a__head(cons(a__nats, _x52))))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(head(head(cons(odds, _x52))))) → a__incr#(a__head(a__head(cons(a__odds, _x52))))mark#(incr(head(s(tail(0))))) → a__incr#(a__head(s(tail(0))))
mark#(incr(head(head(nil)))) → a__incr#(head(head(nil)))mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))
mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(mark(_x61))))))mark#(incr(odds)) → a__incr#(a__incr(pairs))
mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))
mark#(incr(head(head(cons(cons(_x61, _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(mark(_x61), _x62), _x52))))mark#(incr(head(s(nil)))) → a__incr#(head(s(nil)))
mark#(incr(head(s(tail(pairs))))) → a__incr#(a__head(s(a__tail(cons(0, incr(odds))))))mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(head(s(a__tail(a__incr(mark(_x61))))))
mark#(incr(head(pairs))) → a__incr#(a__head(a__pairs))mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(a__head(s(mark(_x61))))))
mark#(incr(head(head(cons(_x51, _x31))))) → a__incr#(a__head(mark(mark(_x51))))mark#(incr(incr(incr(tail(s(_x61)))))) → a__incr#(a__incr(a__incr(a__tail(s(mark(_x61))))))
mark#(incr(head(nats))) → a__incr#(a__head(a__nats))mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))
mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(a__head(mark(_x51)))))
mark#(incr(head(head(pairs)))) → a__incr#(head(head(pairs)))mark#(incr(head(s(odds)))) → a__incr#(a__head(s(odds)))
mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(a__head(s(a__tail(a__incr(mark(_x61))))))mark#(incr(incr(incr(tail(nats))))) → a__incr#(a__incr(a__incr(a__tail(a__nats))))
mark#(incr(head(s(pairs)))) → a__incr#(head(s(pairs)))mark#(incr(incr(incr(pairs)))) → a__incr#(a__incr(a__incr(a__pairs)))
mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))mark#(incr(incr(incr(tail(nil))))) → a__incr#(incr(a__incr(a__tail(nil))))
mark#(incr(head(head(cons(pairs, _x52))))) → a__incr#(a__head(a__head(cons(a__pairs, _x52))))mark#(incr(incr(incr(tail(_x51))))) → a__incr#(incr(a__incr(a__tail(mark(_x51)))))
mark#(incr(head(s(pairs)))) → a__incr#(a__head(s(pairs)))mark#(incr(head(s(tail(tail(_x61)))))) → a__incr#(a__head(s(tail(a__tail(mark(_x61))))))
mark#(incr(odds)) → a__incr#(cons(s(mark(0)), incr(incr(odds))))mark#(incr(head(s(incr(_x51))))) → a__incr#(head(s(a__incr(mark(_x51)))))
mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))mark#(incr(head(head(cons(0, _x52))))) → a__incr#(a__head(a__head(cons(0, _x52))))
mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(head(s(tail(nats))))) → a__incr#(head(s(a__tail(nats))))mark#(incr(head(nil))) → a__incr#(head(nil))
mark#(incr(head(head(_x41)))) → a__incr#(head(head(mark(_x41))))mark#(incr(head(s(tail(head(_x61)))))) → a__incr#(a__head(s(a__tail(a__head(mark(_x61))))))
mark#(incr(nil)) → a__incr#(nil)mark#(incr(head(s(tail(nats))))) → a__incr#(head(s(tail(a__nats))))
mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(head(s(cons(mark(_x51), _x52))))mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))
mark#(incr(head(s(tail(s(_x61)))))) → a__incr#(a__head(s(a__tail(s(mark(_x61))))))mark#(incr(incr(incr(tail(tail(_x61)))))) → a__incr#(a__incr(a__incr(a__tail(a__tail(mark(_x61))))))
mark#(incr(head(odds))) → a__incr#(a__head(a__odds))mark#(incr(X)) → mark#(X)
mark#(incr(head(s(tail(head(_x61)))))) → a__incr#(head(s(a__tail(a__head(mark(_x61))))))mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))
mark#(incr(head(head(incr(_x51))))) → a__incr#(a__head(a__head(a__incr(mark(_x51)))))mark#(incr(head(s(tail(0))))) → a__incr#(head(s(a__tail(0))))
mark#(incr(head(s(tail(nats))))) → a__incr#(head(s(mark(incr(nats)))))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(incr(pairs))) → a__incr#(a__incr(a__pairs))
mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))mark#(incr(incr(incr(tail(odds))))) → a__incr#(a__incr(a__incr(a__tail(a__odds))))
mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))mark#(incr(incr(incr(tail(0))))) → a__incr#(a__incr(a__incr(a__tail(0))))
mark#(incr(incr(incr(tail(nil))))) → a__incr#(a__incr(a__incr(tail(nil))))mark#(incr(head(head(0)))) → a__incr#(head(head(0)))
mark#(incr(head(head(pairs)))) → a__incr#(a__head(a__head(pairs)))mark#(incr(head(head(pairs)))) → a__incr#(a__head(a__head(cons(0, incr(odds)))))
mark#(incr(head(head(head(_x51))))) → a__incr#(a__head(head(a__head(mark(_x51)))))mark#(incr(head(s(tail(_x51))))) → a__incr#(head(s(a__tail(mark(_x51)))))
mark#(incr(head(head(head(_x51))))) → a__incr#(a__head(a__head(a__head(mark(_x51)))))mark#(incr(head(head(cons(head(_x61), _x52))))) → a__incr#(a__head(a__head(cons(a__head(mark(_x61)), _x52))))
mark#(incr(head(s(tail(nats))))) → a__incr#(a__head(s(a__tail(a__nats))))mark#(incr(head(s(head(0))))) → a__incr#(head(s(a__head(0))))
a__incr#(cons(X, XS)) → mark#(X)mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))
mark#(incr(head(s(odds)))) → a__incr#(head(s(a__odds)))mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))
mark#(incr(head(s(odds)))) → a__incr#(a__head(s(a__incr(a__pairs))))mark#(incr(head(s(tail(odds))))) → a__incr#(a__head(s(a__tail(a__odds))))
mark#(incr(head(s(tail(s(_x61)))))) → a__incr#(a__head(s(tail(s(mark(_x61))))))mark#(incr(head(s(tail(cons(_x61, _x62)))))) → a__incr#(head(s(a__tail(cons(mark(_x61), _x62)))))
mark#(incr(head(head(s(_x51))))) → a__incr#(a__head(a__head(s(mark(_x51)))))mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))
mark#(incr(head(head(pairs)))) → a__incr#(head(head(cons(0, incr(odds)))))mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))
mark#(incr(head(head(0)))) → a__incr#(a__head(head(0)))mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))
mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))
mark#(incr(head(head(pairs)))) → a__incr#(head(a__head(a__pairs)))mark#(incr(head(s(s(_x51))))) → a__incr#(head(s(s(mark(_x51)))))
mark#(incr(odds)) → a__incr#(incr(a__pairs))mark#(incr(head(head(_x41)))) → a__incr#(head(a__head(mark(_x41))))
mark#(incr(head(s(0)))) → a__incr#(head(s(0)))mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))
mark#(incr(head(head(tail(_x51))))) → a__incr#(a__head(a__head(a__tail(mark(_x51)))))mark#(incr(incr(odds))) → a__incr#(a__incr(a__odds))
mark#(incr(head(head(s(_x51))))) → a__incr#(a__head(head(s(mark(_x51)))))mark#(incr(head(head(cons(tail(_x61), _x52))))) → a__incr#(a__head(a__head(cons(a__tail(mark(_x61)), _x52))))
mark#(incr(head(head(tail(_x51))))) → a__incr#(a__head(head(a__tail(mark(_x51)))))mark#(incr(head(s(tail(nats))))) → a__incr#(a__head(s(tail(nats))))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(head(s(tail(nil))))) → a__incr#(a__head(s(tail(nil))))
mark#(incr(pairs)) → a__incr#(a__pairs)mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))
mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(head(0))))mark#(incr(head(head(cons(s(_x61), _x52))))) → a__incr#(a__head(a__head(cons(s(mark(_x61)), _x52))))
mark#(incr(head(s(pairs)))) → a__incr#(head(s(cons(0, incr(odds)))))mark#(incr(head(s(tail(pairs))))) → a__incr#(a__head(s(tail(a__pairs))))
mark#(incr(head(s(tail(cons(_x61, _x62)))))) → a__incr#(a__head(s(tail(cons(mark(_x61), _x62)))))mark#(incr(head(s(tail(nil))))) → a__incr#(a__head(s(a__tail(nil))))
mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(a__head(s(tail(a__incr(mark(_x61))))))mark#(incr(head(head(cons(incr(_x61), _x52))))) → a__incr#(a__head(a__head(cons(a__incr(mark(_x61)), _x52))))
mark#(incr(head(s(tail(nats))))) → a__incr#(a__head(s(tail(cons(0, incr(nats))))))mark#(incr(odds)) → a__incr#(incr(cons(0, incr(odds))))
mark#(incr(head(head(nil)))) → a__incr#(head(a__head(nil)))mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))
mark#(incr(head(s(tail(odds))))) → a__incr#(a__head(s(tail(a__odds))))mark#(incr(head(s(tail(odds))))) → a__incr#(head(s(a__tail(a__odds))))
mark#(incr(head(head(nats)))) → a__incr#(a__head(a__head(a__nats)))mark#(incr(head(s(tail(nil))))) → a__incr#(head(s(a__tail(nil))))
mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))
mark#(incr(head(s(head(pairs))))) → a__incr#(a__head(s(a__head(a__pairs))))mark#(incr(head(s(tail(tail(_x61)))))) → a__incr#(a__head(s(a__tail(a__tail(mark(_x61))))))
mark#(incr(head(head(incr(_x51))))) → a__incr#(a__head(head(a__incr(mark(_x51)))))mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(tail(mark(_x51)))))
mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))mark#(incr(head(s(tail(tail(_x61)))))) → a__incr#(head(s(a__tail(a__tail(mark(_x61))))))
mark#(incr(head(head(cons(nil, _x52))))) → a__incr#(a__head(a__head(cons(nil, _x52))))mark#(incr(head(s(tail(pairs))))) → a__incr#(a__head(s(tail(pairs))))
mark#(incr(head(head(odds)))) → a__incr#(a__head(a__head(a__odds)))mark#(incr(incr(incr(odds)))) → a__incr#(a__incr(a__incr(a__odds)))
mark#(incr(head(head(nats)))) → a__incr#(a__head(head(a__nats)))mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))
mark#(incr(incr(incr(tail(cons(_x61, _x62)))))) → a__incr#(a__incr(a__incr(a__tail(cons(mark(_x61), _x62)))))mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))
mark#(incr(head(head(cons(_x51, _x52))))) → a__incr#(head(a__head(cons(mark(_x51), _x52))))mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(incr(a__tail(mark(_x51)))))
mark#(incr(incr(0))) → a__incr#(a__incr(0))mark#(incr(head(s(tail(pairs))))) → a__incr#(head(s(a__tail(a__pairs))))
mark#(incr(head(s(tail(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__tail(cons(mark(_x61), _x62)))))mark#(incr(head(head(pairs)))) → a__incr#(a__head(head(pairs)))
mark#(incr(head(s(tail(head(_x61)))))) → a__incr#(a__head(s(tail(a__head(mark(_x61))))))mark#(incr(incr(incr(tail(pairs))))) → a__incr#(a__incr(a__incr(a__tail(a__pairs))))
mark#(incr(incr(incr(tail(nil))))) → a__incr#(a__incr(incr(a__tail(nil))))mark#(incr(incr(incr(tail(incr(_x61)))))) → a__incr#(a__incr(a__incr(a__tail(a__incr(mark(_x61))))))
mark#(incr(head(s(tail(0))))) → a__incr#(a__head(s(a__tail(0))))mark#(incr(head(s(tail(s(_x61)))))) → a__incr#(head(s(a__tail(s(mark(_x61))))))
mark#(incr(head(s(nats)))) → a__incr#(head(s(nats)))mark#(incr(head(s(tail(_x51))))) → a__incr#(head(s(tail(mark(_x51)))))
mark#(incr(head(head(cons(_x51, _x52))))) → a__incr#(a__head(head(cons(mark(_x51), _x52))))mark#(incr(head(s(head(odds))))) → a__incr#(a__head(s(a__head(a__odds))))
mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))mark#(incr(head(head(odds)))) → a__incr#(a__head(head(a__odds)))
mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))mark#(incr(head(s(tail(pairs))))) → a__incr#(head(s(a__tail(pairs))))

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, head, a__head, nil, cons

Strategy

The right-hand side of the rule mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(a__head(a__head(cons(a__nats, _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
a__incr#(a__head(a__head(cons(nats, _x52)))) 
a__incr#(head(a__head(cons(a__nats, _x52)))) 
a__incr#(a__head(head(cons(a__nats, _x52)))) 
a__incr#(a__head(mark(a__nats))) 
a__incr#(a__head(a__head(cons(cons(0, incr(nats)), _x52)))) 
Thus, the rule mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(a__head(a__head(cons(a__nats, _x52)))) is replaced by the following rules:
mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(a__head(a__head(cons(cons(0, incr(nats)), _x52))))mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(a__head(head(cons(a__nats, _x52))))
mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(a__head(mark(a__nats)))mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(a__head(a__head(cons(nats, _x52))))
mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(head(a__head(cons(a__nats, _x52))))

Problem 28: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(s(X)) → mark#(X)
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(a__pairs), _x62))))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__pairs), _x62), _x52))))
mark#(incr(head(s(tail(pairs))))) → a__incr#(a__head(s(a__tail(cons(0, incr(odds))))))mark#(incr(head(s(nil)))) → a__incr#(head(s(nil)))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(a__tail(a__head(cons(0, incr(nats)))))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__odds))))))
mark#(incr(incr(incr(tail(head(s(s(_x81)))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(mark(_x81))))))))mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(a__head(s(mark(_x61))))))
mark#(incr(head(nats))) → a__incr#(a__head(a__nats))mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))
mark#(incr(incr(incr(tail(s(_x61)))))) → a__incr#(a__incr(a__incr(a__tail(s(mark(_x61))))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(a__tail(head(cons(0, incr(nats)))))))
mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(a__head(mark(_x51)))))mark#(incr(head(head(cons(cons(incr(0), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(incr(0), _x62), _x52))))
mark#(incr(head(odds))) → a__incr#(head(odds))mark#(incr(head(head(pairs)))) → a__incr#(head(head(pairs)))
mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(mark(_x81))), _x62), _x52))))mark#(incr(head(s(odds)))) → a__incr#(a__head(s(odds)))
mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(a__head(s(a__tail(a__incr(mark(_x61))))))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(incr(incr(tail(a__head(a__head(nil))))))
mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(a__head(mark(_x81))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(incr(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(mark(_x91)))), _x62), _x52))))mark#(incr(incr(incr(pairs)))) → a__incr#(a__incr(a__incr(a__pairs)))
mark#(incr(head(head(cons(cons(incr(nil), _x62), _x52))))) → a__incr#(a__head(head(cons(cons(a__incr(nil), _x62), _x52))))mark#(incr(head(tail(_x41)))) → a__incr#(head(a__tail(mark(_x41))))
mark#(incr(incr(incr(tail(head(head(tail(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(mark(_x81))))))))mark#(incr(head(head(cons(pairs, _x52))))) → a__incr#(a__head(a__head(cons(a__pairs, _x52))))
mark#(incr(incr(incr(tail(_x51))))) → a__incr#(incr(a__incr(a__tail(mark(_x51)))))mark#(incr(incr(incr(tail(head(head(nats))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__nats))))))
mark#(incr(head(s(pairs)))) → a__incr#(a__head(s(pairs)))mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(mark(_x71)))))))
mark#(incr(head(head(cons(0, _x52))))) → a__incr#(a__head(a__head(cons(0, _x52))))mark#(incr(head(head(cons(cons(incr(nil), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(nil), _x62))))
mark#(incr(head(pairs))) → a__incr#(head(a__pairs))mark#(incr(incr(incr(tail(head(incr(_x71))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(mark(_x71)))))))
mark#(incr(head(head(_x41)))) → a__incr#(head(head(mark(_x41))))mark#(incr(head(s(tail(head(_x61)))))) → a__incr#(a__head(s(a__tail(a__head(mark(_x61))))))
mark#(incr(nil)) → a__incr#(nil)mark#(incr(incr(incr(tail(head(0)))))) → a__incr#(a__incr(incr(tail(a__head(0)))))
mark#(incr(incr(incr(tail(head(nil)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(nil)))))mark#(incr(incr(incr(tail(head(head(s(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(mark(_x81))))))))
mark#(incr(incr(incr(tail(head(head(incr(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__incr(mark(_x81))))))))mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(a__incr(tail(a__head(head(mark(_x71)))))))
mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))mark#(incr(head(s(tail(s(_x61)))))) → a__incr#(a__head(s(a__tail(s(mark(_x61))))))
mark#(incr(incr(incr(tail(head(0)))))) → a__incr#(a__incr(a__incr(tail(head(0)))))mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(mark(_x71)))))))
mark#(incr(head(s(tail(head(_x61)))))) → a__incr#(head(s(a__tail(a__head(mark(_x61))))))mark#(incr(incr(incr(tail(head(s(odds))))))) → a__incr#(incr(incr(tail(head(s(a__odds))))))
mark#(incr(head(s(tail(0))))) → a__incr#(head(s(a__tail(0))))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(incr(pairs))) → a__incr#(a__incr(a__pairs))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(tail(a__head(cons(0, incr(nats)))))))
mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(mark(0))
mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(mark(_x71)), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(nil))))))
mark#(incr(head(head(pairs)))) → a__incr#(a__head(a__head(pairs)))mark#(incr(head(nats))) → a__incr#(head(a__nats))
mark#(incr(incr(incr(tail(head(s(cons(_x81, _x82)))))))) → a__incr#(incr(incr(tail(a__head(s(cons(mark(_x81), _x82)))))))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(incr(a__incr(tail(head(a__head(nil))))))
mark#(incr(incr(incr(tail(head(pairs)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__pairs)))))mark#(incr(head(s(tail(_x51))))) → a__incr#(head(s(a__tail(mark(_x51)))))
mark#(incr(head(head(cons(cons(s(_x71), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(s(mark(_x71)), _x62), _x52))))mark#(incr(head(head(head(_x51))))) → a__incr#(a__head(a__head(a__head(mark(_x51)))))
mark#(incr(head(head(cons(cons(nil, _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(nil, _x62), _x52))))mark#(incr(incr(incr(tail(head(odds)))))) → a__incr#(a__incr(a__incr(tail(a__head(a__odds)))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(a__tail(head(a__nats)))))mark#(incr(head(head(cons(cons(incr(cons(_x81, _x82)), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(cons(mark(_x81), _x82)), _x62), _x52))))
mark#(incr(incr(incr(tail(head(incr(_x71))))))) → a__incr#(a__incr(incr(tail(a__head(a__incr(mark(_x71)))))))mark#(incr(head(s(tail(nats))))) → a__incr#(a__head(s(a__tail(a__nats))))
mark#(incr(head(head(cons(head(_x61), _x52))))) → a__incr#(a__head(a__head(cons(a__head(mark(_x61)), _x52))))mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
a__incr#(cons(X, XS)) → mark#(X)mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))
mark#(incr(head(s(odds)))) → a__incr#(a__head(s(a__incr(a__pairs))))mark#(incr(incr(incr(tail(head(s(head(_x81)))))))) → a__incr#(incr(incr(tail(a__head(s(a__head(mark(_x81))))))))
mark#(incr(head(s(tail(s(_x61)))))) → a__incr#(a__head(s(tail(s(mark(_x61))))))mark#(incr(head(s(tail(cons(_x61, _x62)))))) → a__incr#(head(s(a__tail(cons(mark(_x61), _x62)))))
mark#(incr(head(head(s(_x51))))) → a__incr#(a__head(a__head(s(mark(_x51)))))mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))
mark#(incr(head(head(cons(cons(pairs, _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__pairs, _x62), _x52))))mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(head(mark(nats)))
mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))mark#(incr(head(head(cons(cons(_x61, _x62), _x31))))) → a__incr#(a__head(mark(cons(mark(_x61), _x62))))
mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))
mark#(incr(head(head(cons(cons(odds, _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__odds, _x62), _x52))))mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))
mark#(incr(head(head(cons(cons(0, _x62), _x52))))) → a__incr#(head(a__head(cons(cons(0, _x62), _x52))))mark#(incr(odds)) → a__incr#(incr(a__pairs))
mark#(incr(head(s(s(_x51))))) → a__incr#(head(s(s(mark(_x51)))))mark#(incr(head(head(_x41)))) → a__incr#(head(a__head(mark(_x41))))
mark#(incr(incr(incr(tail(head(s(incr(_x81)))))))) → a__incr#(incr(incr(tail(a__head(s(a__incr(mark(_x81))))))))mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(tail(head(cons(0, incr(nats)))))))mark#(incr(head(s(tail(nats))))) → a__incr#(a__head(s(tail(nats))))
mark#(incr(head(head(tail(_x51))))) → a__incr#(a__head(head(a__tail(mark(_x51)))))mark#(incr(head(s(tail(nil))))) → a__incr#(a__head(s(tail(nil))))
mark#(incr(pairs)) → a__incr#(a__pairs)mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(head(head(cons(cons(a__incr(a__pairs), _x62), _x52))))
mark#(incr(head(s(pairs)))) → a__incr#(head(s(cons(0, incr(odds)))))mark#(incr(head(s(tail(pairs))))) → a__incr#(a__head(s(tail(a__pairs))))
mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(nil))))))mark#(incr(incr(incr(tail(head(incr(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__incr(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(cons(_x91, _x92))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(cons(mark(_x91), _x92))), _x62), _x52))))mark#(incr(head(cons(_x41, _x42)))) → a__incr#(head(cons(mark(_x41), _x42)))
mark#(incr(head(s(tail(cons(_x61, _x62)))))) → a__incr#(a__head(s(tail(cons(mark(_x61), _x62)))))mark#(incr(head(head(cons(incr(_x61), _x52))))) → a__incr#(a__head(a__head(cons(a__incr(mark(_x61)), _x52))))
mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(a__head(s(tail(a__incr(mark(_x61))))))mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(a__incr(incr(a__tail(a__head(mark(_x61))))))
mark#(incr(head(s(tail(nats))))) → a__incr#(a__head(s(tail(cons(0, incr(nats))))))mark#(incr(head(head(nil)))) → a__incr#(head(a__head(nil)))
mark#(incr(head(s(tail(incr(nats)))))) → a__incr#(head(s(a__tail(a__incr(a__nats)))))mark#(incr(head(head(cons(cons(incr(nats), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(a__nats), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(0))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(0))))))mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))
mark#(incr(head(head(cons(odds, _x52))))) → a__incr#(a__head(head(cons(a__odds, _x52))))mark#(incr(head(s(tail(odds))))) → a__incr#(a__head(s(tail(a__odds))))
mark#(incr(head(s(tail(odds))))) → a__incr#(head(s(a__tail(a__odds))))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x52))))) → a__incr#(head(head(cons(cons(a__incr(mark(_x71)), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(mark(_x71)), _x62))))
mark#(incr(incr(incr(tail(head(odds)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__odds)))))mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x52))))) → a__incr#(a__head(head(cons(cons(a__incr(mark(_x71)), _x62), _x52))))
mark#(incr(head(head(incr(_x51))))) → a__incr#(a__head(head(a__incr(mark(_x51)))))mark#(incr(head(head(cons(cons(incr(head(nil)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(nil)), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(tail(_x81)), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(a__tail(mark(_x81))), _x62), _x52))))mark#(incr(head(head(cons(odds, _x31))))) → a__incr#(a__head(mark(a__odds)))
mark#(incr(head(head(cons(cons(incr(0), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(0), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(nats), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__nats), _x62), _x52))))
mark#(incr(head(s(tail(pairs))))) → a__incr#(a__head(s(tail(pairs))))mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(incr(a__incr(a__tail(a__head(mark(_x61))))))
mark#(incr(head(head(odds)))) → a__incr#(a__head(a__head(a__odds)))mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(a__head(a__head(cons(cons(0, incr(nats)), _x52))))
mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))mark#(incr(head(head(nats)))) → a__incr#(a__head(head(a__nats)))
mark#(incr(head(s(tail(incr(head(_x71))))))) → a__incr#(head(s(a__tail(a__incr(a__head(mark(_x71)))))))mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(incr(a__tail(mark(_x51)))))
mark#(incr(incr(0))) → a__incr#(a__incr(0))mark#(incr(incr(incr(tail(head(0)))))) → a__incr#(incr(a__incr(tail(a__head(0)))))
mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(head(cons(0, incr(nats))))mark#(incr(head(head(pairs)))) → a__incr#(a__head(head(pairs)))
mark#(incr(head(s(tail(head(_x61)))))) → a__incr#(a__head(s(tail(a__head(mark(_x61))))))mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(head(a__nats))
mark#(incr(incr(incr(tail(pairs))))) → a__incr#(a__incr(a__incr(a__tail(a__pairs))))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(cons(0, incr(odds))), _x62), _x52))))
mark#(incr(head(head(cons(cons(head(_x71), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__head(mark(_x71)), _x62), _x52))))mark#(incr(incr(incr(tail(incr(_x61)))))) → a__incr#(a__incr(a__incr(a__tail(a__incr(mark(_x61))))))
mark#(incr(incr(incr(tail(head(head(cons(_x81, _x82)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(cons(mark(_x81), _x82)))))))mark#(incr(head(s(nats)))) → a__incr#(head(s(nats)))
mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(head(mark(_x81))), _x62), _x52))))mark#(incr(head(s(tail(_x51))))) → a__incr#(head(s(tail(mark(_x51)))))
mark#(incr(head(s(head(odds))))) → a__incr#(a__head(s(a__head(a__odds))))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__pairs), _x62), _x52))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(incr(tail(a__head(cons(0, incr(nats)))))))mark#(incr(head(head(cons(cons(incr(cons(_x81, _x82)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(cons(mark(_x81), _x82)), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(incr(_x81)))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__incr(mark(_x81))))))))mark#(incr(head(s(tail(incr(nil)))))) → a__incr#(head(s(a__tail(a__incr(nil)))))
mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(incr(incr(tail(head(s(mark(_x71)))))))mark#(incr(incr(incr(tail(head(nil)))))) → a__incr#(a__incr(incr(tail(a__head(nil)))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(incr(a__pairs), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(nil), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(incr(nil), _x62), _x52))))
mark#(incr(head(s(tail(incr(0)))))) → a__incr#(head(s(a__tail(incr(0)))))mark#(incr(head(head(cons(cons(incr(head(nats)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__nats)), _x62), _x52))))
mark#(incr(head(head(cons(cons(0, _x62), _x31))))) → a__incr#(a__head(mark(cons(0, _x62))))mark#(incr(incr(incr(tail(head(s(tail(_x81)))))))) → a__incr#(incr(incr(tail(a__head(s(a__tail(mark(_x81))))))))
mark#(incr(incr(incr(tail(head(s(0))))))) → a__incr#(a__incr(incr(tail(a__head(s(0))))))mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(pairs)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__pairs)), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(incr(tail(a__head(head(nil))))))
mark#(incr(incr(incr(tail(head(s(s(_x81)))))))) → a__incr#(incr(incr(tail(a__head(s(s(mark(_x81))))))))mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(head(s(a__tail(incr(mark(_x61))))))
mark#(incr(incr(incr(tail(head(s(pairs))))))) → a__incr#(incr(incr(tail(a__head(s(a__pairs))))))mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))
mark#(cons(X1, X2)) → mark#(X1)mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(a__tail(head(cons(0, incr(nats)))))))
mark#(incr(incr(incr(tail(head(odds)))))) → a__incr#(a__incr(incr(tail(a__head(a__odds)))))mark#(incr(incr(incr(tail(head(cons(_x71, _x72))))))) → a__incr#(a__incr(a__incr(tail(a__head(cons(mark(_x71), _x72))))))
mark#(incr(incr(incr(tail(head(s(pairs))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__pairs))))))mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(a__incr(a__incr(tail(head(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(a__head(head(cons(cons(a__incr(a__pairs), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(nil), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(nil), _x62), _x52))))
mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(a__head(mark(a__nats)))mark#(incr(incr(incr(tail(head(s(odds))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__odds))))))
mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))mark#(incr(head(pairs))) → a__incr#(a__head(a__pairs))
mark#(incr(head(head(cons(odds, _x52))))) → a__incr#(a__head(a__head(cons(odds, _x52))))mark#(incr(head(head(cons(_x51, _x31))))) → a__incr#(a__head(mark(mark(_x51))))
mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))mark#(incr(head(head(cons(cons(incr(odds), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__odds), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(incr(mark(_x71)), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x52))))) → a__incr#(head(head(cons(cons(a__incr(a__head(mark(_x81))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(tail(_x81)))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__tail(mark(_x81))))))))mark#(incr(head(head(cons(cons(incr(s(_x81)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(s(mark(_x81))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(a__tail(a__head(a__nats)))))mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(a__incr(incr(tail(head(s(mark(_x71)))))))
mark#(incr(incr(incr(tail(nats))))) → a__incr#(a__incr(a__incr(a__tail(a__nats))))mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__tail(mark(_x91)))), _x62), _x52))))
mark#(incr(head(s(pairs)))) → a__incr#(head(s(pairs)))mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))
mark#(incr(incr(incr(tail(head(s(nil))))))) → a__incr#(a__incr(incr(tail(a__head(s(nil))))))mark#(incr(incr(incr(tail(nil))))) → a__incr#(incr(a__incr(a__tail(nil))))
mark#(incr(head(s(tail(tail(_x61)))))) → a__incr#(a__head(s(tail(a__tail(mark(_x61))))))mark#(incr(odds)) → a__incr#(cons(s(mark(0)), incr(incr(odds))))
mark#(incr(head(s(incr(_x51))))) → a__incr#(head(s(a__incr(mark(_x51)))))mark#(incr(incr(incr(tail(head(s(odds))))))) → a__incr#(incr(incr(tail(head(s(odds))))))
mark#(incr(incr(incr(tail(head(cons(_x71, _x72))))))) → a__incr#(a__incr(incr(tail(a__head(cons(mark(_x71), _x72))))))mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))
mark#(incr(incr(incr(tail(head(nil)))))) → a__incr#(a__incr(a__incr(tail(a__head(nil)))))mark#(incr(head(s(tail(incr(pairs)))))) → a__incr#(head(s(a__tail(a__incr(a__pairs)))))
mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(head(s(tail(nats))))) → a__incr#(head(s(a__tail(nats))))mark#(incr(head(nil))) → a__incr#(head(nil))
mark#(incr(head(s(tail(nats))))) → a__incr#(head(s(tail(a__nats))))mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__odds)), _x62), _x52))))
mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(head(s(cons(mark(_x51), _x52))))mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(head(head(cons(nats, _x52))))
mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(incr(a__incr(tail(a__head(mark(_x61))))))mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(a__incr(incr(tail(head(mark(_x61))))))
mark#(incr(incr(incr(tail(tail(_x61)))))) → a__incr#(a__incr(a__incr(a__tail(a__tail(mark(_x61))))))mark#(incr(head(odds))) → a__incr#(a__head(a__odds))
mark#(incr(head(incr(_x41)))) → a__incr#(head(a__incr(mark(_x41))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(a__tail(mark(0)))))
mark#(incr(X)) → mark#(X)mark#(incr(incr(incr(tail(head(s(cons(_x81, _x82)))))))) → a__incr#(a__incr(incr(tail(a__head(s(cons(mark(_x81), _x82)))))))
mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))mark#(incr(head(head(incr(_x51))))) → a__incr#(a__head(a__head(a__incr(mark(_x51)))))
mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(a__incr(a__incr(tail(a__head(s(mark(_x71)))))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(incr(a__tail(a__head(cons(0, incr(nats)))))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(nats)))))mark#(incr(head(s(tail(nats))))) → a__incr#(head(s(mark(incr(nats)))))
mark#(incr(incr(incr(tail(head(0)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(0)))))mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))
mark#(incr(head(head(cons(cons(incr(incr(_x81)), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(a__incr(mark(_x81))), _x62), _x52))))mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(a__tail(head(a__nats)))))mark#(incr(incr(incr(tail(odds))))) → a__incr#(a__incr(a__incr(a__tail(a__odds))))
mark#(incr(head(head(cons(cons(_x61, _x62), _x52))))) → a__incr#(a__head(head(cons(cons(mark(_x61), _x62), _x52))))mark#(incr(incr(incr(tail(0))))) → a__incr#(a__incr(a__incr(a__tail(0))))
mark#(incr(incr(incr(tail(nil))))) → a__incr#(a__incr(a__incr(tail(nil))))mark#(incr(head(head(0)))) → a__incr#(head(head(0)))
mark#(incr(head(head(cons(cons(incr(head(head(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__head(mark(_x91)))), _x62), _x52))))mark#(incr(head(head(cons(odds, _x52))))) → a__incr#(a__head(a__head(cons(a__incr(a__pairs), _x52))))
mark#(incr(head(head(pairs)))) → a__incr#(a__head(a__head(cons(0, incr(odds)))))mark#(incr(incr(incr(tail(head(tail(_x71))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__tail(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(0), _x62), _x52))))) → a__incr#(a__head(head(cons(cons(a__incr(0), _x62), _x52))))mark#(incr(incr(incr(tail(head(pairs)))))) → a__incr#(a__incr(incr(tail(a__head(a__pairs)))))
mark#(incr(head(s(tail(incr(0)))))) → a__incr#(head(s(tail(a__incr(0)))))mark#(incr(head(head(head(_x51))))) → a__incr#(a__head(head(a__head(mark(_x51)))))
mark#(incr(incr(incr(tail(head(cons(_x71, _x72))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(cons(mark(_x71), _x72))))))mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(a__head(nats))
mark#(incr(head(head(cons(odds, _x52))))) → a__incr#(head(a__head(cons(a__odds, _x52))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(tail(mark(0)))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(pairs), _x62), _x52))))mark#(incr(head(s(head(0))))) → a__incr#(head(s(a__head(0))))
mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))mark#(incr(head(s(odds)))) → a__incr#(head(s(a__odds)))
mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))mark#(incr(head(0))) → a__incr#(head(0))
mark#(incr(head(s(tail(odds))))) → a__incr#(a__head(s(a__tail(a__odds))))mark#(incr(incr(incr(tail(head(s(0))))))) → a__incr#(incr(incr(tail(a__head(s(0))))))
mark#(incr(head(head(pairs)))) → a__incr#(head(head(cons(0, incr(odds)))))mark#(incr(head(head(cons(cons(incr(head(s(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(s(mark(_x91)))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(incr(a__incr(tail(a__head(head(nil))))))mark#(incr(head(s(tail(incr(odds)))))) → a__incr#(head(s(a__tail(a__incr(a__odds)))))
mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(mark(_x71)))))))mark#(incr(head(s(tail(incr(tail(_x71))))))) → a__incr#(head(s(a__tail(a__incr(a__tail(mark(_x71)))))))
mark#(incr(head(head(0)))) → a__incr#(a__head(head(0)))mark#(incr(head(head(pairs)))) → a__incr#(head(a__head(a__pairs)))
mark#(incr(head(s(0)))) → a__incr#(head(s(0)))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(tail(head(a__nats)))))
mark#(incr(head(head(tail(_x51))))) → a__incr#(a__head(a__head(a__tail(mark(_x51)))))mark#(incr(head(head(cons(cons(incr(head(0)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(0)), _x62), _x52))))
mark#(incr(head(head(cons(tail(_x61), _x52))))) → a__incr#(a__head(a__head(cons(a__tail(mark(_x61)), _x52))))mark#(incr(incr(odds))) → a__incr#(a__incr(a__odds))
mark#(incr(head(head(s(_x51))))) → a__incr#(a__head(head(s(mark(_x51)))))mark#(incr(head(head(cons(cons(incr(s(_x81)), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(s(mark(_x81))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(tail(_x81)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__tail(mark(_x81))), _x62), _x52))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(tail(a__head(a__nats)))))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(head(s(tail(incr(cons(_x71, _x72))))))) → a__incr#(head(s(a__tail(a__incr(cons(mark(_x71), _x72))))))
mark#(incr(head(head(cons(s(_x61), _x52))))) → a__incr#(a__head(a__head(cons(s(mark(_x61)), _x52))))mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(head(0))))
mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(head(head(cons(a__nats, _x52))))mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))
mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x31))))) → a__incr#(head(mark(cons(a__incr(a__head(mark(_x81))), _x62))))mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(incr(incr(tail(a__head(mark(_x61))))))
mark#(incr(incr(incr(tail(head(pairs)))))) → a__incr#(a__incr(a__incr(tail(a__head(a__pairs)))))mark#(incr(head(s(tail(nil))))) → a__incr#(a__head(s(a__tail(nil))))
mark#(incr(incr(incr(tail(head(tail(_x71))))))) → a__incr#(a__incr(incr(tail(a__head(a__tail(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(incr(_x81)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__incr(mark(_x81))), _x62), _x52))))
mark#(incr(incr(nats))) → a__incr#(a__incr(cons(0, incr(nats))))mark#(incr(incr(incr(tail(head(s(head(_x81)))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__head(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(odds), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(a__odds), _x62), _x52))))mark#(incr(odds)) → a__incr#(incr(cons(0, incr(odds))))
mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(a__head(head(cons(cons(0, incr(nats)), _x52))))mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__nats))))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(pairs), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(incr(incr(tail(a__head(s(a__nats))))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(a__tail(mark(0)))))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(a__incr(tail(head(head(nil))))))
mark#(incr(head(s(tail(incr(s(_x71))))))) → a__incr#(head(s(a__tail(a__incr(s(mark(_x71)))))))mark#(incr(incr(incr(tail(head(head(pairs))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__pairs))))))
mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(head(a__head(cons(a__nats, _x52))))mark#(incr(head(head(nats)))) → a__incr#(a__head(a__head(a__nats)))
mark#(incr(head(s(tail(nil))))) → a__incr#(head(s(a__tail(nil))))mark#(incr(head(odds))) → a__incr#(head(a__incr(a__pairs)))
mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))mark#(incr(head(s(tail(incr(incr(_x71))))))) → a__incr#(head(s(a__tail(a__incr(a__incr(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(0), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(0), _x62))))mark#(incr(head(s(head(pairs))))) → a__incr#(a__head(s(a__head(a__pairs))))
mark#(incr(incr(incr(tail(head(s(odds))))))) → a__incr#(incr(incr(tail(a__head(s(a__incr(a__pairs)))))))mark#(incr(incr(nats))) → a__incr#(incr(nats))
mark#(incr(incr(nats))) → a__incr#(incr(cons(0, incr(nats))))mark#(incr(head(s(tail(tail(_x61)))))) → a__incr#(a__head(s(a__tail(a__tail(mark(_x61))))))
mark#(incr(incr(incr(tail(head(head(head(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__head(mark(_x81))))))))mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(tail(mark(_x51)))))
mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(head(s(tail(a__incr(mark(_x61))))))
mark#(incr(head(head(cons(cons(_x61, _x62), _x52))))) → a__incr#(head(a__head(cons(cons(mark(_x61), _x62), _x52))))mark#(incr(head(head(cons(cons(tail(_x71), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__tail(mark(_x71)), _x62), _x52))))
mark#(incr(head(s(tail(tail(_x61)))))) → a__incr#(head(s(a__tail(a__tail(mark(_x61))))))mark#(incr(incr(incr(tail(head(tail(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__tail(mark(_x71)))))))
mark#(incr(head(head(cons(nil, _x52))))) → a__incr#(a__head(a__head(cons(nil, _x52))))mark#(incr(incr(incr(odds)))) → a__incr#(a__incr(a__incr(a__odds)))
mark#(incr(head(head(cons(cons(nats, _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__nats, _x62), _x52))))mark#(incr(incr(incr(tail(cons(_x61, _x62)))))) → a__incr#(a__incr(a__incr(a__tail(cons(mark(_x61), _x62)))))
mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))mark#(incr(head(head(cons(_x51, _x52))))) → a__incr#(head(a__head(cons(mark(_x51), _x52))))
mark#(incr(head(s(tail(pairs))))) → a__incr#(head(s(a__tail(a__pairs))))mark#(incr(head(s(tail(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__tail(cons(mark(_x61), _x62)))))
mark#(incr(incr(incr(tail(head(s(nil))))))) → a__incr#(incr(incr(tail(a__head(s(nil))))))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x31))))) → a__incr#(head(mark(cons(a__incr(a__pairs), _x62))))
mark#(incr(incr(incr(tail(nil))))) → a__incr#(a__incr(incr(a__tail(nil))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(a__tail(a__head(a__nats)))))
mark#(incr(head(s(tail(0))))) → a__incr#(a__head(s(a__tail(0))))mark#(incr(head(s(tail(s(_x61)))))) → a__incr#(head(s(a__tail(s(mark(_x61))))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(a__tail(head(nats)))))mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x31))))) → a__incr#(head(mark(cons(a__incr(mark(_x71)), _x62))))
mark#(incr(head(head(cons(_x51, _x52))))) → a__incr#(a__head(head(cons(mark(_x51), _x52))))mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))
mark#(incr(head(head(odds)))) → a__incr#(a__head(head(a__odds)))mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(cons(0, incr(odds))), _x62), _x52))))mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(a__incr(a__incr(a__tail(head(mark(_x61))))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(tail(a__head(a__nats)))))mark#(incr(head(head(cons(cons(cons(_x71, _x72), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(cons(mark(_x71), _x72), _x62), _x52))))
mark#(incr(head(s(tail(pairs))))) → a__incr#(head(s(a__tail(pairs))))

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, head, a__head, nil, cons

Strategy

The right-hand side of the rule mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(a__pairs), _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
a__incr#(a__head(cons(mark(a__incr(a__pairs)), _x32))) 
a__incr#(a__head(mark(cons(a__incr(pairs), _x62)))) 
a__incr#(a__head(mark(cons(a__incr(cons(0, incr(odds))), _x62)))) 
a__incr#(head(mark(cons(a__incr(a__pairs), _x62)))) 
a__incr#(a__head(mark(cons(incr(a__pairs), _x62)))) 
Thus, the rule mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(a__pairs), _x62)))) is replaced by the following rules:
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x31))))) → a__incr#(a__head(mark(cons(incr(a__pairs), _x62))))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(cons(0, incr(odds))), _x62))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(pairs), _x62))))mark#(incr(head(head(cons(cons(incr(pairs), _x32), a__incr(a__pairs)))))) → a__incr#(a__head(cons(mark(a__incr(a__pairs)), _x32)))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x31))))) → a__incr#(head(mark(cons(a__incr(a__pairs), _x62))))

Problem 29: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(s(X)) → mark#(X)
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(mark(_x111)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(cons(0, incr(nats)))))), _x62), _x52))))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(a__nats))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(mark(_x101))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(tail(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(mark(_x81))))))))mark#(incr(head(s(tail(incr(cons(_x71, _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(mark(_x71), _x72))))))
mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(mark(_x71)))))))mark#(incr(head(head(cons(0, _x52))))) → a__incr#(a__head(a__head(cons(0, _x52))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(a__odds))))))mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(head(s(a__head(a__tail(mark(_x61))))))
mark#(incr(incr(incr(tail(head(incr(_x71))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(mark(_x71)))))))mark#(incr(nil)) → a__incr#(nil)
mark#(incr(head(head(cons(cons(incr(head(incr(odds))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(a__odds))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(a__incr(a__pairs)))))))
mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(mark(_x81))), _x62), _x52))))mark#(incr(incr(incr(tail(head(nil)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(nil)))))
mark#(incr(incr(incr(tail(head(head(incr(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__incr(mark(_x81))))))))mark#(incr(incr(incr(tail(head(head(s(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(mark(_x81))))))))
mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))mark#(incr(head(s(tail(s(_x61)))))) → a__incr#(a__head(s(a__tail(s(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(odds)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(a__odds)))), _x62), _x52))))mark#(incr(incr(incr(tail(head(0)))))) → a__incr#(a__incr(a__incr(tail(head(0)))))
mark#(incr(head(s(tail(head(_x61)))))) → a__incr#(head(s(a__tail(a__head(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(a__nats)))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(odds))))))) → a__incr#(incr(incr(tail(head(s(a__odds))))))mark#(incr(head(s(tail(incr(head(_x71))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(mark(_x71)))))))
mark#(incr(head(0))) → a__incr#(a__head(0))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(tail(a__head(cons(0, incr(nats)))))))
mark#(incr(incr(pairs))) → a__incr#(a__incr(a__pairs))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(a__nats)))), _x62), _x52))))
mark#(incr(head(s(tail(incr(incr(_x71))))))) → a__incr#(a__head(s(a__tail(incr(a__incr(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(mark(_x71)), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(mark(_x91)))), _x62))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(_x101)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(mark(_x101))))))))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(cons(0, incr(odds))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(nats)))), _x62), _x52))))
mark#(incr(head(s(head(incr(nats)))))) → a__incr#(head(s(a__head(a__incr(a__nats)))))mark#(incr(incr(incr(tail(head(s(cons(_x81, _x82)))))))) → a__incr#(incr(incr(tail(a__head(s(cons(mark(_x81), _x82)))))))
mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(incr(a__incr(tail(head(a__head(nil))))))mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(a__head(a__odds)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(cons(_x101, _x102)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(cons(mark(_x101), _x102)))), _x62), _x52))))mark#(incr(head(head(cons(cons(s(_x71), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(s(mark(_x71)), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(_x101)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(mark(_x101))))))))))mark#(incr(incr(incr(tail(head(odds)))))) → a__incr#(a__incr(a__incr(tail(a__head(a__odds)))))
mark#(incr(head(s(head(incr(cons(_x71, _x72))))))) → a__incr#(head(s(a__head(a__incr(cons(mark(_x71), _x72))))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(a__tail(head(a__nats)))))
mark#(incr(head(s(tail(nats))))) → a__incr#(a__head(s(a__tail(a__nats))))mark#(incr(head(head(cons(head(_x61), _x52))))) → a__incr#(a__head(a__head(cons(a__head(mark(_x61)), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(incr(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__incr(mark(_x101))))), _x62), _x52))))mark#(incr(head(s(tail(incr(incr(cons(_x81, _x82)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(cons(mark(_x81), _x82)))))))
mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(pairs), _x62))))
mark#(incr(incr(incr(tail(head(head(nats))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(a__nats))))))mark#(incr(incr(incr(tail(s(_x61)))))) → a__incr#(a__incr(incr(a__tail(s(mark(_x61))))))
mark#(incr(head(s(tail(s(_x61)))))) → a__incr#(a__head(s(tail(s(mark(_x61))))))mark#(incr(head(s(tail(cons(_x61, _x62)))))) → a__incr#(head(s(a__tail(cons(mark(_x61), _x62)))))
mark#(incr(head(head(cons(cons(pairs, _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__pairs, _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(head(_x101)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(a__head(mark(_x101))))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(nats))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__nats))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__incr(pairs)))))))
mark#(incr(head(head(cons(cons(incr(0), _x62), _x31))))) → a__incr#(head(mark(cons(incr(0), _x62))))mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))
mark#(incr(head(head(cons(cons(odds, _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__odds, _x62), _x52))))mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))
mark#(incr(head(s(s(_x51))))) → a__incr#(head(s(s(mark(_x51)))))mark#(incr(odds)) → a__incr#(incr(a__pairs))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(a__tail(mark(0)))))mark#(incr(head(head(tail(_x51))))) → a__incr#(a__head(head(a__tail(mark(_x51)))))
mark#(incr(head(s(tail(nats))))) → a__incr#(a__head(s(tail(nats))))mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(head(a__head(mark(_x71)))))))
mark#(incr(head(s(tail(nil))))) → a__incr#(a__head(s(tail(nil))))mark#(incr(head(head(cons(cons(incr(head(incr(head(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(a__head(mark(_x101))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(nats))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__nats))), _x62), _x52))))mark#(incr(head(cons(_x41, _x42)))) → a__incr#(head(cons(mark(_x41), _x42)))
mark#(incr(head(head(cons(incr(_x61), _x52))))) → a__incr#(a__head(a__head(cons(a__incr(mark(_x61)), _x52))))mark#(incr(head(s(tail(nats))))) → a__incr#(a__head(s(tail(cons(0, incr(nats))))))
mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(a__incr(incr(a__tail(a__head(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(s(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(s(mark(_x91)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(tail(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__tail(mark(_x101))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(pairs)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(pairs)), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(incr(tail(a__head(head(a__odds))))))mark#(incr(head(head(cons(cons(incr(nats), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(a__nats), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(pairs)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(cons(0, incr(odds)))), _x62), _x52))))mark#(incr(head(s(head(incr(pairs)))))) → a__incr#(head(s(a__head(a__incr(a__pairs)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__tail(a__head(mark(_x101))))), _x62), _x52))))mark#(incr(head(head(cons(odds, _x52))))) → a__incr#(a__head(head(cons(a__odds, _x52))))
mark#(incr(head(s(tail(odds))))) → a__incr#(a__head(s(tail(a__odds))))mark#(incr(head(s(tail(odds))))) → a__incr#(head(s(a__tail(a__odds))))
mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))mark#(incr(head(nats))) → a__incr#(a__head(nats))
mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x52))))) → a__incr#(head(head(cons(cons(a__incr(mark(_x71)), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(mark(_x71)), _x62))))
mark#(incr(incr(incr(tail(s(nil)))))) → a__incr#(a__incr(incr(tail(s(nil)))))mark#(incr(incr(incr(tail(head(odds)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__odds)))))
mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x52))))) → a__incr#(a__head(head(cons(cons(a__incr(mark(_x71)), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(a__incr(a__pairs))))))))))
mark#(incr(incr(incr(tail(head(s(s(s(_x91))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(s(mark(_x91)))))))))mark#(incr(incr(incr(tail(head(s(s(incr(cons(_x101, _x102)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(cons(mark(_x101), _x102)))))))))
mark#(incr(incr(incr(tail(s(nil)))))) → a__incr#(a__incr(a__incr(tail(s(nil)))))mark#(incr(head(head(cons(cons(incr(tail(_x81)), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(a__tail(mark(_x81))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(nats), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__nats), _x62), _x52))))mark#(incr(head(s(tail(pairs))))) → a__incr#(a__head(s(tail(pairs))))
mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(a__head(a__head(cons(cons(0, incr(nats)), _x52))))mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))
mark#(incr(head(s(tail(incr(head(_x71))))))) → a__incr#(head(s(a__tail(a__incr(a__head(mark(_x71)))))))mark#(incr(head(head(pairs)))) → a__incr#(a__head(head(pairs)))
mark#(incr(head(head(cons(cons(incr(head(tail(cons(_x101, _x102)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(cons(mark(_x101), _x102)))), _x62), _x52))))mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(head(a__nats))
mark#(incr(incr(incr(tail(head(s(s(incr(head(tail(_x111))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(a__tail(mark(_x111)))))))))))mark#(incr(incr(incr(tail(pairs))))) → a__incr#(a__incr(a__incr(a__tail(a__pairs))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(cons(0, incr(odds))), _x62), _x52))))mark#(incr(incr(incr(tail(incr(_x61)))))) → a__incr#(a__incr(a__incr(a__tail(a__incr(mark(_x61))))))
mark#(incr(head(head(cons(cons(head(_x71), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__head(mark(_x71)), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(head(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__head(mark(_x91)))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(cons(_x81, _x82)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(cons(mark(_x81), _x82)))))))mark#(incr(head(head(cons(cons(incr(head(pairs)), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(a__pairs)), _x62))))
mark#(incr(head(s(nats)))) → a__incr#(head(s(nats)))mark#(incr(head(s(head(nil))))) → a__incr#(head(s(a__head(nil))))
mark#(incr(head(s(head(odds))))) → a__incr#(a__head(s(a__head(a__odds))))mark#(incr(head(head(cons(cons(incr(head(tail(head(tail(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(a__tail(mark(_x111)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(incr(tail(a__head(cons(0, incr(nats)))))))mark#(incr(head(head(cons(cons(incr(head(tail(nil))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(nil))), _x62), _x52))))
mark#(incr(incr(incr(tail(s(head(_x71))))))) → a__incr#(a__incr(a__incr(tail(s(a__head(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(mark(_x81))), _x62))))
mark#(incr(incr(incr(tail(head(s(incr(_x81)))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__incr(mark(_x81))))))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(a__odds))))))
mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(incr(incr(tail(a__head(head(nil))))))mark#(incr(incr(incr(tail(head(s(s(incr(cons(_x101, _x102)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(cons(mark(_x101), _x102)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(tail(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(a__tail(mark(_x111)))))), _x62), _x52))))mark#(incr(incr(incr(tail(s(odds)))))) → a__incr#(a__incr(a__incr(tail(s(a__odds)))))
mark#(incr(head(head(cons(cons(incr(head(incr(0))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(0))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(0))))))) → a__incr#(a__incr(incr(tail(a__head(s(0))))))
mark#(incr(head(head(cons(cons(incr(head(nats)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__nats)), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(tail(_x81)))))))) → a__incr#(incr(incr(tail(a__head(s(a__tail(mark(_x81))))))))
mark#(incr(head(head(cons(cons(0, _x62), _x31))))) → a__incr#(a__head(mark(cons(0, _x62))))mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(mark(_x71)))))))
mark#(incr(incr(incr(tail(s(cons(_x71, _x72))))))) → a__incr#(a__incr(a__incr(a__tail(s(cons(mark(_x71), _x72))))))mark#(incr(head(s(head(s(cons(_x71, _x72))))))) → a__incr#(a__head(s(a__head(s(cons(mark(_x71), _x72))))))
mark#(incr(head(head(cons(cons(incr(head(pairs)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__pairs)), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(pairs))))))) → a__incr#(incr(incr(tail(a__head(s(a__pairs))))))
mark#(cons(X1, X2)) → mark#(X1)mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(incr(a__pairs)))))))
mark#(incr(head(head(cons(cons(incr(head(0)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(0)), _x62), _x52))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(a__tail(head(cons(0, incr(nats)))))))
mark#(incr(head(s(head(s(pairs)))))) → a__incr#(a__head(s(a__head(s(a__pairs)))))mark#(incr(incr(incr(tail(head(s(s(incr(s(_x101)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(s(mark(_x101))))))))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(incr(a__tail(head(cons(0, incr(nats)))))))mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(a__incr(a__incr(tail(head(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(a__head(head(cons(cons(a__incr(a__pairs), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(nil), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(nil), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(odds))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__odds))))))mark#(incr(head(head(cons(cons(incr(head(tail(nil))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(nil))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(odds))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__odds))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nil)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(nil)))), _x62), _x52))))
mark#(incr(incr(incr(tail(s(incr(_x71))))))) → a__incr#(a__incr(a__incr(tail(s(a__incr(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x52))))) → a__incr#(head(head(cons(cons(a__incr(a__head(mark(_x81))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(tail(_x81)))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__tail(mark(_x81))))))))mark#(incr(head(head(cons(cons(incr(s(_x81)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(s(mark(_x81))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(nats))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__nats))))))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(a__tail(a__head(a__nats)))))
mark#(incr(head(head(cons(cons(incr(head(nats)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(cons(0, incr(nats)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__tail(mark(_x91)))), _x62), _x52))))
mark#(incr(incr(incr(tail(nats))))) → a__incr#(a__incr(a__incr(a__tail(a__nats))))mark#(incr(head(s(tail(incr(odds)))))) → a__incr#(a__head(s(a__tail(a__incr(a__odds)))))
mark#(incr(incr(incr(tail(nil))))) → a__incr#(incr(a__incr(a__tail(nil))))mark#(incr(incr(incr(tail(head(s(s(incr(0))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(0))))))))
mark#(incr(head(head(cons(cons(incr(head(incr(nil))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(nil))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(s(_x101)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(s(mark(_x101))))))))))
mark#(incr(head(s(tail(tail(_x61)))))) → a__incr#(a__head(s(tail(a__tail(mark(_x61))))))mark#(incr(odds)) → a__incr#(cons(s(mark(0)), incr(incr(odds))))
mark#(incr(head(s(tail(nats))))) → a__incr#(head(s(a__tail(nats))))mark#(incr(incr(incr(tail(head(nil)))))) → a__incr#(a__incr(a__incr(tail(a__head(nil)))))
mark#(incr(head(head(cons(cons(incr(head(tail(incr(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__incr(mark(_x101))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(head(a__odds))))))
mark#(incr(head(s(tail(nats))))) → a__incr#(head(s(tail(a__nats))))mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__odds)), _x62), _x52))))
mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(head(s(cons(mark(_x51), _x52))))mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(head(head(cons(nats, _x52))))
mark#(incr(head(odds))) → a__incr#(a__head(a__odds))mark#(incr(incr(incr(tail(head(s(s(nil)))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(nil)))))))
mark#(incr(incr(incr(tail(head(s(cons(_x81, _x82)))))))) → a__incr#(a__incr(incr(tail(a__head(s(cons(mark(_x81), _x82)))))))mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))
mark#(incr(head(s(tail(incr(incr(s(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(s(mark(_x81))))))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(incr(a__tail(a__head(cons(0, incr(nats)))))))
mark#(incr(head(head(incr(_x51))))) → a__incr#(a__head(a__head(a__incr(mark(_x51)))))mark#(incr(head(s(tail(incr(incr(nil))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(nil))))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(nats)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(head(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(a__head(mark(_x111)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(incr(_x81)), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(a__incr(mark(_x81))), _x62), _x52))))mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))
mark#(incr(head(head(cons(cons(_x61, _x62), _x52))))) → a__incr#(a__head(head(cons(cons(mark(_x61), _x62), _x52))))mark#(incr(head(s(tail(incr(incr(0))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(0))))))
mark#(incr(incr(incr(tail(0))))) → a__incr#(a__incr(a__incr(a__tail(0))))mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(mark(_x101))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(a__tail(a__head(mark(_x101))))), _x62))))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(incr(incr(tail(head(a__head(nil))))))
mark#(incr(head(head(cons(cons(incr(head(head(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__head(mark(_x91)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(mark(_x91)))), _x62), _x52))))
mark#(incr(head(head(pairs)))) → a__incr#(a__head(a__head(cons(0, incr(odds)))))mark#(incr(incr(incr(tail(head(pairs)))))) → a__incr#(a__incr(incr(tail(a__head(a__pairs)))))
mark#(incr(incr(incr(tail(head(s(s(0)))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(0)))))))mark#(incr(head(s(tail(incr(0)))))) → a__incr#(head(s(tail(a__incr(0)))))
mark#(incr(head(head(head(_x51))))) → a__incr#(a__head(head(a__head(mark(_x51)))))mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__head(a__odds)))))))))
mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(a__head(s(a__tail(incr(mark(_x61))))))mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(a__head(nats))
mark#(incr(head(head(cons(odds, _x52))))) → a__incr#(head(a__head(cons(a__odds, _x52))))mark#(incr(head(head(cons(cons(incr(0), _x32), incr(0)))))) → a__incr#(a__head(cons(mark(incr(0)), _x32)))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(tail(mark(0)))))mark#(incr(incr(incr(tail(head(s(s(incr(_x91))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(mark(_x91)))))))))
mark#(incr(head(s(head(0))))) → a__incr#(head(s(a__head(0))))mark#(incr(incr(incr(tail(s(tail(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(s(a__tail(mark(_x71)))))))
mark#(incr(head(s(odds)))) → a__incr#(head(s(a__odds)))mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))
mark#(incr(head(s(tail(odds))))) → a__incr#(a__head(s(a__tail(a__odds))))mark#(incr(incr(incr(tail(head(s(s(incr(head(nil)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(head(nil)))))))))
mark#(incr(incr(incr(tail(head(s(0))))))) → a__incr#(incr(incr(tail(a__head(s(0))))))mark#(incr(head(s(tail(incr(odds)))))) → a__incr#(head(s(a__tail(a__incr(a__odds)))))
mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(mark(_x71)))))))mark#(incr(head(s(head(s(head(_x71))))))) → a__incr#(a__head(s(a__head(s(a__head(mark(_x71)))))))
mark#(incr(head(s(tail(incr(tail(_x71))))))) → a__incr#(head(s(a__tail(a__incr(a__tail(mark(_x71)))))))mark#(incr(head(head(0)))) → a__incr#(a__head(head(0)))
mark#(incr(incr(incr(tail(head(s(s(pairs)))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(pairs)))))))mark#(incr(head(s(tail(incr(incr(tail(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(a__tail(mark(_x81))))))))
mark#(incr(head(s(0)))) → a__incr#(head(s(0)))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(tail(head(a__nats)))))
mark#(incr(head(head(cons(cons(incr(head(0)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(0)), _x62), _x52))))mark#(incr(head(head(tail(_x51))))) → a__incr#(a__head(a__head(a__tail(mark(_x51)))))
mark#(incr(incr(odds))) → a__incr#(a__incr(a__odds))mark#(incr(head(head(cons(tail(_x61), _x52))))) → a__incr#(a__head(a__head(cons(a__tail(mark(_x61)), _x52))))
mark#(incr(head(head(cons(cons(incr(s(_x81)), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(s(mark(_x81))), _x62), _x52))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(tail(a__head(a__nats)))))
mark#(incr(head(s(head(incr(odds)))))) → a__incr#(head(s(a__head(a__incr(a__odds)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(pairs)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(a__pairs)))), _x62), _x52))))
mark#(incr(head(s(head(s(tail(_x71))))))) → a__incr#(a__head(s(a__head(s(a__tail(mark(_x71)))))))mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))
mark#(incr(head(head(cons(s(_x61), _x52))))) → a__incr#(a__head(a__head(cons(s(mark(_x61)), _x52))))mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(incr(incr(tail(a__head(mark(_x61))))))
mark#(incr(incr(incr(tail(head(tail(_x71))))))) → a__incr#(a__incr(incr(tail(a__head(a__tail(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(odds), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(a__odds), _x62), _x52))))
mark#(incr(incr(nats))) → a__incr#(a__incr(cons(0, incr(nats))))mark#(incr(incr(incr(tail(head(s(s(incr(head(pairs)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(a__pairs)))))))))
mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(a__head(head(cons(cons(0, incr(nats)), _x52))))mark#(incr(odds)) → a__incr#(incr(cons(0, incr(odds))))
mark#(incr(incr(incr(tail(s(_x61)))))) → a__incr#(incr(a__incr(tail(s(mark(_x61))))))mark#(incr(incr(incr(tail(s(0)))))) → a__incr#(a__incr(a__incr(tail(s(0)))))
mark#(incr(head(s(tail(incr(s(_x71))))))) → a__incr#(head(s(a__tail(a__incr(s(mark(_x71)))))))mark#(incr(head(head(nats)))) → a__incr#(a__head(a__head(a__nats)))
mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(head(a__head(cons(a__nats, _x52))))mark#(incr(incr(incr(tail(head(head(pairs))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__pairs))))))
mark#(incr(head(s(tail(nil))))) → a__incr#(head(s(a__tail(nil))))mark#(incr(head(head(cons(cons(incr(head(incr(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(head(a__incr(mark(_x91)))), _x62), _x52))))
mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(head(s(head(a__incr(mark(_x61))))))mark#(incr(head(s(tail(incr(incr(_x71))))))) → a__incr#(head(s(a__tail(a__incr(a__incr(mark(_x71)))))))
mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(head(odds)))))))))
mark#(incr(head(s(head(pairs))))) → a__incr#(a__head(s(a__head(a__pairs))))mark#(incr(incr(incr(tail(head(s(odds))))))) → a__incr#(incr(incr(tail(a__head(s(a__incr(a__pairs)))))))
mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(tail(mark(_x51)))))mark#(incr(incr(incr(tail(head(head(head(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__head(mark(_x81))))))))
mark#(incr(incr(incr(tail(s(head(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(s(a__head(mark(_x71)))))))mark#(incr(head(head(cons(cons(tail(_x71), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__tail(mark(_x71)), _x62), _x52))))
mark#(incr(head(s(tail(tail(_x61)))))) → a__incr#(head(s(a__tail(a__tail(mark(_x61))))))mark#(incr(incr(incr(tail(head(tail(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__tail(mark(_x71)))))))
mark#(incr(incr(incr(odds)))) → a__incr#(a__incr(a__incr(a__odds)))mark#(incr(head(head(cons(_x51, _x52))))) → a__incr#(head(a__head(cons(mark(_x51), _x52))))
mark#(incr(head(s(tail(pairs))))) → a__incr#(head(s(a__tail(a__pairs))))mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__head(odds)))))))))
mark#(incr(head(s(tail(incr(pairs)))))) → a__incr#(a__head(s(a__tail(a__incr(a__pairs)))))mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(a__head(odds)))))))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(a__head(odds)))))))))mark#(incr(head(s(head(head(_x61)))))) → a__incr#(head(s(a__head(a__head(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x31))))) → a__incr#(head(mark(cons(a__incr(a__pairs), _x62))))mark#(incr(incr(incr(tail(s(pairs)))))) → a__incr#(a__incr(a__incr(tail(s(a__pairs)))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(a__tail(a__head(a__nats)))))mark#(incr(incr(incr(tail(nil))))) → a__incr#(a__incr(incr(a__tail(nil))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(a__tail(head(nats)))))mark#(incr(head(head(cons(cons(incr(head(incr(tail(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(a__tail(mark(_x101))))), _x62), _x52))))
mark#(incr(head(head(cons(_x51, _x52))))) → a__incr#(a__head(head(cons(mark(_x51), _x52))))mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))
mark#(incr(incr(incr(tail(s(tail(_x71))))))) → a__incr#(a__incr(a__incr(tail(s(a__tail(mark(_x71)))))))mark#(incr(head(head(odds)))) → a__incr#(a__head(head(a__odds)))
mark#(incr(incr(incr(tail(s(odds)))))) → a__incr#(a__incr(a__incr(a__tail(s(a__odds)))))mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(a__incr(a__incr(a__tail(head(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(incr(incr(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(a__incr(mark(_x101))))), _x62), _x52))))mark#(incr(incr(incr(tail(s(nil)))))) → a__incr#(incr(a__incr(a__tail(s(nil)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(cons(_x111, _x112))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(cons(mark(_x111), _x112))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(cons(_x91, _x92))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(cons(mark(_x91), _x92))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(nil))))))mark#(incr(incr(incr(tail(s(_x61)))))) → a__incr#(incr(a__incr(a__tail(s(mark(_x61))))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__incr(a__pairs)))))))mark#(incr(incr(incr(tail(head(s(s(incr(odds))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(odds))))))))
mark#(incr(incr(incr(tail(head(s(s(incr(pairs))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__pairs))))))))mark#(incr(incr(incr(tail(s(s(_x71))))))) → a__incr#(a__incr(a__incr(tail(s(s(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(0)))), _x62), _x52))))mark#(incr(incr(incr(tail(s(cons(_x71, _x72))))))) → a__incr#(a__incr(a__incr(tail(s(cons(mark(_x71), _x72))))))
mark#(incr(head(s(tail(incr(incr(pairs))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(a__pairs))))))mark#(incr(incr(incr(tail(head(s(s(incr(head(cons(_x111, _x112))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(cons(mark(_x111), _x112))))))))))
mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(a__incr(tail(a__head(head(nil))))))mark#(incr(head(s(head(s(nats)))))) → a__incr#(a__head(s(a__head(s(a__nats)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nil)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(nil)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(incr(cons(_x101, _x102)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(cons(mark(_x101), _x102)))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(_x101)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(head(mark(_x101))))))))))mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))
mark#(incr(head(s(head(s(odds)))))) → a__incr#(a__head(s(a__head(s(a__odds)))))mark#(incr(head(odds))) → a__incr#(head(odds))
mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(head(mark(_x71)))))))mark#(incr(incr(incr(tail(head(head(incr(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(a__incr(mark(_x81))))))))
mark#(incr(head(s(odds)))) → a__incr#(a__head(s(odds)))mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(incr(a__tail(a__head(a__head(mark(_x71)))))))
mark#(incr(head(nats))) → a__incr#(a__head(cons(0, incr(nats))))mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(a__head(mark(_x81))), _x62), _x52))))
mark#(incr(incr(incr(pairs)))) → a__incr#(a__incr(a__incr(a__pairs)))mark#(incr(head(head(cons(cons(incr(nil), _x62), _x52))))) → a__incr#(a__head(head(cons(cons(a__incr(nil), _x62), _x52))))
mark#(incr(head(tail(_x41)))) → a__incr#(head(a__tail(mark(_x41))))mark#(incr(incr(incr(tail(head(s(s(incr(head(nil)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__head(nil)))))))))
mark#(incr(head(head(cons(pairs, _x52))))) → a__incr#(a__head(a__head(cons(a__pairs, _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(a__incr(mark(_x111)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(_x51))))) → a__incr#(incr(a__incr(a__tail(mark(_x51)))))mark#(incr(head(s(pairs)))) → a__incr#(a__head(s(pairs)))
mark#(incr(incr(incr(tail(head(head(nats))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__nats))))))mark#(incr(incr(incr(tail(head(s(s(pairs)))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__pairs)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(pairs))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__pairs))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(a__head(a__odds)))))))))
mark#(incr(incr(incr(tail(head(s(s(pairs)))))))) → a__incr#(a__incr(incr(tail(head(s(s(cons(0, incr(odds)))))))))mark#(incr(head(head(cons(cons(incr(nil), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(nil), _x62))))
mark#(incr(head(head(_x41)))) → a__incr#(head(head(mark(_x41))))mark#(incr(head(pairs))) → a__incr#(head(a__pairs))
mark#(incr(head(s(tail(head(_x61)))))) → a__incr#(a__head(s(a__tail(a__head(mark(_x61))))))mark#(incr(incr(incr(tail(head(s(s(incr(_x91))))))))) → a__incr#(a__incr(incr(tail(head(s(s(incr(mark(_x91)))))))))
mark#(incr(incr(incr(tail(head(0)))))) → a__incr#(a__incr(incr(tail(a__head(0)))))mark#(incr(incr(incr(tail(head(s(s(head(_x91))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__head(mark(_x91)))))))))
mark#(incr(head(s(tail(pairs))))) → a__incr#(a__head(s(tail(cons(0, incr(odds))))))mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(a__incr(tail(a__head(head(mark(_x71)))))))
mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(nil))))))mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(nil)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(nil)), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(_x91))))))))) → a__incr#(incr(incr(tail(head(s(s(a__incr(mark(_x91)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(pairs)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(a__pairs)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(s(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(s(mark(_x101))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(0))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(0))), _x62), _x52))))mark#(incr(head(s(tail(0))))) → a__incr#(head(s(a__tail(0))))
mark#(incr(incr(incr(tail(s(incr(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(s(a__incr(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(incr(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(incr(mark(_x91)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(a__incr(mark(_x111)))))), _x62), _x52))))mark#(incr(head(s(head(s(incr(_x71))))))) → a__incr#(a__head(s(a__head(s(a__incr(mark(_x71)))))))
mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(mark(0))
mark#(incr(head(s(head(incr(head(_x71))))))) → a__incr#(head(s(a__head(a__incr(a__head(mark(_x71)))))))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(nil))))))
mark#(incr(head(head(pairs)))) → a__incr#(a__head(a__head(pairs)))mark#(incr(head(nats))) → a__incr#(head(a__nats))
mark#(incr(incr(incr(tail(head(pairs)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__pairs)))))mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(head(s(mark(_x61))))))
mark#(incr(head(s(tail(_x51))))) → a__incr#(head(s(a__tail(mark(_x51)))))mark#(incr(head(head(head(_x51))))) → a__incr#(a__head(a__head(a__head(mark(_x51)))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(incr(tail(head(a__head(a__odds))))))mark#(incr(head(head(cons(cons(nil, _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(nil, _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(odds))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(a__pairs)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(a__nats)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(cons(_x81, _x82)), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(cons(mark(_x81), _x82)), _x62), _x52))))mark#(incr(incr(incr(tail(head(incr(_x71))))))) → a__incr#(a__incr(incr(tail(a__head(a__incr(mark(_x71)))))))
mark#(incr(incr(incr(tail(head(s(s(incr(nil))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(nil))))))))a__incr#(cons(X, XS)) → mark#(X)
mark#(incr(incr(incr(tail(head(s(s(incr(head(nil)))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(a__head(nil)))))))))mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))
mark#(incr(head(s(odds)))) → a__incr#(a__head(s(a__incr(a__pairs))))mark#(incr(head(s(head(incr(nil)))))) → a__incr#(head(s(a__head(a__incr(nil)))))
mark#(incr(incr(incr(tail(head(s(head(_x81)))))))) → a__incr#(incr(incr(tail(a__head(s(a__head(mark(_x81))))))))mark#(incr(head(head(s(_x51))))) → a__incr#(a__head(a__head(s(mark(_x51)))))
mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(head(mark(nats)))
mark#(incr(head(head(cons(cons(incr(head(tail(odds))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__odds))), _x62), _x52))))mark#(incr(head(s(head(s(nil)))))) → a__incr#(a__head(s(a__head(s(nil)))))
mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))mark#(incr(head(head(cons(cons(_x61, _x62), _x31))))) → a__incr#(a__head(mark(cons(mark(_x61), _x62))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(nats)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(a__nats)))))))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(a__odds))))))
mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))mark#(incr(head(head(cons(cons(0, _x62), _x52))))) → a__incr#(head(a__head(cons(cons(0, _x62), _x52))))
mark#(incr(head(head(_x41)))) → a__incr#(head(a__head(mark(_x41))))mark#(incr(incr(incr(tail(head(s(incr(_x81)))))))) → a__incr#(incr(incr(tail(a__head(s(a__incr(mark(_x81))))))))
mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(tail(head(cons(0, incr(nats)))))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(nil)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(a__head(nil)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(mark(_x91)))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(tail(mark(0)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(a__head(mark(_x101))))), _x62), _x52))))
mark#(incr(pairs)) → a__incr#(a__pairs)mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(a__tail(mark(_x91)))), _x62))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(head(head(cons(cons(a__incr(a__pairs), _x62), _x52))))mark#(incr(head(s(pairs)))) → a__incr#(head(s(cons(0, incr(odds)))))
mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(nil))))))mark#(incr(head(s(tail(pairs))))) → a__incr#(a__head(s(tail(a__pairs))))
mark#(incr(incr(incr(tail(head(incr(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__incr(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(mark(_x101))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(cons(_x91, _x92))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(cons(mark(_x91), _x92))), _x62), _x52))))mark#(incr(head(s(tail(cons(_x61, _x62)))))) → a__incr#(a__head(s(tail(cons(mark(_x61), _x62)))))
mark#(incr(incr(incr(tail(head(head(pairs))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(a__pairs))))))mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(a__head(s(tail(a__incr(mark(_x61))))))
mark#(incr(head(head(nil)))) → a__incr#(head(a__head(nil)))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__incr(cons(0, incr(odds)))))))))
mark#(incr(head(s(tail(incr(nats)))))) → a__incr#(head(s(a__tail(a__incr(a__nats)))))mark#(incr(incr(incr(tail(head(s(s(cons(_x91, _x92))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(cons(mark(_x91), _x92))))))))
mark#(incr(incr(incr(tail(head(head(s(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(s(mark(_x81))))))))mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))
mark#(incr(incr(incr(tail(head(head(0))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(0))))))mark#(incr(head(head(incr(_x51))))) → a__incr#(a__head(head(a__incr(mark(_x51)))))
mark#(incr(head(s(tail(incr(tail(_x71))))))) → a__incr#(a__head(s(a__tail(a__incr(a__tail(mark(_x71)))))))mark#(incr(incr(incr(tail(head(s(s(incr(head(s(_x111))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(s(mark(_x111)))))))))))
mark#(incr(head(s(head(s(s(_x71))))))) → a__incr#(a__head(s(a__head(s(s(mark(_x71)))))))mark#(incr(head(s(head(incr(0)))))) → a__incr#(head(s(a__head(a__incr(0)))))
mark#(incr(head(head(cons(odds, _x31))))) → a__incr#(a__head(mark(a__odds)))mark#(incr(head(head(cons(cons(incr(head(nil)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(nil)), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(0), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(0), _x62), _x52))))mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(incr(a__incr(a__tail(a__head(mark(_x61))))))
mark#(incr(head(head(odds)))) → a__incr#(a__head(a__head(a__odds)))mark#(incr(head(head(nats)))) → a__incr#(a__head(head(a__nats)))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(a__incr(a__pairs)))))))mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(incr(a__tail(mark(_x51)))))
mark#(incr(incr(incr(tail(head(s(s(incr(odds))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__odds))))))))mark#(incr(incr(0))) → a__incr#(a__incr(0))
mark#(incr(incr(incr(tail(head(0)))))) → a__incr#(incr(a__incr(tail(a__head(0)))))mark#(incr(incr(incr(tail(s(0)))))) → a__incr#(a__incr(a__incr(a__tail(s(0)))))
mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(head(cons(0, incr(nats))))mark#(incr(head(s(tail(pairs))))) → a__incr#(head(s(a__tail(cons(0, incr(odds))))))
mark#(incr(incr(incr(tail(head(s(s(tail(_x91))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__tail(mark(_x91)))))))))mark#(incr(incr(incr(tail(head(s(s(incr(head(_x101)))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(a__head(mark(_x101))))))))))
mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(mark(_x81))), _x62), _x52))))mark#(incr(head(s(tail(head(_x61)))))) → a__incr#(a__head(s(tail(a__head(mark(_x61))))))
mark#(incr(head(s(head(incr(s(_x71))))))) → a__incr#(head(s(a__head(a__incr(s(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(head(mark(_x81))), _x62), _x52))))
mark#(incr(head(s(tail(_x51))))) → a__incr#(head(s(tail(mark(_x51)))))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__pairs), _x62), _x52))))
mark#(incr(head(s(head(s(_x61)))))) → a__incr#(head(s(a__head(s(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(cons(_x81, _x82)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(cons(mark(_x81), _x82)), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(tail(_x101)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__tail(mark(_x101))))))))))mark#(incr(incr(incr(tail(head(s(s(nats)))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__nats)))))))
mark#(incr(head(s(tail(incr(nil)))))) → a__incr#(head(s(a__tail(a__incr(nil)))))mark#(incr(head(head(cons(cons(incr(head(tail(0))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(0))), _x62), _x52))))
mark#(incr(head(s(head(pairs))))) → a__incr#(head(s(a__head(a__pairs))))mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(incr(incr(tail(head(s(mark(_x71)))))))
mark#(incr(incr(incr(tail(head(nil)))))) → a__incr#(a__incr(incr(tail(a__head(nil)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(a__nats)))), _x62))))
mark#(incr(head(s(head(incr(incr(_x71))))))) → a__incr#(head(s(a__head(a__incr(a__incr(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(incr(pairs))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(a__pairs))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(_x101)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__head(mark(_x101))))))))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(odds))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(s(mark(_x111)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(incr(s(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(s(mark(_x101))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(incr(a__pairs), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(tail(_x101)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__tail(mark(_x101))))))))))
mark#(incr(incr(incr(tail(head(head(tail(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(a__tail(mark(_x81))))))))mark#(incr(head(head(cons(cons(incr(nil), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(incr(nil), _x62), _x52))))
mark#(incr(head(s(tail(incr(0)))))) → a__incr#(head(s(a__tail(incr(0)))))mark#(incr(incr(incr(tail(head(s(s(_x81)))))))) → a__incr#(a__incr(incr(tail(head(s(s(mark(_x81))))))))
mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(incr(tail(a__head(head(nil))))))mark#(incr(head(head(cons(cons(incr(head(incr(nats))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(a__nats))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(nats)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__nats)), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(_x81)))))))) → a__incr#(incr(incr(tail(a__head(s(s(mark(_x81))))))))
mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(head(s(a__tail(incr(mark(_x61))))))mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))
mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(incr(a__incr(a__tail(a__head(a__head(mark(_x71)))))))mark#(incr(incr(incr(tail(head(odds)))))) → a__incr#(a__incr(incr(tail(a__head(a__odds)))))
mark#(incr(incr(incr(tail(head(cons(_x71, _x72))))))) → a__incr#(a__incr(a__incr(tail(a__head(cons(mark(_x71), _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(0)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(nats)), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(a__nats)), _x62))))mark#(incr(incr(incr(tail(head(s(pairs))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__pairs))))))
mark#(incr(head(head(cons(cons(incr(0), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(0), _x62), _x52))))mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(a__head(mark(a__nats)))
mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))mark#(incr(head(pairs))) → a__incr#(a__head(a__pairs))
mark#(incr(head(head(cons(odds, _x52))))) → a__incr#(a__head(a__head(cons(odds, _x52))))mark#(incr(head(head(cons(_x51, _x31))))) → a__incr#(a__head(mark(mark(_x51))))
mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))mark#(incr(head(head(cons(cons(incr(odds), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__odds), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(pairs))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__pairs))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(0), _x62), _x52))))) → a__incr#(a__head(head(cons(cons(incr(0), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(incr(mark(_x71)), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(pairs))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__pairs))))))))
mark#(incr(incr(incr(tail(head(s(s(incr(odds))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(a__odds))))))))mark#(incr(head(s(tail(incr(nats)))))) → a__incr#(a__head(s(a__tail(a__incr(a__nats)))))
mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(a__incr(incr(tail(head(s(mark(_x71)))))))mark#(incr(head(s(head(incr(tail(_x71))))))) → a__incr#(head(s(a__head(a__incr(a__tail(mark(_x71)))))))
mark#(incr(head(s(pairs)))) → a__incr#(head(s(pairs)))mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))
mark#(incr(incr(incr(tail(head(s(nil))))))) → a__incr#(a__incr(incr(tail(a__head(s(nil))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(mark(_x101))))), _x62), _x52))))
mark#(incr(head(s(tail(incr(0)))))) → a__incr#(a__head(s(a__tail(a__incr(0)))))mark#(incr(incr(incr(tail(head(s(s(pairs)))))))) → a__incr#(incr(incr(tail(a__head(s(s(cons(0, incr(odds)))))))))
mark#(incr(head(s(incr(_x51))))) → a__incr#(head(s(a__incr(mark(_x51)))))mark#(incr(incr(incr(tail(head(head(head(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(a__head(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(tail(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__tail(mark(_x101))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(odds))))))) → a__incr#(incr(incr(tail(head(s(odds))))))
mark#(incr(incr(incr(tail(head(cons(_x71, _x72))))))) → a__incr#(a__incr(incr(tail(a__head(cons(mark(_x71), _x72))))))mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))
mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))mark#(incr(head(s(tail(incr(pairs)))))) → a__incr#(head(s(a__tail(a__incr(a__pairs)))))
mark#(incr(nats)) → a__incr#(a__nats)mark#(incr(head(nil))) → a__incr#(head(nil))
mark#(incr(incr(incr(tail(head(s(s(incr(head(incr(_x111))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(a__incr(mark(_x111)))))))))))mark#(incr(head(head(cons(cons(incr(head(incr(_x91))), _x62), _x31))))) → a__incr#(head(mark(cons(a__incr(a__head(a__incr(mark(_x91)))), _x62))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x31))))) → a__incr#(a__head(mark(cons(incr(a__pairs), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(head(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(a__head(mark(_x111)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(incr(a__incr(tail(a__head(mark(_x61))))))mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(a__incr(incr(tail(head(mark(_x61))))))
mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(head(mark(_x51)))))mark#(incr(incr(incr(tail(tail(_x61)))))) → a__incr#(a__incr(a__incr(a__tail(a__tail(mark(_x61))))))
mark#(incr(head(incr(_x41)))) → a__incr#(head(a__incr(mark(_x41))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(a__tail(mark(0)))))
mark#(incr(X)) → mark#(X)mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(a__incr(a__incr(tail(a__head(s(mark(_x71)))))))
mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(head(s(a__head(cons(mark(_x61), _x62)))))mark#(incr(head(s(tail(nats))))) → a__incr#(head(s(mark(incr(nats)))))
mark#(incr(incr(incr(tail(head(0)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(0)))))mark#(incr(incr(incr(tail(head(s(s(incr(head(0)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(0)))))))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(a__tail(head(a__nats)))))mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))
mark#(incr(head(s(head(nats))))) → a__incr#(head(s(a__head(a__nats))))mark#(incr(incr(incr(tail(head(s(s(incr(odds))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(a__odds))))))))
mark#(incr(incr(incr(tail(odds))))) → a__incr#(a__incr(a__incr(a__tail(a__odds))))mark#(incr(incr(incr(tail(nil))))) → a__incr#(a__incr(a__incr(tail(nil))))
mark#(incr(head(head(0)))) → a__incr#(head(head(0)))mark#(incr(head(s(tail(incr(incr(head(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(a__head(mark(_x81))))))))
mark#(incr(head(head(cons(odds, _x52))))) → a__incr#(a__head(a__head(cons(a__incr(a__pairs), _x52))))mark#(incr(incr(incr(tail(head(tail(_x71))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__tail(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(0), _x62), _x52))))) → a__incr#(a__head(head(cons(cons(a__incr(0), _x62), _x52))))mark#(incr(incr(incr(tail(s(nil)))))) → a__incr#(incr(incr(a__tail(s(nil)))))
mark#(incr(head(head(cons(cons(incr(head(incr(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__incr(mark(_x91)))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(head(head(_x111))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(a__head(mark(_x111)))))))))))
mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(head(s(a__head(incr(mark(_x61))))))mark#(incr(incr(incr(tail(head(cons(_x71, _x72))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(cons(mark(_x71), _x72))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(odds)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(a__odds)))), _x62), _x52))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(tail(head(cons(0, incr(nats)))))))
mark#(incr(incr(incr(tail(s(s(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(s(s(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(pairs), _x62), _x52))))
mark#(incr(head(s(tail(incr(incr(odds))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(a__odds))))))mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(mark(_x91)))), _x62), _x52))))
mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))mark#(incr(incr(incr(tail(head(s(s(pairs)))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__pairs)))))))
mark#(incr(head(0))) → a__incr#(head(0))mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(head(a__odds)))))))))
mark#(incr(incr(incr(tail(s(nats)))))) → a__incr#(a__incr(a__incr(tail(s(a__nats)))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(a__tail(head(cons(0, incr(nats)))))))
mark#(incr(head(head(pairs)))) → a__incr#(head(head(cons(0, incr(odds)))))mark#(incr(head(head(cons(cons(incr(head(s(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(s(mark(_x91)))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(incr(a__incr(tail(a__head(head(nil))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(cons(_x111, _x112))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(cons(mark(_x111), _x112))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(_x91))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(mark(_x91)))))))))mark#(incr(head(s(tail(incr(incr(_x71))))))) → a__incr#(a__head(s(tail(a__incr(a__incr(mark(_x71)))))))
mark#(incr(head(head(pairs)))) → a__incr#(head(a__head(a__pairs)))mark#(incr(head(s(head(s(0)))))) → a__incr#(a__head(s(a__head(s(0)))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(a__incr(a__pairs)))))))mark#(incr(head(head(s(_x51))))) → a__incr#(a__head(head(s(mark(_x51)))))
mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__odds)), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(tail(_x81)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__tail(mark(_x81))), _x62), _x52))))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(head(s(tail(incr(cons(_x71, _x72))))))) → a__incr#(head(s(a__tail(a__incr(cons(mark(_x71), _x72))))))
mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x31))))) → a__incr#(head(mark(cons(a__incr(a__head(mark(_x81))), _x62))))mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(head(head(cons(a__nats, _x52))))
mark#(incr(head(s(tail(pairs))))) → a__incr#(a__head(s(mark(incr(odds)))))mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(head(0))))
mark#(incr(incr(incr(tail(head(pairs)))))) → a__incr#(a__incr(a__incr(tail(a__head(a__pairs)))))mark#(incr(head(head(cons(cons(incr(head(nats)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__nats)), _x62), _x52))))
mark#(incr(head(s(tail(nil))))) → a__incr#(a__head(s(a__tail(nil))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(incr(tail(a__head(a__head(a__odds))))))
mark#(incr(head(head(cons(cons(incr(head(pairs)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__pairs)), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(incr(_x81)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__incr(mark(_x81))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(head(_x81)))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__head(mark(_x81))))))))mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__nats))))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(pairs), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(incr(incr(tail(a__head(s(a__nats))))))
mark#(incr(head(s(head(odds))))) → a__incr#(head(s(a__head(a__odds))))mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(mark(_x101))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(a__tail(mark(0)))))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(a__incr(tail(head(head(nil))))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(odds))))))mark#(incr(incr(incr(tail(head(s(s(incr(nil))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(nil))))))))
mark#(incr(head(head(cons(cons(incr(head(pairs)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__pairs)), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(0), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(0), _x62))))
mark#(incr(incr(incr(tail(head(s(s(incr(nats))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__nats))))))))mark#(incr(head(odds))) → a__incr#(head(a__incr(a__pairs)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(a__nats)))), _x62), _x52))))mark#(incr(incr(incr(tail(s(_x61)))))) → a__incr#(a__incr(incr(tail(s(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(nats)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(nats)), _x62), _x52))))mark#(incr(incr(nats))) → a__incr#(incr(cons(0, incr(nats))))
mark#(incr(incr(nats))) → a__incr#(incr(nats))mark#(incr(head(s(tail(incr(nil)))))) → a__incr#(a__head(s(a__tail(a__incr(nil)))))
mark#(incr(head(s(tail(tail(_x61)))))) → a__incr#(a__head(s(a__tail(a__tail(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__tail(mark(_x91)))), _x62), _x52))))
mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(head(s(tail(a__incr(mark(_x61))))))
mark#(incr(head(head(cons(cons(_x61, _x62), _x52))))) → a__incr#(head(a__head(cons(cons(mark(_x61), _x62), _x52))))mark#(incr(head(s(tail(incr(s(_x71))))))) → a__incr#(a__head(s(a__tail(a__incr(s(mark(_x71)))))))
mark#(incr(incr(incr(tail(s(pairs)))))) → a__incr#(a__incr(a__incr(a__tail(s(a__pairs)))))mark#(incr(head(head(cons(cons(incr(head(tail(s(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(s(mark(_x101))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(odds)))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__odds)))))))mark#(incr(head(head(cons(nil, _x52))))) → a__incr#(a__head(a__head(cons(nil, _x52))))
mark#(incr(head(head(cons(cons(nats, _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__nats, _x62), _x52))))mark#(incr(incr(incr(tail(head(head(0))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(0))))))
mark#(incr(incr(incr(tail(cons(_x61, _x62)))))) → a__incr#(a__incr(a__incr(a__tail(cons(mark(_x61), _x62)))))mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))
mark#(incr(head(s(tail(incr(incr(incr(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(a__incr(mark(_x81))))))))mark#(incr(incr(incr(tail(s(nats)))))) → a__incr#(a__incr(a__incr(a__tail(s(a__nats)))))
mark#(incr(head(s(tail(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__tail(cons(mark(_x61), _x62)))))mark#(incr(incr(incr(tail(head(s(nil))))))) → a__incr#(incr(incr(tail(a__head(s(nil))))))
mark#(incr(head(s(tail(incr(incr(_x71))))))) → a__incr#(a__head(s(a__tail(a__incr(incr(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(pairs), _x32), a__incr(a__pairs)))))) → a__incr#(a__head(cons(mark(a__incr(a__pairs)), _x32)))
mark#(incr(incr(incr(tail(head(head(cons(_x81, _x82)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(cons(mark(_x81), _x82)))))))mark#(incr(head(s(tail(s(_x61)))))) → a__incr#(head(s(a__tail(s(mark(_x61))))))
mark#(incr(head(s(tail(0))))) → a__incr#(a__head(s(a__tail(0))))mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x31))))) → a__incr#(head(mark(cons(a__incr(mark(_x71)), _x62))))
mark#(incr(incr(incr(tail(head(s(s(incr(0))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(0))))))))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(cons(0, incr(odds))), _x62), _x52))))
mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))mark#(incr(head(head(cons(cons(incr(head(incr(_x91))), _x62), _x52))))) → a__incr#(head(head(cons(cons(a__incr(a__head(a__incr(mark(_x91)))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(head(a__incr(a__pairs)))))))mark#(incr(head(head(cons(cons(cons(_x71, _x72), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(cons(mark(_x71), _x72), _x62), _x52))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(tail(a__head(a__nats)))))mark#(incr(head(s(tail(pairs))))) → a__incr#(head(s(a__tail(pairs))))

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, head, a__head, nil, cons

Strategy

The right-hand side of the rule mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(mark(_x111)))))), _x62), _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
a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__nats))))), _x62), _x52)))) 
a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(cons(mark(_x121), _x122)))))), _x62), _x52)))) 
a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__tail(mark(_x121))))))), _x62), _x52)))) 
a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__incr(mark(_x121))))))), _x62), _x52)))) 
a__incr#(head(mark(cons(incr(head(a__tail(a__head(s(mark(_x111)))))), _x62)))) 
a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(mark(_x111)))))), _x62), _x52)))) 
a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(nil))))), _x62), _x52)))) 
a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(mark(_x111)))))), _x62), _x52)))) 
a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(0))))), _x62), _x52)))) 
a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(mark(_x121))))))), _x62), _x52)))) 
a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(s(mark(_x111)))))), _x62), _x52)))) 
a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__pairs))))), _x62), _x52)))) 
a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__head(mark(_x121))))))), _x62), _x52)))) 
a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__odds))))), _x62), _x52)))) 
Thus, the rule mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(mark(_x111)))))), _x62), _x52)))) is replaced by the following rules:
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(incr(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__incr(mark(_x121))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(0))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(0))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(pairs))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__pairs))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(head(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__head(mark(_x121))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(mark(_x121))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(tail(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__tail(mark(_x121))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(nats))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__nats))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(nil))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(nil))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(cons(_x121, _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(cons(mark(_x121), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(mark(_x111)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(s(mark(_x111)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(mark(_x111)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(odds))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__odds))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(s(mark(_x111)))))), _x62), _x52))))

Problem 30: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(_x131))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(mark(_x131)))))))), _x62), _x52))))mark#(s(X)) → mark#(X)
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(_x121)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(mark(_x121))))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(incr(a__pairs)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(nil))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(nil))))), _x62))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(_x101)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(mark(_x101))))))))))
mark#(incr(incr(incr(tail(head(head(s(nil)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(nil)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(_x121, _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(mark(_x121), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(incr(a__pairs))), _x62), _x52))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(a__tail(head(a__nats)))))
mark#(incr(head(s(tail(nats))))) → a__incr#(a__head(s(a__tail(a__nats))))mark#(incr(head(head(cons(head(_x61), _x52))))) → a__incr#(a__head(a__head(cons(a__head(mark(_x61)), _x52))))
mark#(incr(incr(incr(tail(head(head(nats))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(a__nats))))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(incr(_x111))))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(a__incr(mark(_x111)))))))))))
mark#(incr(head(s(tail(s(_x61)))))) → a__incr#(a__head(s(tail(s(mark(_x61))))))mark#(incr(head(head(cons(cons(pairs, _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__pairs, _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(nats))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__nats))), _x62), _x52))))mark#(incr(head(s(head(incr(nats)))))) → a__incr#(head(s(head(a__incr(a__nats)))))
mark#(incr(head(head(cons(cons(incr(0), _x62), _x31))))) → a__incr#(head(mark(cons(incr(0), _x62))))mark#(incr(head(s(s(_x51))))) → a__incr#(head(s(s(mark(_x51)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(_x131))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(mark(_x131)))))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(0))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(0))))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(a__tail(mark(0)))))mark#(incr(head(s(tail(nats))))) → a__incr#(a__head(s(tail(nats))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(tail(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__tail(mark(_x121))))))), _x62), _x52))))mark#(incr(head(s(tail(nil))))) → a__incr#(a__head(s(tail(nil))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(pairs)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__pairs)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(nil)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(nil)))))))))
mark#(incr(head(cons(_x41, _x42)))) → a__incr#(head(cons(mark(_x41), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(nats))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__nats))), _x62), _x52))))
mark#(incr(head(head(cons(incr(_x61), _x52))))) → a__incr#(a__head(a__head(cons(a__incr(mark(_x61)), _x52))))mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(a__incr(incr(a__tail(a__head(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(s(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(s(mark(_x91)))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(head(a__head(a__odds))))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(incr(tail(a__head(head(a__odds))))))mark#(incr(head(head(cons(cons(incr(head(pairs)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(pairs)), _x62), _x52))))
mark#(incr(head(s(head(incr(pairs)))))) → a__incr#(head(s(a__head(a__incr(a__pairs)))))mark#(incr(head(head(cons(cons(incr(head(pairs)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(cons(0, incr(odds)))), _x62), _x52))))
mark#(incr(head(s(tail(odds))))) → a__incr#(a__head(s(tail(a__odds))))mark#(incr(incr(incr(tail(head(head(tail(odds)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(a__odds)))))))
mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))mark#(incr(head(nats))) → a__incr#(a__head(nats))
mark#(incr(head(s(tail(incr(head(head(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(a__head(mark(_x81))))))))mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(mark(_x71)), _x62))))
mark#(incr(incr(incr(tail(head(odds)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__odds)))))mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x52))))) → a__incr#(a__head(head(cons(cons(a__incr(mark(_x71)), _x62), _x52))))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(nats))))))mark#(incr(incr(incr(tail(s(nil)))))) → a__incr#(a__incr(a__incr(tail(s(nil)))))
mark#(incr(head(head(cons(cons(incr(tail(_x81)), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(a__tail(mark(_x81))), _x62), _x52))))mark#(incr(head(s(tail(pairs))))) → a__incr#(a__head(s(tail(pairs))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(tail(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(a__tail(mark(_x121))))))), _x62), _x52))))mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(0)))), _x62))))mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(incr(a__incr(a__tail(a__head(s(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(cons(_x101, _x102)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(cons(mark(_x101), _x102)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__tail(head(mark(_x101))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(tail(_x111))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(a__tail(mark(_x111)))))))))))mark#(incr(head(s(tail(incr(head(s(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(s(mark(_x81))))))))
mark#(incr(incr(incr(tail(incr(_x61)))))) → a__incr#(a__incr(a__incr(a__tail(a__incr(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(cons(0, incr(odds))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(head(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__head(mark(_x91)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(pairs)), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(a__pairs)), _x62))))
mark#(incr(incr(incr(tail(head(head(cons(_x81, _x82)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(cons(mark(_x81), _x82)))))))mark#(incr(head(s(nats)))) → a__incr#(head(s(nats)))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(head(_x111))))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(a__head(mark(_x111)))))))))))mark#(incr(head(s(head(odds))))) → a__incr#(a__head(s(a__head(a__odds))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(incr(tail(a__head(cons(0, incr(nats)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(tail(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(a__tail(mark(_x111)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__nats)))), _x62), _x52))))mark#(incr(incr(incr(tail(s(head(_x71))))))) → a__incr#(a__incr(a__incr(tail(s(a__head(mark(_x71)))))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(a__odds))))))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(incr(incr(tail(a__head(head(nil))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(tail(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(a__tail(mark(_x111)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__tail(head(a__nats)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(incr(0))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(0))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(pairs))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(a__pairs))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(nats)))), _x62), _x52))))mark#(incr(head(head(cons(cons(0, _x62), _x31))))) → a__incr#(a__head(mark(cons(0, _x62))))
mark#(incr(head(head(cons(cons(incr(head(nats)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__nats)), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(0))))))) → a__incr#(a__incr(incr(tail(a__head(s(0))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(cons(0, incr(nats)))))), _x62), _x52))))mark#(incr(incr(incr(tail(s(cons(_x71, _x72))))))) → a__incr#(a__incr(a__incr(a__tail(s(cons(mark(_x71), _x72))))))
mark#(incr(head(s(tail(incr(cons(pairs, _x72))))))) → a__incr#(head(s(a__tail(a__incr(cons(pairs, _x72))))))mark#(incr(incr(incr(tail(head(incr(nats))))))) → a__incr#(a__incr(a__incr(tail(a__head(incr(a__nats))))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(incr(a__pairs)))))))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(a__tail(head(cons(0, incr(nats)))))))mark#(incr(incr(incr(tail(head(s(s(incr(s(_x101)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(s(mark(_x101))))))))))
mark#(incr(head(s(head(s(pairs)))))) → a__incr#(a__head(s(a__head(s(a__pairs)))))mark#(incr(head(s(head(incr(nats)))))) → a__incr#(head(s(a__head(incr(a__nats)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(mark(0)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(a__head(head(cons(cons(a__incr(a__pairs), _x62), _x52))))
mark#(incr(head(s(tail(incr(head(_x71))))))) → a__incr#(a__head(s(a__tail(incr(a__head(mark(_x71)))))))mark#(incr(head(s(tail(s(pairs)))))) → a__incr#(a__head(s(a__tail(s(a__pairs)))))
mark#(incr(head(head(cons(cons(incr(head(tail(odds))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__odds))), _x62), _x52))))mark#(incr(incr(incr(tail(s(incr(_x71))))))) → a__incr#(a__incr(a__incr(tail(s(a__incr(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x52))))) → a__incr#(head(head(cons(cons(a__incr(a__head(mark(_x81))), _x62), _x52))))mark#(incr(head(s(tail(incr(head(odds))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(a__odds))))))
mark#(incr(incr(incr(tail(head(s(s(incr(nats))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__nats))))))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(a__tail(a__head(a__nats)))))
mark#(incr(head(head(cons(cons(incr(head(nats)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(cons(0, incr(nats)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__tail(mark(_x91)))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(incr(a__tail(head(s(a__nats))))))mark#(incr(incr(incr(tail(nil))))) → a__incr#(incr(a__incr(a__tail(nil))))
mark#(incr(incr(incr(tail(head(s(s(incr(0))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(0))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(s(s(mark(_x121))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(incr(nil))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(nil))), _x62), _x52))))mark#(incr(incr(incr(tail(head(nil)))))) → a__incr#(a__incr(a__incr(tail(a__head(nil)))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(head(a__odds))))))mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(incr(incr(a__tail(a__head(s(a__nats))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(incr(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__incr(mark(_x121))))))), _x62), _x52))))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(head(s(cons(mark(_x51), _x52))))
mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(mark(_x81))), _x62), _x52))))mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(head(head(cons(nats, _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(head(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__head(mark(_x121))))))), _x62), _x52))))mark#(incr(head(odds))) → a__incr#(a__head(a__odds))
mark#(incr(head(s(tail(incr(cons(pairs, _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(cons(0, incr(odds)), _x72))))))mark#(incr(head(s(tail(incr(incr(s(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(s(mark(_x81))))))))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(head(s(a__tail(incr(a__incr(cons(0, incr(nats))))))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(incr(a__tail(a__head(cons(0, incr(nats)))))))
mark#(incr(head(head(incr(_x51))))) → a__incr#(a__head(a__head(a__incr(mark(_x51)))))mark#(incr(head(s(tail(incr(incr(nil))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(nil))))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(nats)))))mark#(incr(incr(incr(tail(head(s(head(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(a__head(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(head(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(a__head(mark(_x111)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(0)))))) → a__incr#(a__incr(incr(tail(head(0)))))
mark#(incr(head(s(tail(incr(incr(0))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(0))))))mark#(incr(incr(incr(tail(0))))) → a__incr#(a__incr(a__incr(a__tail(0))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(a__tail(a__head(mark(_x101))))), _x62))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(tail(_x111))))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(a__tail(mark(_x111)))))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(nats))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(a__nats))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(tail(head(mark(_x101))))), _x62), _x52))))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(tail(incr(a__incr(a__nats))))))mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(a__head(nats))
mark#(incr(head(head(cons(odds, _x52))))) → a__incr#(head(a__head(cons(a__odds, _x52))))mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(tail(incr(a__incr(cons(0, incr(nats))))))))
mark#(incr(incr(incr(tail(head(s(s(incr(_x91))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(mark(_x91)))))))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(tail(mark(0)))))
mark#(incr(head(s(head(0))))) → a__incr#(head(s(a__head(0))))mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))
mark#(incr(head(s(odds)))) → a__incr#(head(s(a__odds)))mark#(incr(head(s(tail(odds))))) → a__incr#(a__head(s(a__tail(a__odds))))
mark#(incr(incr(incr(tail(head(s(0))))))) → a__incr#(incr(incr(tail(a__head(s(0))))))mark#(incr(incr(incr(tail(head(head(s(0)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(0)))))))
mark#(incr(head(s(head(s(head(_x71))))))) → a__incr#(a__head(s(a__head(s(a__head(mark(_x71)))))))mark#(incr(head(s(tail(incr(tail(_x71))))))) → a__incr#(head(s(a__tail(a__incr(a__tail(mark(_x71)))))))
mark#(incr(head(head(0)))) → a__incr#(a__head(head(0)))mark#(incr(incr(incr(tail(head(incr(_x71))))))) → a__incr#(a__incr(a__incr(tail(a__head(incr(mark(_x71)))))))
mark#(incr(head(s(0)))) → a__incr#(head(s(0)))mark#(incr(incr(incr(tail(head(head(tail(nats)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(a__nats)))))))
mark#(incr(head(head(tail(_x51))))) → a__incr#(a__head(a__head(a__tail(mark(_x51)))))mark#(incr(incr(incr(tail(head(s(odds))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(a__odds))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(head(0)))), _x62))))mark#(incr(incr(incr(tail(head(incr(0))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(0))))))
mark#(incr(head(head(cons(s(_x61), _x52))))) → a__incr#(a__head(a__head(cons(s(mark(_x61)), _x52))))mark#(incr(head(s(head(s(tail(_x71))))))) → a__incr#(a__head(s(a__head(s(a__tail(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(cons(0, incr(nats)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(s(mark(_x111)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(0)))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(tail(tail(_x91))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(a__tail(mark(_x91)))))))))
mark#(incr(head(head(cons(cons(incr(odds), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(a__odds), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(_x101)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(incr(mark(_x101))))))))))
mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(a__head(head(cons(cons(0, incr(nats)), _x52))))mark#(incr(incr(incr(tail(s(_x61)))))) → a__incr#(incr(a__incr(tail(s(mark(_x61))))))
mark#(incr(incr(incr(tail(head(head(tail(pairs)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(a__pairs)))))))mark#(incr(incr(incr(tail(s(0)))))) → a__incr#(a__incr(a__incr(tail(s(0)))))
mark#(incr(head(head(cons(cons(incr(head(s(_x91))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(s(mark(_x91)))), _x62), _x52))))mark#(incr(head(s(tail(nil))))) → a__incr#(head(s(a__tail(nil))))
mark#(incr(head(head(nats)))) → a__incr#(a__head(a__head(a__nats)))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(odds)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__odds)))))), _x62), _x52))))
mark#(incr(head(s(head(tail(nil)))))) → a__incr#(head(s(a__head(a__tail(nil)))))mark#(incr(head(s(tail(incr(incr(_x71))))))) → a__incr#(head(s(a__tail(a__incr(a__incr(mark(_x71)))))))
mark#(incr(incr(incr(tail(head(s(odds))))))) → a__incr#(incr(incr(tail(a__head(s(a__incr(a__pairs)))))))mark#(incr(incr(incr(tail(head(head(head(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__head(mark(_x81))))))))
mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(tail(mark(_x51)))))mark#(incr(head(head(cons(cons(tail(_x71), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__tail(mark(_x71)), _x62), _x52))))
mark#(incr(head(s(tail(tail(_x61)))))) → a__incr#(head(s(a__tail(a__tail(mark(_x61))))))mark#(incr(incr(incr(tail(head(tail(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__tail(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(nil)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(nil)))))), _x62), _x52))))mark#(incr(head(s(tail(s(odds)))))) → a__incr#(a__head(s(a__tail(s(a__odds)))))
mark#(incr(incr(incr(tail(head(incr(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(a__odds))))))mark#(incr(head(head(cons(_x51, _x52))))) → a__incr#(head(a__head(cons(mark(_x51), _x52))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(head(a__head(a__incr(a__pairs)))))))mark#(incr(head(s(tail(s(incr(_x71))))))) → a__incr#(a__head(s(a__tail(s(a__incr(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(a__incr(mark(_x111)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(a__head(odds)))))))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(a__head(odds)))))))))mark#(incr(head(s(head(head(_x61)))))) → a__incr#(head(s(a__head(a__head(mark(_x61))))))
mark#(incr(incr(incr(tail(s(pairs)))))) → a__incr#(a__incr(a__incr(tail(s(a__pairs)))))mark#(incr(head(s(tail(incr(cons(pairs, _x51))))))) → a__incr#(head(s(a__tail(cons(s(mark(a__pairs)), incr(_x51))))))
mark#(incr(incr(incr(tail(head(head(s(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(head(s(mark(_x81))))))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(incr(tail(a__head(a__head(a__incr(a__pairs)))))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(a__tail(head(nats)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(nats))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__nats))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(incr(tail(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(a__tail(mark(_x101))))), _x62), _x52))))mark#(incr(head(head(cons(_x51, _x52))))) → a__incr#(a__head(head(cons(mark(_x51), _x52))))
mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))mark#(incr(head(head(odds)))) → a__incr#(a__head(head(a__odds)))
mark#(incr(incr(incr(tail(s(tail(_x71))))))) → a__incr#(a__incr(a__incr(tail(s(a__tail(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(cons(_x111, _x112))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(cons(mark(_x111), _x112))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(incr(incr(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(a__incr(mark(_x101))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(tail(s(_x91))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(s(mark(_x91)))))))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(head(head(a__odds))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(cons(_x111, _x112))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(cons(mark(_x111), _x112))))), _x62), _x52))))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(head(s(tail(a__incr(a__incr(a__nats))))))mark#(incr(head(head(cons(cons(incr(head(cons(_x91, _x92))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(cons(mark(_x91), _x92))), _x62), _x52))))
mark#(incr(incr(incr(tail(s(_x61)))))) → a__incr#(incr(a__incr(a__tail(s(mark(_x61))))))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(nil))))))
mark#(incr(head(s(tail(s(nats)))))) → a__incr#(a__head(s(a__tail(s(a__nats)))))mark#(incr(incr(incr(tail(head(s(s(incr(odds))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(odds))))))))
mark#(incr(head(s(tail(incr(cons(nil, _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(nil, _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(pairs))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__pairs))))), _x62), _x52))))
mark#(incr(incr(incr(tail(s(cons(_x71, _x72))))))) → a__incr#(a__incr(a__incr(tail(s(cons(mark(_x71), _x72))))))mark#(incr(head(s(tail(incr(incr(pairs))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(a__pairs))))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(cons(_x111, _x112))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(cons(mark(_x111), _x112))))))))))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(a__incr(tail(a__head(head(nil))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(mark(_x101))))), _x62), _x52))))mark#(incr(head(s(head(s(nats)))))) → a__incr#(a__head(s(a__head(s(a__nats)))))
mark#(incr(head(head(cons(cons(incr(head(incr(cons(_x101, _x102)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(cons(mark(_x101), _x102)))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(s(nats)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(a__nats)))))))
mark#(incr(head(s(head(s(odds)))))) → a__incr#(a__head(s(a__head(s(a__odds)))))mark#(incr(incr(incr(tail(head(head(s(pairs)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(a__pairs)))))))
mark#(incr(head(s(tail(incr(cons(tail(_x81), _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(a__tail(mark(_x81)), _x72))))))mark#(incr(incr(incr(tail(head(head(incr(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(a__incr(mark(_x81))))))))
mark#(incr(head(nats))) → a__incr#(a__head(cons(0, incr(nats))))mark#(incr(incr(incr(tail(head(incr(nats))))))) → a__incr#(incr(a__incr(tail(a__head(a__incr(a__nats))))))
mark#(incr(incr(incr(pairs)))) → a__incr#(a__incr(a__incr(a__pairs)))mark#(incr(incr(incr(tail(head(s(s(incr(head(nil)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__head(nil)))))))))
mark#(incr(head(s(head(tail(cons(0, _x72))))))) → a__incr#(head(s(head(a__tail(cons(0, _x72))))))mark#(incr(incr(incr(tail(head(s(s(pairs)))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__pairs)))))))
mark#(incr(head(s(head(tail(tail(_x71))))))) → a__incr#(head(s(head(a__tail(a__tail(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(_x121)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(s(s(mark(_x121))))))), _x62))))
mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(a__incr(tail(a__head(s(a__nats))))))mark#(incr(head(pairs))) → a__incr#(head(a__pairs))
mark#(incr(incr(incr(tail(head(s(s(incr(_x91))))))))) → a__incr#(a__incr(incr(tail(head(s(s(incr(mark(_x91)))))))))mark#(incr(incr(incr(tail(head(0)))))) → a__incr#(a__incr(incr(tail(a__head(0)))))
mark#(incr(incr(incr(tail(head(s(s(head(_x91))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__head(mark(_x91)))))))))mark#(incr(head(s(tail(pairs))))) → a__incr#(a__head(s(tail(cons(0, incr(odds))))))
mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(a__incr(tail(a__head(head(mark(_x71)))))))mark#(incr(incr(pairs))) → a__incr#(a__incr(cons(0, incr(odds))))
mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(mark(_x71)))))))mark#(incr(incr(incr(tail(head(s(s(incr(_x91))))))))) → a__incr#(incr(incr(tail(head(s(s(a__incr(mark(_x91)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(0))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(0))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(pairs)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(a__pairs)))), _x62), _x52))))
mark#(incr(head(s(tail(0))))) → a__incr#(head(s(a__tail(0))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(cons(_x121, _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(cons(mark(_x121), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(odds)), _x62), _x52))))mark#(incr(head(s(head(s(incr(_x71))))))) → a__incr#(a__head(s(a__head(s(a__incr(mark(_x71)))))))
mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(mark(0))mark#(incr(head(s(head(incr(head(_x71))))))) → a__incr#(head(s(a__head(a__incr(a__head(mark(_x71)))))))
mark#(incr(head(s(tail(incr(cons(_x71, _x72))))))) → a__incr#(a__head(s(tail(a__incr(cons(mark(_x71), _x72))))))mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(head(s(mark(_x61))))))
mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(cons(0, incr(nats))))))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(a__head(head(a__incr(a__pairs)))))))
mark#(incr(head(head(cons(cons(nil, _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(nil, _x62), _x52))))mark#(incr(head(s(tail(incr(head(pairs))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(a__pairs))))))
mark#(incr(incr(pairs))) → a__incr#(a__incr(pairs))mark#(incr(incr(incr(tail(head(incr(_x71))))))) → a__incr#(a__incr(incr(tail(a__head(a__incr(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(nil))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(incr(nil))))), _x62), _x52))))mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(a__tail(incr(incr(a__nats))))))
a__incr#(cons(X, XS)) → mark#(X)mark#(incr(incr(incr(tail(head(s(s(incr(nil))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(nil))))))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(nil)))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(a__head(nil)))))))))mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(_x111))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(mark(_x111)))))), _x62))))mark#(incr(head(s(head(incr(nil)))))) → a__incr#(head(s(a__head(a__incr(nil)))))
mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(head(mark(nats)))mark#(incr(head(head(cons(cons(_x61, _x62), _x31))))) → a__incr#(a__head(mark(cons(mark(_x61), _x62))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(nats)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(a__nats)))))))))mark#(incr(head(s(tail(s(s(_x71))))))) → a__incr#(a__head(s(a__tail(s(s(mark(_x71)))))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(pairs)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(a__pairs)))))))))mark#(incr(head(s(tail(incr(head(nil))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(nil))))))
mark#(incr(incr(incr(tail(head(s(incr(_x81)))))))) → a__incr#(incr(incr(tail(a__head(s(a__incr(mark(_x81))))))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(tail(head(cons(0, incr(nats)))))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(tail(mark(0)))))mark#(incr(head(head(cons(cons(incr(head(head(_x91))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__head(mark(_x91)))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(incr(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__incr(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(mark(_x101))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(cons(_x91, _x92))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(cons(mark(_x91), _x92))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(cons(0, incr(nats)))))), _x62), _x52))))
mark#(incr(head(s(tail(cons(_x61, _x62)))))) → a__incr#(a__head(s(tail(cons(mark(_x61), _x62)))))mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(a__head(s(tail(a__incr(mark(_x61))))))
mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(incr(a__incr(tail(head(head(nil))))))mark#(incr(incr(incr(tail(head(head(s(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(s(mark(_x81))))))))
mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))mark#(incr(incr(incr(tail(head(incr(head(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(a__head(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(odds))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(a__odds))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(incr(a__incr(a__tail(a__head(mark(_x61))))))
mark#(incr(head(head(odds)))) → a__incr#(a__head(a__head(a__odds)))mark#(incr(head(s(head(tail(cons(nil, _x72))))))) → a__incr#(head(s(head(a__tail(cons(nil, _x72))))))
mark#(incr(head(head(nats)))) → a__incr#(a__head(head(a__nats)))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__nats)))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(a__incr(a__pairs)))))))mark#(incr(incr(0))) → a__incr#(a__incr(0))
mark#(incr(incr(incr(tail(head(0)))))) → a__incr#(incr(a__incr(tail(a__head(0)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(nil))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(nil))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(tail(_x91))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__tail(mark(_x91)))))))))mark#(incr(head(s(tail(pairs))))) → a__incr#(head(s(a__tail(cons(0, incr(odds))))))
mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(head(cons(0, incr(nats))))mark#(incr(incr(incr(tail(head(s(s(incr(head(_x101)))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(a__head(mark(_x101))))))))))
mark#(incr(head(s(tail(head(_x61)))))) → a__incr#(a__head(s(tail(a__head(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(mark(_x121))))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(tail(_x101)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__tail(mark(_x101))))))))))mark#(incr(incr(incr(tail(head(s(s(nats)))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__nats)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(tail(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__tail(mark(_x111)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(0))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(0))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(tail(0)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(0)))))))mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(incr(incr(tail(head(s(mark(_x71)))))))
mark#(incr(incr(incr(tail(head(nil)))))) → a__incr#(a__incr(incr(tail(a__head(nil)))))mark#(incr(head(s(head(incr(incr(_x71))))))) → a__incr#(head(s(a__head(a__incr(a__incr(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(incr(pairs))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(a__pairs))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(0)))), _x62), _x52))))
mark#(incr(incr(pairs))) → a__incr#(incr(a__pairs))mark#(incr(head(head(cons(cons(incr(head(incr(s(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(s(mark(_x101))))), _x62), _x52))))
mark#(incr(head(s(tail(s(cons(_x71, _x72))))))) → a__incr#(a__head(s(a__tail(s(cons(mark(_x71), _x72))))))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(incr(a__pairs), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(tail(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(a__tail(mark(_x81))))))))mark#(incr(incr(incr(tail(head(s(s(_x81)))))))) → a__incr#(incr(incr(tail(a__head(s(s(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(nats)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__nats)), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(incr(a__incr(a__tail(a__head(a__head(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(cons(_x131, _x132))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(cons(mark(_x131), _x132))))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(cons(_x71, _x72))))))) → a__incr#(a__incr(a__incr(tail(a__head(cons(mark(_x71), _x72))))))
mark#(incr(incr(incr(tail(head(s(pairs))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__pairs))))))mark#(incr(head(head(cons(cons(incr(head(nats)), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(a__nats)), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(0)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(incr(_x131))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__incr(mark(_x131)))))))), _x62), _x52))))
mark#(incr(head(head(cons(_x51, _x31))))) → a__incr#(a__head(mark(mark(_x51))))mark#(incr(head(head(cons(cons(incr(odds), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__odds), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(mark(_x111)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(incr(mark(_x71)), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(pairs))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__pairs))))))))mark#(incr(incr(incr(tail(head(incr(s(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(s(mark(_x81))))))))
mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(a__incr(incr(tail(head(s(mark(_x71)))))))mark#(incr(incr(incr(tail(head(s(nil))))))) → a__incr#(a__incr(incr(tail(a__head(s(nil))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(mark(_x101))))), _x62), _x52))))mark#(incr(head(s(tail(incr(0)))))) → a__incr#(a__head(s(a__tail(a__incr(0)))))
mark#(incr(incr(incr(tail(head(head(head(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(a__head(mark(_x81))))))))mark#(incr(head(s(incr(_x51))))) → a__incr#(head(s(a__incr(mark(_x51)))))
mark#(incr(head(s(head(tail(odds)))))) → a__incr#(head(s(a__head(a__tail(a__odds)))))mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))
mark#(incr(incr(incr(tail(head(cons(_x71, _x72))))))) → a__incr#(a__incr(incr(tail(a__head(cons(mark(_x71), _x72))))))mark#(incr(head(s(tail(incr(head(tail(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(a__tail(mark(_x81))))))))
mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))mark#(incr(incr(incr(tail(head(s(s(incr(head(incr(_x111))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(a__incr(mark(_x111)))))))))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x31))))) → a__incr#(a__head(mark(cons(incr(a__pairs), _x62))))mark#(incr(head(incr(_x41)))) → a__incr#(head(a__incr(mark(_x41))))
mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(head(mark(_x51)))))mark#(incr(X)) → mark#(X)
mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(a__incr(a__incr(tail(a__head(s(mark(_x71)))))))mark#(incr(head(s(head(incr(nats)))))) → a__incr#(head(s(a__head(a__incr(nats)))))
mark#(incr(head(s(head(tail(cons(pairs, _x72))))))) → a__incr#(head(s(head(a__tail(cons(a__pairs, _x72))))))mark#(incr(incr(incr(tail(head(s(s(incr(head(0)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(0)))))))))
mark#(incr(head(s(tail(incr(head(_x71))))))) → a__incr#(a__head(s(tail(a__incr(a__head(mark(_x71)))))))mark#(incr(head(s(head(nats))))) → a__incr#(head(s(a__head(a__nats))))
mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))mark#(incr(incr(incr(tail(head(s(s(incr(odds))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(a__odds))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(s(mark(_x111)))))), _x62), _x52))))mark#(incr(head(head(cons(odds, _x52))))) → a__incr#(a__head(a__head(cons(a__incr(a__pairs), _x52))))
mark#(incr(head(head(cons(cons(incr(0), _x62), _x52))))) → a__incr#(a__head(head(cons(cons(a__incr(0), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(incr(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__incr(mark(_x91)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__incr(pairs))), _x62), _x52))))mark#(incr(head(s(tail(incr(head(_x71))))))) → a__incr#(a__head(s(a__tail(a__incr(head(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(odds)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(a__odds)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(pairs)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(a__pairs)))), _x62), _x52))))
mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))mark#(incr(incr(incr(tail(head(s(s(pairs)))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__pairs)))))))
mark#(incr(head(head(cons(cons(incr(head(cons(_x91, _x92))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(cons(mark(_x91), _x92))), _x62), _x52))))mark#(incr(incr(incr(tail(head(0)))))) → a__incr#(incr(a__incr(tail(head(0)))))
mark#(incr(head(head(cons(cons(incr(head(s(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(s(mark(_x91)))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(tail(_x81)))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(a__tail(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(cons(_x111, _x112))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(cons(mark(_x111), _x112))))), _x62), _x52))))mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(head(s(head(tail(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(tail(_x81)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__tail(mark(_x81))), _x62), _x52))))mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(head(0))))
mark#(incr(head(s(tail(pairs))))) → a__incr#(a__head(s(mark(incr(odds)))))mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x31))))) → a__incr#(head(mark(cons(a__incr(a__head(mark(_x81))), _x62))))
mark#(incr(incr(incr(tail(head(s(s(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(s(mark(_x81))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(nats)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(nats)))), _x62), _x52))))mark#(incr(incr(incr(tail(head(pairs)))))) → a__incr#(a__incr(a__incr(tail(a__head(a__pairs)))))
mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__incr(cons(0, incr(odds))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(s(_x81)))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(s(mark(_x81))))))))
mark#(incr(head(s(tail(nil))))) → a__incr#(a__head(s(a__tail(nil))))mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(head(s(a__tail(a__incr(a__incr(nats))))))
mark#(incr(head(head(cons(cons(incr(incr(_x81)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__incr(mark(_x81))), _x62), _x52))))mark#(incr(incr(incr(tail(head(incr(incr(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(a__incr(mark(_x81))))))))
mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(incr(incr(tail(a__head(s(a__nats))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(mark(_x101))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(a__incr(tail(head(head(nil))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(s(mark(_x111)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(nil))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(nil))))))))mark#(incr(head(head(cons(cons(incr(0), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(0), _x62))))
mark#(incr(incr(incr(tail(head(incr(cons(_x81, _x82)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(cons(mark(_x81), _x82)))))))mark#(incr(incr(nats))) → a__incr#(incr(cons(0, incr(nats))))
mark#(incr(head(s(tail(incr(nil)))))) → a__incr#(a__head(s(a__tail(a__incr(nil)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(nil))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(nil))))), _x62), _x52))))
mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(head(s(tail(a__incr(mark(_x61))))))mark#(incr(head(head(cons(nil, _x52))))) → a__incr#(a__head(a__head(cons(nil, _x52))))
mark#(incr(incr(incr(tail(head(s(s(odds)))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__odds)))))))mark#(incr(head(head(cons(cons(nats, _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__nats, _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(0))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(0))))), _x62), _x52))))mark#(incr(incr(incr(tail(cons(_x61, _x62)))))) → a__incr#(a__incr(a__incr(a__tail(cons(mark(_x61), _x62)))))
mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(a__incr(a__tail(head(s(a__nats))))))mark#(incr(incr(incr(tail(s(nats)))))) → a__incr#(a__incr(a__incr(a__tail(s(a__nats)))))
mark#(incr(head(s(tail(incr(incr(_x71))))))) → a__incr#(a__head(s(a__tail(a__incr(incr(mark(_x71)))))))mark#(incr(incr(incr(tail(head(incr(nats))))))) → a__incr#(a__incr(incr(tail(a__head(a__incr(a__nats))))))
mark#(incr(head(s(tail(0))))) → a__incr#(a__head(s(a__tail(0))))mark#(incr(incr(incr(tail(head(s(s(incr(0))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(0))))))))
mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(head(s(mark(_x71)))))))mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(head(a__incr(a__pairs)))))))mark#(incr(head(s(tail(pairs))))) → a__incr#(head(s(a__tail(pairs))))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(tail(incr(incr(cons(0, incr(nats))))))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(a__incr(pairs)))))))
mark#(incr(head(s(tail(s(0)))))) → a__incr#(a__head(s(a__tail(s(0)))))mark#(incr(head(s(head(tail(nats)))))) → a__incr#(head(s(head(a__tail(nats)))))
mark#(incr(head(s(head(tail(incr(_x71))))))) → a__incr#(head(s(a__head(a__tail(a__incr(mark(_x71)))))))mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))
mark#(incr(incr(incr(tail(head(s(odds))))))) → a__incr#(incr(incr(tail(head(s(a__incr(a__pairs)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(nats)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__nats)))))), _x62), _x52))))
mark#(incr(head(s(head(tail(cons(_x71, _x51))))))) → a__incr#(head(s(head(mark(_x51)))))mark#(incr(head(s(head(tail(pairs)))))) → a__incr#(head(s(a__head(a__tail(a__pairs)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(head(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(a__head(mark(_x121))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(odds)), _x62), _x52))))
mark#(incr(head(s(head(tail(head(_x71))))))) → a__incr#(head(s(a__head(a__tail(a__head(mark(_x71)))))))mark#(incr(head(s(head(incr(nats)))))) → a__incr#(head(s(a__head(a__incr(cons(0, incr(nats)))))))
mark#(incr(head(head(cons(cons(incr(head(incr(odds))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(a__odds))), _x62), _x52))))mark#(incr(incr(incr(tail(head(nil)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(nil)))))
mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))mark#(incr(incr(incr(tail(head(head(incr(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__incr(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(odds)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(a__odds)))), _x62), _x52))))mark#(incr(head(s(tail(head(_x61)))))) → a__incr#(head(s(a__tail(a__head(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(a__nats)))), _x62), _x52))))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(tail(a__head(cons(0, incr(nats)))))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(0)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(0)))))))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(_x101)))))))))) → a__incr#(incr(incr(tail(head(s(s(a__incr(a__incr(mark(_x101))))))))))mark#(incr(head(s(tail(incr(incr(_x71))))))) → a__incr#(a__head(s(a__tail(incr(a__incr(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(mark(_x71)), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(mark(_x91)))), _x62))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(cons(0, incr(odds))), _x62))))mark#(incr(head(s(head(tail(pairs)))))) → a__incr#(head(s(head(a__tail(a__pairs)))))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(a__tail(incr(cons(s(mark(0)), incr(incr(nats))))))))mark#(incr(incr(incr(tail(head(s(cons(_x81, _x82)))))))) → a__incr#(incr(incr(tail(a__head(s(cons(mark(_x81), _x82)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(s(mark(_x111)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(a__head(a__odds)))))))))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(head(s(a__tail(incr(incr(cons(0, incr(nats))))))))mark#(incr(incr(incr(tail(head(incr(_x71))))))) → a__incr#(incr(a__incr(tail(a__head(a__incr(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(cons(_x101, _x102)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(cons(mark(_x101), _x102)))), _x62), _x52))))mark#(incr(head(s(tail(incr(head(cons(_x81, _x82)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(cons(mark(_x81), _x82)))))))
mark#(incr(head(head(cons(cons(s(_x71), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(s(mark(_x71)), _x62), _x52))))mark#(incr(incr(incr(tail(head(odds)))))) → a__incr#(a__incr(a__incr(tail(a__head(a__odds)))))
mark#(incr(incr(incr(tail(head(incr(nil))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(nil))))))mark#(incr(head(s(head(incr(cons(_x71, _x72))))))) → a__incr#(head(s(a__head(a__incr(cons(mark(_x71), _x72))))))
mark#(incr(head(head(cons(cons(incr(head(tail(incr(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__incr(mark(_x101))))), _x62), _x52))))mark#(incr(head(s(tail(incr(incr(cons(_x81, _x82)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(cons(mark(_x81), _x82)))))))
mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(pairs), _x62))))
mark#(incr(head(s(head(tail(s(_x71))))))) → a__incr#(head(s(a__head(a__tail(s(mark(_x71)))))))mark#(incr(incr(incr(tail(s(_x61)))))) → a__incr#(a__incr(incr(a__tail(s(mark(_x61))))))
mark#(incr(head(s(tail(cons(_x61, _x62)))))) → a__incr#(head(s(a__tail(cons(mark(_x61), _x62)))))mark#(incr(incr(incr(tail(head(s(s(incr(head(_x101)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(a__head(mark(_x101))))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(0))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(0))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__incr(pairs)))))))
mark#(incr(head(head(cons(cons(odds, _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__odds, _x62), _x52))))mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))
mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(a__tail(head(a__nats)))), _x62))))
mark#(incr(head(s(head(tail(tail(_x71))))))) → a__incr#(head(s(a__head(a__tail(a__tail(mark(_x71)))))))mark#(incr(head(s(head(tail(cons(head(_x81), _x72))))))) → a__incr#(head(s(head(a__tail(cons(a__head(mark(_x81)), _x72))))))
mark#(incr(odds)) → a__incr#(incr(a__pairs))mark#(incr(head(s(tail(incr(head(nats))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(a__nats))))))
mark#(incr(incr(incr(tail(head(head(tail(_x81)))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(a__tail(mark(_x81))))))))mark#(incr(head(head(tail(_x51))))) → a__incr#(a__head(head(a__tail(mark(_x51)))))
mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(head(a__head(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(incr(head(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(a__head(mark(_x101))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(mark(_x111)))))), _x62), _x52))))mark#(incr(head(s(tail(incr(cons(incr(_x81), _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(a__incr(mark(_x81)), _x72))))))
mark#(incr(head(s(head(tail(cons(incr(_x81), _x72))))))) → a__incr#(head(s(head(a__tail(cons(a__incr(mark(_x81)), _x72))))))mark#(incr(head(head(cons(cons(incr(head(nil)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(nil)), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(incr(a__tail(a__head(s(nats))))))mark#(incr(head(s(tail(nats))))) → a__incr#(a__head(s(tail(cons(0, incr(nats))))))
mark#(incr(head(head(cons(cons(incr(head(tail(tail(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__tail(mark(_x101))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(a__nats)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(incr(_x91))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__incr(mark(_x91)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(nats), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(a__nats), _x62), _x52))))
mark#(incr(head(head(cons(odds, _x52))))) → a__incr#(a__head(head(cons(a__odds, _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__tail(a__head(mark(_x101))))), _x62), _x52))))
mark#(incr(head(s(tail(odds))))) → a__incr#(head(s(a__tail(a__odds))))mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x52))))) → a__incr#(head(head(cons(cons(a__incr(mark(_x71)), _x62), _x52))))
mark#(incr(incr(incr(tail(s(nil)))))) → a__incr#(a__incr(incr(tail(s(nil)))))mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(a__incr(a__pairs))))))))))
mark#(incr(incr(incr(tail(head(head(s(s(_x91))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(s(mark(_x91)))))))))mark#(incr(incr(incr(tail(head(s(s(s(_x91))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(s(mark(_x91)))))))))
mark#(incr(incr(incr(tail(head(s(s(incr(cons(_x101, _x102)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(cons(mark(_x101), _x102)))))))))mark#(incr(head(head(cons(cons(incr(nats), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__nats), _x62), _x52))))
mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(a__head(a__head(cons(cons(0, incr(nats)), _x52))))mark#(incr(head(s(tail(incr(head(_x71))))))) → a__incr#(head(s(a__tail(a__incr(a__head(mark(_x71)))))))
mark#(incr(head(head(pairs)))) → a__incr#(a__head(head(pairs)))mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(head(a__nats))
mark#(incr(incr(incr(tail(pairs))))) → a__incr#(a__incr(a__incr(a__tail(a__pairs))))mark#(incr(head(head(cons(cons(head(_x71), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__head(mark(_x71)), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(s(head(_x91))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(a__head(mark(_x91)))))))))mark#(incr(head(s(head(nil))))) → a__incr#(head(s(a__head(nil))))
mark#(incr(head(head(cons(cons(incr(head(tail(nil))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(nil))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(incr(_x81)))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__incr(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(mark(_x81))), _x62))))mark#(incr(incr(incr(tail(head(s(s(incr(cons(_x101, _x102)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(cons(mark(_x101), _x102)))))))))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(head(s(a__tail(a__incr(a__incr(cons(0, incr(nats))))))))mark#(incr(incr(incr(tail(head(head(tail(head(_x91))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(a__head(mark(_x91)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(head(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(a__head(mark(_x111)))))), _x62), _x52))))mark#(incr(incr(incr(tail(s(odds)))))) → a__incr#(a__incr(a__incr(tail(s(a__odds)))))
mark#(incr(incr(incr(tail(head(s(tail(_x81)))))))) → a__incr#(incr(incr(tail(a__head(s(a__tail(mark(_x81))))))))mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(mark(_x71)))))))
mark#(incr(head(s(head(s(cons(_x71, _x72))))))) → a__incr#(a__head(s(a__head(s(cons(mark(_x71), _x72))))))mark#(incr(head(head(cons(cons(incr(head(pairs)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__pairs)), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(s(cons(_x91, _x92))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(cons(mark(_x91), _x92))))))))mark#(incr(incr(incr(tail(head(s(pairs))))))) → a__incr#(incr(incr(tail(a__head(s(a__pairs))))))
mark#(incr(head(head(cons(cons(incr(head(0)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(0)), _x62), _x52))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(incr(a__tail(head(cons(0, incr(nats)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(tail(a__head(cons(0, incr(nats)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(a__incr(a__incr(tail(head(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(nil), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(nil), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(odds))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__odds))))))
mark#(incr(incr(incr(tail(head(head(s(_x81)))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(s(mark(_x81))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(cons(0, incr(nats)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(nil))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(nil))), _x62), _x52))))mark#(incr(incr(incr(tail(head(incr(nats))))))) → a__incr#(a__incr(a__incr(tail(head(a__incr(a__nats))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nil)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(nil)))), _x62), _x52))))mark#(incr(head(s(tail(incr(head(incr(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(a__incr(mark(_x81))))))))
mark#(incr(incr(incr(tail(head(s(tail(_x81)))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__tail(mark(_x81))))))))mark#(incr(head(head(cons(cons(incr(s(_x81)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(s(mark(_x81))), _x62), _x52))))
mark#(incr(incr(incr(tail(nats))))) → a__incr#(a__incr(a__incr(a__tail(a__nats))))mark#(incr(head(s(tail(incr(odds)))))) → a__incr#(a__head(s(a__tail(a__incr(a__odds)))))
mark#(incr(incr(incr(tail(head(s(s(incr(s(_x101)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(s(mark(_x101))))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x32), incr(a__head(a__tail(head(0))))))))) → a__incr#(head(cons(mark(incr(a__head(a__tail(head(0))))), _x32)))
mark#(incr(head(s(tail(tail(_x61)))))) → a__incr#(a__head(s(tail(a__tail(mark(_x61))))))mark#(incr(odds)) → a__incr#(cons(s(mark(0)), incr(incr(odds))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nil)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(nil)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(incr(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__incr(mark(_x101))))), _x62), _x52))))
mark#(incr(head(s(tail(nats))))) → a__incr#(head(s(a__tail(nats))))mark#(incr(head(head(cons(cons(incr(head(tail(head(cons(_x111, _x112))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(mark(_x111), _x112))))), _x62), _x52))))
mark#(incr(head(s(tail(nats))))) → a__incr#(head(s(tail(a__nats))))mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__odds)), _x62), _x52))))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(tail(a__incr(a__incr(a__nats))))))mark#(incr(incr(incr(tail(head(s(s(nil)))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(nil)))))))
mark#(incr(incr(incr(tail(head(s(cons(_x81, _x82)))))))) → a__incr#(a__incr(incr(tail(a__head(s(cons(mark(_x81), _x82)))))))mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(head(head(cons(cons(incr(incr(_x81)), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(a__incr(mark(_x81))), _x62), _x52))))
mark#(incr(head(head(cons(cons(_x61, _x62), _x52))))) → a__incr#(a__head(head(cons(cons(mark(_x61), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(mark(_x101))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(mark(_x91)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(head(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__head(mark(_x91)))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(incr(incr(tail(head(a__head(nil))))))mark#(incr(head(head(pairs)))) → a__incr#(a__head(a__head(cons(0, incr(odds)))))
mark#(incr(incr(incr(tail(head(pairs)))))) → a__incr#(a__incr(incr(tail(a__head(a__pairs)))))mark#(incr(head(head(head(_x51))))) → a__incr#(a__head(head(a__head(mark(_x51)))))
mark#(incr(head(s(tail(incr(0)))))) → a__incr#(head(s(tail(a__incr(0)))))mark#(incr(incr(incr(tail(head(s(s(0)))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(0)))))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__head(a__odds)))))))))mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(a__head(s(a__tail(incr(mark(_x61))))))
mark#(incr(head(s(head(tail(nats)))))) → a__incr#(head(s(a__head(a__tail(a__nats)))))mark#(incr(head(head(cons(0, _x31))))) → a__incr#(a__head(mark(0)))
mark#(incr(head(head(cons(cons(incr(0), _x32), incr(0)))))) → a__incr#(a__head(cons(mark(incr(0)), _x32)))mark#(incr(incr(incr(tail(head(s(s(incr(incr(nats)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(a__nats)))))))))
mark#(incr(head(s(head(tail(0)))))) → a__incr#(head(s(a__head(a__tail(0)))))mark#(incr(head(head(cons(cons(incr(head(0)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(0)), _x62), _x52))))
mark#(incr(incr(incr(tail(s(tail(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(s(a__tail(mark(_x71)))))))mark#(incr(incr(incr(tail(head(s(s(incr(head(nil)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(head(nil)))))))))
mark#(incr(head(s(tail(incr(odds)))))) → a__incr#(head(s(a__tail(a__incr(a__odds)))))mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(mark(_x71)))))))
mark#(incr(incr(incr(tail(head(s(s(pairs)))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(pairs)))))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(tail(head(a__nats)))))
mark#(incr(head(s(tail(incr(incr(tail(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(a__tail(mark(_x81))))))))mark#(incr(head(s(tail(incr(cons(pairs, _x72))))))) → a__incr#(head(s(a__tail(incr(cons(a__pairs, _x72))))))
mark#(incr(head(head(cons(cons(incr(head(0)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(0)), _x62), _x52))))mark#(incr(head(head(cons(tail(_x61), _x52))))) → a__incr#(a__head(a__head(cons(a__tail(mark(_x61)), _x52))))
mark#(incr(incr(odds))) → a__incr#(a__incr(a__odds))mark#(incr(head(head(cons(cons(incr(s(_x81)), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(s(mark(_x81))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(tail(a__head(a__nats)))))mark#(incr(head(s(head(incr(odds)))))) → a__incr#(head(s(a__head(a__incr(a__odds)))))
mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))mark#(incr(head(head(cons(cons(incr(head(tail(head(pairs)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(a__pairs)))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(incr(incr(tail(a__head(mark(_x61))))))mark#(incr(incr(incr(tail(head(tail(_x71))))))) → a__incr#(a__incr(incr(tail(a__head(a__tail(mark(_x71)))))))
mark#(incr(incr(nats))) → a__incr#(a__incr(cons(0, incr(nats))))mark#(incr(odds)) → a__incr#(incr(cons(0, incr(odds))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(pairs)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(a__pairs)))))))))mark#(incr(head(s(tail(incr(cons(pairs, _x72))))))) → a__incr#(head(s(a__tail(a__incr(cons(cons(0, incr(odds)), _x72))))))
mark#(incr(head(s(tail(incr(s(_x71))))))) → a__incr#(head(s(a__tail(a__incr(s(mark(_x71)))))))mark#(incr(incr(incr(tail(head(incr(nats))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(nats))))))
mark#(incr(incr(incr(tail(head(head(pairs))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__pairs))))))mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(head(a__head(cons(a__nats, _x52))))
mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(head(s(head(a__incr(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(incr(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(head(a__incr(mark(_x91)))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(nil))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(nil))))))mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(head(odds)))))))))
mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))mark#(incr(head(s(head(pairs))))) → a__incr#(a__head(s(a__head(a__pairs))))
mark#(incr(incr(incr(tail(s(head(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(s(a__head(mark(_x71)))))))mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(a__incr(incr(a__tail(a__head(s(mark(_x71)))))))
mark#(incr(head(s(tail(incr(cons(odds, _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(a__odds, _x72))))))mark#(incr(head(s(tail(incr(cons(_x71, _x72))))))) → a__incr#(a__head(s(a__tail(incr(cons(mark(_x71), _x72))))))
mark#(incr(incr(incr(odds)))) → a__incr#(a__incr(a__incr(a__odds)))mark#(incr(head(s(tail(incr(cons(pairs, _x72))))))) → a__incr#(head(s(tail(a__incr(cons(a__pairs, _x72))))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(_x101)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(incr(a__incr(mark(_x101))))))))))mark#(incr(head(s(tail(pairs))))) → a__incr#(head(s(a__tail(a__pairs))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__head(odds)))))))))mark#(incr(head(s(head(tail(cons(s(_x81), _x72))))))) → a__incr#(head(s(head(a__tail(cons(s(mark(_x81)), _x72))))))
mark#(incr(head(s(tail(incr(pairs)))))) → a__incr#(a__head(s(a__tail(a__incr(a__pairs)))))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x31))))) → a__incr#(head(mark(cons(a__incr(a__pairs), _x62))))
mark#(incr(incr(incr(tail(nil))))) → a__incr#(a__incr(incr(a__tail(nil))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(a__tail(a__head(a__nats)))))
mark#(incr(head(s(tail(incr(cons(0, _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(0, _x72))))))mark#(incr(incr(incr(tail(s(odds)))))) → a__incr#(a__incr(a__incr(a__tail(s(a__odds)))))
mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(a__incr(a__incr(a__tail(head(mark(_x61))))))mark#(incr(incr(incr(tail(s(nil)))))) → a__incr#(incr(a__incr(a__tail(s(nil)))))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(a__tail(incr(a__incr(nats))))))mark#(incr(incr(incr(tail(head(head(s(odds)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(a__odds)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(odds)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__odds)))), _x62), _x52))))mark#(incr(head(s(tail(incr(cons(pairs, _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(pairs, _x72))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(a__tail(head(mark(_x101))))), _x62))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__incr(a__pairs)))))))
mark#(incr(incr(incr(tail(head(s(s(incr(pairs))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__pairs))))))))mark#(incr(head(s(tail(incr(cons(pairs, _x51))))))) → a__incr#(a__head(s(a__tail(cons(s(mark(a__pairs)), incr(_x51))))))
mark#(incr(incr(incr(tail(head(head(tail(incr(_x91))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(a__incr(mark(_x91)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(mark(_x111)))))), _x62), _x52))))
mark#(incr(head(s(tail(s(tail(_x71))))))) → a__incr#(a__head(s(a__tail(s(a__tail(mark(_x71)))))))mark#(incr(incr(incr(tail(s(s(_x71))))))) → a__incr#(a__incr(a__incr(tail(s(s(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(0)))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(tail(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(head(a__tail(mark(_x81))))))))
mark#(incr(head(s(head(tail(cons(cons(_x81, _x82), _x72))))))) → a__incr#(head(s(head(a__tail(cons(cons(mark(_x81), _x82), _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__tail(head(0)))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(s(tail(_x91))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(a__tail(mark(_x91)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(0)))), _x62), _x52))))
mark#(incr(head(s(head(tail(cons(odds, _x72))))))) → a__incr#(head(s(head(a__tail(cons(a__odds, _x72))))))mark#(incr(incr(incr(tail(head(head(s(incr(_x91))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(a__incr(mark(_x91)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nil)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(nil)))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(head(_x101)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(head(mark(_x101))))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(0)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(0)))))), _x62), _x52))))mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))
mark#(incr(head(head(cons(0, _x52))))) → a__incr#(head(a__head(cons(0, _x52))))mark#(incr(head(odds))) → a__incr#(head(odds))
mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(head(mark(_x71)))))))mark#(incr(head(s(odds)))) → a__incr#(a__head(s(odds)))
mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(incr(a__tail(a__head(a__head(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(a__head(mark(_x81))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(mark(_x101))))), _x62))))mark#(incr(head(head(cons(cons(incr(nil), _x62), _x52))))) → a__incr#(a__head(head(cons(cons(a__incr(nil), _x62), _x52))))
mark#(incr(head(tail(_x41)))) → a__incr#(head(a__tail(mark(_x41))))mark#(incr(head(head(cons(pairs, _x52))))) → a__incr#(a__head(a__head(cons(a__pairs, _x52))))
mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(incr(a__tail(a__head(s(cons(0, incr(nats))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(a__incr(mark(_x111)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(_x51))))) → a__incr#(incr(a__incr(a__tail(mark(_x51)))))mark#(incr(incr(incr(tail(head(head(nats))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__nats))))))
mark#(incr(head(s(pairs)))) → a__incr#(a__head(s(pairs)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(incr(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(a__incr(mark(_x121))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(pairs))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__pairs))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(a__head(a__odds)))))))))
mark#(incr(incr(incr(tail(head(s(s(pairs)))))))) → a__incr#(a__incr(incr(tail(head(s(s(cons(0, incr(odds)))))))))mark#(incr(head(head(cons(cons(incr(nil), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(nil), _x62))))
mark#(incr(head(head(_x41)))) → a__incr#(head(head(mark(_x41))))mark#(incr(head(s(tail(head(_x61)))))) → a__incr#(a__head(s(a__tail(a__head(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(incr(mark(_x111)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(nil))))))
mark#(incr(head(head(cons(cons(incr(head(nil)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(nil)), _x62), _x52))))mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(head(s(a__tail(a__incr(incr(a__nats))))))
mark#(incr(head(head(cons(cons(incr(head(tail(s(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(s(mark(_x101))))), _x62), _x52))))mark#(incr(incr(incr(tail(s(incr(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(s(a__incr(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(incr(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(incr(mark(_x91)))), _x62), _x52))))mark#(incr(head(s(head(tail(nats)))))) → a__incr#(head(s(head(tail(a__nats)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(a__incr(mark(_x111)))))), _x62), _x52))))mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))
mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(nil))))))mark#(incr(head(head(pairs)))) → a__incr#(a__head(a__head(pairs)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(tail(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(a__tail(mark(_x111)))))), _x62), _x52))))mark#(incr(head(nats))) → a__incr#(head(a__nats))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(nats)))), _x62))))mark#(incr(incr(incr(tail(head(incr(pairs))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(a__pairs))))))
mark#(incr(incr(incr(tail(head(pairs)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__pairs)))))mark#(incr(head(s(tail(_x51))))) → a__incr#(head(s(a__tail(mark(_x51)))))
mark#(incr(head(head(head(_x51))))) → a__incr#(a__head(a__head(a__head(mark(_x51)))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(incr(tail(head(a__head(a__odds))))))
mark#(incr(incr(incr(tail(head(s(s(incr(odds))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(a__pairs)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(a__nats)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nil)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(nil)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(cons(_x81, _x82)), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(cons(mark(_x81), _x82)), _x62), _x52))))
mark#(incr(head(s(tail(incr(cons(head(_x81), _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(a__head(mark(_x81)), _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(_x111))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(tail(head(a__incr(mark(_x111)))))), _x62), _x52))))
mark#(incr(head(s(odds)))) → a__incr#(a__head(s(a__incr(a__pairs))))mark#(incr(incr(incr(tail(head(s(head(_x81)))))))) → a__incr#(incr(incr(tail(a__head(s(a__head(mark(_x81))))))))
mark#(incr(head(head(s(_x51))))) → a__incr#(a__head(a__head(s(mark(_x51)))))mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(tail(odds))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__odds))), _x62), _x52))))mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))
mark#(incr(head(s(head(s(nil)))))) → a__incr#(a__head(s(a__head(s(nil)))))mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(a__odds))))))mark#(incr(head(head(cons(cons(0, _x62), _x52))))) → a__incr#(head(a__head(cons(cons(0, _x62), _x52))))
mark#(incr(head(head(_x41)))) → a__incr#(head(a__head(mark(_x41))))mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))
mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(mark(_x91)))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(head(nil)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(a__head(nil)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(a__head(mark(_x101))))), _x62), _x52))))mark#(incr(pairs)) → a__incr#(a__pairs)
mark#(incr(head(s(head(tail(0)))))) → a__incr#(head(s(head(a__tail(0)))))mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(a__tail(mark(_x91)))), _x62))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(head(head(cons(cons(a__incr(a__pairs), _x62), _x52))))mark#(incr(head(s(pairs)))) → a__incr#(head(s(cons(0, incr(odds)))))
mark#(incr(head(s(tail(pairs))))) → a__incr#(a__head(s(tail(a__pairs))))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(nil))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(head(_x131))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__head(mark(_x131)))))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(tail(cons(_x91, _x92))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(cons(mark(_x91), _x92))))))))
mark#(incr(incr(incr(tail(head(head(pairs))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(a__pairs))))))mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(head(s(a__head(tail(mark(_x61))))))
mark#(incr(head(head(nil)))) → a__incr#(head(a__head(nil)))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__incr(cons(0, incr(odds)))))))))
mark#(incr(head(s(tail(incr(nats)))))) → a__incr#(head(s(a__tail(a__incr(a__nats)))))mark#(incr(incr(incr(tail(head(s(s(cons(_x91, _x92))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(cons(mark(_x91), _x92))))))))
mark#(incr(incr(incr(tail(head(head(0))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(0))))))mark#(incr(incr(incr(tail(head(s(tail(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(a__tail(mark(_x81))))))))
mark#(incr(head(s(head(tail(s(_x71))))))) → a__incr#(head(s(head(a__tail(s(mark(_x71)))))))mark#(incr(head(head(incr(_x51))))) → a__incr#(a__head(head(a__incr(mark(_x51)))))
mark#(incr(head(s(tail(incr(tail(_x71))))))) → a__incr#(a__head(s(a__tail(a__incr(a__tail(mark(_x71)))))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(cons(_x111, _x112))))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(cons(mark(_x111), _x112))))))))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(s(_x111))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(s(mark(_x111)))))))))))mark#(incr(head(s(head(s(s(_x71))))))) → a__incr#(a__head(s(a__head(s(s(mark(_x71)))))))
mark#(incr(head(s(head(incr(0)))))) → a__incr#(head(s(a__head(a__incr(0)))))mark#(incr(head(head(cons(cons(incr(head(nil)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(nil)), _x62), _x52))))
mark#(incr(head(head(cons(odds, _x31))))) → a__incr#(a__head(mark(a__odds)))mark#(incr(head(head(cons(cons(incr(0), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(0), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(odds))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__odds))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(odds))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__odds))))))))
mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(incr(a__tail(mark(_x51)))))mark#(incr(incr(incr(tail(s(0)))))) → a__incr#(a__incr(a__incr(a__tail(s(0)))))
mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(mark(_x81))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__incr(a__pairs))), _x62), _x52))))
mark#(incr(head(s(head(incr(s(_x71))))))) → a__incr#(head(s(a__head(a__incr(s(mark(_x71)))))))mark#(incr(head(s(tail(_x51))))) → a__incr#(head(s(tail(mark(_x51)))))
mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(head(mark(_x81))), _x62), _x52))))mark#(incr(head(s(head(tail(cons(nats, _x72))))))) → a__incr#(head(s(head(a__tail(cons(a__nats, _x72))))))
mark#(incr(head(s(head(s(_x61)))))) → a__incr#(head(s(a__head(s(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__pairs), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(cons(_x81, _x82)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(cons(mark(_x81), _x82)), _x62), _x52))))mark#(incr(head(s(tail(incr(cons(_x71, _x51))))))) → a__incr#(a__head(s(a__tail(cons(s(mark(mark(_x71))), incr(_x51))))))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(head(s(a__tail(incr(a__incr(a__nats))))))mark#(incr(head(s(tail(s(head(_x71))))))) → a__incr#(a__head(s(a__tail(s(a__head(mark(_x71)))))))
mark#(incr(head(s(tail(incr(nil)))))) → a__incr#(head(s(a__tail(a__incr(nil)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(pairs)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__pairs)))), _x62), _x52))))
mark#(incr(head(s(head(pairs))))) → a__incr#(head(s(a__head(a__pairs))))mark#(incr(head(head(cons(cons(incr(head(tail(head(head(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__head(mark(_x111)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(a__nats)))), _x62))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(s(_x111))))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(s(mark(_x111)))))))))))
mark#(incr(head(s(head(tail(cons(tail(_x81), _x72))))))) → a__incr#(head(s(head(a__tail(cons(a__tail(mark(_x81)), _x72))))))mark#(incr(incr(incr(tail(head(s(s(incr(head(_x101)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__head(mark(_x101))))))))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(odds))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(s(mark(_x111)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(tail(_x101)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__tail(mark(_x101))))))))))mark#(incr(head(s(tail(incr(0)))))) → a__incr#(head(s(a__tail(incr(0)))))
mark#(incr(head(head(cons(cons(incr(nil), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(incr(nil), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(_x81)))))))) → a__incr#(a__incr(incr(tail(head(s(s(mark(_x81))))))))
mark#(incr(head(s(head(tail(nil)))))) → a__incr#(head(s(head(a__tail(nil)))))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(incr(tail(a__head(head(nil))))))
mark#(incr(head(s(head(tail(nats)))))) → a__incr#(head(s(head(tail(cons(0, incr(nats)))))))mark#(incr(head(head(cons(cons(incr(head(incr(nats))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(a__nats))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(nats)))), _x62), _x52))))mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(head(s(a__tail(incr(mark(_x61))))))
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(incr(incr(incr(tail(head(odds)))))) → a__incr#(a__incr(incr(tail(a__head(a__odds)))))
mark#(incr(incr(incr(tail(head(incr(_x71))))))) → a__incr#(a__incr(a__incr(tail(head(a__incr(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(0), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(0), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(incr(a__incr(a__tail(a__head(s(a__nats))))))mark#(incr(head(s(head(tail(head(_x71))))))) → a__incr#(head(s(head(a__tail(a__head(mark(_x71)))))))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(a__tail(a__incr(incr(a__nats))))))mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(a__head(mark(a__nats)))
mark#(incr(head(s(tail(s(nil)))))) → a__incr#(a__head(s(a__tail(s(nil)))))mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))
mark#(incr(head(pairs))) → a__incr#(a__head(a__pairs))mark#(incr(head(head(cons(odds, _x52))))) → a__incr#(a__head(a__head(cons(odds, _x52))))
mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))mark#(incr(head(head(cons(cons(incr(head(tail(pairs))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__pairs))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(0), _x62), _x52))))) → a__incr#(a__head(head(cons(cons(incr(0), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(tail(_x81)))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(a__tail(mark(_x81))))))))
mark#(incr(head(s(head(tail(odds)))))) → a__incr#(head(s(head(a__tail(a__odds)))))mark#(incr(head(s(head(tail(nats)))))) → a__incr#(head(s(head(mark(incr(nats))))))
mark#(incr(head(s(tail(incr(cons(pairs, _x72))))))) → a__incr#(a__head(s(a__tail(incr(cons(a__pairs, _x72))))))mark#(incr(incr(incr(tail(head(s(s(incr(odds))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(a__odds))))))))
mark#(incr(head(s(tail(incr(nats)))))) → a__incr#(a__head(s(a__tail(a__incr(a__nats)))))mark#(incr(head(s(head(incr(tail(_x71))))))) → a__incr#(head(s(a__head(a__incr(a__tail(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(cons(0, incr(nats)))))), _x62), _x52))))mark#(incr(head(s(pairs)))) → a__incr#(head(s(pairs)))
mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))mark#(incr(incr(incr(tail(head(s(s(pairs)))))))) → a__incr#(incr(incr(tail(a__head(s(s(cons(0, incr(odds)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(tail(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__tail(mark(_x101))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(odds))))))) → a__incr#(incr(incr(tail(head(s(odds))))))
mark#(incr(nats)) → a__incr#(a__nats)mark#(incr(head(s(tail(incr(pairs)))))) → a__incr#(head(s(a__tail(a__incr(a__pairs)))))
mark#(incr(head(nil))) → a__incr#(head(nil))mark#(incr(head(s(head(tail(incr(_x71))))))) → a__incr#(head(s(head(a__tail(a__incr(mark(_x71)))))))
mark#(incr(incr(incr(tail(head(incr(nats))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(cons(0, incr(nats))))))))mark#(incr(head(head(cons(cons(incr(head(incr(_x91))), _x62), _x31))))) → a__incr#(head(mark(cons(a__incr(a__head(a__incr(mark(_x91)))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(head(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(a__head(mark(_x111)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(incr(a__incr(tail(a__head(mark(_x61))))))
mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(a__incr(incr(tail(head(mark(_x61))))))mark#(incr(incr(incr(tail(tail(_x61)))))) → a__incr#(a__incr(a__incr(a__tail(a__tail(mark(_x61))))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(a__tail(mark(0)))))mark#(incr(head(s(tail(incr(head(0))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(0))))))
mark#(incr(head(s(tail(incr(cons(nats, _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(a__nats, _x72))))))mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(head(s(a__head(cons(mark(_x61), _x62)))))
mark#(incr(head(s(tail(nats))))) → a__incr#(head(s(mark(incr(nats)))))mark#(incr(incr(incr(tail(head(0)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(0)))))
mark#(incr(incr(incr(tail(head(s(cons(_x81, _x82)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(cons(mark(_x81), _x82)))))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(a__tail(head(a__nats)))))
mark#(incr(incr(incr(tail(odds))))) → a__incr#(a__incr(a__incr(a__tail(a__odds))))mark#(incr(incr(incr(tail(nil))))) → a__incr#(a__incr(a__incr(tail(nil))))
mark#(incr(head(s(tail(incr(incr(head(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(a__head(mark(_x81))))))))mark#(incr(head(head(0)))) → a__incr#(head(head(0)))
mark#(incr(incr(incr(tail(head(tail(_x71))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__tail(mark(_x71)))))))mark#(incr(incr(incr(tail(s(nil)))))) → a__incr#(incr(incr(a__tail(s(nil)))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(head(_x111))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(a__head(mark(_x111)))))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(head(a__nats)))), _x62))))
mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(head(s(a__head(incr(mark(_x61))))))mark#(incr(incr(incr(tail(head(cons(_x71, _x72))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(cons(mark(_x71), _x72))))))
mark#(incr(incr(incr(tail(head(head(tail(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(tail(mark(_x81))))))))mark#(incr(incr(incr(tail(head(head(tail(nil)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(nil)))))))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(cons(0, incr(nats))))))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(tail(head(cons(0, incr(nats)))))))
mark#(incr(incr(incr(tail(s(s(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(s(s(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(pairs), _x62), _x52))))
mark#(incr(head(s(tail(incr(incr(odds))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(a__odds))))))mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(mark(_x91)))), _x62), _x52))))
mark#(incr(head(0))) → a__incr#(head(0))mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(head(a__odds)))))))))
mark#(incr(incr(incr(tail(s(nats)))))) → a__incr#(a__incr(a__incr(tail(s(a__nats)))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(a__tail(head(cons(0, incr(nats)))))))
mark#(incr(head(s(tail(incr(cons(pairs, _x72))))))) → a__incr#(a__head(s(tail(a__incr(cons(a__pairs, _x72))))))mark#(incr(head(head(pairs)))) → a__incr#(head(head(cons(0, incr(odds)))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(odds))))))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(incr(a__incr(tail(a__head(head(nil))))))
mark#(incr(head(head(cons(0, _x52))))) → a__incr#(a__head(head(cons(0, _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(_x91))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(mark(_x91)))))))))
mark#(incr(head(s(tail(incr(incr(_x71))))))) → a__incr#(a__head(s(tail(a__incr(a__incr(mark(_x71)))))))mark#(incr(head(head(pairs)))) → a__incr#(head(a__head(a__pairs)))
mark#(incr(head(s(head(s(0)))))) → a__incr#(a__head(s(a__head(s(0)))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(a__incr(a__pairs)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(s(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(s(mark(_x121))))))), _x62), _x52))))mark#(incr(head(head(s(_x51))))) → a__incr#(a__head(head(s(mark(_x51)))))
mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__odds)), _x62), _x52))))mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))
mark#(incr(head(s(tail(incr(cons(_x71, _x72))))))) → a__incr#(head(s(a__tail(a__incr(cons(mark(_x71), _x72))))))mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(head(head(cons(a__nats, _x52))))
mark#(incr(head(s(tail(incr(cons(cons(_x81, _x82), _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(cons(mark(_x81), _x82), _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(odds)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(a__odds)))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(pairs))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(a__pairs))))))mark#(incr(head(head(cons(cons(incr(head(nats)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__nats)), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(nil))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(tail(head(a__incr(nil))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(pairs)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__pairs)), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(incr(tail(a__head(a__head(a__odds))))))mark#(incr(head(s(tail(incr(cons(s(_x81), _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(s(mark(_x81)), _x72))))))
mark#(incr(incr(incr(tail(head(s(head(_x81)))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__head(mark(_x81))))))))mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__nats))))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(pairs), _x62), _x52))))mark#(incr(head(s(head(odds))))) → a__incr#(head(s(a__head(a__odds))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(a__tail(mark(0)))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(a__incr(cons(0, incr(odds)))))))))
mark#(incr(head(s(head(tail(cons(_x71, _x72))))))) → a__incr#(head(s(a__head(a__tail(cons(mark(_x71), _x72))))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(odds))))))
mark#(incr(head(head(cons(cons(incr(head(pairs)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__pairs)), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(nats))))))
mark#(incr(incr(incr(tail(head(head(s(_x81)))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(s(mark(_x81))))))))mark#(incr(head(odds))) → a__incr#(head(a__incr(a__pairs)))
mark#(incr(incr(incr(tail(head(s(s(incr(nats))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__nats))))))))mark#(incr(incr(incr(tail(s(_x61)))))) → a__incr#(a__incr(incr(tail(s(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(a__nats)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(nats)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(nats)), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(incr(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(a__incr(mark(_x81))))))))mark#(incr(incr(nats))) → a__incr#(incr(nats))
mark#(incr(head(s(tail(tail(_x61)))))) → a__incr#(a__head(s(a__tail(a__tail(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__tail(mark(_x91)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(_x61, _x62), _x52))))) → a__incr#(head(a__head(cons(cons(mark(_x61), _x62), _x52))))mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))
mark#(incr(head(s(tail(incr(s(_x71))))))) → a__incr#(a__head(s(a__tail(a__incr(s(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(s(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(s(mark(_x101))))), _x62), _x52))))
mark#(incr(incr(incr(tail(s(pairs)))))) → a__incr#(a__incr(a__incr(a__tail(s(a__pairs)))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(odds)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(a__odds)))))))))
mark#(incr(incr(incr(tail(head(head(0))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(0))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(mark(0)))), _x62), _x52))))
mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))mark#(incr(head(s(tail(incr(incr(incr(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(a__incr(mark(_x81))))))))
mark#(incr(incr(incr(tail(head(incr(tail(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(a__tail(mark(_x81))))))))mark#(incr(head(s(tail(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__tail(cons(mark(_x61), _x62)))))
mark#(incr(incr(incr(tail(head(s(nil))))))) → a__incr#(incr(incr(tail(a__head(s(nil))))))mark#(incr(head(head(cons(cons(incr(pairs), _x32), a__incr(a__pairs)))))) → a__incr#(a__head(cons(mark(a__incr(a__pairs)), _x32)))
mark#(incr(incr(incr(tail(head(head(cons(_x81, _x82)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(cons(mark(_x81), _x82)))))))mark#(incr(head(s(tail(s(_x61)))))) → a__incr#(head(s(a__tail(s(mark(_x61))))))
mark#(incr(head(s(head(tail(cons(_x71, _x72))))))) → a__incr#(head(s(head(tail(cons(mark(_x71), _x72))))))mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x31))))) → a__incr#(head(mark(cons(a__incr(mark(_x71)), _x62))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(cons(0, incr(odds))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(incr(_x91))), _x62), _x52))))) → a__incr#(head(head(cons(cons(a__incr(a__head(a__incr(mark(_x91)))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(tail(a__head(a__nats)))))mark#(incr(head(head(cons(cons(cons(_x71, _x72), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(cons(mark(_x71), _x72), _x62), _x52))))

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, head, a__head, nil, cons

Strategy

The right-hand side of the rule mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(_x131))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(mark(_x131)))))))), _x62), _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
a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(s(mark(_x131)))))))), _x62), _x52)))) 
a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(a__head(mark(_x141))))))))), _x62), _x52)))) 
a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(cons(mark(_x141), _x142)))))))), _x62), _x52)))) 
a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(s(s(s(mark(_x131)))))))), _x62), _x52)))) 
a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(0))))))), _x62), _x52)))) 
a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(a__nats))))))), _x62), _x52)))) 
a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(s(mark(_x141))))))))), _x62), _x52)))) 
a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(a__odds))))))), _x62), _x52)))) 
a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(a__pairs))))))), _x62), _x52)))) 
a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(a__tail(mark(_x141))))))))), _x62), _x52)))) 
a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(nil))))))), _x62), _x52)))) 
a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(a__incr(mark(_x141))))))))), _x62), _x52)))) 
a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(mark(_x131)))))))), _x62), _x52)))) 
a__incr#(head(mark(cons(incr(head(a__tail(a__head(s(s(s(mark(_x131)))))))), _x62)))) 
Thus, the rule mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(_x131))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(mark(_x131)))))))), _x62), _x52)))) is replaced by the following rules:
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(cons(_x141, _x142)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(cons(mark(_x141), _x142)))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(_x131))))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(s(s(s(mark(_x131)))))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(_x131))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(mark(_x131)))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(tail(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(a__tail(mark(_x141))))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(odds))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(a__odds))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(s(mark(_x141))))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(nats))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(a__nats))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(_x131))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(s(mark(_x131)))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(nil))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(nil))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(a__incr(mark(_x141))))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(head(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(a__head(mark(_x141))))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(pairs))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(a__pairs))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(_x131))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(s(s(s(mark(_x131)))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(0))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(0))))))), _x62), _x52))))

Problem 31: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(head(cons(head(cons(0, _x72)), _x52))))) → a__incr#(a__head(a__head(cons(head(cons(0, _x72)), _x52))))mark#(s(X)) → mark#(X)
mark#(incr(head(head(cons(head(cons(0, _x72)), _x52))))) → a__incr#(a__head(head(cons(a__head(cons(0, _x72)), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(0), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(s(0), _x132))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(s(a__incr(mark(_x221))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(head(nats))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(a__nats))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nil, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(nil)), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(tail(_x151))))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(s(a__tail(mark(_x151)))))))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(incr(_x111))))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(a__incr(mark(_x111)))))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(odds))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(a__odds))), _x122)))))), _x62), _x52))))
mark#(incr(head(s(tail(s(_x61)))))) → a__incr#(a__head(s(tail(s(mark(_x61))))))mark#(incr(head(head(cons(cons(pairs, _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__pairs, _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(0)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(0)), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(nats))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__nats))), _x62), _x52))))
mark#(incr(head(s(head(incr(nats)))))) → a__incr#(head(s(head(a__incr(a__nats)))))mark#(incr(head(head(cons(cons(incr(0), _x62), _x31))))) → a__incr#(head(mark(cons(incr(0), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(pairs), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(pairs)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(a__pairs), _x132))))), incr(_x91))))))), _x32)))mark#(incr(head(s(s(_x51))))) → a__incr#(head(s(s(mark(_x51)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(_x131))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(mark(_x131)))))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(0)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(0)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(head(_x131))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(a__head(mark(_x131)))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(_x131, _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(cons(mark(_x131), _x132))), _x122)))))), _x62))))
mark#(incr(incr(incr(tail(head(s(0))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(0))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(pairs, _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(a__pairs, _x212))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(cons(_x171, _x172)), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(s(cons(mark(_x171), _x172)), _x132))), _x122)))))), _x62))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(a__tail(mark(0)))))
mark#(incr(head(s(tail(nats))))) → a__incr#(a__head(s(tail(nats))))mark#(incr(head(head(cons(head(cons(nats, _x72)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(cons(a__nats, _x72)), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(tail(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__tail(mark(_x121))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(0)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(0)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(tail(nil))))) → a__incr#(a__head(s(tail(nil))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(incr(cons(a__tail(a__head(mark(_x141))), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(incr(a__pairs))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x151))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(mark(s(mark(a__nats)))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(pairs)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__pairs)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(nil)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(nil)))))))))
mark#(incr(head(cons(_x41, _x42)))) → a__incr#(head(cons(mark(_x41), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(nats))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__nats))), _x62), _x52))))
mark#(incr(head(head(cons(incr(_x61), _x52))))) → a__incr#(a__head(a__head(cons(a__incr(mark(_x61)), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(nil)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(nil)), _x122)))))), _x62))))
mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(a__incr(incr(a__tail(a__head(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(mark(_x141))), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(s(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(s(mark(_x91)))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(head(a__head(a__odds))))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(incr(tail(a__head(head(a__odds))))))mark#(incr(head(head(cons(cons(incr(head(pairs)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(pairs)), _x62), _x52))))
mark#(incr(head(s(head(incr(pairs)))))) → a__incr#(head(s(a__head(a__incr(a__pairs)))))mark#(incr(head(head(cons(cons(incr(head(pairs)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(cons(0, incr(odds)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(mark(_x141))))), incr(_x101)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(_x231, _x232))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(cons(mark(_x231), _x232))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(tail(odds))))) → a__incr#(a__head(s(tail(a__odds))))mark#(incr(incr(incr(tail(head(head(tail(odds)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(a__odds)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(mark(s(a__incr(mark(_x221))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(head(nats))) → a__incr#(a__head(nats))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(nats), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(s(a__nats))), incr(_x101)))))), _x62), _x52))))
mark#(incr(head(s(tail(incr(head(head(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(a__head(mark(_x81))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(s(_x221), _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(s(mark(_x221)), _x212))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(mark(_x71)), _x62))))mark#(incr(incr(incr(tail(head(odds)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__odds)))))
mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x52))))) → a__incr#(a__head(head(cons(cons(a__incr(mark(_x71)), _x62), _x52))))mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(nats))))))
mark#(incr(incr(incr(tail(s(nil)))))) → a__incr#(a__incr(a__incr(tail(s(nil)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(incr(_x161)), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(s(a__incr(mark(_x161))))), incr(_x101)))))), _x62), _x52))))
mark#(incr(head(head(cons(head(cons(s(_x81), _x72)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(cons(s(mark(_x81)), _x72)), _x52))))mark#(incr(head(head(cons(cons(incr(tail(_x81)), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(a__tail(mark(_x81))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(0))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(0))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(0)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(s(s(0)))))), _x62), _x52))))
mark#(incr(head(s(tail(pairs))))) → a__incr#(a__head(s(tail(pairs))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(pairs)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__pairs)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(tail(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(a__tail(mark(_x121))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(incr(_x241)))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__tail(a__incr(mark(_x241))))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(_x131))))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(s(s(s(mark(_x131)))))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(_x131), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(tail(mark(_x131)), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(0)))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x161))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(mark(s(mark(_x151)))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(odds)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(a__odds)), _x122)))))), _x62))))
mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(incr(a__incr(a__tail(a__head(s(mark(_x71)))))))mark#(incr(head(head(cons(head(cons(pairs, _x72)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(cons(pairs, _x72)), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(cons(_x101, _x102)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(cons(mark(_x101), _x102)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__tail(head(mark(_x101))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(tail(_x111))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(a__tail(mark(_x111)))))))))))mark#(incr(head(s(tail(incr(head(s(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(s(mark(_x81))))))))
mark#(incr(incr(incr(tail(incr(_x61)))))) → a__incr#(a__incr(a__incr(a__tail(a__incr(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(cons(0, incr(odds))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(head(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__head(mark(_x91)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(pairs)), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(a__pairs)), _x62))))
mark#(incr(incr(incr(tail(head(head(cons(_x81, _x82)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(cons(mark(_x81), _x82)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(0)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(0)), _x122)))))), _x62), _x52))))
mark#(incr(head(s(nats)))) → a__incr#(head(s(nats)))mark#(incr(incr(incr(tail(head(s(s(incr(incr(head(_x111))))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(a__head(mark(_x111)))))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(mark(_x141))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(head(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(a__head(mark(_x151)))), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(head(pairs), _x52))))) → a__incr#(a__head(a__head(cons(a__head(a__pairs), _x52))))mark#(incr(head(s(head(odds))))) → a__incr#(a__head(s(a__head(a__odds))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(_x231))), _x191))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__tail(mark(_x231)))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(tail(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(a__tail(mark(_x111)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(incr(tail(a__head(cons(0, incr(nats)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(nats), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(nats)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__nats), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__nats)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(_x121, _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(mark(_x121), _x122)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(s(head(_x71))))))) → a__incr#(a__incr(a__incr(tail(s(a__head(mark(_x71)))))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(a__odds))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(cons(_x141, _x142)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(cons(mark(_x141), _x142)), _x122)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(incr(incr(tail(a__head(head(nil))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(pairs)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(a__pairs)), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(tail(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(a__tail(mark(_x111)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(0)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(0)), _x122)))))), _x62))))mark#(incr(head(head(cons(head(cons(_x71, _x72)), _x52))))) → a__incr#(head(a__head(cons(a__head(cons(mark(_x71), _x72)), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(odds, _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__odds, _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__tail(head(a__nats)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(tail(_x221), _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(cons(a__tail(mark(_x221)), _x202))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(odds, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(a__odds)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(incr(0))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(0))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(pairs))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(a__pairs))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(s(nil)))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(s(nil)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(_x201, _x191))), _x161))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(mark(s(mark(mark(_x201))))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(head(_x141)))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(a__head(mark(_x141))))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(nats)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(odds), _x132))), _x91)))))), _x32), incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__odds), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__odds), _x132))))), incr(_x91))))))), _x32)))mark#(incr(head(head(cons(cons(incr(head(nats)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__nats)), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(0))))))) → a__incr#(a__incr(incr(tail(a__head(s(0))))))mark#(incr(head(head(cons(cons(0, _x62), _x31))))) → a__incr#(a__head(mark(cons(0, _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(cons(0, incr(nats)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(cons(_x141, _x142)))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(cons(mark(_x141), _x142)))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(tail(_x201)), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(tail(_x201))), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(a__tail(mark(_x201))), _x132))))), incr(_x91))))))), _x32)))mark#(incr(incr(incr(tail(s(cons(_x71, _x72))))))) → a__incr#(a__incr(a__incr(a__tail(s(cons(mark(_x71), _x72))))))
mark#(incr(head(s(tail(incr(cons(pairs, _x72))))))) → a__incr#(head(s(a__tail(a__incr(cons(pairs, _x72))))))mark#(incr(incr(incr(tail(head(incr(nats))))))) → a__incr#(a__incr(a__incr(tail(a__head(incr(a__nats))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(tail(_x161)), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(s(a__tail(mark(_x161))))), incr(_x101)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(head(_x131))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(a__head(mark(_x131)))), _x122)))))), _x62))))
mark#(cons(X1, X2)) → mark#(X1)mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(incr(a__pairs)))))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(a__tail(head(cons(0, incr(nats)))))))mark#(incr(incr(incr(tail(head(s(s(incr(s(_x101)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(s(mark(_x101))))))))))
mark#(incr(head(s(head(s(pairs)))))) → a__incr#(a__head(s(a__head(s(a__pairs)))))mark#(incr(head(s(head(incr(nats)))))) → a__incr#(head(s(a__head(incr(a__nats)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(_x231))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(incr(a__tail(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(mark(0)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(s(_x231))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(s(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(_x191)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(a__head(mark(_x191))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(incr(_x171)), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(s(a__incr(mark(_x171))), _x132))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(a__head(head(cons(cons(a__incr(a__pairs), _x62), _x52))))
mark#(incr(head(s(tail(incr(head(_x71))))))) → a__incr#(a__head(s(a__tail(incr(a__head(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(_x171)), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(s(a__head(mark(_x171))), _x132))), _x122)))))), _x62))))
mark#(incr(head(s(tail(s(pairs)))))) → a__incr#(a__head(s(a__tail(s(a__pairs)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(odds), _x151))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(mark(s(a__odds))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(odds))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__odds))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(_x131), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(incr(cons(a__tail(mark(_x131)), _x122)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(s(incr(_x71))))))) → a__incr#(a__incr(a__incr(tail(s(a__incr(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(cons(_x141, _x142)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(cons(mark(_x141), _x142)))))))), _x62), _x52))))
mark#(incr(head(head(cons(head(cons(0, _x72)), _x31))))) → a__incr#(a__head(mark(a__head(cons(0, _x72)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(tail(_x131))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(a__tail(mark(_x131)))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x52))))) → a__incr#(head(head(cons(cons(a__incr(a__head(mark(_x81))), _x62), _x52))))mark#(incr(head(s(tail(incr(head(odds))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(a__odds))))))
mark#(incr(incr(incr(tail(head(s(s(incr(nats))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__nats))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(nil), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(nil), _x122)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(a__tail(a__head(a__nats)))))mark#(incr(head(head(cons(cons(incr(head(nats)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(cons(0, incr(nats)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(nil))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(nil))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__tail(mark(_x91)))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(incr(a__tail(head(s(a__nats))))))mark#(incr(incr(incr(tail(nil))))) → a__incr#(incr(a__incr(a__tail(nil))))
mark#(incr(incr(incr(tail(head(s(s(incr(0))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(0))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(s(s(mark(_x121))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(incr(nil))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(nil))), _x62), _x52))))mark#(incr(incr(incr(tail(head(nil)))))) → a__incr#(a__incr(a__incr(tail(a__head(nil)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(incr(_x221), _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(cons(a__incr(mark(_x221)), _x202))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(head(a__odds))))))
mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(incr(incr(a__tail(a__head(s(a__nats))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(cons(0, incr(nats)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(incr(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__incr(mark(_x121))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(0, _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(0)), incr(_x101)))))), _x62), _x52))))
mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(head(s(cons(mark(_x51), _x52))))mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(mark(_x81))), _x62), _x52))))
mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(head(head(cons(nats, _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(_x151)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(tail(head(cons(s(mark(_x151)), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(head(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__head(mark(_x121))))))), _x62), _x52))))mark#(incr(head(odds))) → a__incr#(a__head(a__odds))
mark#(incr(head(head(cons(head(_x61), _x52))))) → a__incr#(a__head(head(cons(a__head(mark(_x61)), _x52))))mark#(incr(head(s(tail(incr(cons(pairs, _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(cons(0, incr(odds)), _x72))))))
mark#(incr(head(s(tail(incr(incr(s(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(s(mark(_x81))))))))mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(head(s(a__tail(incr(a__incr(cons(0, incr(nats))))))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(incr(a__tail(a__head(cons(0, incr(nats)))))))mark#(incr(head(head(incr(_x51))))) → a__incr#(a__head(a__head(a__incr(mark(_x51)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(nats))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__tail(a__nats))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(s(tail(incr(incr(nil))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(nil))))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(nats)))))mark#(incr(incr(incr(tail(head(s(head(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(a__head(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(head(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(a__head(mark(_x111)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(0)))))) → a__incr#(a__incr(incr(tail(head(0)))))
mark#(incr(head(s(tail(incr(incr(0))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(0))))))mark#(incr(incr(incr(tail(0))))) → a__incr#(a__incr(a__incr(a__tail(0))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(a__tail(a__head(mark(_x101))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(nats))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(a__nats))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(tail(_x111))))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(a__tail(mark(_x111)))))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(0, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(0)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(cons(_x151, _x152), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(cons(mark(_x151), _x152))), incr(_x101)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(tail(head(mark(_x101))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(s(nil)))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(s(nil)))))))mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(tail(incr(a__incr(a__nats))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(nats))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(s(a__nats))))))), _x62), _x52))))mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(a__head(nats))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(tail(incr(a__incr(cons(0, incr(nats))))))))mark#(incr(head(head(cons(odds, _x52))))) → a__incr#(head(a__head(cons(a__odds, _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(_x151)), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(tail(mark(0)))))
mark#(incr(incr(incr(tail(head(s(s(incr(_x91))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(mark(_x91)))))))))mark#(incr(head(s(head(0))))) → a__incr#(head(s(a__head(0))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(_x211, _x192), mark(_x211)))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(cons(mark(mark(_x211)), _x192)), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(tail(_x221)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__tail(mark(_x221))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(pairs))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(a__pairs))), _x122)))))), _x62), _x52))))
mark#(incr(head(s(odds)))) → a__incr#(head(s(a__odds)))mark#(incr(head(s(tail(odds))))) → a__incr#(a__head(s(a__tail(a__odds))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(cons(s(mark(_x151)), _x132))), _x122)))))), _x62))))mark#(incr(incr(incr(tail(head(s(0))))))) → a__incr#(incr(incr(tail(a__head(s(0))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(head(_x221), _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(a__head(mark(_x221)), _x212))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(head(s(0)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(0)))))))
mark#(incr(head(s(head(s(head(_x71))))))) → a__incr#(a__head(s(a__head(s(a__head(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(_x231))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(s(a__incr(a__tail(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(tail(incr(tail(_x71))))))) → a__incr#(head(s(a__tail(a__incr(a__tail(mark(_x71)))))))mark#(incr(head(head(0)))) → a__incr#(a__head(head(0)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(head(mark(_x141))), _x122)))))), _x62))))mark#(incr(incr(incr(tail(head(incr(_x71))))))) → a__incr#(a__incr(a__incr(tail(a__head(incr(mark(_x71)))))))
mark#(incr(head(s(0)))) → a__incr#(head(s(0)))mark#(incr(incr(incr(tail(head(head(tail(nats)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(a__nats)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(odds)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(a__incr(a__pairs))), _x122)))))), _x62))))mark#(incr(head(head(tail(_x51))))) → a__incr#(a__head(a__head(a__tail(mark(_x51)))))
mark#(incr(incr(incr(tail(head(s(odds))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(a__odds))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(head(0)))), _x62))))
mark#(incr(incr(incr(tail(head(incr(0))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(0))))))mark#(incr(head(head(cons(s(_x61), _x52))))) → a__incr#(a__head(a__head(cons(s(mark(_x61)), _x52))))
mark#(incr(head(s(head(s(tail(_x71))))))) → a__incr#(a__head(s(a__head(s(a__tail(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(odds), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(tail(a__head(cons(s(a__odds), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(mark(_x141))))), incr(_x101)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(_x151)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(_x151)), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(incr(_x191)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__incr(mark(_x191))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(cons(0, incr(nats)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(s(mark(_x111)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(0)))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(tail(tail(_x91))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(a__tail(mark(_x91)))))))))mark#(incr(head(head(cons(cons(incr(odds), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(a__odds), _x62), _x52))))
mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(a__head(head(cons(cons(0, incr(nats)), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(_x101)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(incr(mark(_x101))))))))))
mark#(incr(incr(incr(tail(s(_x61)))))) → a__incr#(incr(a__incr(tail(s(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(head(_x151), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(a__head(mark(_x151)))), incr(_x101)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(tail(pairs)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(a__pairs)))))))mark#(incr(incr(incr(tail(s(0)))))) → a__incr#(a__incr(a__incr(tail(s(0)))))
mark#(incr(head(head(nats)))) → a__incr#(a__head(a__head(a__nats)))mark#(incr(head(head(cons(cons(incr(head(s(_x91))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(s(mark(_x91)))), _x62), _x52))))
mark#(incr(head(s(tail(nil))))) → a__incr#(head(s(a__tail(nil))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(odds)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__odds)))))), _x62), _x52))))
mark#(incr(head(s(head(tail(nil)))))) → a__incr#(head(s(a__head(a__tail(nil)))))mark#(incr(head(s(tail(incr(incr(_x71))))))) → a__incr#(head(s(a__tail(a__incr(a__incr(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(incr(_x201)), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(incr(_x201))), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__incr(mark(_x201))), _x132))))), incr(_x91))))))), _x32)))mark#(incr(incr(incr(tail(head(s(odds))))))) → a__incr#(incr(incr(tail(a__head(s(a__incr(a__pairs)))))))
mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(tail(mark(_x51)))))mark#(incr(incr(incr(tail(head(head(head(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__head(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(_x131, _x132))), _x122)))))), _x32), incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(mark(_x131), _x132))), _x122))))))))))) → a__incr#(head(cons(mark(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(mark(_x131), _x132))), _x122))))))), _x32)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(s(_x191)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(s(mark(_x191))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(tail(_x71), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__tail(mark(_x71)), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(_x131), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(mark(_x131)), _x122)))))), _x62), _x52))))
mark#(incr(head(s(tail(tail(_x61)))))) → a__incr#(head(s(a__tail(a__tail(mark(_x61))))))mark#(incr(incr(incr(tail(head(tail(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__tail(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(nil)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(nil)))))), _x62), _x52))))mark#(incr(head(s(tail(s(odds)))))) → a__incr#(a__head(s(a__tail(s(a__odds)))))
mark#(incr(incr(incr(tail(head(incr(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(a__odds))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(nats)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__nats)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(_x51, _x52))))) → a__incr#(head(a__head(cons(mark(_x51), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(pairs), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(s(a__pairs))), incr(_x101)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(head(a__head(a__incr(a__pairs)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(a__incr(mark(_x111)))))), _x62), _x52))))
mark#(incr(head(s(tail(s(incr(_x71))))))) → a__incr#(a__head(s(a__tail(s(a__incr(mark(_x71)))))))mark#(incr(head(head(cons(head(0), _x52))))) → a__incr#(a__head(a__head(cons(a__head(0), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(odds, _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(a__odds)), incr(_x101)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(a__head(odds)))))))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(a__head(odds)))))))))mark#(incr(head(s(head(head(_x61)))))) → a__incr#(head(s(a__head(a__head(mark(_x61))))))
mark#(incr(incr(incr(tail(s(pairs)))))) → a__incr#(a__incr(a__incr(tail(s(a__pairs)))))mark#(incr(head(s(tail(incr(cons(pairs, _x51))))))) → a__incr#(head(s(a__tail(cons(s(mark(a__pairs)), incr(_x51))))))
mark#(incr(incr(incr(tail(head(head(s(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(head(s(mark(_x81))))))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(incr(tail(a__head(a__head(a__incr(a__pairs)))))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(a__tail(head(nats)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(nats))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__nats))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(incr(tail(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(a__tail(mark(_x101))))), _x62), _x52))))mark#(incr(head(head(cons(_x51, _x52))))) → a__incr#(a__head(head(cons(mark(_x51), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(nil), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(s(nil), _x132))), _x122)))))), _x62))))mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))
mark#(incr(head(head(odds)))) → a__incr#(a__head(head(a__odds)))mark#(incr(incr(incr(tail(s(tail(_x71))))))) → a__incr#(a__incr(a__incr(tail(s(a__tail(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(cons(_x111, _x112))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(cons(mark(_x111), _x112))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(incr(incr(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(a__incr(mark(_x101))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(tail(s(_x91))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(s(mark(_x91)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(s(mark(_x151)))), _x122)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(head(head(a__odds))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(tail(_x191)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__tail(mark(_x191))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(cons(_x111, _x112))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(cons(mark(_x111), _x112))))), _x62), _x52))))mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(head(s(tail(a__incr(a__incr(a__nats))))))
mark#(incr(head(head(cons(cons(incr(head(cons(_x91, _x92))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(cons(mark(_x91), _x92))), _x62), _x52))))mark#(incr(incr(incr(tail(s(_x61)))))) → a__incr#(incr(a__incr(a__tail(s(mark(_x61))))))
mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(nil))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(nats, _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(a__nats, _x132))), _x122)))))), _x62))))
mark#(incr(head(s(tail(s(nats)))))) → a__incr#(a__head(s(a__tail(s(a__nats)))))mark#(incr(incr(incr(tail(head(s(s(incr(odds))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(odds))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(pairs, _x191))), _x151))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(mark(s(mark(a__pairs)))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(pairs), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__pairs), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(incr(pairs))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(nats)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(head(mark(_x141))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(head(_x161)))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(a__head(mark(_x161))))), _x122)))))), _x62), _x52))))
mark#(incr(head(s(tail(incr(cons(nil, _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(nil, _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(odds)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(incr(cons(a__tail(a__head(a__odds)), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(pairs))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__pairs))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(s(_x201)), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(_x201))), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(s(mark(_x201))), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(incr(incr(tail(s(cons(_x71, _x72))))))) → a__incr#(a__incr(a__incr(tail(s(cons(mark(_x71), _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(incr(_x131))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(a__incr(mark(_x131)))))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(s(nil)))))))) → a__incr#(a__incr(a__incr(tail(a__head(head(s(nil)))))))mark#(incr(head(s(tail(incr(incr(pairs))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(a__pairs))))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(cons(_x111, _x112))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(cons(mark(_x111), _x112))))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(incr(_x141)))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(a__incr(mark(_x141))))), _x122)))))), _x62))))
mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(a__incr(tail(a__head(head(nil))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(mark(_x101))))), _x62), _x52))))
mark#(incr(head(s(head(s(nats)))))) → a__incr#(a__head(s(a__head(s(a__nats)))))mark#(incr(head(head(cons(cons(incr(head(incr(cons(_x101, _x102)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(cons(mark(_x101), _x102)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(incr(_x131))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(a__incr(mark(_x131)))), _x122)))))), _x62))))mark#(incr(incr(incr(tail(head(head(s(nats)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(a__nats)))))))
mark#(incr(head(s(head(s(odds)))))) → a__incr#(a__head(s(a__head(s(a__odds)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(incr(_x161)))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(a__incr(mark(_x161))))), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x151))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(s(mark(_x151)))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(head(_x151), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(a__head(mark(_x151)), _x132))), _x122)))))), _x62))))
mark#(incr(incr(incr(tail(head(head(s(pairs)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(a__pairs)))))))mark#(incr(head(s(tail(incr(cons(tail(_x81), _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(a__tail(mark(_x81)), _x72))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(_x131))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(s(s(a__tail(mark(_x131)))))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(incr(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(a__incr(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(_x131))))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(a__head(s(s(s(mark(_x131)))))))), _x62))))mark#(incr(head(nats))) → a__incr#(a__head(cons(0, incr(nats))))
mark#(incr(incr(incr(tail(head(incr(nats))))))) → a__incr#(incr(a__incr(tail(a__head(a__incr(a__nats))))))mark#(incr(incr(incr(pairs)))) → a__incr#(a__incr(a__incr(a__pairs)))
mark#(incr(incr(incr(tail(head(s(s(incr(head(nil)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__head(nil)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(s(s(s(s(mark(_x141))))))))), _x62), _x52))))
mark#(incr(head(s(head(tail(cons(0, _x72))))))) → a__incr#(head(s(head(a__tail(cons(0, _x72))))))mark#(incr(incr(incr(tail(head(s(s(pairs)))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__pairs)))))))
mark#(incr(head(s(head(tail(tail(_x71))))))) → a__incr#(head(s(head(a__tail(a__tail(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(_x121)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(s(s(mark(_x121))))))), _x62))))
mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(a__incr(tail(a__head(s(a__nats))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(nats)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(a__nats)))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(s(_x161)), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(s(s(mark(_x161))))), incr(_x101)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(cons(_x131, _x132))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(s(s(cons(mark(_x131), _x132))))))), _x62), _x52))))
mark#(incr(head(pairs))) → a__incr#(head(a__pairs))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(_x131))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(tail(a__head(s(s(s(mark(_x131)))))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(_x91))))))))) → a__incr#(a__incr(incr(tail(head(s(s(incr(mark(_x91)))))))))mark#(incr(head(head(cons(head(head(_x71)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(a__head(mark(_x71))), _x52))))
mark#(incr(incr(incr(tail(head(0)))))) → a__incr#(a__incr(incr(tail(a__head(0)))))mark#(incr(incr(incr(tail(head(s(s(head(_x91))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__head(mark(_x91)))))))))
mark#(incr(head(head(cons(head(cons(_x71, _x51)), mark(_x71)))))) → a__incr#(a__head(a__head(cons(mark(mark(_x71)), _x52))))mark#(incr(head(s(tail(pairs))))) → a__incr#(a__head(s(tail(cons(0, incr(odds))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(nil), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(nil)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(nil), _x132))))), incr(_x91))))))), _x32)))mark#(incr(head(head(cons(head(cons(_x71, _x72)), _x52))))) → a__incr#(a__head(a__head(cons(head(cons(mark(_x71), _x72)), _x52))))
mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(a__incr(tail(a__head(head(mark(_x71)))))))mark#(incr(incr(pairs))) → a__incr#(a__incr(cons(0, incr(odds))))
mark#(incr(head(head(cons(head(cons(0, _x72)), _x52))))) → a__incr#(head(a__head(cons(a__head(cons(0, _x72)), _x52))))mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(tail(a__head(mark(_x141))), _x122)))))), _x62))))mark#(incr(incr(incr(tail(head(s(s(incr(_x91))))))))) → a__incr#(incr(incr(tail(head(s(s(a__incr(mark(_x91)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(0))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(0))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(pairs)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(a__pairs)))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(nats)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(a__nats)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(nil))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(a__incr(nil))))), _x62))))
mark#(incr(head(s(tail(0))))) → a__incr#(head(s(a__tail(0))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(nil, _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(nil, _x212))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(cons(_x121, _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(cons(mark(_x121), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x91)))))), _x32), incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(_x151)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(_x151)), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(odds)), _x62), _x52))))mark#(incr(head(s(head(s(incr(_x71))))))) → a__incr#(a__head(s(a__head(s(a__incr(mark(_x71)))))))
mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(mark(0))mark#(incr(head(s(head(incr(head(_x71))))))) → a__incr#(head(s(a__head(a__incr(a__head(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(a__nats)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(a__nats)), _x132))))), incr(_x91))))))), _x32)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(nats))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(a__nats))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(s(mark(_x151)))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(pairs))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__tail(a__pairs))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(odds)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(s(a__odds)))))))), _x62), _x52))))mark#(incr(head(s(tail(incr(cons(_x71, _x72))))))) → a__incr#(a__head(s(tail(a__incr(cons(mark(_x71), _x72))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(cons(_x131, _x132), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(cons(mark(_x131), _x132), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(0), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(0)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(0), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(head(s(mark(_x61))))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(a__head(head(a__incr(a__pairs)))))))
mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(cons(0, incr(nats))))))))mark#(incr(incr(incr(tail(head(head(s(nil)))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(s(nil)))))))
mark#(incr(head(head(cons(cons(nil, _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(nil, _x62), _x52))))mark#(incr(head(s(tail(incr(head(pairs))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(a__pairs))))))
mark#(incr(incr(pairs))) → a__incr#(a__incr(pairs))mark#(incr(incr(incr(tail(head(incr(_x71))))))) → a__incr#(a__incr(incr(tail(a__head(a__incr(mark(_x71)))))))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(a__tail(incr(incr(a__nats))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(_x201, _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(head(cons(mark(_x201), _x202))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(nil))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(incr(nil))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(head(_x131), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__head(mark(_x131)), _x122)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(nil))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(nil))))))))a__incr#(cons(X, XS)) → mark#(X)
mark#(incr(incr(incr(tail(head(s(s(incr(head(nil)))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(a__head(nil)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(head(_x131))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(a__head(mark(_x131)))))))), _x62), _x52))))
mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(_x111))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(mark(_x111)))))), _x62))))
mark#(incr(head(s(head(incr(nil)))))) → a__incr#(head(s(a__head(a__incr(nil)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(cons(a__nats, _x202))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(head(mark(nats)))mark#(incr(head(head(cons(cons(_x61, _x62), _x31))))) → a__incr#(a__head(mark(cons(mark(_x61), _x62))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(nats)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(a__nats)))))))))mark#(incr(head(s(tail(s(s(_x71))))))) → a__incr#(a__head(s(a__tail(s(s(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(_x191)), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(mark(_x191))), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(mark(_x191))), _x132))))), incr(_x91))))))), _x32)))mark#(incr(incr(incr(tail(head(s(s(incr(incr(pairs)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(a__pairs)))))))))
mark#(incr(head(s(tail(incr(head(nil))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(nil))))))mark#(incr(incr(incr(tail(head(s(incr(_x81)))))))) → a__incr#(incr(incr(tail(a__head(s(a__incr(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(nil))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(nil))))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(tail(head(cons(0, incr(nats)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(nats))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(s(s(s(a__nats))))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(tail(mark(0)))))
mark#(incr(head(head(cons(cons(incr(head(head(_x91))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__head(mark(_x91)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(0, _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(cons(0, _x202))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(s(_x141)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(s(mark(_x141))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(incr(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(a__incr(mark(_x151)))), _x122)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(incr(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__incr(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(mark(_x101))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(cons(_x91, _x92))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(cons(mark(_x91), _x92))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(cons(_x141, _x142)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(cons(mark(_x141), _x142)))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(cons(0, incr(nats)))))), _x62), _x52))))mark#(incr(head(s(tail(cons(_x61, _x62)))))) → a__incr#(a__head(s(tail(cons(mark(_x61), _x62)))))
mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(a__head(s(tail(a__incr(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(incr(mark(_x221))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(_x131, _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(head(cons(mark(_x131), _x132))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), a__incr(mark(_x221))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(s(mark(a__incr(mark(_x221))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(incr(a__incr(tail(head(head(nil))))))mark#(incr(incr(incr(tail(head(head(s(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(s(mark(_x81))))))))
mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))mark#(incr(incr(incr(tail(head(incr(head(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(a__head(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(odds)))))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(a__head(s(s(s(a__incr(a__odds)))))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(0), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(0))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(pairs)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(a__pairs)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(nil)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(s(nil)))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(odds))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(a__odds))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(odds), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__odds))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(_x141)))))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(a__head(s(s(s(a__incr(mark(_x141))))))))), _x62))))mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(incr(a__incr(a__tail(a__head(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(_x191)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(a__head(mark(_x191))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(odds)))) → a__incr#(a__head(a__head(a__odds)))
mark#(incr(head(s(head(tail(cons(nil, _x72))))))) → a__incr#(head(s(head(a__tail(cons(nil, _x72))))))mark#(incr(head(head(nats)))) → a__incr#(a__head(head(a__nats)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__nats)))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(a__incr(a__pairs)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(tail(_x191)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__tail(mark(_x191))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(_x201, _x191))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(mark(_x201))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(odds)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(a__odds)))))), _x62), _x52))))mark#(incr(incr(0))) → a__incr#(a__incr(0))
mark#(incr(incr(incr(tail(head(0)))))) → a__incr#(incr(a__incr(tail(a__head(0)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(nil))))), _x32), incr(a__head(tail(head(a__incr(nil)))))))))) → a__incr#(head(cons(mark(incr(a__head(tail(head(a__incr(nil)))))), _x32)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(nil))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(nil))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(tail(_x91))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__tail(mark(_x91)))))))))
mark#(incr(head(s(tail(pairs))))) → a__incr#(head(s(a__tail(cons(0, incr(odds))))))mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(head(cons(0, incr(nats))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(_x101)))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(a__head(mark(_x101))))))))))mark#(incr(head(s(tail(head(_x61)))))) → a__incr#(a__head(s(tail(a__head(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(mark(_x121))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(nil)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(nil)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(s(s(incr(tail(_x101)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__tail(mark(_x101))))))))))mark#(incr(incr(incr(tail(head(s(s(nats)))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__nats)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(tail(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__tail(mark(_x111)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(0))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(0))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(head(_x151))))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(s(a__head(mark(_x151)))))))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(tail(0)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(0)))))))
mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(incr(incr(tail(head(s(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(head(cons(s(mark(_x151)), _x132))), _x122)))))), _x62))))
mark#(incr(incr(incr(tail(head(nil)))))) → a__incr#(a__incr(incr(tail(a__head(nil)))))mark#(incr(head(head(cons(head(cons(pairs, _x72)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(cons(cons(0, incr(odds)), _x72)), _x52))))
mark#(incr(head(s(head(incr(incr(_x71))))))) → a__incr#(head(s(a__head(a__incr(a__incr(mark(_x71)))))))mark#(incr(head(s(tail(nats))))) → a__incr#(head(s(a__tail(a__nats))))
mark#(incr(head(head(cons(cons(incr(head(incr(pairs))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(a__pairs))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(0)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(_x211, _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(mark(cons(mark(_x211), _x212))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(s(s(s(a__incr(mark(_x141))))))))), _x62), _x52))))
mark#(incr(incr(pairs))) → a__incr#(incr(a__pairs))mark#(incr(head(head(cons(cons(incr(head(incr(s(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(s(mark(_x101))))), _x62), _x52))))
mark#(incr(head(s(tail(s(cons(_x71, _x72))))))) → a__incr#(a__head(s(a__tail(s(cons(mark(_x71), _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(incr(_x201)), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(incr(_x201))), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(a__incr(mark(_x201))), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(incr(a__pairs), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(tail(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(a__tail(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(_x141)))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(mark(_x141))))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(odds), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(odds)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__odds), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(s(_x201)), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(_x201))), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(s(mark(_x201))), _x132))))), incr(_x91))))))), _x32)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(_x151)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(mark(a__tail(head(cons(s(mark(_x151)), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(cons(_x151, _x152), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(cons(mark(_x151), _x152), _x132))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(nats)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__nats)), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(_x81)))))))) → a__incr#(incr(incr(tail(a__head(s(s(mark(_x81))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(pairs)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(a__pairs)), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(nil, _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(nil, _x122)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(incr(a__incr(a__tail(a__head(a__head(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(odds)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(tail(a__head(a__odds)), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(cons(_x131, _x132))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(cons(mark(_x131), _x132))))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(cons(_x71, _x72))))))) → a__incr#(a__incr(a__incr(tail(a__head(cons(mark(_x71), _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(pairs)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(a__pairs)))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(nats)), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(a__nats)), _x62))))mark#(incr(incr(incr(tail(head(s(pairs))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__pairs))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(0)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(0))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(0))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(nats))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(nats))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(mark(_x151)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(incr(_x131))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__incr(mark(_x131)))))))), _x62), _x52))))mark#(incr(head(head(cons(_x51, _x31))))) → a__incr#(a__head(mark(mark(_x51))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(s(_x201))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(s(mark(_x201)))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(nats), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(nats)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(a__nats), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(odds), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__odds), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(head(_x131))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(s(s(a__head(mark(_x131)))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(incr(mark(_x71)), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(mark(_x111)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(_x131, _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(cons(mark(_x131), _x132))), _x122)))))), _x62))))mark#(incr(incr(incr(tail(head(s(s(incr(pairs))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__pairs))))))))
mark#(incr(incr(incr(tail(head(incr(s(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(s(mark(_x81))))))))mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(a__incr(incr(tail(head(s(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(0, _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(0, _x212))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(s(nil))))))) → a__incr#(a__incr(incr(tail(a__head(s(nil))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(tail(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__tail(mark(_x141))))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(nats)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(a__nats)), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(mark(_x101))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(incr(_x151))))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(a__incr(mark(_x151)))))))))), _x62), _x52))))
mark#(incr(head(s(tail(incr(0)))))) → a__incr#(a__head(s(a__tail(a__incr(0)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(pairs, _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(cons(a__pairs, _x202))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(head(head(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(a__head(mark(_x81))))))))mark#(incr(head(s(incr(_x51))))) → a__incr#(head(s(a__incr(mark(_x51)))))
mark#(incr(head(s(head(tail(odds)))))) → a__incr#(head(s(a__head(a__tail(a__odds)))))mark#(incr(incr(incr(tail(head(cons(_x71, _x72))))))) → a__incr#(a__incr(incr(tail(a__head(cons(mark(_x71), _x72))))))
mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))
mark#(incr(head(s(tail(incr(head(tail(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(a__tail(mark(_x81))))))))mark#(incr(incr(incr(tail(head(s(s(incr(head(incr(_x111))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(a__incr(mark(_x111)))))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(cons(_x241, _x242)))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__tail(cons(mark(_x241), _x242)))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(odds, _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(a__odds, _x212))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x31))))) → a__incr#(a__head(mark(cons(incr(a__pairs), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nil, _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(cons(nil, _x202))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(_x211), mark(_x211)))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(s(mark(mark(_x211)))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(odds))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__tail(a__odds))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(_x211), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(s(mark(_x211)))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(incr(_x41)))) → a__incr#(head(a__incr(mark(_x41))))
mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(head(mark(_x51)))))mark#(incr(X)) → mark#(X)
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(nats), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__nats), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(a__incr(a__incr(tail(a__head(s(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(incr(_x191)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__incr(mark(_x191))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(s(head(incr(nats)))))) → a__incr#(head(s(a__head(a__incr(nats)))))
mark#(incr(head(s(head(tail(cons(pairs, _x72))))))) → a__incr#(head(s(head(a__tail(cons(a__pairs, _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(0))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(s(0))))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(0)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(0)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(_x141)))))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(a__head(s(s(s(s(mark(_x141))))))))), _x62))))
mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))mark#(incr(head(s(head(nats))))) → a__incr#(head(s(a__head(a__nats))))
mark#(incr(head(s(tail(incr(head(_x71))))))) → a__incr#(a__head(s(tail(a__incr(a__head(mark(_x71)))))))mark#(incr(incr(incr(tail(head(s(s(incr(odds))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(a__odds))))))))
mark#(incr(head(head(cons(head(nats), _x52))))) → a__incr#(a__head(a__head(cons(a__head(a__nats), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(pairs, _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__pairs, _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(s(mark(_x111)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(head(mark(_x141))), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(odds, _x52))))) → a__incr#(a__head(a__head(cons(a__incr(a__pairs), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(0), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(0)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(0), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(pairs)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(a__pairs)), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(0), _x62), _x52))))) → a__incr#(a__head(head(cons(cons(a__incr(0), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(tail(_x131))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(a__tail(mark(_x131)))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(incr(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__incr(mark(_x91)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__incr(pairs))), _x62), _x52))))mark#(incr(head(s(tail(incr(head(_x71))))))) → a__incr#(a__head(s(a__tail(a__incr(head(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(0)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(0)))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(nats)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(a__nats)), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(head(cons(pairs, _x51)), a__pairs))))) → a__incr#(a__head(a__head(cons(mark(a__pairs), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(odds)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(a__odds)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(_x121, _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(mark(_x121), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(pairs)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(a__pairs)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(odds)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(odds)), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(tail(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(a__tail(mark(_x151)))), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(nil), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(nil))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))
mark#(incr(incr(incr(tail(head(s(s(pairs)))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__pairs)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x151))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(s(mark(_x151)))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(mark(_x151)))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(cons(_x91, _x92))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(cons(mark(_x91), _x92))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(0)))))) → a__incr#(incr(a__incr(tail(head(0)))))mark#(incr(head(head(cons(cons(incr(head(s(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(s(mark(_x91)))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(tail(_x81)))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(a__tail(mark(_x81))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(cons(_x111, _x112))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(cons(mark(_x111), _x112))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(pairs, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(mark(a__pairs)), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(s(mark(_x141))))))))), _x62), _x52))))
mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(head(s(head(tail(mark(_x61))))))mark#(incr(head(head(cons(head(s(_x71)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(s(mark(_x71))), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(nats, _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(a__nats, _x212))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(_x231))), a__incr(a__tail(mark(_x231)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(s(mark(a__incr(a__tail(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(incr(tail(a__head(a__head(incr(a__pairs)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(nil))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__tail(nil))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(tail(_x81)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__tail(mark(_x81))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(s(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x31))))) → a__incr#(head(mark(cons(a__incr(a__head(mark(_x81))), _x62))))mark#(incr(head(s(tail(pairs))))) → a__incr#(a__head(s(mark(incr(odds)))))
mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(head(0))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(nats)))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(pairs)))))) → a__incr#(a__incr(a__incr(tail(a__head(a__pairs)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(nats)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__incr(cons(0, incr(odds))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(s(_x81)))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(s(mark(_x81))))))))
mark#(incr(head(s(tail(nil))))) → a__incr#(a__head(s(a__tail(nil))))mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(head(s(a__tail(a__incr(a__incr(nats))))))
mark#(incr(head(head(cons(cons(incr(incr(_x81)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__incr(mark(_x81))), _x62), _x52))))mark#(incr(incr(incr(tail(head(incr(incr(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(a__incr(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(tail(_x201)), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(tail(_x201))), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__tail(mark(_x201))), _x132))))), incr(_x91))))))), _x32)))mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(incr(incr(tail(a__head(s(a__nats))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(odds)))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(a__odds)))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(mark(_x101))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(a__incr(tail(head(head(nil))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(head(_x221)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__head(mark(_x221))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(s(mark(_x111)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x151))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(head(s(mark(_x151)))), _x122)))))), _x62))))
mark#(incr(incr(incr(tail(head(s(s(incr(nil))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(nil))))))))mark#(incr(head(head(cons(head(cons(pairs, _x72)), _x52))))) → a__incr#(head(a__head(cons(a__head(cons(a__pairs, _x72)), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(nats))))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(s(s(s(a__nats))))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), _x191))), _x161))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(mark(s(mark(s(a__incr(mark(_x221))))))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(_x191)), _x151))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(mark(s(a__head(mark(_x191))))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(0))))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(s(s(s(0))))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(0), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(s(0))), incr(_x101)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(0), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(0), _x62))))
mark#(incr(incr(incr(tail(head(incr(cons(_x81, _x82)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(cons(mark(_x81), _x82)))))))mark#(incr(incr(nats))) → a__incr#(incr(cons(0, incr(nats))))
mark#(incr(head(s(tail(incr(nil)))))) → a__incr#(a__head(s(a__tail(a__incr(nil)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(nil))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(nil))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(cons(_x221, _x222), _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(cons(mark(_x221), _x222), _x212))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(_x211), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(mark(s(mark(_x211)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(tail(_x151))))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(a__tail(mark(_x151)))))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(head(cons(s(mark(a__nats)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(head(s(tail(a__incr(mark(_x61))))))mark#(incr(head(head(cons(nil, _x52))))) → a__incr#(a__head(a__head(cons(nil, _x52))))
mark#(incr(incr(incr(tail(head(s(s(odds)))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__odds)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(odds)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(a__odds)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(incr(mark(_x141))))))))), _x62), _x52))))mark#(incr(head(head(cons(head(cons(nil, _x72)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(cons(nil, _x72)), _x52))))
mark#(incr(head(head(cons(cons(nats, _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__nats, _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(nil)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(nil)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(0))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(0))))), _x62), _x52))))mark#(incr(incr(incr(tail(cons(_x61, _x62)))))) → a__incr#(a__incr(a__incr(a__tail(cons(mark(_x61), _x62)))))
mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(a__incr(a__tail(head(s(a__nats))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(tail(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(a__tail(mark(_x151)))), _x122)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(s(nats)))))) → a__incr#(a__incr(a__incr(a__tail(s(a__nats)))))mark#(incr(head(s(tail(incr(incr(_x71))))))) → a__incr#(a__head(s(a__tail(a__incr(incr(mark(_x71)))))))
mark#(incr(incr(incr(tail(head(incr(nats))))))) → a__incr#(a__incr(incr(tail(a__head(a__incr(a__nats))))))mark#(incr(head(s(tail(0))))) → a__incr#(a__head(s(a__tail(0))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(cons(_x191, _x192)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(cons(mark(_x191), _x192)), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(s(s(incr(0))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(0))))))))
mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(head(s(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(odds)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(head(a__odds)), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(_x151, _x152))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(cons(mark(_x151), _x152))), _x122)))))), _x62), _x52))))mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(nil)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(nil)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(head(a__incr(a__pairs)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(_x201, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(mark(_x201))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(head(mark(_x141))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(pairs)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(s(s(a__pairs)))))), _x62), _x52))))mark#(incr(head(s(tail(pairs))))) → a__incr#(head(s(a__tail(pairs))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(incr(cons(0, incr(odds)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(mark(_x141))), _x122)))))), _x62))))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(tail(incr(incr(cons(0, incr(nats))))))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(a__incr(pairs)))))))
mark#(incr(head(s(tail(s(0)))))) → a__incr#(a__head(s(a__tail(s(0)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x151))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(s(mark(_x151)))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(tail(_x151), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(a__tail(mark(_x151)), _x132))), _x122)))))), _x62))))mark#(incr(head(s(head(tail(nats)))))) → a__incr#(head(s(head(a__tail(nats)))))
mark#(incr(head(s(head(tail(incr(_x71))))))) → a__incr#(head(s(a__head(a__tail(a__incr(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(incr(_x231))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__incr(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(nil), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(nil)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(nil), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(0))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(0))), _x122)))))), _x62))))mark#(incr(incr(incr(tail(head(s(odds))))))) → a__incr#(incr(incr(tail(head(s(a__incr(a__pairs)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(incr(_x131))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(a__incr(mark(_x131)))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(_x121, _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(incr(cons(mark(_x121), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(nats)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__nats)))))), _x62), _x52))))mark#(incr(head(s(head(tail(cons(_x71, _x51))))))) → a__incr#(head(s(head(mark(_x51)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(s(_x161)))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(s(mark(_x161))))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(nats))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__nats))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(_x151), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(s(mark(mark(_x151)))), incr(_x101)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(_x101)))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(a__incr(mark(_x101))))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(odds)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(incr(a__odds)))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(s(_x151))))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(s(mark(_x151)))))))))), _x62), _x52))))
mark#(incr(head(s(head(tail(pairs)))))) → a__incr#(head(s(a__head(a__tail(a__pairs)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(s(_x171)), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(s(s(mark(_x171))), _x132))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(incr(_x211), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(a__incr(mark(_x211)))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(pairs)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(a__pairs)), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(s(_x191)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(s(mark(_x191))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(head(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(a__head(mark(_x121))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(odds)), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(0), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(0), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(nil)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(nil)), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(nil))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(nil))))))), _x62), _x52))))
mark#(incr(head(head(cons(head(_x61), _x31))))) → a__incr#(a__head(mark(a__head(mark(_x61)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(odds, _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(a__odds, _x132))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(nats), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__nats), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x32), incr(a__head(tail(head(incr(cons(a__tail(a__head(mark(_x141))), _x122))))))))))) → a__incr#(head(cons(mark(incr(a__head(tail(head(incr(cons(a__tail(a__head(mark(_x141))), _x122))))))), _x32)))
mark#(incr(head(s(head(tail(head(_x71))))))) → a__incr#(head(s(a__head(a__tail(a__head(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(_x231))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(mark(s(a__incr(a__tail(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(incr(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(a__incr(mark(_x151)))), _x122)))))), _x62), _x52))))mark#(incr(head(s(head(incr(nats)))))) → a__incr#(head(s(a__head(a__incr(cons(0, incr(nats)))))))
mark#(incr(head(head(cons(cons(incr(head(incr(odds))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(a__odds))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(nil), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(s(nil))), incr(_x101)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(_x121, _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(cons(s(mark(mark(_x121))), incr(_x101)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(_x131))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(s(s(s(mark(_x131)))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(incr(_x131))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(s(s(a__incr(mark(_x131)))))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(nil)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(nil)))))
mark#(incr(head(head(cons(head(_x61), _x52))))) → a__incr#(a__head(a__head(cons(head(mark(_x61)), _x52))))mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))
mark#(incr(incr(incr(tail(head(head(incr(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__incr(mark(_x81))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(odds)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(a__odds)))), _x62), _x52))))
mark#(incr(head(s(tail(head(_x61)))))) → a__incr#(head(s(a__tail(a__head(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(mark(_x141))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(a__nats)))), _x62), _x52))))mark#(incr(head(s(tail(nats))))) → a__incr#(a__head(s(a__tail(cons(0, incr(nats))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(0)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(0)), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(tail(_x141)))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(a__tail(mark(_x141))))), _x122)))))), _x62))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(s(_x111))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(s(mark(_x111)))))))))))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(_x121, _x122)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(tail(head(a__incr(cons(mark(_x121), _x122)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(tail(a__head(cons(0, incr(nats)))))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(0)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(0)))))))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(_x101)))))))))) → a__incr#(incr(incr(tail(head(s(s(a__incr(a__incr(mark(_x101))))))))))
mark#(incr(head(s(tail(incr(incr(_x71))))))) → a__incr#(a__head(s(a__tail(incr(a__incr(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(mark(_x71)), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(_x201)), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(head(_x201))), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(a__head(mark(_x201))), _x132))))), incr(_x91))))))), _x32)))mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(mark(_x91)))), _x62))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(cons(0, incr(odds))), _x62))))mark#(incr(head(s(head(tail(pairs)))))) → a__incr#(head(s(head(a__tail(a__pairs)))))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(a__tail(incr(cons(s(mark(0)), incr(incr(nats))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(odds)), _x122)))))), _x32), incr(a__head(tail(head(incr(cons(a__tail(a__head(a__odds)), _x122))))))))))) → a__incr#(head(cons(mark(incr(a__head(tail(head(incr(cons(a__tail(a__head(a__odds)), _x122))))))), _x32)))
mark#(incr(incr(incr(tail(head(s(cons(_x81, _x82)))))))) → a__incr#(incr(incr(tail(a__head(s(cons(mark(_x81), _x82)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(s(mark(_x111)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(a__head(a__odds)))))))))mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(head(s(a__tail(incr(incr(cons(0, incr(nats))))))))
mark#(incr(incr(incr(tail(head(incr(_x71))))))) → a__incr#(incr(a__incr(tail(a__head(a__incr(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(cons(_x101, _x102)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(cons(mark(_x101), _x102)))), _x62), _x52))))
mark#(incr(head(s(tail(incr(head(cons(_x81, _x82)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(cons(mark(_x81), _x82)))))))mark#(incr(head(head(cons(cons(s(_x71), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(s(mark(_x71)), _x62), _x52))))
mark#(incr(incr(incr(tail(head(odds)))))) → a__incr#(a__incr(a__incr(tail(a__head(a__odds)))))mark#(incr(incr(incr(tail(head(incr(nil))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(nil))))))
mark#(incr(head(head(cons(head(cons(head(_x81), _x72)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(cons(a__head(mark(_x81)), _x72)), _x52))))mark#(incr(head(s(head(incr(cons(_x71, _x72))))))) → a__incr#(head(s(a__head(a__incr(cons(mark(_x71), _x72))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(0), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(0), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(incr(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__incr(mark(_x101))))), _x62), _x52))))
mark#(incr(head(s(tail(incr(incr(cons(_x81, _x82)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(cons(mark(_x81), _x82)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(mark(_x141))), _x122)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(nil)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(nil)))))))))mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(pairs), _x62))))mark#(incr(head(s(head(tail(s(_x71))))))) → a__incr#(head(s(a__head(a__tail(s(mark(_x71)))))))
mark#(incr(incr(incr(tail(s(_x61)))))) → a__incr#(a__incr(incr(a__tail(s(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(odds)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(a__odds)), _x122)))))), _x62), _x52))))
mark#(incr(head(s(tail(cons(_x61, _x62)))))) → a__incr#(head(s(a__tail(cons(mark(_x61), _x62)))))mark#(incr(incr(incr(tail(head(s(s(incr(head(_x101)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(a__head(mark(_x101))))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(s(mark(_x151)))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(_x141)))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(tail(a__head(s(s(s(s(mark(_x141))))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(0))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(0))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(pairs), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(pairs)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__pairs), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__incr(pairs)))))))mark#(incr(head(head(cons(cons(odds, _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__odds, _x62), _x52))))
mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(a__tail(head(a__nats)))), _x62))))mark#(incr(head(s(head(tail(tail(_x71))))))) → a__incr#(head(s(a__head(a__tail(a__tail(mark(_x71)))))))
mark#(incr(head(s(head(tail(cons(head(_x81), _x72))))))) → a__incr#(head(s(head(a__tail(cons(a__head(mark(_x81)), _x72))))))mark#(incr(odds)) → a__incr#(incr(a__pairs))
mark#(incr(head(s(tail(incr(head(nats))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(a__nats))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(_x151), _x101)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(tail(head(cons(s(mark(s(mark(_x151)))), incr(_x101)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(tail(_x81)))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(a__tail(mark(_x81))))))))mark#(incr(head(head(tail(_x51))))) → a__incr#(a__head(head(a__tail(mark(_x51)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(_x151)), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(head(a__head(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(head(_x131))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(a__head(mark(_x131)))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(nil, _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(nil, _x132))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(incr(head(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(a__head(mark(_x101))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(mark(_x111)))))), _x62), _x52))))
mark#(incr(head(s(tail(incr(cons(incr(_x81), _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(a__incr(mark(_x81)), _x72))))))mark#(incr(head(head(cons(cons(incr(head(nil)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(nil)), _x62), _x52))))
mark#(incr(head(s(head(tail(cons(incr(_x81), _x72))))))) → a__incr#(head(s(head(a__tail(cons(a__incr(mark(_x81)), _x72))))))mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(incr(a__tail(a__head(s(nats))))))
mark#(incr(head(s(tail(nats))))) → a__incr#(a__head(s(tail(cons(0, incr(nats))))))mark#(incr(head(head(cons(cons(incr(head(tail(tail(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__tail(mark(_x101))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(a__nats)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(incr(_x91))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__incr(mark(_x91)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(nats), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(a__nats), _x62), _x52))))mark#(incr(head(head(cons(odds, _x52))))) → a__incr#(a__head(head(cons(a__odds, _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__tail(a__head(mark(_x101))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), _x191))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(mark(_x221))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(tail(odds))))) → a__incr#(head(s(a__tail(a__odds))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(_x131, _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(cons(mark(_x131), _x132))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(odds), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(odds)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(a__odds), _x132))))), incr(_x91))))))), _x32)))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(head(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(a__head(mark(_x141))))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(incr(_x221), _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(a__incr(mark(_x221)), _x212))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(nil)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(s(s(nil)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x52))))) → a__incr#(head(head(cons(cons(a__incr(mark(_x71)), _x62), _x52))))mark#(incr(incr(incr(tail(s(nil)))))) → a__incr#(a__incr(incr(tail(s(nil)))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(a__incr(a__pairs))))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(0, _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(0, _x132))), _x122)))))), _x62))))
mark#(incr(incr(incr(tail(head(head(s(s(_x91))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(s(mark(_x91)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(_x201, _x202))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(cons(mark(_x201), _x202))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(incr(incr(tail(head(s(s(s(_x91))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(s(mark(_x91)))))))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(incr(pairs)))))))
mark#(incr(incr(incr(tail(head(s(s(incr(cons(_x101, _x102)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(cons(mark(_x101), _x102)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(_x131))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(mark(_x131)))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(cons(s(mark(_x151)), _x132))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(nats), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__nats), _x62), _x52))))
mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(a__head(a__head(cons(cons(0, incr(nats)), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(odds), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(s(a__odds), _x132))), _x122)))))), _x62))))
mark#(incr(head(s(tail(incr(head(_x71))))))) → a__incr#(head(s(a__tail(a__incr(a__head(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(tail(a__head(mark(_x141))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(nats)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(s(a__nats)))))))), _x62), _x52))))mark#(incr(head(head(cons(head(cons(incr(_x81), _x72)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(cons(a__incr(mark(_x81)), _x72)), _x52))))
mark#(incr(head(head(pairs)))) → a__incr#(a__head(head(pairs)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(mark(a__nats)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(_x211), _x191))), _x161))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(mark(s(mark(s(mark(_x211)))))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(head(a__nats))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(s(_x151))))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(s(s(mark(_x151)))))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(_x201)), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(head(_x201))), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(mark(_x201))), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(head(cons(0, _x51)), 0))))) → a__incr#(a__head(a__head(cons(mark(0), _x52))))mark#(incr(incr(incr(tail(pairs))))) → a__incr#(a__incr(a__incr(a__tail(a__pairs))))
mark#(incr(head(head(cons(cons(head(_x71), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__head(mark(_x71)), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(s(head(_x91))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(a__head(mark(_x91)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(_x151), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(a__tail(mark(_x151)))), incr(_x101)))))), _x62), _x52))))mark#(incr(head(s(head(nil))))) → a__incr#(head(s(a__head(nil))))
mark#(incr(head(head(cons(cons(incr(head(tail(nil))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(nil))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(incr(_x81)))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__incr(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(mark(_x81))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(tail(_x171)), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(s(a__tail(mark(_x171))), _x132))), _x122)))))), _x62))))
mark#(incr(incr(incr(tail(head(s(s(incr(cons(_x101, _x102)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(cons(mark(_x101), _x102)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(_x211, _x212), _x191))), _x161))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(mark(s(mark(cons(mark(_x211), _x212))))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x151))), _x122)))))), _x32), incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(mark(_x151)))), _x122))))))))))) → a__incr#(head(cons(mark(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(mark(_x151)))), _x122))))))), _x32)))mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(head(s(a__tail(a__incr(a__incr(cons(0, incr(nats))))))))
mark#(incr(incr(incr(tail(head(head(tail(head(_x91))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(a__head(mark(_x91)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(head(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(a__head(mark(_x111)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(s(odds)))))) → a__incr#(a__incr(a__incr(tail(s(a__odds)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(nats))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(a__nats))), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(pairs, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(pairs)), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x131))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(s(mark(_x131)))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(pairs)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(a__pairs)), _x122)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(tail(_x81)))))))) → a__incr#(incr(incr(tail(a__head(s(a__tail(mark(_x81))))))))
mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(tail(_x221), _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(a__tail(mark(_x221)), _x212))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(head(s(cons(_x71, _x72))))))) → a__incr#(a__head(s(a__head(s(cons(mark(_x71), _x72))))))mark#(incr(head(head(cons(cons(incr(head(pairs)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__pairs)), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(s(cons(_x91, _x92))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(cons(mark(_x91), _x92))))))))mark#(incr(incr(incr(tail(head(s(pairs))))))) → a__incr#(incr(incr(tail(a__head(s(a__pairs))))))
mark#(incr(head(head(cons(cons(incr(head(0)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(0)), _x62), _x52))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(incr(a__tail(head(cons(0, incr(nats)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(tail(a__head(cons(0, incr(nats)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(a__incr(a__incr(tail(head(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(nil), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(nil), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(cons(_x111, _x112))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(cons(mark(_x111), _x112))))))))))
mark#(incr(incr(incr(tail(head(s(odds))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__odds))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(nats)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(a__nats)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(tail(_x141)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__tail(mark(_x141))), _x122)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(s(_x81)))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(s(mark(_x81))))))))
mark#(incr(incr(incr(tail(head(incr(nats))))))) → a__incr#(a__incr(a__incr(tail(head(a__incr(a__nats))))))mark#(incr(head(head(cons(cons(incr(head(tail(nil))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(nil))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(cons(0, incr(nats)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nil)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(nil)))), _x62), _x52))))
mark#(incr(head(s(tail(incr(head(incr(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(a__incr(mark(_x81))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(pairs))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(a__pairs))), _x122)))))), _x62))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(odds)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(a__odds)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(nil)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(nil)), _x122)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(tail(_x81)))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__tail(mark(_x81))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(odds)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(s(s(a__odds)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(s(_x81)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(s(mark(_x81))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(tail(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(a__tail(mark(_x141))))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(odds), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__odds), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(_x151), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(cons(s(mark(s(mark(_x151)))), incr(_x101)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(nats))))) → a__incr#(a__incr(a__incr(a__tail(a__nats))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(_x131), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(a__tail(mark(_x131)))), incr(_x101)))))), _x62), _x52))))
mark#(incr(head(s(tail(incr(odds)))))) → a__incr#(a__head(s(a__tail(a__incr(a__odds)))))mark#(incr(incr(incr(tail(head(s(s(incr(s(_x101)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(s(mark(_x101))))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x32), incr(a__head(a__tail(head(0))))))))) → a__incr#(head(cons(mark(incr(a__head(a__tail(head(0))))), _x32)))mark#(incr(head(s(tail(tail(_x61)))))) → a__incr#(a__head(s(tail(a__tail(mark(_x61))))))
mark#(incr(odds)) → a__incr#(cons(s(mark(0)), incr(incr(odds))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nil)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(nil)))), _x62), _x52))))
mark#(incr(head(s(tail(nats))))) → a__incr#(head(s(a__tail(nats))))mark#(incr(head(head(cons(cons(incr(head(tail(incr(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__incr(mark(_x101))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(cons(_x111, _x112))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(mark(_x111), _x112))))), _x62), _x52))))mark#(incr(head(s(tail(nats))))) → a__incr#(head(s(tail(a__nats))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(head(_x221), _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(cons(a__head(mark(_x221)), _x202))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(nats)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(a__nats)), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(nats), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__nats))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__odds)), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(cons(_x161, _x162)), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(s(cons(mark(_x161), _x162)))), incr(_x101)))))), _x62), _x52))))mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(tail(a__incr(a__incr(a__nats))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x171))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(_x151)), _x171))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(mark(s(mark(_x151)))))), incr(_x91))))))), _x32)))mark#(incr(incr(incr(tail(head(s(s(nil)))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(nil)))))))
mark#(incr(head(head(cons(head(cons(_x71, _x72)), _x52))))) → a__incr#(a__head(head(cons(a__head(cons(mark(_x71), _x72)), _x52))))mark#(incr(incr(incr(tail(head(s(cons(_x81, _x82)))))))) → a__incr#(a__incr(incr(tail(a__head(s(cons(mark(_x81), _x82)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(s(_x221)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(s(mark(_x221))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(0), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(0), _x122)))))), _x62), _x52))))
mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(head(_x201))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(a__head(mark(_x201)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(incr(_x151))))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(s(a__incr(mark(_x151)))))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(odds), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__odds), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(pairs, _x191))), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(a__pairs)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(a__pairs)), _x132))))), incr(_x91))))))), _x32)))mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))
mark#(incr(head(head(cons(cons(incr(incr(_x81)), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(a__incr(mark(_x81))), _x62), _x52))))mark#(incr(head(head(cons(cons(_x61, _x62), _x52))))) → a__incr#(a__head(head(cons(cons(mark(_x61), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(mark(_x101))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(mark(_x91)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(head(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__head(mark(_x91)))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(incr(incr(tail(head(a__head(nil))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(head(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(a__head(mark(_x151)))), _x122)))))), _x62), _x52))))mark#(incr(head(head(pairs)))) → a__incr#(a__head(a__head(cons(0, incr(odds)))))
mark#(incr(incr(incr(tail(head(pairs)))))) → a__incr#(a__incr(incr(tail(a__head(a__pairs)))))mark#(incr(head(head(cons(head(cons(pairs, _x72)), _x52))))) → a__incr#(a__head(a__head(cons(head(cons(a__pairs, _x72)), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(cons(_x201, _x202)), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(_x201, _x202))), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(cons(mark(_x201), _x202)), _x132))))), incr(_x91))))))), _x32)))mark#(incr(head(head(head(_x51))))) → a__incr#(a__head(head(a__head(mark(_x51)))))
mark#(incr(head(s(tail(incr(0)))))) → a__incr#(head(s(tail(a__incr(0)))))mark#(incr(incr(incr(tail(head(s(s(0)))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(0)))))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__head(a__odds)))))))))mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(a__head(s(a__tail(incr(mark(_x61))))))
mark#(incr(head(s(head(tail(nats)))))) → a__incr#(head(s(a__head(a__tail(a__nats)))))mark#(incr(head(head(cons(0, _x31))))) → a__incr#(a__head(mark(0)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(_x201, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(mark(mark(_x201))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(0), _x32), incr(0)))))) → a__incr#(a__head(cons(mark(incr(0)), _x32)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(odds))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(a__odds))), _x122)))))), _x62))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(nats)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(a__nats)))))))))
mark#(incr(head(s(head(tail(0)))))) → a__incr#(head(s(a__head(a__tail(0)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(_x121, _x101)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(tail(head(cons(s(mark(mark(_x121))), incr(_x101)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(odds), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(head(cons(s(a__odds), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(0)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(0)), _x62), _x52))))
mark#(incr(incr(incr(tail(s(tail(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(s(a__tail(mark(_x71)))))))mark#(incr(incr(incr(tail(head(s(s(incr(head(nil)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(head(nil)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(incr(_x131), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__incr(mark(_x131)), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(s(_x241)))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__tail(s(mark(_x241))))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(tail(incr(odds)))))) → a__incr#(head(s(a__tail(a__incr(a__odds)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(odds)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__odds)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(odds), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(odds), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(odds))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(a__odds))))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(pairs)))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(pairs)))))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(tail(head(a__nats)))))mark#(incr(head(s(tail(incr(incr(tail(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(a__tail(mark(_x81))))))))
mark#(incr(head(s(tail(incr(cons(pairs, _x72))))))) → a__incr#(head(s(a__tail(incr(cons(a__pairs, _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(nil))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(nil))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(0)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(0)), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(_x151), _x101)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(s(mark(_x151)))), incr(_x101)))))), _x62))))
mark#(incr(incr(odds))) → a__incr#(a__incr(a__odds))mark#(incr(head(head(cons(tail(_x61), _x52))))) → a__incr#(a__head(a__head(cons(a__tail(mark(_x61)), _x52))))
mark#(incr(head(head(cons(cons(incr(s(_x81)), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(s(mark(_x81))), _x62), _x52))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(tail(a__head(a__nats)))))
mark#(incr(head(s(head(incr(odds)))))) → a__incr#(head(s(a__head(a__incr(a__odds)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(pairs)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(a__pairs)))), _x62), _x52))))
mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(incr(incr(tail(a__head(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(_x151, _x152))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(mark(_x151), _x152))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(incr(_x141)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__incr(mark(_x141))), _x122)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(tail(_x71))))))) → a__incr#(a__incr(incr(tail(a__head(a__tail(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(_x201, _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(a__head(cons(mark(_x201), _x202))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(nats))) → a__incr#(a__incr(cons(0, incr(nats))))mark#(incr(odds)) → a__incr#(incr(cons(0, incr(odds))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(pairs)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(a__pairs)))))))))mark#(incr(head(s(tail(incr(cons(pairs, _x72))))))) → a__incr#(head(s(a__tail(a__incr(cons(cons(0, incr(odds)), _x72))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(nil), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(nil), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(s(tail(incr(s(_x71))))))) → a__incr#(head(s(a__tail(a__incr(s(mark(_x71)))))))
mark#(incr(incr(incr(tail(head(incr(nats))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(nats))))))mark#(incr(incr(incr(tail(head(head(pairs))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__pairs))))))
mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(head(a__head(cons(a__nats, _x52))))mark#(incr(incr(incr(tail(head(s(nil))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(nil))))))
mark#(incr(head(head(cons(cons(incr(head(incr(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(head(a__incr(mark(_x91)))), _x62), _x52))))mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(head(s(head(a__incr(mark(_x61))))))
mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(head(odds)))))))))
mark#(incr(head(s(head(pairs))))) → a__incr#(a__head(s(a__head(a__pairs))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(cons(_x221, _x222)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(cons(mark(_x221), _x222)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(a__incr(incr(a__tail(a__head(s(mark(_x71)))))))mark#(incr(incr(incr(tail(s(head(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(s(a__head(mark(_x71)))))))
mark#(incr(head(s(tail(incr(cons(odds, _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(a__odds, _x72))))))mark#(incr(head(s(tail(incr(cons(_x71, _x72))))))) → a__incr#(a__head(s(a__tail(incr(cons(mark(_x71), _x72))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x32), incr(a__head(tail(head(a__incr(cons(a__tail(a__head(mark(_x141))), _x122))))))))))) → a__incr#(head(cons(mark(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(mark(_x141))), _x122))))))), _x32)))mark#(incr(incr(incr(odds)))) → a__incr#(a__incr(a__incr(a__odds)))
mark#(incr(head(s(tail(incr(cons(pairs, _x72))))))) → a__incr#(head(s(tail(a__incr(cons(a__pairs, _x72))))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(_x101)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(incr(a__incr(mark(_x101))))))))))
mark#(incr(head(s(tail(pairs))))) → a__incr#(head(s(a__tail(a__pairs))))mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__head(odds)))))))))
mark#(incr(head(s(head(tail(cons(s(_x81), _x72))))))) → a__incr#(head(s(head(a__tail(cons(s(mark(_x81)), _x72))))))mark#(incr(head(s(tail(incr(pairs)))))) → a__incr#(a__head(s(a__tail(a__incr(a__pairs)))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x31))))) → a__incr#(head(mark(cons(a__incr(a__pairs), _x62))))mark#(incr(incr(incr(tail(nil))))) → a__incr#(a__incr(incr(a__tail(nil))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(a__tail(a__head(a__nats)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(pairs, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(0, incr(odds)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(tail(incr(cons(0, _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(0, _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(head(_x161)), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(s(a__head(mark(_x161))))), incr(_x101)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(pairs, _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(a__pairs, _x132))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(_x131), _x122)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(mark(_x131)), _x122)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(s(odds)))))) → a__incr#(a__incr(a__incr(a__tail(s(a__odds)))))mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(a__incr(a__incr(a__tail(head(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(_x211), _x191))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(mark(_x211)))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(s(nil)))))) → a__incr#(incr(a__incr(a__tail(s(nil)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x122)))))), _x32), incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(s(mark(_x151)), _x132))), _x122))))))))))) → a__incr#(head(cons(mark(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(s(mark(_x151)), _x132))), _x122))))))), _x32)))mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(a__tail(incr(a__incr(nats))))))
mark#(incr(incr(incr(tail(head(head(s(odds)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(a__odds)))))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(tail(head(a__nats)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(odds)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__odds)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(s(_x141)))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(s(mark(_x141))))), _x122)))))), _x62))))
mark#(incr(head(s(tail(incr(cons(pairs, _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(pairs, _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(a__tail(head(mark(_x101))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(_x131))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(s(s(s(mark(_x131)))))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__incr(a__pairs)))))))
mark#(incr(incr(incr(tail(head(s(s(incr(pairs))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__pairs))))))))mark#(incr(head(s(tail(incr(cons(pairs, _x51))))))) → a__incr#(a__head(s(a__tail(cons(s(mark(a__pairs)), incr(_x51))))))
mark#(incr(incr(incr(tail(head(head(tail(incr(_x91))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(a__incr(mark(_x91)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(mark(_x111)))))), _x62), _x52))))
mark#(incr(head(s(tail(s(tail(_x71))))))) → a__incr#(a__head(s(a__tail(s(a__tail(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(head(_x241)))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__tail(a__head(mark(_x241))))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(s(s(_x71))))))) → a__incr#(a__incr(a__incr(tail(s(s(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(tail(a__head(mark(_x141))), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(nats)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(a__nats)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(pairs))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__pairs))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(nats)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(a__nats)), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(incr(_x151), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(a__incr(mark(_x151)))), incr(_x101)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(tail(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(head(a__tail(mark(_x81))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(0)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(odds))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__odds))))))), _x62), _x52))))mark#(incr(head(head(cons(head(incr(_x71)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(a__incr(mark(_x71))), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__tail(head(0)))), _x62), _x52))))mark#(incr(head(s(head(tail(cons(cons(_x81, _x82), _x72))))))) → a__incr#(head(s(head(a__tail(cons(cons(mark(_x81), _x82), _x72))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(0)))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(s(tail(_x91))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(a__tail(mark(_x91)))))))))
mark#(incr(head(s(head(tail(cons(odds, _x72))))))) → a__incr#(head(s(head(a__tail(cons(a__odds, _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(nil)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(nil)), _x122)))))), _x62))))
mark#(incr(incr(incr(tail(head(head(s(incr(_x91))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(a__incr(mark(_x91)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nil)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(nil)))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(_x101)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(head(mark(_x101))))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(nats, _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(a__nats)), incr(_x101)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(0)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(0)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(pairs, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(a__pairs)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(_x191)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(mark(_x191))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(a__incr(cons(tail(a__head(mark(_x141))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(_x211, _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(cons(mark(_x211), _x212))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))
mark#(incr(head(head(cons(0, _x52))))) → a__incr#(head(a__head(cons(0, _x52))))mark#(incr(head(odds))) → a__incr#(head(odds))
mark#(incr(head(head(cons(head(_x61), _x52))))) → a__incr#(head(a__head(cons(a__head(mark(_x61)), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(_x121)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(tail(head(s(s(mark(_x121))))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(head(mark(_x71)))))))mark#(incr(head(s(odds)))) → a__incr#(a__head(s(odds)))
mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(incr(a__tail(a__head(a__head(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(a__head(mark(_x81))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(cons(_x151, _x152))))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(s(cons(mark(_x151), _x152))))))))), _x62), _x52))))mark#(incr(head(head(cons(head(nil), _x52))))) → a__incr#(a__head(a__head(cons(a__head(nil), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(0)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(0)), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(mark(_x101))))), _x62))))
mark#(incr(head(head(cons(head(cons(tail(_x81), _x72)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(cons(a__tail(mark(_x81)), _x72)), _x52))))mark#(incr(head(head(cons(cons(incr(nil), _x62), _x52))))) → a__incr#(a__head(head(cons(cons(a__incr(nil), _x62), _x52))))
mark#(incr(head(tail(_x41)))) → a__incr#(head(a__tail(mark(_x41))))mark#(incr(head(head(cons(pairs, _x52))))) → a__incr#(a__head(a__head(cons(a__pairs, _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(a__nats)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(a__nats)), _x132))))), incr(_x91))))))), _x32)))mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(incr(a__tail(a__head(s(cons(0, incr(nats))))))))
mark#(incr(incr(incr(tail(_x51))))) → a__incr#(incr(a__incr(a__tail(mark(_x51)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(a__incr(mark(_x111)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(_x131), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(s(mark(_x131)), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(mark(a__nats)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(_x101)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(a__incr(mark(_x101))))))))))mark#(incr(incr(incr(tail(head(head(nats))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__nats))))))
mark#(incr(head(s(pairs)))) → a__incr#(a__head(s(pairs)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(incr(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(a__incr(mark(_x121))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(_x191)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(head(mark(_x191))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(pairs))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__pairs))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(a__head(a__odds)))))))))mark#(incr(incr(incr(tail(head(s(s(pairs)))))))) → a__incr#(a__incr(incr(tail(head(s(s(cons(0, incr(odds)))))))))
mark#(incr(head(head(cons(cons(incr(nil), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(nil), _x62))))mark#(incr(head(head(_x41)))) → a__incr#(head(head(mark(_x41))))
mark#(incr(head(s(tail(head(_x61)))))) → a__incr#(a__head(s(a__tail(a__head(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(0)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(s(0)))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(incr(mark(_x111)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(nil))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(incr(_x151), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(a__incr(mark(_x151)), _x132))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(nil)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(nil)), _x62), _x52))))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(head(s(a__tail(a__incr(incr(a__nats))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x32), incr(a__head(tail(head(a__incr(cons(tail(a__head(mark(_x141))), _x122))))))))))) → a__incr#(head(cons(mark(incr(a__head(tail(head(a__incr(cons(tail(a__head(mark(_x141))), _x122))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(head(cons(s(mark(_x151)), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(s(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(s(mark(_x101))))), _x62), _x52))))
mark#(incr(incr(incr(tail(s(incr(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(s(a__incr(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(_x201, _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(a__head(cons(mark(_x201), _x202))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(incr(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(incr(mark(_x91)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(a__incr(mark(_x111)))))), _x62), _x52))))
mark#(incr(head(s(head(tail(nats)))))) → a__incr#(head(s(head(tail(a__nats)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(nats)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(s(s(a__nats)))))), _x62), _x52))))
mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(tail(_x161)))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(a__tail(mark(_x161))))), _x122)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(nil))))))mark#(incr(head(head(pairs)))) → a__incr#(a__head(a__head(pairs)))
mark#(incr(head(nats))) → a__incr#(head(a__nats))mark#(incr(head(head(cons(cons(incr(head(tail(head(tail(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(a__tail(mark(_x111)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(nats)))), _x62))))mark#(incr(incr(incr(tail(head(incr(pairs))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(a__pairs))))))
mark#(incr(incr(incr(tail(head(pairs)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__pairs)))))mark#(incr(head(s(tail(_x51))))) → a__incr#(head(s(a__tail(mark(_x51)))))
mark#(incr(head(head(head(_x51))))) → a__incr#(a__head(a__head(a__head(mark(_x51)))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(incr(tail(head(a__head(a__odds))))))
mark#(incr(incr(incr(tail(head(s(s(incr(odds))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(a__pairs)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x151))), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(s(mark(_x151)))))), incr(_x101)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(a__nats)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nil)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(nil)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(cons(_x81, _x82)), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(cons(mark(_x81), _x82)), _x62), _x52))))mark#(incr(head(head(cons(head(cons(cons(_x81, _x82), _x72)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(cons(cons(mark(_x81), _x82), _x72)), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(mark(_x141))), _x122)))))), _x62), _x52))))mark#(incr(head(s(tail(incr(cons(head(_x81), _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(a__head(mark(_x81)), _x72))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(_x121, _x101)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(mark(_x121))), incr(_x101)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(_x111))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(tail(head(a__incr(mark(_x111)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(0)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(0)), _x122)))))), _x62))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(tail(_x111))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(a__tail(mark(_x111)))))))))))
mark#(incr(head(s(odds)))) → a__incr#(a__head(s(a__incr(a__pairs))))mark#(incr(incr(incr(tail(head(s(head(_x81)))))))) → a__incr#(incr(incr(tail(a__head(s(a__head(mark(_x81))))))))
mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))mark#(incr(head(head(s(_x51))))) → a__incr#(a__head(a__head(s(mark(_x51)))))
mark#(incr(head(head(cons(cons(incr(head(tail(odds))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__odds))), _x62), _x52))))mark#(incr(head(s(head(s(nil)))))) → a__incr#(a__head(s(a__head(s(nil)))))
mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(_x131, _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(mark(_x131), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(a__odds))))))mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))
mark#(incr(head(head(cons(cons(0, _x62), _x52))))) → a__incr#(head(a__head(cons(cons(0, _x62), _x52))))mark#(incr(head(head(_x41)))) → a__incr#(head(a__head(mark(_x41))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(0, incr(nats)))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))
mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(mark(_x91)))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(head(nil)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(a__head(nil)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(a__head(mark(_x101))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(nil)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(nil)))))))), _x62), _x52))))
mark#(incr(pairs)) → a__incr#(a__pairs)mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(a__tail(mark(_x91)))), _x62))))
mark#(incr(head(s(head(tail(0)))))) → a__incr#(head(s(head(a__tail(0)))))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(head(head(cons(cons(a__incr(a__pairs), _x62), _x52))))
mark#(incr(head(s(pairs)))) → a__incr#(head(s(cons(0, incr(odds)))))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(nil))))))
mark#(incr(head(s(tail(pairs))))) → a__incr#(a__head(s(tail(a__pairs))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(nats, _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__nats, _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(head(_x131))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__head(mark(_x131)))))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(tail(cons(_x91, _x92))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(cons(mark(_x91), _x92))))))))
mark#(incr(incr(incr(tail(head(head(pairs))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(a__pairs))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(pairs)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(a__pairs)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(head(s(a__head(tail(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(incr(_x131))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(a__incr(mark(_x131)))), _x122)))))), _x62))))
mark#(incr(head(head(nil)))) → a__incr#(head(a__head(nil)))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(odds)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(a__incr(a__pairs))))))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__incr(cons(0, incr(odds)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x161))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(mark(s(mark(_x151)))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(tail(incr(nats)))))) → a__incr#(head(s(a__tail(a__incr(a__nats)))))mark#(incr(incr(incr(tail(head(s(s(cons(_x91, _x92))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(cons(mark(_x91), _x92))))))))
mark#(incr(incr(incr(tail(head(head(0))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(0))))))mark#(incr(incr(incr(tail(head(s(tail(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(a__tail(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(0))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__tail(0))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(head(tail(_x71)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(a__tail(mark(_x71))), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(cons(_x151, _x152))))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(cons(mark(_x151), _x152))))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x121))), s(mark(_x151)))))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(mark(s(mark(_x151)))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(cons(s(mark(_x151)), _x132))), _x122)))))), _x62))))mark#(incr(head(s(head(tail(s(_x71))))))) → a__incr#(head(s(head(a__tail(s(mark(_x71)))))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(head(a__head(incr(a__pairs)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(nats))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(cons(0, incr(nats))))))))), _x62), _x52))))
mark#(incr(head(head(incr(_x51))))) → a__incr#(a__head(head(a__incr(mark(_x51)))))mark#(incr(head(s(tail(incr(tail(_x71))))))) → a__incr#(a__head(s(a__tail(a__incr(a__tail(mark(_x71)))))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(cons(_x111, _x112))))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(cons(mark(_x111), _x112))))))))))mark#(incr(incr(incr(tail(head(s(s(incr(head(s(_x111))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(s(mark(_x111)))))))))))
mark#(incr(head(s(head(s(s(_x71))))))) → a__incr#(a__head(s(a__head(s(s(mark(_x71)))))))mark#(incr(head(s(tail(nats))))) → a__incr#(a__head(s(a__tail(nats))))
mark#(incr(head(s(head(incr(0)))))) → a__incr#(head(s(a__head(a__incr(0)))))mark#(incr(head(head(cons(odds, _x31))))) → a__incr#(a__head(mark(a__odds)))
mark#(incr(head(head(cons(cons(incr(head(nil)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(nil)), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(odds))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__odds))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(0), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(0), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(_x101)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(incr(mark(_x101))))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(cons(_x191, _x192)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(cons(mark(_x191), _x192)), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(cons(_x131, _x132))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(cons(mark(_x131), _x132))))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(odds))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__odds))))))))mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(incr(a__tail(mark(_x51)))))
mark#(incr(incr(incr(tail(s(0)))))) → a__incr#(a__incr(a__incr(a__tail(s(0)))))mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(mark(_x81))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__incr(a__pairs))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(nil))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(nil))), _x122)))))), _x62))))
mark#(incr(head(s(head(incr(s(_x71))))))) → a__incr#(head(s(a__head(a__incr(s(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(tail(_x201))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(a__tail(mark(_x201)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(tail(_x51))))) → a__incr#(head(s(tail(mark(_x51)))))mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(head(mark(_x81))), _x62), _x52))))
mark#(incr(head(s(head(tail(cons(nats, _x72))))))) → a__incr#(head(s(head(a__tail(cons(a__nats, _x72))))))mark#(incr(head(s(head(s(_x61)))))) → a__incr#(head(s(a__head(s(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__pairs), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(_x151)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(_x151)), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(cons(_x81, _x82)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(cons(mark(_x81), _x82)), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(odds, _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(cons(a__odds, _x202))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(head(_x211), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(a__head(mark(_x211)))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(head(odds), _x52))))) → a__incr#(a__head(a__head(cons(a__head(a__odds), _x52))))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(head(s(a__tail(incr(a__incr(a__nats))))))mark#(incr(head(s(tail(incr(cons(_x71, _x51))))))) → a__incr#(a__head(s(a__tail(cons(s(mark(mark(_x71))), incr(_x51))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(cons(_x161, _x162)))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(cons(mark(_x161), _x162)))), _x122)))))), _x62), _x52))))mark#(incr(head(s(tail(incr(nil)))))) → a__incr#(head(s(a__tail(a__incr(nil)))))
mark#(incr(head(s(tail(s(head(_x71))))))) → a__incr#(a__head(s(a__tail(s(a__head(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(pairs)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__pairs)))), _x62), _x52))))
mark#(incr(head(s(head(pairs))))) → a__incr#(head(s(a__head(a__pairs))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(pairs), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__pairs), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(head(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__head(mark(_x111)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x151))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(mark(s(mark(a__nats)))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(tail(_x131))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(a__tail(mark(_x131)))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(a__nats)))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(pairs), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__pairs))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(s(_x111))))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(s(mark(_x111)))))))))))
mark#(incr(head(s(head(tail(cons(tail(_x81), _x72))))))) → a__incr#(head(s(head(a__tail(cons(a__tail(mark(_x81)), _x72))))))mark#(incr(incr(incr(tail(head(s(s(incr(head(_x101)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__head(mark(_x101))))))))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(odds))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(_x231))), _x191))), _x161))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(mark(s(mark(s(a__incr(a__tail(mark(_x231)))))))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(s(mark(_x111)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(tail(_x101)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__tail(mark(_x101))))))))))
mark#(incr(head(s(tail(incr(0)))))) → a__incr#(head(s(a__tail(incr(0)))))mark#(incr(head(head(cons(cons(incr(nil), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(incr(nil), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(_x81)))))))) → a__incr#(a__incr(incr(tail(head(s(s(mark(_x81))))))))mark#(incr(head(s(head(tail(nil)))))) → a__incr#(head(s(head(a__tail(nil)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(odds)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(s(s(s(a__incr(a__odds)))))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(incr(tail(a__head(head(nil))))))
mark#(incr(head(s(head(tail(nats)))))) → a__incr#(head(s(head(tail(cons(0, incr(nats)))))))mark#(incr(head(head(cons(cons(incr(head(incr(nats))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(a__nats))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(nats)))), _x62), _x52))))mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(head(s(a__tail(incr(mark(_x61))))))
mark#(incr(head(s(tail(nats))))) → a__incr#(a__head(s(tail(a__nats))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(_x131))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(s(mark(_x131)))))))), _x62), _x52))))
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(odds)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(a__odds)), _x122)))))), _x62))))
mark#(incr(incr(incr(tail(head(odds)))))) → a__incr#(a__incr(incr(tail(a__head(a__odds)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(a__incr(mark(_x141))))))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(incr(_x71))))))) → a__incr#(a__incr(a__incr(tail(head(a__incr(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(pairs))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(a__pairs))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(0), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(0), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(incr(a__incr(a__tail(a__head(s(a__nats))))))
mark#(incr(head(s(head(tail(head(_x71))))))) → a__incr#(head(s(head(a__tail(a__head(mark(_x71)))))))mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(a__tail(a__incr(incr(a__nats))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(nil), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(nil), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(head(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__head(mark(_x141))))))))), _x62), _x52))))
mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(a__head(mark(a__nats)))mark#(incr(head(s(tail(s(nil)))))) → a__incr#(a__head(s(a__tail(s(nil)))))
mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(incr(cons(0, incr(odds))))), _x62), _x52))))
mark#(incr(head(pairs))) → a__incr#(a__head(a__pairs))mark#(incr(head(head(cons(odds, _x52))))) → a__incr#(a__head(a__head(cons(odds, _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(_x131))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(s(s(s(mark(_x131)))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(_x211, _x212), _x191))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(mark(_x211), _x212))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))mark#(incr(head(head(cons(cons(incr(head(tail(pairs))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__pairs))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(0), _x62), _x52))))) → a__incr#(a__head(head(cons(cons(incr(0), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(0))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(s(s(s(0))))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(tail(_x81)))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(a__tail(mark(_x81))))))))mark#(incr(head(s(head(tail(odds)))))) → a__incr#(head(s(head(a__tail(a__odds)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(tail(_x211), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(a__tail(mark(_x211)))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(s(head(tail(nats)))))) → a__incr#(head(s(head(mark(incr(nats))))))
mark#(incr(head(s(tail(incr(cons(pairs, _x72))))))) → a__incr#(a__head(s(a__tail(incr(cons(a__pairs, _x72))))))mark#(incr(incr(incr(tail(head(s(s(incr(odds))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(a__odds))))))))
mark#(incr(head(s(tail(incr(nats)))))) → a__incr#(a__head(s(a__tail(a__incr(a__nats)))))mark#(incr(head(s(head(incr(tail(_x71))))))) → a__incr#(head(s(a__head(a__incr(a__tail(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(cons(0, incr(nats)))))), _x62), _x52))))mark#(incr(head(s(pairs)))) → a__incr#(head(s(pairs)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(nats)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(a__nats)), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(0, _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(0, _x122)))))), _x62), _x52))))
mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(a__head(head(incr(a__pairs)))))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(head(_x111))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(a__head(mark(_x111)))))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(_x221), _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(cons(s(mark(_x221)), _x202))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(s(s(pairs)))))))) → a__incr#(incr(incr(tail(a__head(s(s(cons(0, incr(odds)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(tail(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__tail(mark(_x101))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(odds))))))) → a__incr#(incr(incr(tail(head(s(odds))))))mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(head(s(tail(incr(pairs)))))) → a__incr#(head(s(a__tail(a__incr(a__pairs)))))mark#(incr(head(nil))) → a__incr#(head(nil))
mark#(incr(head(s(head(tail(incr(_x71))))))) → a__incr#(head(s(head(a__tail(a__incr(mark(_x71)))))))mark#(incr(incr(incr(tail(head(incr(nats))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(cons(0, incr(nats))))))))
mark#(incr(head(head(cons(cons(incr(head(incr(_x91))), _x62), _x31))))) → a__incr#(head(mark(cons(a__incr(a__head(a__incr(mark(_x91)))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(pairs, _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(a__pairs)), incr(_x101)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(head(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(a__head(mark(_x111)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(incr(a__incr(tail(a__head(mark(_x61))))))
mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(a__incr(incr(tail(head(mark(_x61))))))mark#(incr(incr(incr(tail(tail(_x61)))))) → a__incr#(a__incr(a__incr(a__tail(a__tail(mark(_x61))))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(incr(_x111))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(a__incr(mark(_x111)))))))))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(incr(a__tail(head(a__nats)))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(a__tail(mark(0)))))mark#(incr(head(s(tail(incr(head(0))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(0))))))
mark#(incr(head(s(tail(incr(cons(nats, _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(a__nats, _x72))))))mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(head(s(a__head(cons(mark(_x61), _x62)))))
mark#(incr(head(s(tail(nats))))) → a__incr#(head(s(mark(incr(nats)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(incr(cons(a__tail(a__head(mark(_x141))), _x122)))))), _x62))))
mark#(incr(incr(incr(tail(head(0)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(0)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(head(_x151))))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(a__head(mark(_x151)))))))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(cons(_x81, _x82)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(cons(mark(_x81), _x82)))))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(a__tail(head(a__nats)))))
mark#(incr(incr(incr(tail(odds))))) → a__incr#(a__incr(a__incr(a__tail(a__odds))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(odds), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(s(a__odds))), incr(_x101)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(nil))))) → a__incr#(a__incr(a__incr(tail(nil))))mark#(incr(head(s(tail(incr(incr(head(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(a__head(mark(_x81))))))))
mark#(incr(head(head(0)))) → a__incr#(head(head(0)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(pairs), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(s(a__pairs), _x132))), _x122)))))), _x62))))
mark#(incr(incr(incr(tail(head(tail(_x71))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__tail(mark(_x71)))))))mark#(incr(incr(incr(tail(s(nil)))))) → a__incr#(incr(incr(a__tail(s(nil)))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(head(_x111))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(a__head(mark(_x111)))))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(head(a__nats)))), _x62))))
mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(head(s(a__head(incr(mark(_x61))))))mark#(incr(incr(incr(tail(head(cons(_x71, _x72))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(cons(mark(_x71), _x72))))))
mark#(incr(incr(incr(tail(head(head(tail(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(tail(mark(_x81))))))))mark#(incr(incr(incr(tail(head(head(tail(nil)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(nil)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(_x121)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(tail(a__head(s(s(mark(_x121))))))), _x62), _x52))))mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(cons(0, incr(nats))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(nats), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__nats), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(head(cons(odds, _x72)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(cons(a__odds, _x72)), _x52))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(tail(head(cons(0, incr(nats)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x131))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(s(mark(_x131)))), _x122)))))), _x62))))
mark#(incr(incr(incr(tail(s(s(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(s(s(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(_x201, _x202))), _x161))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(mark(s(a__head(cons(mark(_x201), _x202))))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(pairs), _x62), _x52))))mark#(incr(head(s(tail(incr(incr(odds))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(a__odds))))))
mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(mark(_x91)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(odds), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__incr(a__pairs)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(0))) → a__incr#(head(0))mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(head(a__odds)))))))))
mark#(incr(incr(incr(tail(s(nats)))))) → a__incr#(a__incr(a__incr(tail(s(a__nats)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(odds)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(a__odds)), _x122)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(a__tail(head(cons(0, incr(nats)))))))mark#(incr(head(s(tail(incr(cons(pairs, _x72))))))) → a__incr#(a__head(s(tail(a__incr(cons(a__pairs, _x72))))))
mark#(incr(head(head(pairs)))) → a__incr#(head(head(cons(0, incr(odds)))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(odds))))))
mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(incr(a__incr(tail(a__head(head(nil))))))mark#(incr(head(head(cons(head(cons(pairs, _x72)), _x52))))) → a__incr#(a__head(head(cons(a__head(cons(a__pairs, _x72)), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(incr(_x201))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(a__incr(mark(_x201)))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(0, _x52))))) → a__incr#(a__head(head(cons(0, _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(_x91))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(mark(_x91)))))))))mark#(incr(head(s(tail(incr(incr(_x71))))))) → a__incr#(a__head(s(tail(a__incr(a__incr(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(head(s(mark(_x151)))), _x122)))))), _x62), _x52))))mark#(incr(head(head(pairs)))) → a__incr#(head(a__head(a__pairs)))
mark#(incr(head(s(head(s(0)))))) → a__incr#(a__head(s(a__head(s(0)))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(a__incr(a__pairs)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(s(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(s(mark(_x121))))))), _x62), _x52))))mark#(incr(head(head(s(_x51))))) → a__incr#(a__head(head(s(mark(_x51)))))
mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__odds)), _x62), _x52))))mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))
mark#(incr(head(s(tail(incr(cons(_x71, _x72))))))) → a__incr#(head(s(a__tail(a__incr(cons(mark(_x71), _x72))))))mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(head(head(cons(a__nats, _x52))))
mark#(incr(head(s(tail(incr(cons(cons(_x81, _x82), _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(cons(mark(_x81), _x82), _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(odds)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(a__odds)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(pairs)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(s(a__pairs)))))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(pairs))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(a__pairs))))))
mark#(incr(head(head(cons(cons(incr(head(nats)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__nats)), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(pairs)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(a__pairs)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(nil))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(tail(head(a__incr(nil))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(pairs)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__pairs)), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(incr(tail(a__head(a__head(a__odds))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(nats), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(s(a__nats), _x132))), _x122)))))), _x62))))
mark#(incr(head(s(tail(incr(cons(s(_x81), _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(s(mark(_x81)), _x72))))))mark#(incr(incr(incr(tail(head(s(head(_x81)))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__head(mark(_x81))))))))
mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__nats))))))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(pairs), _x62), _x52))))
mark#(incr(head(s(head(odds))))) → a__incr#(head(s(a__head(a__odds))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(a__tail(mark(0)))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(a__incr(cons(0, incr(odds)))))))))mark#(incr(head(s(head(tail(cons(_x71, _x72))))))) → a__incr#(head(s(a__head(a__tail(cons(mark(_x71), _x72))))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(odds))))))mark#(incr(head(head(cons(head(cons(pairs, _x72)), _x31))))) → a__incr#(a__head(mark(a__head(cons(a__pairs, _x72)))))
mark#(incr(head(head(cons(cons(incr(head(pairs)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__pairs)), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(nats))))))
mark#(incr(incr(incr(tail(head(head(s(_x81)))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(s(mark(_x81))))))))mark#(incr(head(odds))) → a__incr#(head(a__incr(a__pairs)))
mark#(incr(incr(incr(tail(head(s(s(incr(nats))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__nats))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(pairs), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__pairs), _x122)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(a__tail(head(nats)))))mark#(incr(incr(incr(tail(s(_x61)))))) → a__incr#(a__incr(incr(tail(s(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(a__nats)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(nats)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(nats)), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(incr(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(a__incr(mark(_x81))))))))mark#(incr(incr(nats))) → a__incr#(incr(nats))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x151))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(s(mark(_x151)))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(tail(_x241)))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__tail(a__tail(mark(_x241))))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(tail(tail(_x61)))))) → a__incr#(a__head(s(a__tail(a__tail(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(head(mark(_x141))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__tail(mark(_x91)))), _x62), _x52))))mark#(incr(head(head(cons(cons(_x61, _x62), _x52))))) → a__incr#(head(a__head(cons(cons(mark(_x61), _x62), _x52))))
mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))mark#(incr(head(s(tail(incr(s(_x71))))))) → a__incr#(a__head(s(a__tail(a__incr(s(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(s(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(s(mark(_x101))))), _x62), _x52))))mark#(incr(incr(incr(tail(s(pairs)))))) → a__incr#(a__incr(a__incr(a__tail(s(a__pairs)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x131))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(mark(_x131)))), _x122)))))), _x62))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(odds)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(a__odds)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(_x221, _x222), _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(cons(cons(mark(_x221), _x222), _x202))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(cons(_x201, _x202)), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(_x201, _x202))), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(cons(mark(_x201), _x202)), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(_x131), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(mark(_x131)), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(nil, _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(nil)), incr(_x101)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(0))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(0))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(mark(0)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(_x131, _x121))), mark(_x131))))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(mark(mark(_x131))), _x122)))))), _x62))))mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))
mark#(incr(head(s(tail(incr(incr(incr(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(a__incr(mark(_x81))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(head(_x231))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__head(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(incr(tail(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(a__tail(mark(_x81))))))))mark#(incr(head(s(tail(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__tail(cons(mark(_x61), _x62)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(nats)), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(s(nil))))))) → a__incr#(incr(incr(tail(a__head(s(nil))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(0)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(0)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(nil)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(nil)), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(pairs), _x32), a__incr(a__pairs)))))) → a__incr#(a__head(cons(mark(a__incr(a__pairs)), _x32)))mark#(incr(incr(incr(tail(head(head(cons(_x81, _x82)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(cons(mark(_x81), _x82)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(_x231))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(tail(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(s(tail(s(_x61)))))) → a__incr#(head(s(a__tail(s(mark(_x61))))))
mark#(incr(head(s(head(tail(cons(_x71, _x72))))))) → a__incr#(head(s(head(tail(cons(mark(_x71), _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(odds)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(odds)))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x31))))) → a__incr#(head(mark(cons(a__incr(mark(_x71)), _x62))))mark#(incr(head(head(cons(head(cons(_x71, _x72)), _x31))))) → a__incr#(a__head(mark(a__head(cons(mark(_x71), _x72)))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(cons(0, incr(odds))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(incr(_x91))), _x62), _x52))))) → a__incr#(head(head(cons(cons(a__incr(a__head(a__incr(mark(_x91)))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(tail(a__head(a__nats)))))mark#(incr(head(head(cons(cons(cons(_x71, _x72), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(cons(mark(_x71), _x72), _x62), _x52))))

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, head, a__head, nil, cons

Strategy

The right-hand side of the rule mark#(incr(head(head(cons(head(cons(0, _x72)), _x52))))) → a__incr#(a__head(a__head(cons(head(cons(0, _x72)), _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
a__incr#(a__head(head(cons(head(cons(0, _x72)), _x52)))) 
a__incr#(head(a__head(cons(head(cons(0, _x72)), _x52)))) 
a__incr#(a__head(mark(head(cons(0, _x72))))) 
Thus, the rule mark#(incr(head(head(cons(head(cons(0, _x72)), _x52))))) → a__incr#(a__head(a__head(cons(head(cons(0, _x72)), _x52)))) is replaced by the following rules:
mark#(incr(head(head(cons(head(cons(0, _x72)), _x31))))) → a__incr#(a__head(mark(head(cons(0, _x72)))))mark#(incr(head(head(cons(head(cons(0, _x72)), _x52))))) → a__incr#(head(a__head(cons(head(cons(0, _x72)), _x52))))
mark#(incr(head(head(cons(head(cons(0, _x72)), _x52))))) → a__incr#(a__head(head(cons(head(cons(0, _x72)), _x52))))

Problem 32: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(odds))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(odds))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(a__odds))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(s(s(incr(incr(nil)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(nil)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(nats))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__nats))), _x62), _x52))))mark#(incr(head(head(cons(incr(_x61), _x52))))) → a__incr#(a__head(a__head(cons(a__incr(mark(_x61)), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(mark(_x141))), _x122)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(incr(tail(a__head(head(a__odds))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(mark(_x141))))), incr(_x101)))))), _x62), _x52))))mark#(incr(head(s(head(incr(pairs)))))) → a__incr#(head(s(a__head(a__incr(a__pairs)))))
mark#(incr(head(head(cons(cons(incr(head(pairs)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(cons(0, incr(odds)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(_x231, _x232))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(cons(mark(_x231), _x232))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(tail(odds))))) → a__incr#(a__head(s(tail(a__odds))))mark#(incr(incr(incr(tail(head(head(tail(odds)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(a__odds)))))))
mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(mark(s(a__incr(mark(_x221))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(nil)))), _x232))), a__incr(mark(cons(head(s(s(incr(nil)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(nil)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(nats))) → a__incr#(a__head(nats))
mark#(incr(head(s(tail(incr(head(head(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(a__head(mark(_x81))))))))mark#(incr(incr(incr(tail(head(odds)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__odds)))))
mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x52))))) → a__incr#(a__head(head(cons(cons(a__incr(mark(_x71)), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x232))), a__incr(mark(cons(head(s(_x271)), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(a__incr(cons(a__head(s(mark(_x271))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(0))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(0))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(tail(_x81)), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(a__tail(mark(_x81))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(0)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(s(s(0)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(tail(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(a__tail(mark(_x121))))))), _x62), _x52))))
mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))mark#(incr(head(head(cons(head(cons(0, _x72)), _x31))))) → a__incr#(a__head(mark(head(cons(0, _x72)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(_x131))))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(s(s(s(mark(_x131)))))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x161))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(mark(s(mark(_x151)))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(incr(a__incr(a__tail(a__head(s(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(cons(_x101, _x102)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(cons(mark(_x101), _x102)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__tail(head(mark(_x101))))), _x62), _x52))))mark#(incr(head(s(tail(incr(head(s(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(s(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(head(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__head(mark(_x91)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(pairs)), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(a__pairs)), _x62))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(head(_x111))))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(a__head(mark(_x111)))))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(incr(nats))), a__incr(mark(incr(nats)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(s(mark(a__incr(a__incr(a__nats))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(_x231, _x232))), a__incr(mark(cons(_x231, _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(mark(_x231), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(s(head(odds))))) → a__incr#(a__head(s(a__head(a__odds))))
mark#(incr(head(head(cons(head(pairs), _x52))))) → a__incr#(a__head(a__head(cons(a__head(a__pairs), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(nats), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(nats)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__nats), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(incr(incr(tail(s(head(_x71))))))) → a__incr#(a__incr(a__incr(tail(s(a__head(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(_x121, _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(mark(_x121), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(_x251), _x232))), a__incr(mark(cons(head(_x251), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(mark(_x251)), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(odds))), _x232))), a__incr(mark(cons(head(s(s(odds))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__odds))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(_x251), _x232))), a__incr(mark(cons(head(_x251), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(mark(_x251)), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(a__odds))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(_x231, _x232))), a__incr(mark(cons(_x231, _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(incr(cons(mark(_x231), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(pairs)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(a__pairs)), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(tail(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(a__tail(mark(_x111)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(0))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(0))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(0))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(0)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(0)), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x221))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(cons(s(mark(head(s(s(a__incr(mark(_x291))))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(s(_x231))), a__incr(mark(s(_x231)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(s(mark(a__incr(s(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__tail(head(a__nats)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(incr(0))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(0))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(s(nil)))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(s(nil)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(nats)), _x232))), a__incr(mark(cons(head(s(nats)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(a__nats)), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(_x201, _x191))), _x161))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(mark(s(mark(mark(_x201))))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(nats)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(odds), _x132))), _x91)))))), _x32), incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__odds), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__odds), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(cons(_x141, _x142)))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(cons(mark(_x141), _x142)))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(tail(_x201)), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(tail(_x201))), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(a__tail(mark(_x201))), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(s(tail(incr(cons(pairs, _x72))))))) → a__incr#(head(s(a__tail(a__incr(cons(pairs, _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(tail(_x161)), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(s(a__tail(mark(_x161))))), incr(_x101)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(head(_x131))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(a__head(mark(_x131)))), _x122)))))), _x62))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(incr(a__pairs)))))))
mark#(incr(head(s(head(incr(nats)))))) → a__incr#(head(s(a__head(incr(a__nats)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(s(_x231))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(s(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(tail(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(s(s(head(_x61)))))) → a__incr#(head(s(s(a__head(mark(_x61))))))
mark#(incr(head(s(tail(s(pairs)))))) → a__incr#(a__head(s(a__tail(s(a__pairs)))))mark#(incr(head(head(cons(cons(incr(head(tail(odds))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__odds))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(0), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(cons(s(0), _x132))), _x122)))))), _x62))))mark#(incr(incr(incr(tail(s(incr(_x71))))))) → a__incr#(a__incr(a__incr(tail(s(a__incr(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(cons(_x141, _x142)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(cons(mark(_x141), _x142)))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(nats)))), _x232))), a__incr(mark(cons(head(s(s(incr(nats)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__nats)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(head(cons(0, _x72)), _x31))))) → a__incr#(a__head(mark(a__head(cons(0, _x72)))))mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x52))))) → a__incr#(head(head(cons(cons(a__incr(a__head(mark(_x81))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(tail(_x131))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(a__tail(mark(_x131)))), _x122)))))), _x62))))mark#(incr(head(s(tail(incr(head(odds))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(a__odds))))))
mark#(incr(incr(incr(tail(head(head(nats))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(a__nats))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(tail(_x241))), _x232))), a__incr(mark(cons(head(s(tail(_x241))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(a__tail(mark(_x241)))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(_x231, _x232))), a__incr(mark(cons(_x231, _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(a__incr(cons(mark(_x231), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(s(s(incr(nats))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__nats))))))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(a__tail(a__head(a__nats)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(nil), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(nil), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(_x241), _x232))), a__incr(mark(cons(head(_x241), _x232)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(mark(_x241)), _x232))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(nats)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(cons(0, incr(nats)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__tail(mark(_x91)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(nil))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(nil))), _x122)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(incr(a__tail(head(s(a__nats))))))mark#(incr(incr(incr(tail(head(s(s(incr(0))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(0))))))))
mark#(incr(incr(incr(tail(head(head(nats))))))) → a__incr#(a__incr(a__incr(a__tail(head(a__head(a__nats))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(incr(_x221), _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(cons(a__incr(mark(_x221)), _x202))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(incr(_x151), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(cons(a__incr(mark(_x151)), _x132))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(cons(0, incr(nats)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(0, _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(0)), incr(_x101)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x151))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(tail(mark(s(mark(a__nats)))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(tail(mark(s(mark(a__nats)))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(mark(_x81))), _x62), _x52))))mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(head(head(cons(nats, _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(_x151)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(tail(head(cons(s(mark(_x151)), _x132))))), incr(_x91))))))), _x32)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(odds, _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(cons(a__odds, _x132))), _x122)))))), _x62))))
mark#(incr(head(odds))) → a__incr#(a__head(a__odds))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(head(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__head(mark(_x121))))))), _x62), _x52))))
mark#(incr(head(s(tail(incr(incr(s(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(s(mark(_x81))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(nats)), _x232))), a__incr(mark(cons(head(s(nats)), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(a__nats)), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(incr(_x51))))) → a__incr#(a__head(a__head(a__incr(mark(_x51)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(nil))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(nil))))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(head(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(a__head(mark(_x81))))))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(nats)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(nats, _x232))), a__incr(mark(cons(nats, _x232)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(nats, _x232))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(nats)), _x232))), a__incr(mark(cons(head(s(nats)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(a__nats)), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(s(_x321)))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(s(_x321)))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(s(mark(_x321))))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(0)))))) → a__incr#(a__incr(incr(tail(head(0)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(a__tail(a__head(mark(_x101))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(0, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(0)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(tail(_x111))))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(a__tail(mark(_x111)))))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(tail(head(mark(_x101))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(cons(_x301, _x302))))), _x232))), a__incr(mark(cons(head(s(s(incr(cons(_x301, _x302))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(cons(mark(_x301), _x302))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(odds, _x52))))) → a__incr#(head(a__head(cons(a__odds, _x52))))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(tail(incr(a__incr(cons(0, incr(nats))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(nil)))), _x232))), a__incr(mark(cons(head(s(s(incr(nil)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(nil)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(tail(mark(0)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(head(incr(nats)))))) → a__incr#(head(s(head(incr(a__nats)))))mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x221))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(cons(s(mark(head(s(s(a__incr(mark(_x291))))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(cons(s(mark(_x151)), _x132))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(head(_x221), _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(a__head(mark(_x221)), _x212))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(_x231))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(s(a__incr(a__tail(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(head(s(head(_x71))))))) → a__incr#(a__head(s(a__head(s(a__head(mark(_x71)))))))mark#(incr(incr(incr(tail(head(head(s(0)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(0)))))))
mark#(incr(incr(incr(tail(head(incr(_x71))))))) → a__incr#(a__incr(a__incr(tail(a__head(incr(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(head(mark(_x141))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(odds)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(a__incr(a__pairs))), _x122)))))), _x62))))mark#(incr(incr(incr(tail(head(s(odds))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(a__odds))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(_x131))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(a__tail(mark(_x131)))))))), _x62), _x52))))mark#(incr(head(s(head(s(tail(_x71))))))) → a__incr#(a__head(s(a__head(s(a__tail(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(incr(_x261), _x242))), _x232))), a__incr(mark(cons(head(s(cons(incr(_x261), _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(a__incr(mark(_x261)), _x242))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(mark(_x141))))), incr(_x101)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(odds), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(tail(a__head(cons(s(a__odds), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(_x151)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(_x151)), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(head(s(s(a__incr(mark(_x291))))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(cons(0, incr(nats)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(s(mark(_x111)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(0)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(odds), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(a__odds), _x62), _x52))))mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(a__head(head(cons(cons(0, incr(nats)), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(head(_x151), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(a__head(mark(_x151)))), incr(_x101)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(tail(pairs)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(a__pairs)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(0)), _x232))), a__incr(mark(cons(head(s(0)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(0)), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(head(mark(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(tail(nil))))) → a__incr#(head(s(a__tail(nil))))mark#(incr(head(head(cons(cons(incr(head(s(_x91))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(s(mark(_x91)))), _x62), _x52))))
mark#(incr(head(s(tail(incr(incr(_x71))))))) → a__incr#(head(s(a__tail(a__incr(a__incr(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nil, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(mark(nil)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(incr(_x201)), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(incr(_x201))), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__incr(mark(_x201))), _x132))))), incr(_x91))))))), _x32)))mark#(incr(incr(incr(tail(head(head(head(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__head(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nil, _x191))), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(nil)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(nil)), _x132))))), incr(_x91))))))), _x32)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(pairs)), a__incr(mark(pairs))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(a__incr(a__pairs)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(s(_x191)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(s(mark(_x191))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(0)))), _x232))), a__incr(mark(cons(head(s(s(incr(0)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(0)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(s(tail(tail(_x61)))))) → a__incr#(head(s(a__tail(a__tail(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(_x131), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(mark(_x131)), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(_x241, _x242))), _x232))), a__incr(mark(cons(head(s(cons(_x241, _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(a__tail(mark(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(mark(_x241), _x242))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(nil))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(nil))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(nil))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(incr(cons(a__tail(head(mark(_x141))), _x122)))))), _x62), _x52))))
mark#(incr(head(s(tail(s(incr(_x71))))))) → a__incr#(a__head(s(a__tail(s(a__incr(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(a__incr(mark(_x111)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(a__head(odds)))))))))mark#(incr(head(s(head(head(_x61)))))) → a__incr#(head(s(a__head(a__head(mark(_x61))))))
mark#(incr(incr(incr(tail(s(pairs)))))) → a__incr#(a__incr(a__incr(tail(s(a__pairs)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(_x231, _x232))), a__incr(mark(cons(_x231, _x232)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(incr(cons(mark(_x231), _x232))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(head(s(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(head(s(mark(_x81))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(nats)), a__incr(mark(nats))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(a__nats)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(a__tail(head(nats)))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(incr(tail(a__head(a__head(a__incr(a__pairs)))))))
mark#(incr(head(head(cons(_x51, _x52))))) → a__incr#(a__head(head(cons(mark(_x51), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(odds)), _x232))), a__incr(mark(cons(head(s(odds)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(a__odds)), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))mark#(incr(head(head(odds)))) → a__incr#(a__head(head(a__odds)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(0)), a__incr(mark(0))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(0)))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(cons(_x111, _x112))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(cons(mark(_x111), _x112))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(incr(incr(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(a__incr(mark(_x101))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), a__incr(mark(_x221))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(mark(_x221))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(head(s(tail(a__incr(a__incr(a__nats))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(0), _x121))), s(0))))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(mark(s(0))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(nats, _x232))), a__incr(mark(cons(nats, _x232)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(cons(0, incr(nats)), _x232))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(odds)))), _x232))), a__incr(mark(cons(head(s(s(incr(odds)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__odds)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(_x231, _x232))), a__incr(mark(cons(_x231, _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(mark(_x231), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(nil))))))
mark#(incr(incr(incr(tail(s(_x61)))))) → a__incr#(incr(a__incr(a__tail(s(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(pairs, _x191))), _x151))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(mark(s(mark(a__pairs)))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(nats)), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(incr(_x241))), _x232))), a__incr(mark(cons(head(s(incr(_x241))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(a__incr(mark(_x241)))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(odds)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(incr(cons(a__tail(a__head(a__odds)), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(pairs))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__pairs))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(incr(a__tail(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(s(cons(_x71, _x72))))))) → a__incr#(a__incr(a__incr(tail(s(cons(mark(_x71), _x72))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(incr(_x131))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(a__incr(mark(_x131)))))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(s(nil)))))))) → a__incr#(a__incr(a__incr(tail(a__head(head(s(nil)))))))
mark#(incr(head(s(tail(incr(incr(pairs))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(a__pairs))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(nil)))), _x232))), a__incr(mark(cons(head(s(s(incr(nil)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(nil)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(incr(incr(tail(head(head(s(nats)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(a__nats)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(incr(_x131))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(a__incr(mark(_x131)))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(_x301))))), _x232)))))), _x181))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(mark(_x301)))))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(s(head(s(odds)))))) → a__incr#(a__head(s(a__head(s(a__odds)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(s(a__incr(mark(_x291))))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(s(s(_x151))))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(s(s(mark(_x151)))))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x151))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(s(mark(_x151)))))), incr(_x91)))))), _x62))))mark#(incr(head(s(tail(incr(cons(tail(_x81), _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(a__tail(mark(_x81)), _x72))))))
mark#(incr(incr(incr(tail(head(head(s(pairs)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(a__pairs)))))))mark#(incr(incr(incr(tail(head(head(incr(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(a__incr(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(_x131))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(s(s(a__tail(mark(_x131)))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(_x131))))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(a__head(s(s(s(mark(_x131)))))))), _x62))))
mark#(incr(incr(incr(tail(head(incr(nats))))))) → a__incr#(incr(a__incr(tail(a__head(a__incr(a__nats))))))mark#(incr(incr(incr(pairs)))) → a__incr#(a__incr(a__incr(a__pairs)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(s(s(s(s(mark(_x141))))))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(pairs)))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__pairs)))))))
mark#(incr(head(s(head(incr(nats)))))) → a__incr#(head(s(head(a__incr(nats)))))mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(a__incr(tail(a__head(s(a__nats))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(nats)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(a__nats)))))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(_x91))))))))) → a__incr#(a__incr(incr(tail(head(s(s(incr(mark(_x91)))))))))
mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(a__incr(tail(a__head(head(mark(_x71)))))))mark#(incr(incr(pairs))) → a__incr#(a__incr(cons(0, incr(odds))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(nats))), _x232))), a__incr(mark(cons(head(s(s(nats))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__nats))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(pairs)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(a__pairs)))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(nats)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(a__nats)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(nil))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(a__incr(nil))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(nats))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(a__nats))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(nil, _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(nil, _x212))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(nats)), a__incr(mark(nats))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(a__nats)))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(s(head(incr(head(_x71))))))) → a__incr#(head(s(a__head(a__incr(a__head(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(pairs))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__tail(a__pairs))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(odds)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(s(a__odds)))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(nats))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(nats))), _x62), _x52))))mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(head(s(mark(_x61))))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(a__head(head(a__incr(a__pairs)))))))mark#(incr(incr(incr(tail(head(head(s(nil)))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(s(nil)))))))
mark#(incr(head(s(tail(incr(head(pairs))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(a__pairs))))))mark#(incr(incr(pairs))) → a__incr#(a__incr(pairs))
mark#(incr(incr(incr(tail(head(incr(_x71))))))) → a__incr#(a__incr(incr(tail(a__head(a__incr(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(nil))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(incr(nil))))), _x62), _x52))))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(a__tail(incr(incr(a__nats))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(head(_x131), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__head(mark(_x131)), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(head(_x131))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(a__head(mark(_x131)))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(_x111))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(mark(_x111)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(nil)))), _x232))), a__incr(mark(cons(head(s(s(incr(nil)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(nil)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(cons(a__nats, _x202))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(head(mark(nats)))mark#(incr(head(head(cons(cons(_x61, _x62), _x31))))) → a__incr#(a__head(mark(cons(mark(_x61), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(mark(s(a__incr(mark(_x221))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(_x191)), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(mark(_x191))), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(mark(_x191))), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(s(tail(s(s(_x71))))))) → a__incr#(a__head(s(a__tail(s(s(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(pairs, _x212), _x191))), _x161))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(mark(s(mark(cons(a__pairs, _x212))))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(s(incr(_x81)))))))) → a__incr#(incr(incr(tail(a__head(s(a__incr(mark(_x81))))))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(tail(mark(0)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(0, _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(cons(0, _x202))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(incr(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__incr(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(mark(_x101))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(cons(_x91, _x92))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(cons(mark(_x91), _x92))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(nil)), a__incr(mark(nil))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(nil)))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(s(tail(cons(_x61, _x62)))))) → a__incr#(a__head(s(tail(cons(mark(_x61), _x62)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(cons(0, incr(nats)))))), _x62), _x52))))mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(a__head(s(tail(a__incr(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(odds)), _x232))), a__incr(mark(cons(head(s(odds)), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(a__odds)), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(incr(mark(_x221))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), a__incr(mark(_x221))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(s(mark(a__incr(mark(_x221))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(head(s(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(s(mark(_x81))))))))
mark#(incr(incr(incr(tail(head(incr(head(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(a__head(mark(_x81))))))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(pairs)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(a__pairs)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(_x141)))))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(a__head(s(s(s(a__incr(mark(_x141))))))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(_x231, _x232))), a__incr(mark(cons(_x231, _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(mark(_x231), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(head(tail(cons(nil, _x72))))))) → a__incr#(head(s(head(a__tail(cons(nil, _x72))))))mark#(incr(head(head(nats)))) → a__incr#(a__head(head(a__nats)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(tail(_x191)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__tail(mark(_x191))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__nats)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(_x201, _x191))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(mark(_x201))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), a__incr(mark(_x221))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(s(mark(incr(mark(_x221))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(odds)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(a__odds)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x232))), a__incr(mark(cons(head(s(_x271)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(s(mark(s(mark(a__incr(cons(a__head(s(mark(_x271))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(incr(incr(tail(head(0)))))) → a__incr#(incr(a__incr(tail(a__head(0)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(nil))))), _x32), incr(a__head(tail(head(a__incr(nil)))))))))) → a__incr#(head(cons(mark(incr(a__head(tail(head(a__incr(nil)))))), _x32)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x232))), a__incr(mark(cons(head(s(_x271)), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(mark(_x271))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(head(cons(0, incr(nats))))
mark#(incr(head(s(tail(pairs))))) → a__incr#(head(s(a__tail(cons(0, incr(odds))))))mark#(incr(incr(incr(tail(head(s(s(tail(_x91))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__tail(mark(_x91)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(nil))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(nil))))), _x62), _x52))))mark#(incr(head(s(tail(head(_x61)))))) → a__incr#(a__head(s(tail(a__head(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(incr(incr(_x241)))), a__incr(mark(incr(incr(_x241))))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(s(mark(a__incr(a__incr(a__incr(mark(_x241))))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(head(_x291)))), _x232))), a__incr(mark(cons(head(s(s(head(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__head(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(0)))), _x221))), a__incr(mark(cons(head(s(s(incr(0)))), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(cons(s(mark(head(s(s(a__incr(0)))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(pairs)))), _x232))), a__incr(mark(cons(head(s(s(incr(pairs)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__pairs)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(incr(incr(tail(head(s(s(incr(tail(_x101)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__tail(mark(_x101))))))))))mark#(incr(incr(incr(tail(head(s(s(nats)))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__nats)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(tail(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__tail(mark(_x111)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(0))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(0))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(pairs)))), _x232))), a__incr(mark(cons(head(s(s(incr(pairs)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__pairs)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(head(cons(s(mark(_x151)), _x132))), _x122)))))), _x62))))
mark#(incr(head(head(cons(head(cons(pairs, _x72)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(cons(cons(0, incr(odds)), _x72)), _x52))))mark#(incr(head(s(head(incr(incr(_x71))))))) → a__incr#(head(s(a__head(a__incr(a__incr(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(incr(pairs))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(a__pairs))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(s(s(s(a__incr(mark(_x141))))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(_x211, _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(mark(cons(mark(_x211), _x212))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(incr(a__pairs), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(s(_x241))), a__incr(mark(s(_x241)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(s(mark(_x241)))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(odds), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(odds)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__odds), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(_x151)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(mark(a__tail(head(cons(s(mark(_x151)), _x132))))), incr(_x91))))))), _x32)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(incr(head(_x241)))), a__incr(mark(incr(head(_x241))))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(s(mark(a__incr(a__incr(a__head(mark(_x241))))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(cons(_x71, _x72))))))) → a__incr#(a__incr(a__incr(tail(a__head(cons(mark(_x71), _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(pairs)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(a__pairs)))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(0)))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(pairs))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__pairs))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(nats))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(nats))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(0)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(a__head(0)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), a__incr(mark(_x221))))), _x161))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(mark(_x221))))))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(_x51, _x31))))) → a__incr#(a__head(mark(mark(_x51))))
mark#(incr(head(head(cons(cons(incr(odds), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__odds), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(odds)))), _x232))), a__incr(mark(cons(head(s(s(incr(odds)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__odds)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(head(_x131))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(s(s(a__head(mark(_x131)))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(0)), _x232))), a__incr(mark(cons(head(s(0)), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(0)), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(incr(mark(_x71)), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(nil)))), _x232))), a__incr(mark(cons(head(s(s(incr(nil)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(nil)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x221))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(cons(s(a__head(mark(s(s(a__incr(mark(_x291))))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(incr(s(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(s(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(a__tail(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(a__incr(incr(tail(head(s(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(tail(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__tail(mark(_x141))))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(incr(_x151))))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(a__incr(mark(_x151)))))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(mark(_x101))))), _x62), _x52))))mark#(incr(head(s(tail(s(0)))))) → a__incr#(a__head(s(tail(s(0)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(pairs, _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(cons(a__pairs, _x202))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(head(head(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(a__head(mark(_x81))))))))
mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))mark#(incr(incr(incr(tail(head(cons(_x71, _x72))))))) → a__incr#(a__incr(incr(tail(a__head(cons(mark(_x71), _x72))))))
mark#(incr(head(s(tail(incr(head(tail(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(a__tail(mark(_x81))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(pairs, _x192), a__pairs))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(cons(mark(a__pairs), _x192)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(incr(_x111))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(a__incr(mark(_x111)))))))))))mark#(incr(head(head(cons(head(cons(0, _x72)), _x52))))) → a__incr#(a__head(head(cons(head(cons(0, _x72)), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(cons(_x241, _x242)))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__tail(cons(mark(_x241), _x242)))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(_x211), mark(_x211)))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(s(mark(mark(_x211)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(odds))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__tail(a__odds))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(_x211), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(s(mark(_x211)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(head(mark(_x51)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(nats), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__nats), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(a__incr(a__incr(tail(a__head(s(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(incr(_x191)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__incr(mark(_x191))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(head(tail(cons(pairs, _x72))))))) → a__incr#(head(s(head(a__tail(cons(a__pairs, _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(0))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(s(0))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x151))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(mark(s(mark(a__nats)))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(tail(_x261), _x242))), _x232))), a__incr(mark(cons(head(s(cons(tail(_x261), _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(tail(mark(_x261)), _x242))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(tail(incr(head(_x71))))))) → a__incr#(a__head(s(tail(a__incr(a__head(mark(_x71)))))))mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(pairs, _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__pairs, _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(incr(cons(a__head(s(s(a__incr(a__tail(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(a__tail(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(head(mark(_x141))), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(pairs)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(a__pairs)), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(0), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(0)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(0), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(0), _x62), _x52))))) → a__incr#(a__head(head(cons(cons(a__incr(0), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(incr(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__incr(mark(_x91)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(odds)))), _x232))), a__incr(mark(cons(head(s(s(incr(odds)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__odds)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(s(tail(incr(head(_x71))))))) → a__incr#(a__head(s(a__tail(a__incr(head(mark(_x71)))))))
mark#(incr(head(head(cons(head(cons(pairs, _x51)), a__pairs))))) → a__incr#(a__head(a__head(cons(mark(a__pairs), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(odds)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(a__odds)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(_x121, _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(mark(_x121), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(odds)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(odds)), _x122)))))), _x62))))
mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x151))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(s(mark(_x151)))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(incr(pairs))), a__incr(mark(incr(pairs)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(s(mark(a__incr(a__incr(a__pairs))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(nats)), a__incr(mark(nats))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(s(mark(a__incr(a__nats)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(s(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(s(mark(_x91)))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(tail(_x81)))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(a__tail(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(s(mark(_x141))))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(nats)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(s(a__incr(a__nats)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(head(nats))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(head(a__nats))))))mark#(incr(head(head(cons(head(s(_x71)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(s(mark(_x71))), _x52))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(incr(tail(a__head(a__head(incr(a__pairs)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(nil))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__tail(nil))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(head(0))))mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__incr(cons(0, incr(odds))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(nats)))), _x62), _x52))))mark#(incr(incr(incr(tail(head(pairs)))))) → a__incr#(a__incr(a__incr(tail(a__head(a__pairs)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(tail(_x321)))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(tail(_x321)))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(a__tail(mark(_x321))))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(head(s(_x81)))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(s(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(0)), _x151))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(mark(s(a__head(0)))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(mark(s(a__head(0)))))), incr(_x91))))))), _x32)))mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(head(s(a__tail(a__incr(a__incr(nats))))))
mark#(incr(incr(incr(tail(head(incr(incr(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(a__incr(mark(_x81))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(odds)), a__incr(mark(odds))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(a__odds)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(tail(_x201)), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(tail(_x201))), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__tail(mark(_x201))), _x132))))), incr(_x91))))))), _x32)))mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(incr(incr(tail(a__head(s(a__nats))))))
mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(a__incr(tail(head(head(nil))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(head(_x221)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__head(mark(_x221))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(s(mark(_x111)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x151))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(head(s(mark(_x151)))), _x122)))))), _x62))))
mark#(incr(incr(incr(tail(head(s(s(incr(nil))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(nil))))))))mark#(incr(head(head(cons(head(cons(pairs, _x72)), _x52))))) → a__incr#(head(a__head(cons(a__head(cons(a__pairs, _x72)), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(nats))))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(s(s(s(a__nats))))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), a__incr(mark(_x221))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(s(mark(a__incr(mark(_x221))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), _x191))), _x161))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(mark(s(mark(s(a__incr(mark(_x221))))))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(0), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(0), _x62))))
mark#(incr(incr(incr(tail(head(incr(cons(_x81, _x82)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(cons(mark(_x81), _x82)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(odds, _x232))), a__incr(mark(cons(odds, _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__odds, _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(incr(nats))) → a__incr#(incr(cons(0, incr(nats))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(pairs, _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(mark(cons(a__pairs, _x212))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(tail(incr(nil)))))) → a__incr#(a__head(s(a__tail(a__incr(nil)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(nil))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(nil))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(tail(_x151))))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(a__tail(mark(_x151)))))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(_x211), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(mark(s(mark(_x211)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(cons(_x221, _x222), _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(cons(mark(_x221), _x222), _x212))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(a__head(mark(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(tail(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(a__tail(mark(_x141))))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(0)))), _x232))), a__incr(mark(cons(head(s(s(incr(0)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(0)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(nil, _x52))))) → a__incr#(a__head(a__head(cons(nil, _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(incr(mark(_x141))))))))), _x62), _x52))))
mark#(incr(incr(incr(tail(s(nats)))))) → a__incr#(a__incr(a__incr(a__tail(s(a__nats)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(pairs, _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(pairs, _x212))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(_x281))), _x232))), a__incr(mark(cons(head(s(s(_x281))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(a__incr(cons(a__head(s(s(mark(_x281)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(tail(0), _x242))), _x232))), a__incr(mark(cons(head(s(cons(tail(0), _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(a__tail(0), _x242))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(cons(_x191, _x192)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(cons(mark(_x191), _x192)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(head(s(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(odds)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(head(a__odds)), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(_x151, _x152))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(cons(mark(_x151), _x152))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(nil)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(nil)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(pairs)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(s(s(a__pairs)))))), _x62), _x52))))mark#(incr(head(s(tail(pairs))))) → a__incr#(head(s(a__tail(pairs))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(incr(cons(0, incr(odds)))))))))mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(tail(incr(incr(cons(0, incr(nats))))))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(a__incr(pairs)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x151))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(s(mark(_x151)))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(pairs, _x242))), _x232))), a__incr(mark(cons(head(s(cons(pairs, _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(a__pairs, _x242))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(s(head(tail(incr(_x71))))))) → a__incr#(head(s(a__head(a__tail(a__incr(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(0)), _x151))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(mark(s(a__head(0)))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(_x281, _x282))), _x232))), a__incr(mark(cons(head(s(cons(_x281, _x282))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(cons(mark(_x281), _x282))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(incr(_x231))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__incr(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(odds)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(incr(cons(a__tail(a__head(a__odds)), _x122)))))), _x62), _x52))))mark#(incr(head(s(head(tail(cons(_x71, _x51))))))) → a__incr#(head(s(head(mark(_x51)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(nats)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__nats)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(nats))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__nats))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(incr(_x241))), _x232))), a__incr(mark(cons(head(s(incr(_x241))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(a__incr(mark(_x241)))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(s(head(tail(pairs)))))) → a__incr#(head(s(a__head(a__tail(a__pairs)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(0))), _x232))), a__incr(mark(cons(head(s(s(0))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(0))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(_x251), _x232))), a__incr(mark(cons(head(_x251), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(mark(_x251)), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(s(_x171)), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(s(s(mark(_x171))), _x132))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(incr(cons(head(s(s(a__incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(incr(_x211), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(a__incr(mark(_x211)))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(s(incr(_x151))))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(s(a__incr(mark(_x151)))))))))), _x62), _x52))))
mark#(incr(head(head(cons(head(cons(nats, _x72)), _x52))))) → a__incr#(a__head(head(cons(a__head(cons(a__nats, _x72)), _x52))))mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(odds)), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(0), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(0), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(head(_x61), _x31))))) → a__incr#(a__head(mark(a__head(mark(_x61)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(odds, _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(a__odds, _x132))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x32), incr(a__head(tail(head(incr(cons(a__tail(a__head(mark(_x141))), _x122))))))))))) → a__incr#(head(cons(mark(incr(a__head(tail(head(incr(cons(a__tail(a__head(mark(_x141))), _x122))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(incr(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(a__incr(mark(_x151)))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(_x131))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(s(s(s(mark(_x131)))))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(incr(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__incr(mark(_x81))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(odds)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(a__odds)))), _x62), _x52))))
mark#(incr(head(s(tail(head(_x61)))))) → a__incr#(head(s(a__tail(a__head(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x232))), a__incr(mark(cons(head(s(_x271)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(a__tail(mark(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(mark(_x271))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(mark(_x141))))), incr(_x91)))))), _x62))))mark#(incr(head(s(tail(nats))))) → a__incr#(a__head(s(a__tail(cons(0, incr(nats))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(0)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(0)), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(s(tail(_x151))))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(s(a__tail(mark(_x151)))))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(tail(_x141)))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(a__tail(mark(_x141))))), _x122)))))), _x62))))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(head(_x151), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(cons(a__head(mark(_x151)), _x132))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(nats)), a__incr(mark(nats))))), _x151))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(a__nats)))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(pairs)), a__incr(mark(pairs))))), _x151))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(a__pairs)))))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(_x101)))))))))) → a__incr#(incr(incr(tail(head(s(s(a__incr(a__incr(mark(_x101))))))))))
mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(mark(_x71)), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(_x201)), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(head(_x201))), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(a__head(mark(_x201))), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x151))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(mark(s(mark(nats)))))), incr(_x91)))))), _x62))))mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(a__tail(incr(cons(s(mark(0)), incr(incr(nats))))))))
mark#(incr(incr(incr(tail(head(s(cons(_x81, _x82)))))))) → a__incr#(incr(incr(tail(a__head(s(cons(mark(_x81), _x82)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(s(mark(_x111)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(_x281))), _x221))), a__incr(mark(cons(head(s(s(_x281))), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(cons(s(mark(a__head(s(s(mark(_x281)))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(cons(_x101, _x102)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(cons(mark(_x101), _x102)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(pairs, _x212), _x191))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(a__pairs, _x212))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(s(_x71), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(s(mark(_x71)), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(nil)))), _x232))), a__incr(mark(cons(head(s(s(incr(nil)))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(head(s(s(a__incr(nil)))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(incr(nil))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(nil))))))
mark#(incr(head(s(tail(s(nats)))))) → a__incr#(a__head(s(tail(s(a__nats)))))mark#(incr(head(s(head(incr(cons(_x71, _x72))))))) → a__incr#(head(s(a__head(a__incr(cons(mark(_x71), _x72))))))
mark#(incr(head(head(cons(head(cons(head(_x81), _x72)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(cons(a__head(mark(_x81)), _x72)), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(nats)))), _x232))), a__incr(mark(cons(head(s(s(incr(nats)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__nats)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(0), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(0), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(incr(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__incr(mark(_x101))))), _x62), _x52))))
mark#(incr(head(s(tail(incr(incr(cons(_x81, _x82)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(cons(mark(_x81), _x82)))))))mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(pairs), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(nil)))), _x232))), a__incr(mark(cons(head(s(s(incr(nil)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(incr(cons(head(s(s(a__incr(nil)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x201))), a__incr(mark(cons(head(s(_x271)), _x201)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(cons(s(mark(a__head(s(mark(_x271))))), incr(_x201))))))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(s(s(incr(head(_x101)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(a__head(mark(_x101))))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(s(mark(_x151)))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(s(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(s(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(s(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(0))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(0))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__incr(pairs)))))))
mark#(incr(head(head(cons(cons(odds, _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__odds, _x62), _x52))))mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(a__tail(head(a__nats)))), _x62))))mark#(incr(head(s(head(tail(tail(_x71))))))) → a__incr#(head(s(a__head(a__tail(a__tail(mark(_x71)))))))
mark#(incr(head(s(head(tail(cons(head(_x81), _x72))))))) → a__incr#(head(s(head(a__tail(cons(a__head(mark(_x81)), _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(incr(cons(a__head(s(s(a__incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(pairs)), _x232))), a__incr(mark(cons(head(s(pairs)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(a__pairs)), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(s(tail(incr(head(nats))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(a__nats))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(_x151), _x101)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(tail(head(cons(s(mark(s(mark(_x151)))), incr(_x101)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(pairs)), _x232))), a__incr(mark(cons(head(s(pairs)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(a__pairs)), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(tail(_x51))))) → a__incr#(a__head(head(a__tail(mark(_x51)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(head(_x131))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(a__head(mark(_x131)))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(nil, _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(nil, _x132))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(incr(head(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(a__head(mark(_x101))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x221))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(cons(s(mark(head(s(s(incr(mark(_x291))))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(cons(_x291, _x292)))), _x232))), a__incr(mark(cons(head(s(s(cons(_x291, _x292)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(cons(mark(_x291), _x292)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(incr(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(incr(cons(a__tail(a__head(a__incr(mark(_x151)))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(nil)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(nil)), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(incr(a__tail(a__head(s(nats))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(tail(nil), _x242))), _x232))), a__incr(mark(cons(head(s(cons(tail(nil), _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(a__tail(nil), _x242))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(tail(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__tail(mark(_x101))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(incr(_x91))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__incr(mark(_x91)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__tail(a__head(mark(_x101))))), _x62), _x52))))mark#(incr(head(s(tail(odds))))) → a__incr#(head(s(a__tail(a__odds))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), _x191))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(mark(_x221))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(0)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(incr(cons(a__tail(a__head(0)), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(_x131, _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(cons(mark(_x131), _x132))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(odds), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(odds)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(a__odds), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(incr(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(incr(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(a__incr(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x52))))) → a__incr#(head(head(cons(cons(a__incr(mark(_x71)), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(incr(_x221), _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(a__incr(mark(_x221)), _x212))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(incr(incr(tail(s(nil)))))) → a__incr#(a__incr(incr(tail(s(nil)))))mark#(incr(incr(incr(tail(head(head(s(s(_x91))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(s(mark(_x91)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(s(s(incr(cons(_x101, _x102)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(cons(mark(_x101), _x102)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(_x131))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(mark(_x131)))))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(nats))))))) → a__incr#(incr(a__incr(a__tail(a__head(a__head(nats))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(head(_x241))), _x232))), a__incr(mark(cons(head(s(head(_x241))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(a__head(mark(_x241)))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), a__incr(mark(_x221))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(a__incr(mark(_x221))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(nats)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(s(a__nats)))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nil, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(nil)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(pairs)))) → a__incr#(a__head(head(pairs)))mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(head(a__nats))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(pairs, _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(cons(0, incr(odds)), _x212))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(head(s(head(_x91))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(a__head(mark(_x91)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(_x151, _x152))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(incr(cons(a__tail(a__head(cons(mark(_x151), _x152))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(incr(_x251), _x232))), a__incr(mark(cons(incr(_x251), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__incr(mark(_x251)), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(_x241, _x242))), _x232))), a__incr(mark(cons(head(s(cons(_x241, _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(head(s(cons(mark(_x241), _x242))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(nil))), _x232))), a__incr(mark(cons(head(s(s(nil))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(nil))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(nil))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(nil))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(nil, _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(cons(nil, _x132))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(mark(_x81))), _x62))))mark#(incr(incr(incr(tail(head(s(incr(_x81)))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__incr(mark(_x81))))))))
mark#(incr(incr(incr(tail(head(s(s(incr(cons(_x101, _x102)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(cons(mark(_x101), _x102)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(_x211, _x212), _x191))), _x161))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(mark(s(mark(cons(mark(_x211), _x212))))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x151))), _x122)))))), _x32), incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(mark(_x151)))), _x122))))))))))) → a__incr#(head(cons(mark(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(mark(_x151)))), _x122))))))), _x32)))mark#(incr(incr(incr(tail(head(head(tail(head(_x91))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(a__head(mark(_x91)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(head(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(a__head(mark(_x111)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(pairs, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(pairs)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(_x131))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(tail(mark(_x131)))))))), _x62), _x52))))mark#(incr(head(s(tail(s(incr(_x71))))))) → a__incr#(a__head(s(tail(s(a__incr(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x131))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(s(mark(_x131)))), _x122)))))), _x62))))mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x221))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(cons(mark(s(mark(head(s(s(a__incr(mark(_x291)))))))), incr(_x221)))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(s(head(s(cons(_x71, _x72))))))) → a__incr#(a__head(s(a__head(s(cons(mark(_x71), _x72))))))
mark#(incr(head(head(cons(cons(incr(head(pairs)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__pairs)), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(odds)), _x232))), a__incr(mark(cons(head(s(odds)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(a__odds)), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x201))), a__incr(mark(cons(head(s(_x271)), _x201)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(cons(s(mark(a__head(s(mark(_x271))))), incr(_x201))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(s(_x251), _x232))), a__incr(mark(cons(s(_x251), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(s(mark(_x251)), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(incr(incr(tail(head(s(pairs))))))) → a__incr#(incr(incr(tail(a__head(s(a__pairs))))))mark#(incr(head(head(cons(cons(incr(head(0)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(0)), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(nil)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(incr(cons(a__tail(a__head(nil)), _x122)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(incr(a__tail(head(cons(0, incr(nats)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(cons(_x151, _x152), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(cons(cons(mark(_x151), _x152), _x132))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(nats, _x242))), _x232))), a__incr(mark(cons(head(s(cons(nats, _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(a__nats, _x242))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(nil), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(nil), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(nats)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(a__nats)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(head(s(_x81)))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(s(mark(_x81))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(_x241, _x242))), _x232))), a__incr(mark(cons(head(s(cons(_x241, _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(mark(_x241), _x242))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(cons(0, incr(nats)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(nil))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(nil))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nil)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(nil)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(pairs))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(a__pairs))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(tail(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(a__tail(mark(_x141))))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(odds), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__odds), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(_x151), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(cons(s(mark(s(mark(_x151)))), incr(_x101)))))), _x62), _x52))))mark#(incr(incr(incr(tail(nats))))) → a__incr#(a__incr(a__incr(a__tail(a__nats))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(tail(_x261), _x242))), _x201))), a__incr(mark(cons(head(s(cons(tail(_x261), _x242))), _x201)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(cons(s(mark(a__head(s(cons(a__tail(mark(_x261)), _x242))))), incr(_x201))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(incr(cons(_x241, _x242)))), a__incr(mark(incr(cons(_x241, _x242))))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(s(mark(a__incr(a__incr(cons(mark(_x241), _x242)))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(_x131), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(a__tail(mark(_x131)))), incr(_x101)))))), _x62), _x52))))mark#(incr(head(s(tail(tail(_x61)))))) → a__incr#(a__head(s(tail(a__tail(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x32), incr(a__head(a__tail(head(0))))))))) → a__incr#(head(cons(mark(incr(a__head(a__tail(head(0))))), _x32)))mark#(incr(head(head(cons(cons(incr(head(tail(incr(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__incr(mark(_x101))))), _x62), _x52))))
mark#(incr(head(s(tail(nats))))) → a__incr#(head(s(a__tail(nats))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(tail(incr(_x281)), _x242))), _x232))), a__incr(mark(cons(head(s(cons(tail(incr(_x281)), _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(a__tail(a__incr(mark(_x281))), _x242))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(nats)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(a__nats)), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__odds)), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(0)), a__incr(mark(0))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(0)))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(nats, _x232))), a__incr(mark(cons(nats, _x232)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(incr(cons(a__nats, _x232))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(cons(_x161, _x162)), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(s(cons(mark(_x161), _x162)))), incr(_x101)))))), _x62), _x52))))mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(tail(a__incr(a__incr(a__nats))))))
mark#(incr(incr(incr(tail(head(s(s(nil)))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(nil)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x171))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(_x151)), _x171))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(mark(s(mark(_x151)))))), incr(_x91))))))), _x32)))
mark#(incr(incr(incr(tail(head(s(cons(_x81, _x82)))))))) → a__incr#(a__incr(incr(tail(a__head(s(cons(mark(_x81), _x82)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(head(_x201))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(a__head(mark(_x201)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(pairs)))), _x221))), a__incr(mark(cons(head(s(s(incr(pairs)))), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(cons(s(mark(head(s(s(a__incr(a__pairs)))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(s(tail(s(odds)))))) → a__incr#(a__head(s(tail(s(odds)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(tail(head(incr(cons(a__tail(a__head(mark(_x141))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(incr(cons(a__head(s(s(a__incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(mark(_x91)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(pairs)), _x232))), a__incr(mark(cons(head(s(pairs)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(a__pairs)), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(head(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(a__head(mark(_x151)))), _x122)))))), _x62), _x52))))mark#(incr(head(head(pairs)))) → a__incr#(a__head(a__head(cons(0, incr(odds)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(cons(_x201, _x202)), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(_x201, _x202))), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(cons(mark(_x201), _x202)), _x132))))), incr(_x91))))))), _x32)))mark#(incr(head(head(cons(head(cons(pairs, _x72)), _x52))))) → a__incr#(a__head(a__head(cons(head(cons(a__pairs, _x72)), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(incr(nil))), a__incr(mark(incr(nil)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(s(mark(a__incr(a__incr(nil))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(s(s(0)))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(0)))))))
mark#(incr(head(head(head(_x51))))) → a__incr#(a__head(head(a__head(mark(_x51)))))mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__head(a__odds)))))))))
mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(a__head(s(a__tail(incr(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(incr(_x271)), _x232))), a__incr(mark(cons(head(incr(_x271)), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(a__incr(mark(_x271))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(head(tail(nats)))))) → a__incr#(head(s(a__head(a__tail(a__nats)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(nil)), a__incr(mark(nil))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(s(mark(a__incr(nil)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(0, _x31))))) → a__incr#(a__head(mark(0)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(_x201, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(mark(mark(_x201))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(nats)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(a__nats)))))))))mark#(incr(head(s(s(0))))) → a__incr#(head(s(s(0))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(odds), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(head(cons(s(a__odds), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(0)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(0)), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x151))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(mark(s(mark(cons(0, incr(nats)))))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(s(tail(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(s(a__tail(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(nats)))), _x232))), a__incr(mark(cons(head(s(s(incr(nats)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__nats)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(s(s(incr(head(nil)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(head(nil)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(s(_x241)))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__tail(s(mark(_x241))))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(incr(_x131), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__incr(mark(_x131)), _x122)))))), _x62), _x52))))
mark#(incr(head(s(tail(incr(odds)))))) → a__incr#(head(s(a__tail(a__incr(a__odds)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(odds)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__odds)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(odds), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(odds), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(head(nats))))))) → a__incr#(incr(incr(a__tail(a__head(a__head(a__nats))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(s(head(_x151))))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(s(a__head(mark(_x151)))))))))), _x62), _x52))))mark#(incr(head(s(s(s(_x61)))))) → a__incr#(head(s(s(s(mark(_x61))))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(tail(head(a__nats)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(_x151), _x101)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(s(mark(_x151)))), incr(_x101)))))), _x62))))
mark#(incr(head(head(cons(tail(_x61), _x52))))) → a__incr#(a__head(a__head(cons(a__tail(mark(_x61)), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(cons(_x321, _x322)))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(cons(_x321, _x322)))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(cons(mark(_x321), _x322)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(_x251), _x232))), a__incr(mark(cons(head(_x251), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(mark(_x251)), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(pairs)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(a__pairs)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(s(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(tail(s(mark(_x141))))))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(incr(incr(tail(a__head(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(_x151, _x152))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(mark(_x151), _x152))), _x122)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(tail(_x71))))))) → a__incr#(a__incr(incr(tail(a__head(a__tail(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(_x201, _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(a__head(cons(mark(_x201), _x202))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(head(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(incr(cons(a__tail(a__head(a__head(mark(_x151)))), _x122)))))), _x62), _x52))))mark#(incr(head(s(tail(incr(cons(pairs, _x72))))))) → a__incr#(head(s(a__tail(a__incr(cons(cons(0, incr(odds)), _x72))))))
mark#(incr(odds)) → a__incr#(incr(cons(0, incr(odds))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nil, _x191))), _x151))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(mark(s(mark(nil)))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(head(_x241))), _x232))), a__incr(mark(cons(head(s(head(_x241))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(a__head(mark(_x241)))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(_x241))), a__incr(mark(tail(_x241)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(a__tail(mark(_x241)))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(tail(s(_x61)))))) → a__incr#(head(s(tail(s(mark(_x61))))))mark#(incr(incr(incr(tail(head(s(nil))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(nil))))))
mark#(incr(head(s(head(pairs))))) → a__incr#(a__head(s(a__head(a__pairs))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(cons(_x221, _x222)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(cons(mark(_x221), _x222)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(tail(_x261), _x242))), _x232))), a__incr(mark(cons(head(s(cons(tail(_x261), _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(a__tail(mark(_x261)), _x242))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(s(head(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(s(a__head(mark(_x71)))))))
mark#(incr(head(s(tail(incr(cons(odds, _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(a__odds, _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(incr(_x281))), _x232))), a__incr(mark(cons(head(s(incr(_x281))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(a__incr(mark(_x281)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x32), incr(a__head(tail(head(a__incr(cons(a__tail(a__head(mark(_x141))), _x122))))))))))) → a__incr#(head(cons(mark(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(mark(_x141))), _x122))))))), _x32)))mark#(incr(incr(incr(odds)))) → a__incr#(a__incr(a__incr(a__odds)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(nil)), _x232))), a__incr(mark(cons(head(s(nil)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(nil)), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(incr(_x231))), a__incr(mark(incr(_x231)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(s(mark(incr(a__incr(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(tail(pairs))))) → a__incr#(head(s(a__tail(a__pairs))))mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__head(odds)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(cons(_x301, _x302))))), _x232))), a__incr(mark(cons(head(s(s(incr(cons(_x301, _x302))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(cons(mark(_x301), _x302))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(a__tail(a__head(a__nats)))))
mark#(incr(incr(incr(tail(nil))))) → a__incr#(a__incr(incr(a__tail(nil))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(nil)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(s(a__incr(nil)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(pairs, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(0, incr(odds)))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(_x131), _x122)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(mark(_x131)), _x122)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(s(odds)))))) → a__incr#(a__incr(a__incr(a__tail(s(a__odds)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(odds)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(s(a__incr(a__odds)))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(nats)), _x232))), a__incr(mark(cons(head(s(nats)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(a__nats)), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(_x211), _x191))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(mark(_x211)))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(s(nil)))))) → a__incr#(incr(a__incr(a__tail(s(nil)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x122)))))), _x32), incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(s(mark(_x151)), _x132))), _x122))))))))))) → a__incr#(head(cons(mark(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(s(mark(_x151)), _x132))), _x122))))))), _x32)))mark#(incr(incr(incr(tail(head(head(s(odds)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(a__odds)))))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(tail(head(a__nats)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(odds)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__odds)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(odds)))), _x221))), a__incr(mark(cons(head(s(s(incr(odds)))), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(cons(s(mark(head(s(s(a__incr(a__odds)))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(tail(_x251), _x232))), a__incr(mark(cons(tail(_x251), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__tail(mark(_x251)), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__incr(a__pairs)))))))mark#(incr(incr(incr(tail(head(head(tail(incr(_x91))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(a__incr(mark(_x91)))))))))
mark#(incr(head(s(tail(s(nil)))))) → a__incr#(a__head(s(tail(s(nil)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(mark(_x111)))))), _x62), _x52))))
mark#(incr(head(s(tail(s(tail(_x71))))))) → a__incr#(a__head(s(a__tail(s(a__tail(mark(_x71)))))))mark#(incr(incr(incr(tail(s(s(_x71))))))) → a__incr#(a__incr(a__incr(tail(s(s(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(nats)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(a__nats)), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(pairs))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__pairs))))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(tail(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(head(a__tail(mark(_x81))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(odds))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__odds))))))), _x62), _x52))))
mark#(incr(head(s(head(tail(cons(cons(_x81, _x82), _x72))))))) → a__incr#(head(s(head(a__tail(cons(cons(mark(_x81), _x82), _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__tail(head(0)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(0)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(nil)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(nil)), _x122)))))), _x62))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(_x101)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(head(mark(_x101))))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(pairs)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(s(a__incr(a__pairs)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(pairs, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(a__pairs)), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(_x191)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(mark(_x191))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(a__incr(cons(tail(a__head(mark(_x141))), _x122)))))), _x62))))mark#(incr(head(head(cons(0, _x52))))) → a__incr#(head(a__head(cons(0, _x52))))
mark#(incr(head(odds))) → a__incr#(head(odds))mark#(incr(head(head(cons(cons(incr(head(tail(nats))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__nats))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x221))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(cons(s(mark(head(s(s(a__incr(mark(_x291))))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(s(odds)))) → a__incr#(a__head(s(odds)))
mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(incr(a__tail(a__head(a__head(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(cons(_x151, _x152))))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(s(cons(mark(_x151), _x152))))))))), _x62), _x52))))
mark#(incr(head(head(cons(head(nil), _x52))))) → a__incr#(a__head(a__head(cons(a__head(nil), _x52))))mark#(incr(head(head(cons(head(cons(tail(_x81), _x72)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(cons(a__tail(mark(_x81)), _x72)), _x52))))
mark#(incr(head(head(cons(cons(incr(nil), _x62), _x52))))) → a__incr#(a__head(head(cons(cons(a__incr(nil), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(tail(_x271)), _x232))), a__incr(mark(cons(head(tail(_x271)), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(a__tail(mark(_x271))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(tail(_x41)))) → a__incr#(head(a__tail(mark(_x41))))mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(incr(a__tail(a__head(s(cons(0, incr(nats))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(a__nats)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(a__nats)), _x132))))), incr(_x91))))))), _x32)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(mark(a__nats)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(_x131), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(s(mark(_x131)), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(a__incr(mark(_x111)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(_x51))))) → a__incr#(incr(a__incr(a__tail(mark(_x51)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(0)))), _x232))), a__incr(mark(cons(head(s(s(incr(0)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(0)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(pairs)))) → a__incr#(a__head(s(pairs)))mark#(incr(incr(incr(tail(head(head(nats))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__nats))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(_x191)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(head(mark(_x191))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(a__head(a__odds)))))))))
mark#(incr(incr(incr(tail(head(s(s(pairs)))))))) → a__incr#(a__incr(incr(tail(head(s(s(cons(0, incr(odds)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(_x231, _x232))), a__incr(mark(cons(_x231, _x232)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(a__incr(cons(mark(_x231), _x232))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(_x41)))) → a__incr#(head(head(mark(_x41))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(0)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(s(0)))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(s(_x291)))), _x232))), a__incr(mark(cons(head(s(s(s(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(s(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(incr(mark(_x111)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(s(nats)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(s(a__nats)))))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(nil))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(incr(_x151), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(a__incr(mark(_x151)), _x132))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(nil)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(nil)), _x62), _x52))))mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(head(s(a__tail(a__incr(incr(a__nats))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(head(cons(s(mark(_x151)), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x32), incr(a__head(tail(head(a__incr(cons(tail(a__head(mark(_x141))), _x122))))))))))) → a__incr#(head(cons(mark(incr(a__head(tail(head(a__incr(cons(tail(a__head(mark(_x141))), _x122))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(head(tail(s(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(s(mark(_x101))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(_x201, _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(a__head(cons(mark(_x201), _x202))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(s(incr(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(s(a__incr(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(odds)), a__incr(mark(odds))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(a__odds)))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(head(tail(nats)))))) → a__incr#(head(s(head(tail(a__nats)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(a__incr(mark(_x111)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(nats))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(cons(0, incr(nats))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(nats, _x232))), a__incr(mark(cons(nats, _x232)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(a__incr(cons(a__nats, _x232))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(tail(_x161)))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(a__tail(mark(_x161))))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(0)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(a__head(0)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(tail(_x281))), _x232))), a__incr(mark(cons(head(s(tail(_x281))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(a__tail(mark(_x281)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(_x281))), _x232))), a__incr(mark(cons(head(s(s(_x281))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(incr(cons(a__head(s(s(mark(_x281)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(incr(_x231))), a__incr(mark(incr(_x231)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(a__incr(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), a__incr(mark(_x221))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(mark(_x221))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(tail(_x51))))) → a__incr#(head(s(a__tail(mark(_x51)))))mark#(incr(head(head(head(_x51))))) → a__incr#(a__head(a__head(a__head(mark(_x51)))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(incr(tail(head(a__head(a__odds))))))mark#(incr(incr(incr(tail(head(s(s(incr(odds))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(a__pairs)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(a__nats)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(incr(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(incr(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(a__incr(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(tail(incr(cons(head(_x81), _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(a__head(mark(_x81)), _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(_x111))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(tail(head(a__incr(mark(_x111)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(0)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(0)), _x122)))))), _x62))))mark#(incr(head(s(odds)))) → a__incr#(a__head(s(a__incr(a__pairs))))
mark#(incr(head(head(s(_x51))))) → a__incr#(a__head(a__head(s(mark(_x51)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x232))), a__incr(mark(cons(head(s(_x271)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(mark(_x271))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(s(incr(mark(_x221))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(0, incr(nats)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(nil)))), _x232))), a__incr(mark(cons(head(s(s(incr(nil)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(nil)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(nil)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(nil)))))))), _x62), _x52))))mark#(incr(pairs)) → a__incr#(a__pairs)
mark#(incr(head(s(head(tail(0)))))) → a__incr#(head(s(head(a__tail(0)))))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(head(head(cons(cons(a__incr(a__pairs), _x62), _x52))))
mark#(incr(head(s(tail(pairs))))) → a__incr#(a__head(s(tail(a__pairs))))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(nil))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(head(_x131))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__head(mark(_x131)))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(nats, _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__nats, _x122)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(tail(cons(_x91, _x92))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(cons(mark(_x91), _x92))))))))mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(head(s(a__head(tail(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(incr(_x131))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(a__incr(mark(_x131)))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(0)), _x232))), a__incr(mark(cons(head(s(0)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(0)), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(nil)))) → a__incr#(head(a__head(nil)))mark#(incr(head(s(tail(incr(nats)))))) → a__incr#(head(s(a__tail(a__incr(a__nats)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x161))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(mark(s(mark(_x151)))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(s(tail(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(a__tail(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(incr(_x231))), a__incr(mark(incr(_x231)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(s(mark(a__incr(incr(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(_x281))), _x232))), a__incr(mark(cons(head(s(s(_x281))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(mark(_x281)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(cons(_x301, _x302))))), _x232))), a__incr(mark(cons(head(s(s(incr(cons(_x301, _x302))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(cons(mark(_x301), _x302))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(cons(_x151, _x152))))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(cons(mark(_x151), _x152))))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x121))), s(mark(_x151)))))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(mark(s(mark(_x151)))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(_x241))), _x232))), a__incr(mark(cons(head(s(s(_x241))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(s(mark(_x241)))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(cons(s(mark(_x151)), _x132))), _x122)))))), _x62))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(head(a__head(incr(a__pairs)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(pairs))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(a__pairs))))))), _x62), _x52))))mark#(incr(head(s(head(incr(0)))))) → a__incr#(head(s(a__head(a__incr(0)))))
mark#(incr(head(head(cons(cons(incr(head(nil)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(nil)), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(_x101)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(incr(mark(_x101))))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(cons(_x131, _x132))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(cons(mark(_x131), _x132))))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(odds))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__odds))))))))mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(incr(a__tail(mark(_x51)))))
mark#(incr(incr(incr(tail(s(0)))))) → a__incr#(a__incr(a__incr(a__tail(s(0)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(tail(s(tail(_x71))))))) → a__incr#(a__head(s(tail(s(a__tail(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__incr(a__pairs))), _x62), _x52))))
mark#(incr(head(s(head(incr(s(_x71))))))) → a__incr#(head(s(a__head(a__incr(s(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(tail(_x51))))) → a__incr#(head(s(tail(mark(_x51)))))mark#(incr(head(s(head(tail(cons(nats, _x72))))))) → a__incr#(head(s(head(a__tail(cons(a__nats, _x72))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(nats, _x211))), a__incr(mark(cons(nats, _x211)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(cons(s(mark(a__nats)), incr(_x211))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(s(head(s(_x61)))))) → a__incr#(head(s(a__head(s(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(0))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(0))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x232))), a__incr(mark(cons(head(s(_x271)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(incr(cons(a__head(s(mark(_x271))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(head(s(a__tail(incr(a__incr(a__nats))))))mark#(incr(head(s(tail(s(head(_x71))))))) → a__incr#(a__head(s(a__tail(s(a__head(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(pairs)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__pairs)))), _x62), _x52))))mark#(incr(head(s(head(pairs))))) → a__incr#(head(s(a__head(a__pairs))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(head(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__head(mark(_x111)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x151))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(mark(s(mark(a__nats)))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(pairs), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__pairs))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(s(_x111))))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(s(mark(_x111)))))))))))
mark#(incr(head(s(head(tail(cons(tail(_x81), _x72))))))) → a__incr#(head(s(head(a__tail(cons(a__tail(mark(_x81)), _x72))))))mark#(incr(head(s(tail(s(cons(_x71, _x72))))))) → a__incr#(a__head(s(tail(s(cons(mark(_x71), _x72))))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(_x101)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__head(mark(_x101))))))))))mark#(incr(head(s(tail(s(odds)))))) → a__incr#(head(s(tail(s(a__odds)))))
mark#(incr(head(head(cons(head(cons(0, _x72)), _x52))))) → a__incr#(head(a__head(cons(head(cons(0, _x72)), _x52))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(odds))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(_x231))), _x191))), _x161))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(mark(s(mark(s(a__incr(a__tail(mark(_x231)))))))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(s(mark(_x111)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(nats)))), _x232))), a__incr(mark(cons(head(s(s(incr(nats)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(a__nats)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(nil), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(incr(nil), _x62), _x52))))
mark#(incr(head(s(tail(incr(0)))))) → a__incr#(head(s(a__tail(incr(0)))))mark#(incr(incr(incr(tail(head(s(s(_x81)))))))) → a__incr#(a__incr(incr(tail(head(s(s(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(head(_x271)), _x232))), a__incr(mark(cons(head(head(_x271)), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(a__head(mark(_x271))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(s(head(tail(nats)))))) → a__incr#(head(s(head(tail(cons(0, incr(nats)))))))
mark#(incr(incr(incr(tail(head(head(nats))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(nats))))))mark#(incr(head(s(head(incr(nats)))))) → a__incr#(head(s(head(a__incr(cons(0, incr(nats)))))))
mark#(incr(head(s(tail(nats))))) → a__incr#(a__head(s(tail(a__nats))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(odds)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(a__odds)), _x122)))))), _x62))))
mark#(incr(incr(incr(tail(head(odds)))))) → a__incr#(a__incr(incr(tail(a__head(a__odds)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(0)))), _x232))), a__incr(mark(cons(head(s(s(incr(0)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(0)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(pairs))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(a__pairs))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(0), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(0), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(head(_x231))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(s(a__incr(a__head(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(nil), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(nil), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(a__tail(a__incr(incr(a__nats))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(_x231, _x221))), a__incr(mark(cons(_x231, _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(cons(s(mark(mark(_x231))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))mark#(incr(head(head(cons(odds, _x52))))) → a__incr#(a__head(a__head(cons(odds, _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(0), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(cons(s(0), _x132))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(_x231, _x211))), a__incr(mark(cons(_x231, _x211)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(cons(s(mark(mark(_x231))), incr(_x211))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(pairs))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__pairs))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(0), _x62), _x52))))) → a__incr#(a__head(head(cons(cons(incr(0), _x62), _x52))))
mark#(incr(head(s(head(tail(nats)))))) → a__incr#(head(s(head(mark(incr(nats))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(0), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(head(cons(s(0), _x132))), _x122)))))), _x62))))
mark#(incr(head(s(tail(incr(cons(pairs, _x72))))))) → a__incr#(a__head(s(a__tail(incr(cons(a__pairs, _x72))))))mark#(incr(head(s(tail(incr(nats)))))) → a__incr#(a__head(s(a__tail(a__incr(a__nats)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(cons(0, incr(nats)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(_x231, _x232))), a__incr(mark(cons(_x231, _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(a__incr(cons(mark(_x231), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(nats)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(a__nats)), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(0, _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(0, _x122)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(a__head(head(incr(a__pairs)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(incr(s(_x241)))), a__incr(mark(incr(s(_x241))))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(s(mark(a__incr(a__incr(s(mark(_x241))))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(_x221), _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(cons(s(mark(_x221)), _x202))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(s(s(pairs)))))))) → a__incr#(incr(incr(tail(a__head(s(s(cons(0, incr(odds)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(tail(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__tail(mark(_x101))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(nats))))))) → a__incr#(incr(a__incr(a__tail(head(a__head(a__nats))))))
mark#(incr(incr(incr(tail(head(s(odds))))))) → a__incr#(incr(incr(tail(head(s(odds))))))mark#(incr(head(s(tail(incr(pairs)))))) → a__incr#(head(s(a__tail(a__incr(a__pairs)))))
mark#(incr(nats)) → a__incr#(a__nats)mark#(incr(head(nil))) → a__incr#(head(nil))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(head(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(head(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__head(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(s(head(tail(incr(_x71))))))) → a__incr#(head(s(head(a__tail(a__incr(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x232))), a__incr(mark(cons(head(s(_x271)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(mark(_x271))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(incr(nats))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(cons(0, incr(nats))))))))
mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(incr(a__incr(tail(a__head(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(head(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(a__head(mark(_x111)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(pairs, _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(a__pairs)), incr(_x101)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(a__incr(incr(tail(head(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(_x231, _x232))), a__incr(mark(cons(_x231, _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(mark(_x231), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(tail(_x61)))))) → a__incr#(a__incr(a__incr(a__tail(a__tail(mark(_x61))))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(a__tail(mark(0)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(head(_x151))))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(a__head(mark(_x151)))))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(a__incr(cons(head(s(s(incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(0)))) → a__incr#(head(head(0)))
mark#(incr(incr(incr(tail(nil))))) → a__incr#(a__incr(a__incr(tail(nil))))mark#(incr(incr(incr(tail(s(nil)))))) → a__incr#(incr(incr(a__tail(s(nil)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(head(a__nats)))), _x62))))mark#(incr(incr(incr(tail(head(cons(_x71, _x72))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(cons(mark(_x71), _x72))))))
mark#(incr(incr(incr(tail(head(head(tail(nil)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(nil)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(nats), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__nats), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(head(cons(odds, _x72)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(cons(a__odds, _x72)), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(nil)))), _x221))), a__incr(mark(cons(head(s(s(incr(nil)))), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(cons(s(mark(head(s(s(a__incr(nil)))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(_x201, _x202))), _x161))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(mark(s(a__head(cons(mark(_x201), _x202))))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(pairs), _x62), _x52))))
mark#(incr(head(s(tail(incr(incr(odds))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(a__odds))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(odds), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__incr(a__pairs)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(odds)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(a__odds)), _x122)))))), _x62), _x52))))mark#(incr(head(head(pairs)))) → a__incr#(head(head(cons(0, incr(odds)))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(odds))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(incr(_x201))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(a__incr(mark(_x201)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(head(cons(pairs, _x72)), _x52))))) → a__incr#(a__head(head(cons(a__head(cons(a__pairs, _x72)), _x52))))mark#(incr(head(head(cons(0, _x52))))) → a__incr#(a__head(head(cons(0, _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(_x91))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(mark(_x91)))))))))mark#(incr(head(s(tail(incr(incr(_x71))))))) → a__incr#(a__head(s(tail(a__incr(a__incr(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(s(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(s(mark(_x121))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(nats))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(cons(0, incr(nats))))))))), _x62), _x52))))
mark#(incr(head(s(tail(incr(cons(_x71, _x72))))))) → a__incr#(head(s(a__tail(a__incr(cons(mark(_x71), _x72))))))mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(head(head(cons(a__nats, _x52))))
mark#(incr(head(s(tail(incr(cons(cons(_x81, _x82), _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(cons(mark(_x81), _x82), _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(odds)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(a__odds)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(pairs)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(s(a__pairs)))))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(pairs))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(a__pairs))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(nil))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(tail(head(a__incr(nil))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(incr(tail(a__head(a__head(a__odds))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(nats), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(s(a__nats), _x132))), _x122)))))), _x62))))mark#(incr(head(s(head(odds))))) → a__incr#(head(s(a__head(a__odds))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(a__tail(mark(0)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(nats, _x232))), a__incr(mark(cons(nats, _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__nats, _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(a__tail(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(s(head(tail(cons(_x71, _x72))))))) → a__incr#(head(s(a__head(a__tail(cons(mark(_x71), _x72))))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(a__incr(cons(0, incr(odds)))))))))mark#(incr(head(head(cons(cons(incr(head(pairs)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__pairs)), _x62), _x52))))
mark#(incr(head(head(cons(head(cons(pairs, _x72)), _x31))))) → a__incr#(a__head(mark(a__head(cons(a__pairs, _x72)))))mark#(incr(incr(incr(tail(head(head(s(_x81)))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(s(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(_x231))), a__incr(mark(tail(_x231)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(a__tail(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(a__nats)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(nats)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(nats)), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(incr(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(a__incr(mark(_x81))))))))
mark#(incr(incr(nats))) → a__incr#(incr(nats))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x151))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(s(mark(_x151)))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__tail(mark(_x91)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(incr(cons(a__tail(a__head(s(mark(_x151)))), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(_x61, _x62), _x52))))) → a__incr#(head(a__head(cons(cons(mark(_x61), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(s(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(s(mark(_x101))))), _x62), _x52))))
mark#(incr(incr(incr(tail(s(pairs)))))) → a__incr#(a__incr(a__incr(a__tail(s(a__pairs)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x131))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(mark(_x131)))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(_x221, _x222), _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(cons(cons(mark(_x221), _x222), _x202))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(cons(_x201, _x202)), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(_x201, _x202))), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(cons(mark(_x201), _x202)), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(_x131), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(mark(_x131)), _x122)))))), _x62))))mark#(incr(incr(incr(tail(head(head(0))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(0))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(_x131, _x121))), mark(_x131))))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(mark(mark(_x131))), _x122)))))), _x62))))mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(nil)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(nil)), _x122)))))), _x62))))mark#(incr(incr(incr(tail(head(head(cons(_x81, _x82)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(cons(mark(_x81), _x82)))))))
mark#(incr(head(s(tail(s(_x61)))))) → a__incr#(head(s(a__tail(s(mark(_x61))))))mark#(incr(head(s(head(tail(cons(_x71, _x72))))))) → a__incr#(head(s(head(tail(cons(mark(_x71), _x72))))))
mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x31))))) → a__incr#(head(mark(cons(a__incr(mark(_x71)), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(s(_x231))), a__incr(mark(s(_x231)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(s(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(head(cons(_x71, _x72)), _x31))))) → a__incr#(a__head(mark(a__head(cons(mark(_x71), _x72)))))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(cons(0, incr(odds))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(incr(_x91))), _x62), _x52))))) → a__incr#(head(head(cons(cons(a__incr(a__head(a__incr(mark(_x91)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x232))), a__incr(mark(cons(head(s(_x271)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(head(s(mark(_x271))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(_x131, _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(a__incr(cons(tail(a__head(cons(mark(_x131), _x132))), _x122)))))), _x62))))mark#(s(X)) → mark#(X)
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(tail(_x261), _x242))), _x232))), a__incr(mark(cons(head(s(cons(tail(_x261), _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(s(mark(s(mark(a__incr(cons(a__head(s(cons(a__tail(mark(_x261)), _x242))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(incr(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(incr(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__incr(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(_x301))))), _x241))), a__incr(mark(cons(head(s(s(incr(tail(_x301))))), _x241)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(cons(s(mark(a__head(s(s(a__incr(a__tail(mark(_x301)))))))), incr(_x241))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(incr(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(incr(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__incr(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(cons(_x301, _x302))))), _x232))), a__incr(mark(cons(head(s(s(incr(cons(_x301, _x302))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(cons(mark(_x301), _x302))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), a__incr(mark(_x221))))), _x161))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(mark(s(s(mark(a__incr(mark(_x221))))))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(head(cons(nats, _x72)), _x52))))) → a__incr#(a__head(a__head(cons(head(cons(a__nats, _x72)), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(s(_x241), _x232))), a__incr(mark(cons(s(_x241), _x232)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(s(mark(_x241)), _x232))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(s(cons(_x61, _x62)))))) → a__incr#(head(s(s(cons(mark(_x61), _x62)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(_x231, _x232))), a__incr(mark(cons(_x231, _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(incr(cons(mark(_x231), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(tail(s(_x281)), _x242))), _x232))), a__incr(mark(cons(head(s(cons(tail(s(_x281)), _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(a__tail(s(mark(_x281))), _x242))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x151))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(s(mark(mark(a__nats)))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(incr(_x231))), a__incr(mark(incr(_x231)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(head(cons(s(s(mark(a__incr(a__incr(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), _x191))), _x161))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(mark(s(mark(s(a__incr(mark(_x221))))))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(nil, _x232))), a__incr(mark(cons(nil, _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(nil, _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(odds, _x232))), a__incr(mark(cons(odds, _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__odds, _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(pairs)))), _x232))), a__incr(mark(cons(head(s(s(incr(pairs)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(a__pairs)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(s(s(incr(incr(incr(_x111))))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(a__incr(mark(_x111)))))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(tail(_x151))))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(s(a__tail(mark(_x151)))))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(tail(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(incr(cons(a__tail(a__head(a__tail(mark(_x151)))), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(odds))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(a__odds))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(pairs, _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__pairs, _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(0), _x62), _x31))))) → a__incr#(head(mark(cons(incr(0), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(pairs), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(pairs)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(a__pairs), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(0)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(0)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(head(_x131))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(a__head(mark(_x131)))), _x122)))))), _x62))))
mark#(incr(incr(incr(tail(head(s(0))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(0))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(cons(_x171, _x172)), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(s(cons(mark(_x171), _x172)), _x132))), _x122)))))), _x62))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(a__tail(mark(0)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(nats)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(incr(cons(a__tail(a__head(a__nats)), _x122)))))), _x62), _x52))))
mark#(incr(head(s(tail(nats))))) → a__incr#(a__head(s(tail(nats))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(tail(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__tail(mark(_x121))))))), _x62), _x52))))
mark#(incr(head(s(tail(nil))))) → a__incr#(a__head(s(tail(nil))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(0)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(0)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x221))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(cons(s(mark(a__head(s(s(a__incr(mark(_x291))))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(nats)), a__incr(mark(nats))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(a__nats)))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(pairs)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__pairs)))))), _x62), _x52))))mark#(incr(head(cons(_x41, _x42)))) → a__incr#(head(cons(mark(_x41), _x42)))
mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(a__incr(incr(a__tail(a__head(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(nil)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(nil)), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(s(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(s(mark(_x91)))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(head(a__head(a__odds))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(0)), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(0)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(0)), _x132))))), incr(_x91))))))), _x32)))mark#(incr(head(head(cons(cons(incr(head(pairs)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(pairs)), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(nats), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(s(a__nats))), incr(_x101)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(s(_x221), _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(s(mark(_x221)), _x212))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(_x71), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(mark(_x71)), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(incr(odds))), a__incr(mark(incr(odds)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(s(mark(a__incr(a__incr(a__odds))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(nats))))))mark#(incr(incr(incr(tail(s(nil)))))) → a__incr#(a__incr(a__incr(tail(s(nil)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(incr(_x161)), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(s(a__incr(mark(_x161))))), incr(_x101)))))), _x62), _x52))))mark#(incr(head(head(cons(head(cons(s(_x81), _x72)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(cons(s(mark(_x81)), _x72)), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(0, _x232))), a__incr(mark(cons(0, _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(0, _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(s(tail(pairs))))) → a__incr#(a__head(s(tail(pairs))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(pairs)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__pairs)))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(incr(_x241)))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__tail(a__incr(mark(_x241))))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(_x131), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(tail(mark(_x131)), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(incr(_x231))), a__incr(mark(incr(_x231)))))), _x161))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(mark(s(s(mark(a__incr(a__incr(mark(_x231)))))))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(0)))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(odds)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(a__odds)), _x122)))))), _x62))))
mark#(incr(head(head(cons(head(cons(pairs, _x72)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(cons(pairs, _x72)), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(pairs)), a__incr(mark(pairs))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(s(mark(a__incr(a__pairs)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(tail(_x111))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(a__tail(mark(_x111)))))))))))mark#(incr(incr(incr(tail(incr(_x61)))))) → a__incr#(a__incr(a__incr(a__tail(a__incr(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(cons(0, incr(odds))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(cons(_x81, _x82)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(cons(mark(_x81), _x82)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(0)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(0)), _x122)))))), _x62), _x52))))mark#(incr(head(s(nats)))) → a__incr#(head(s(nats)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(mark(_x141))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(head(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(a__head(mark(_x151)))), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(_x231))), _x191))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__tail(mark(_x231)))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(tail(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(a__tail(mark(_x111)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(incr(tail(a__head(cons(0, incr(nats)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__nats)))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(incr(incr(tail(a__head(head(nil))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(cons(_x141, _x142)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(cons(mark(_x141), _x142)), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), a__incr(mark(_x221))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(mark(_x221))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(incr(_x241))), _x232))), a__incr(mark(cons(head(s(incr(_x241))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(a__incr(mark(_x241)))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(odds, _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__odds, _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(head(cons(_x71, _x72)), _x52))))) → a__incr#(head(a__head(cons(a__head(cons(mark(_x71), _x72)), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(tail(_x221), _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(cons(a__tail(mark(_x221)), _x202))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(odds, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(a__odds)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(pairs))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(a__pairs))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(head(_x141)))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(a__head(mark(_x141))))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(0, _x62), _x31))))) → a__incr#(a__head(mark(cons(0, _x62))))mark#(incr(incr(incr(tail(head(s(0))))))) → a__incr#(a__incr(incr(tail(a__head(s(0))))))
mark#(incr(head(head(cons(cons(incr(head(nats)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__nats)), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(cons(0, incr(nats)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(s(cons(_x71, _x72))))))) → a__incr#(a__incr(a__incr(a__tail(s(cons(mark(_x71), _x72))))))mark#(incr(incr(incr(tail(head(incr(nats))))))) → a__incr#(a__incr(a__incr(tail(a__head(incr(a__nats))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(pairs))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(pairs))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(a__pairs))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(s(a__incr(mark(_x291))))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(a__tail(head(cons(0, incr(nats)))))))
mark#(incr(head(s(head(s(pairs)))))) → a__incr#(a__head(s(a__head(s(a__pairs)))))mark#(incr(incr(incr(tail(head(s(s(incr(s(_x101)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(s(mark(_x101))))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(head(_x311))))), _x221))), a__incr(mark(cons(head(s(s(incr(head(_x311))))), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(cons(s(mark(head(s(s(a__incr(a__head(mark(_x311)))))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(head(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(head(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(a__head(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(mark(0)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(_x231))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(incr(a__tail(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(_x191)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(a__head(mark(_x191))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(incr(_x171)), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(s(a__incr(mark(_x171))), _x132))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(a__head(head(cons(cons(a__incr(a__pairs), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(nats)), a__incr(mark(nats))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(incr(a__nats)))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(tail(incr(head(_x71))))))) → a__incr#(a__head(s(a__tail(incr(a__head(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(s(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(s(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(s(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(_x171)), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(s(a__head(mark(_x171))), _x132))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(cons(_x301, _x302))))), _x232))), a__incr(mark(cons(head(s(s(incr(cons(_x301, _x302))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(cons(mark(_x301), _x302))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(odds), _x151))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(mark(s(a__odds))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(_x131), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(incr(cons(a__tail(mark(_x131)), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(incr(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(a__incr(mark(_x141))))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(s(cons(_x151, _x152))))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(s(cons(mark(_x151), _x152))))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(tail(_x241), _x232))), a__incr(mark(cons(tail(_x241), _x232)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__tail(mark(_x241)), _x232))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(_x241, _x242))), _x232))), a__incr(mark(cons(head(s(cons(_x241, _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(mark(_x241), _x242))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(nats)), a__incr(mark(nats))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(0, incr(nats)))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(nil))))) → a__incr#(incr(a__incr(a__tail(nil))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(s(s(mark(_x121))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(incr(nil))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(nil))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(s(a__incr(mark(_x291))))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(0)), _x232))), a__incr(mark(cons(head(s(0)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(0)), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(incr(cons(head(s(s(a__incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(nil)))))) → a__incr#(a__incr(a__incr(tail(a__head(nil)))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(head(a__odds))))))mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(incr(incr(a__tail(a__head(s(a__nats))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(incr(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__incr(mark(_x121))))))), _x62), _x52))))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(head(s(cons(mark(_x51), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(_x241, _x242))), _x201))), a__incr(mark(cons(head(s(cons(_x241, _x242))), _x201)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(cons(s(mark(a__head(s(cons(mark(_x241), _x242))))), incr(_x201))))))))), incr(_x91))))))), _x42)))mark#(incr(head(s(tail(incr(cons(pairs, _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(cons(0, incr(odds)), _x72))))))
mark#(incr(head(head(cons(head(_x61), _x52))))) → a__incr#(a__head(head(cons(a__head(mark(_x61)), _x52))))mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(head(s(a__tail(incr(a__incr(cons(0, incr(nats))))))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(incr(a__tail(a__head(cons(0, incr(nats)))))))mark#(incr(head(s(tail(incr(incr(nil))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(nil))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(nats))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__tail(a__nats))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(head(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(a__head(mark(_x111)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(pairs)))), _x232))), a__incr(mark(cons(head(s(s(incr(pairs)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(a__pairs)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(odds)))), _x232))), a__incr(mark(cons(head(s(s(incr(odds)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(a__odds)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(_x231))), a__incr(mark(tail(_x231)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(s(mark(a__incr(a__tail(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(s(tail(incr(incr(0))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(0))))))
mark#(incr(incr(incr(tail(0))))) → a__incr#(a__incr(a__incr(a__tail(0))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(nats))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(a__nats))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(cons(_x151, _x152), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(cons(mark(_x151), _x152))), incr(_x101)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(s(nil)))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(s(nil)))))))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(tail(incr(a__incr(a__nats))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(nats))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(s(a__nats))))))), _x62), _x52))))
mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(a__head(nats))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(_x151)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(s(s(incr(_x91))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(mark(_x91)))))))))mark#(incr(head(s(head(0))))) → a__incr#(head(s(a__head(0))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(_x211, _x192), mark(_x211)))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(cons(mark(mark(_x211)), _x192)), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(tail(_x221)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__tail(mark(_x221))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(pairs))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(a__pairs))), _x122)))))), _x62), _x52))))mark#(incr(head(s(odds)))) → a__incr#(head(s(a__odds)))
mark#(incr(head(s(tail(odds))))) → a__incr#(a__head(s(a__tail(a__odds))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(cons(_x311, _x312))))), _x221))), a__incr(mark(cons(head(s(s(incr(cons(_x311, _x312))))), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(cons(s(mark(head(s(s(a__incr(cons(mark(_x311), _x312))))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(incr(incr(tail(head(s(0))))))) → a__incr#(incr(incr(tail(a__head(s(0))))))mark#(incr(head(s(tail(incr(tail(_x71))))))) → a__incr#(head(s(a__tail(a__incr(a__tail(mark(_x71)))))))
mark#(incr(head(head(0)))) → a__incr#(a__head(head(0)))mark#(incr(head(s(0)))) → a__incr#(head(s(0)))
mark#(incr(incr(incr(tail(head(head(tail(nats)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(a__nats)))))))mark#(incr(head(head(tail(_x51))))) → a__incr#(a__head(a__head(a__tail(mark(_x51)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(head(0)))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(nil)), _x232))), a__incr(mark(cons(head(s(nil)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(nil)), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(incr(incr(tail(head(incr(0))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(0))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x232))), a__incr(mark(cons(head(s(_x271)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(mark(_x271))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(s(_x61), _x52))))) → a__incr#(a__head(a__head(cons(s(mark(_x61)), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(incr(_x191)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__incr(mark(_x191))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(nats), _x232))), a__incr(mark(cons(head(nats), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(a__nats), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(incr(incr(tail(head(head(tail(tail(_x91))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(a__tail(mark(_x91)))))))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(_x101)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(incr(mark(_x101))))))))))
mark#(incr(incr(incr(tail(s(_x61)))))) → a__incr#(incr(a__incr(tail(s(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(0, _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(cons(0, _x132))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(_x251), _x232))), a__incr(mark(cons(head(_x251), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(incr(cons(a__head(mark(_x251)), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(s(0)))))) → a__incr#(a__incr(a__incr(tail(s(0)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(nil, _x232))), a__incr(mark(cons(nil, _x232)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(nil, _x232))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(nats)))) → a__incr#(a__head(a__head(a__nats)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(odds)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__odds)))))), _x62), _x52))))mark#(incr(head(s(head(tail(nil)))))) → a__incr#(head(s(a__head(a__tail(nil)))))
mark#(incr(head(s(s(nil))))) → a__incr#(head(s(s(nil))))mark#(incr(incr(incr(tail(head(s(odds))))))) → a__incr#(incr(incr(tail(a__head(s(a__incr(a__pairs)))))))
mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(tail(mark(_x51)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(_x131, _x132))), _x122)))))), _x32), incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(mark(_x131), _x132))), _x122))))))))))) → a__incr#(head(cons(mark(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(mark(_x131), _x132))), _x122))))))), _x32)))
mark#(incr(head(head(cons(cons(tail(_x71), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__tail(mark(_x71)), _x62), _x52))))mark#(incr(incr(incr(tail(head(tail(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__tail(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(nil)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(nil)))))), _x62), _x52))))mark#(incr(head(s(tail(s(odds)))))) → a__incr#(a__head(s(a__tail(s(a__odds)))))
mark#(incr(incr(incr(tail(head(incr(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(a__odds))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(tail(head(_x281)), _x242))), _x232))), a__incr(mark(cons(head(s(cons(tail(head(_x281)), _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(a__tail(a__head(mark(_x281))), _x242))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x221))), a__incr(mark(cons(head(s(_x271)), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(cons(s(mark(a__head(s(mark(_x271))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(nats)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__nats)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(_x51, _x52))))) → a__incr#(head(a__head(cons(mark(_x51), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(pairs), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(s(a__pairs))), incr(_x101)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(head(a__head(a__incr(a__pairs)))))))mark#(incr(head(head(cons(head(0), _x52))))) → a__incr#(a__head(a__head(cons(a__head(0), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(_x281))), _x232))), a__incr(mark(cons(head(s(s(_x281))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(mark(_x281)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(odds, _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(a__odds)), incr(_x101)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(a__head(odds)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(0), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(cons(s(0), _x132))), _x122)))))), _x62))))
mark#(incr(head(s(tail(incr(cons(pairs, _x51))))))) → a__incr#(head(s(a__tail(cons(s(mark(a__pairs)), incr(_x51))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(nats))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__nats))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(incr(tail(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(a__tail(mark(_x101))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(tail(odds), _x242))), _x232))), a__incr(mark(cons(head(s(cons(tail(odds), _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(a__tail(a__odds), _x242))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(pairs)))), _x232))), a__incr(mark(cons(head(s(s(incr(pairs)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__pairs)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(nil), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(s(nil), _x132))), _x122)))))), _x62))))
mark#(incr(incr(incr(tail(s(tail(_x71))))))) → a__incr#(a__incr(a__incr(tail(s(a__tail(mark(_x71)))))))mark#(incr(incr(incr(tail(head(head(tail(s(_x91))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(s(mark(_x91)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(s(mark(_x151)))), _x122)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(head(head(a__odds))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(tail(_x191)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__tail(mark(_x191))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(cons(_x111, _x112))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(cons(mark(_x111), _x112))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(tail(_x261), _x242))), _x232))), a__incr(mark(cons(head(s(cons(tail(_x261), _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(head(s(cons(a__tail(mark(_x261)), _x242))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(cons(_x91, _x92))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(cons(mark(_x91), _x92))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(nats))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__nats))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(nats, _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(a__nats, _x132))), _x122)))))), _x62))))
mark#(incr(head(s(tail(s(nats)))))) → a__incr#(a__head(s(a__tail(s(a__nats)))))mark#(incr(incr(incr(tail(head(s(s(incr(odds))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(odds))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(pairs), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__pairs), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(incr(pairs))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(incr(_x241))), a__incr(mark(incr(_x241)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(a__incr(mark(_x241)))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(head(mark(_x141))), _x122)))))), _x62), _x52))))
mark#(incr(head(s(tail(s(pairs)))))) → a__incr#(a__head(s(tail(s(a__pairs)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(head(_x161)))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(a__head(mark(_x161))))), _x122)))))), _x62), _x52))))
mark#(incr(head(s(tail(incr(cons(nil, _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(nil, _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(s(_x201)), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(_x201))), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(s(mark(_x201))), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(incr(cons(head(s(s(a__incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(s(s(incr(head(cons(_x111, _x112))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(cons(mark(_x111), _x112))))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(incr(_x141)))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(a__incr(mark(_x141))))), _x122)))))), _x62))))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(a__incr(tail(a__head(head(nil))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(mark(_x101))))), _x62), _x52))))
mark#(incr(head(s(head(s(nats)))))) → a__incr#(a__head(s(a__head(s(a__nats)))))mark#(incr(head(head(cons(cons(incr(head(incr(cons(_x101, _x102)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(cons(mark(_x101), _x102)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(incr(_x161)))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(a__incr(mark(_x161))))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(head(_x151), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(a__head(mark(_x151)), _x132))), _x122)))))), _x62))))
mark#(incr(head(nats))) → a__incr#(a__head(cons(0, incr(nats))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(incr(_x251), _x232))), a__incr(mark(cons(incr(_x251), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__incr(mark(_x251)), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x232))), a__incr(mark(cons(head(s(_x271)), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(mark(_x271))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(s(s(incr(head(nil)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__head(nil)))))))))
mark#(incr(head(s(head(tail(cons(0, _x72))))))) → a__incr#(head(s(head(a__tail(cons(0, _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(cons(_x251, _x252), _x232))), a__incr(mark(cons(cons(_x251, _x252), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(cons(mark(_x251), _x252), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(head(tail(tail(_x71))))))) → a__incr#(head(s(head(a__tail(a__tail(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(_x121)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(s(s(mark(_x121))))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(odds, _x242))), _x232))), a__incr(mark(cons(head(s(cons(odds, _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(a__odds, _x242))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(nats, _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(cons(a__nats, _x132))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(s(_x161)), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(s(s(mark(_x161))))), incr(_x101)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(cons(_x131, _x132))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(s(s(cons(mark(_x131), _x132))))))), _x62), _x52))))
mark#(incr(head(pairs))) → a__incr#(head(a__pairs))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(_x131))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(tail(a__head(s(s(s(mark(_x131)))))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(0)))))) → a__incr#(a__incr(incr(tail(a__head(0)))))mark#(incr(head(head(cons(head(head(_x71)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(a__head(mark(_x71))), _x52))))
mark#(incr(incr(incr(tail(head(s(s(head(_x91))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__head(mark(_x91)))))))))mark#(incr(head(head(cons(head(cons(_x71, _x51)), mark(_x71)))))) → a__incr#(a__head(a__head(cons(mark(mark(_x71)), _x52))))
mark#(incr(head(s(tail(pairs))))) → a__incr#(a__head(s(tail(cons(0, incr(odds))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(nil), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(nil)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(nil), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(head(cons(_x71, _x72)), _x52))))) → a__incr#(a__head(a__head(cons(head(cons(mark(_x71), _x72)), _x52))))mark#(incr(head(head(cons(head(cons(0, _x72)), _x52))))) → a__incr#(head(a__head(cons(a__head(cons(0, _x72)), _x52))))
mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(nats)), a__incr(mark(nats))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(nats)))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(tail(a__head(mark(_x141))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), _x191))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(s(a__incr(mark(_x221))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(incr(incr(tail(head(s(s(incr(_x91))))))))) → a__incr#(incr(incr(tail(head(s(s(a__incr(mark(_x91)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(0))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(0))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(odds))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(a__odds))))))), _x62), _x52))))mark#(incr(head(s(tail(0))))) → a__incr#(head(s(a__tail(0))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(cons(_x121, _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(cons(mark(_x121), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x91)))))), _x32), incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(_x151)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(_x151)), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(odds)), _x62), _x52))))mark#(incr(head(s(head(s(incr(_x71))))))) → a__incr#(a__head(s(a__head(s(a__incr(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(_x131))))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(s(s(a__tail(mark(_x131)))))))), _x62))))mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(mark(0))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(a__nats)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(a__nats)), _x132))))), incr(_x91))))))), _x32)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(nats))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(a__nats))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(s(mark(_x151)))), _x122)))))), _x62), _x52))))mark#(incr(head(s(tail(incr(cons(_x71, _x72))))))) → a__incr#(a__head(s(tail(a__incr(cons(mark(_x71), _x72))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(cons(_x131, _x132), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(cons(mark(_x131), _x132), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(0), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(0)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(0), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(cons(0, incr(nats))))))))mark#(incr(head(head(cons(cons(nil, _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(nil, _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(s(odds)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(s(a__odds)))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(_x201, _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(head(cons(mark(_x201), _x202))), _x132))))), incr(_x91)))))), _x62))))
a__incr#(cons(X, XS)) → mark#(X)mark#(incr(incr(incr(tail(head(s(s(incr(nil))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(nil))))))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(nil)))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(a__head(nil)))))))))mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nil, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(nil), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(s(head(incr(nil)))))) → a__incr#(head(s(a__head(a__incr(nil)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(pairs)), a__incr(mark(pairs))))), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(a__pairs)))), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(a__pairs)))), _x132))))), incr(_x91))))))), _x32)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x232))), a__incr(mark(cons(head(s(_x271)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(a__tail(mark(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(mark(_x271))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(s(s(incr(head(nats)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(a__nats)))))))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(pairs)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(a__pairs)))))))))mark#(incr(head(s(tail(incr(head(nil))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(nil))))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(tail(head(cons(0, incr(nats)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(nil))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(nil))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(nats))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(s(s(s(a__nats))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(head(_x91))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__head(mark(_x91)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(s(_x141)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(s(mark(_x141))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(incr(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(a__incr(mark(_x151)))), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(cons(_x141, _x142)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(cons(mark(_x141), _x142)))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(nats))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__nats))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(pairs), _x232))), a__incr(mark(cons(head(pairs), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(a__pairs), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(pairs, _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(cons(a__pairs, _x132))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(_x131, _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(head(cons(mark(_x131), _x132))), _x122)))))), _x62))))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(incr(a__incr(tail(head(head(nil))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(incr(cons(a__head(s(s(a__incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(_x231, _x232))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(s(a__incr(cons(mark(_x231), _x232))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(0)), _x151))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(s(mark(a__head(0)))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(odds)))))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(a__head(s(s(s(a__incr(a__odds)))))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(nats))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(nats))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(a__nats))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(0), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(0))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(tail(_x291)))), _x232))), a__incr(mark(cons(head(s(s(tail(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__tail(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(nil)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(s(nil)))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(odds))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(a__odds))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(odds), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__odds))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(s(tail(s(odds)))))) → a__incr#(a__head(s(tail(s(a__incr(a__pairs))))))
mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(incr(a__incr(a__tail(a__head(mark(_x61))))))mark#(incr(head(head(odds)))) → a__incr#(a__head(a__head(a__odds)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(_x191)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(a__head(mark(_x191))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(a__incr(a__pairs)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(head(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(head(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(a__head(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(0))) → a__incr#(a__incr(0))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(head(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(head(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(a__head(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(nats))))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(s(s(a__tail(a__nats))))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(odds)), a__incr(mark(odds))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(s(mark(a__incr(a__odds)))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(s(s(incr(head(_x101)))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(a__head(mark(_x101))))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(mark(_x121))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(tail(pairs), _x242))), _x232))), a__incr(mark(cons(head(s(cons(tail(pairs), _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(a__tail(a__pairs), _x242))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(nil)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(nil)))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(head(tail(0)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__tail(0)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(head(_x151))))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(s(a__head(mark(_x151)))))))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(incr(incr(tail(head(s(mark(_x71)))))))
mark#(incr(incr(incr(tail(head(nil)))))) → a__incr#(a__incr(incr(tail(a__head(nil)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(s(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(s(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(s(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(incr(incr(tail(head(head(nats))))))) → a__incr#(incr(a__incr(a__tail(a__head(a__head(cons(0, incr(nats))))))))mark#(incr(head(s(tail(nats))))) → a__incr#(head(s(a__tail(a__nats))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(0)))), _x62), _x52))))mark#(incr(incr(pairs))) → a__incr#(incr(a__pairs))
mark#(incr(head(s(tail(s(cons(_x71, _x72))))))) → a__incr#(a__head(s(a__tail(s(cons(mark(_x71), _x72))))))mark#(incr(head(head(cons(cons(incr(head(incr(s(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(s(mark(_x101))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(incr(_x201)), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(incr(_x201))), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(a__incr(mark(_x201))), _x132))))), incr(_x91))))))), _x32)))mark#(incr(incr(incr(tail(head(head(tail(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(a__tail(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(_x141)))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(mark(_x141))))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(cons(_x261, _x262), _x242))), _x232))), a__incr(mark(cons(head(s(cons(cons(_x261, _x262), _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(cons(mark(_x261), _x262), _x242))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(s(_x251), _x232))), a__incr(mark(cons(s(_x251), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(s(mark(_x251)), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(cons(_x151, _x152), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(cons(mark(_x151), _x152), _x132))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(s(_x201)), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(_x201))), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(s(mark(_x201))), _x132))))), incr(_x91))))))), _x32)))mark#(incr(incr(incr(tail(head(s(s(_x81)))))))) → a__incr#(incr(incr(tail(a__head(s(s(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(nats)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__nats)), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(nil, _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(nil, _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(pairs)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(a__pairs)), _x122)))))), _x62))))mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(incr(a__incr(a__tail(a__head(a__head(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(cons(_x131, _x132))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(cons(mark(_x131), _x132))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(odds)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(tail(a__head(a__odds)), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(nats)), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(a__nats)), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(s(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(s(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(s(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(pairs)), a__incr(mark(pairs))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(a__pairs)))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(0))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(0))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(incr(_x131))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__incr(mark(_x131)))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(mark(_x151)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(tail(_x151), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(cons(a__tail(mark(_x151)), _x132))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(s(_x201))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(s(mark(_x201)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(nats), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(nats)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(a__nats), _x132))))), incr(_x91))))))), _x32)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(mark(_x111)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(_x131, _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(cons(mark(_x131), _x132))), _x122)))))), _x62))))mark#(incr(incr(incr(tail(head(s(s(incr(pairs))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__pairs))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x232))), a__incr(mark(cons(head(s(_x271)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(s(mark(s(mark(a__incr(cons(a__head(s(mark(_x271))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(s(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(s(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(s(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(0, _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(0, _x212))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(s(nil))))))) → a__incr#(a__incr(incr(tail(a__head(s(nil))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(nats)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(a__nats)), _x122)))))), _x62))))mark#(incr(head(s(tail(incr(0)))))) → a__incr#(a__head(s(a__tail(a__incr(0)))))
mark#(incr(head(s(head(tail(odds)))))) → a__incr#(head(s(a__head(a__tail(a__odds)))))mark#(incr(head(s(incr(_x51))))) → a__incr#(head(s(a__incr(mark(_x51)))))
mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), a__incr(mark(_x221))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(incr(mark(_x221))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(odds, _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(a__odds, _x212))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x31))))) → a__incr#(a__head(mark(cons(incr(a__pairs), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nil, _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(cons(nil, _x202))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(incr(_x41)))) → a__incr#(head(a__incr(mark(_x41))))
mark#(incr(X)) → mark#(X)mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(pairs, _x232))), a__incr(mark(cons(pairs, _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__pairs, _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(head(incr(nats)))))) → a__incr#(head(s(a__head(a__incr(nats)))))mark#(incr(incr(incr(tail(head(s(s(incr(head(0)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(0)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(_x141)))))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(a__head(s(s(s(s(mark(_x141))))))))), _x62))))mark#(incr(head(s(head(nats))))) → a__incr#(head(s(a__head(a__nats))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(tail(_x261), _x242))), _x232))), a__incr(mark(cons(head(s(cons(tail(_x261), _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(incr(cons(a__head(s(cons(a__tail(mark(_x261)), _x242))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(s(s(incr(odds))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(a__odds))))))))
mark#(incr(head(head(cons(head(nats), _x52))))) → a__incr#(a__head(a__head(cons(a__head(a__nats), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(nats))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(tail(a__nats))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(s(mark(_x111)))))), _x62), _x52))))mark#(incr(head(head(cons(odds, _x52))))) → a__incr#(a__head(a__head(cons(a__incr(a__pairs), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(pairs, _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(cons(a__pairs, _x212))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(tail(_x131))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(a__tail(mark(_x131)))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__incr(pairs))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(0)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(0)))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(nats)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(a__nats)), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(nil)))), _x232))), a__incr(mark(cons(head(s(s(incr(nil)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(nil)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(_x281))), _x232))), a__incr(mark(cons(head(s(s(_x281))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(mark(_x281)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(pairs)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(a__pairs)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(nil)))), _x221))), a__incr(mark(cons(head(s(s(incr(nil)))), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(cons(s(mark(head(s(s(a__incr(nil)))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(s(pairs)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(s(a__pairs)))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(tail(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(a__tail(mark(_x151)))), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(nil), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(nil))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(incr(pairs))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(pairs)))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__pairs)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(mark(_x151)))), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(cons(_x91, _x92))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(cons(mark(_x91), _x92))), _x62), _x52))))mark#(incr(incr(incr(tail(head(0)))))) → a__incr#(incr(a__incr(tail(head(0)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(cons(_x111, _x112))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(cons(mark(_x111), _x112))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(_x251), _x221))), a__incr(mark(cons(head(_x251), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(cons(s(mark(a__head(mark(_x251)))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(pairs, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(mark(a__pairs)), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(head(s(head(tail(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x232))), a__incr(mark(cons(head(s(_x271)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(head(s(mark(_x271))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(nats, _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(a__nats, _x212))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(_x231))), a__incr(a__tail(mark(_x231)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(s(mark(a__incr(a__tail(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(tail(_x81)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__tail(mark(_x81))), _x62), _x52))))
mark#(incr(head(s(tail(pairs))))) → a__incr#(a__head(s(mark(incr(odds)))))mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x31))))) → a__incr#(head(mark(cons(a__incr(a__head(mark(_x81))), _x62))))
mark#(incr(incr(incr(tail(head(s(s(_x81)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(s(mark(_x81))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(nats)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(s(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(a__tail(s(mark(_x141))))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(s(0)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(s(0)))))))), _x62), _x52))))
mark#(incr(head(s(tail(nil))))) → a__incr#(a__head(s(a__tail(nil))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(nil)))), _x232))), a__incr(mark(cons(head(s(s(incr(nil)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(incr(nil)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(tail(_x261), _x242))), _x232))), a__incr(mark(cons(head(s(cons(tail(_x261), _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(a__tail(mark(_x261)), _x242))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(incr(_x81)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__incr(mark(_x81))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(_x131, _x121))), mark(_x131))))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(a__incr(cons(a__tail(mark(mark(_x131))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(mark(_x101))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(odds)))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(a__odds)))))))), _x62), _x52))))mark#(incr(head(head(cons(head(cons(nats, _x72)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(cons(cons(0, incr(nats)), _x72)), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(_x241, _x242))), _x232))), a__incr(mark(cons(head(s(cons(_x241, _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(mark(_x241), _x242))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(0))))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(s(s(s(0))))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(_x191)), _x151))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(mark(s(a__head(mark(_x191))))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(0), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(s(0))), incr(_x101)))))), _x62), _x52))))
mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(head(s(tail(a__incr(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(head(cons(s(mark(a__nats)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(nats))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(nats))))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(odds)))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__odds)))))))
mark#(incr(head(s(s(nats))))) → a__incr#(head(s(s(a__nats))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(odds)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(a__odds)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(nats, _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__nats, _x62), _x52))))
mark#(incr(head(head(cons(head(cons(nil, _x72)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(cons(nil, _x72)), _x52))))mark#(incr(incr(incr(tail(cons(_x61, _x62)))))) → a__incr#(a__incr(a__incr(a__tail(cons(mark(_x61), _x62)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(0))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(0))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(nil)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(nil)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x232))), a__incr(mark(cons(head(s(_x271)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(incr(cons(a__head(s(mark(_x271))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(a__incr(a__tail(head(s(a__nats))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(tail(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(a__tail(mark(_x151)))), _x122)))))), _x62), _x52))))mark#(incr(head(s(tail(incr(incr(_x71))))))) → a__incr#(a__head(s(a__tail(a__incr(incr(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(0)))), _x232))), a__incr(mark(cons(head(s(s(incr(0)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(0)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(head(_x241))), a__incr(mark(head(_x241)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(a__head(mark(_x241)))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(incr(incr(tail(head(incr(nats))))))) → a__incr#(a__incr(incr(tail(a__head(a__incr(a__nats))))))mark#(incr(head(s(tail(0))))) → a__incr#(a__head(s(a__tail(0))))
mark#(incr(incr(incr(tail(head(s(s(incr(0))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(0))))))))mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(head(a__incr(a__pairs)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(_x201, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(mark(_x201))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(head(mark(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(head(mark(_x141))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(a__tail(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(mark(_x141))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x221))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(cons(s(mark(head(s(s(a__incr(mark(_x291))))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x232))), a__incr(mark(cons(head(s(_x271)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(mark(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(mark(_x271))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(tail(s(0)))))) → a__incr#(a__head(s(a__tail(s(0)))))mark#(incr(head(s(head(tail(nats)))))) → a__incr#(head(s(head(a__tail(nats)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(tail(_x151), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(a__tail(mark(_x151)), _x132))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(pairs, _x232))), a__incr(mark(cons(pairs, _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__pairs, _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), a__incr(mark(_x221))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(incr(mark(_x221))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(nil)), a__incr(mark(nil))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(nil)))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(incr(incr(tail(head(s(odds))))))) → a__incr#(incr(incr(tail(head(s(a__incr(a__pairs)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(0))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(0))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(nil), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(nil)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(nil), _x132))))), incr(_x91))))))), _x32)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(nats)))), _x232))), a__incr(mark(cons(head(s(s(incr(nats)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(a__nats)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(incr(_x131))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(a__incr(mark(_x131)))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(0)))), _x232))), a__incr(mark(cons(head(s(s(incr(0)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(0)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(_x121, _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(incr(cons(mark(_x121), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(nats))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(cons(0, incr(nats))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), a__incr(mark(_x221))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(a__incr(mark(_x221))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(pairs)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(incr(cons(a__tail(a__head(a__pairs)), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(s(_x161)))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(s(mark(_x161))))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(_x151), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(s(mark(mark(_x151)))), incr(_x101)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(s(_x151))))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(s(mark(_x151)))))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(odds)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(incr(a__odds)))))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(_x101)))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(a__incr(mark(_x101))))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(pairs)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(a__pairs)), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(s(_x191)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(s(mark(_x191))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(head(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(a__head(mark(_x121))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(nil)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(nil)), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(nil))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(nil))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(nats), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__nats), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(s(head(tail(head(_x71))))))) → a__incr#(head(s(a__head(a__tail(a__head(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(_x231))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(head(cons(s(mark(s(a__incr(a__tail(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x221))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(head(cons(s(s(mark(cons(s(mark(head(s(s(a__incr(mark(_x291))))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(pairs))), _x232))), a__incr(mark(cons(head(s(s(pairs))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__pairs))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(incr(odds))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(a__odds))), _x62), _x52))))
mark#(incr(head(s(head(incr(nats)))))) → a__incr#(head(s(a__head(a__incr(cons(0, incr(nats)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(_x121, _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(cons(s(mark(mark(_x121))), incr(_x101)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(nil), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(s(nil))), incr(_x101)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(nil)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(nil)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(incr(_x131))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(s(s(a__incr(mark(_x131)))))))), _x62), _x52))))mark#(incr(head(head(cons(head(_x61), _x52))))) → a__incr#(a__head(a__head(cons(head(mark(_x61)), _x52))))
mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(s(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(s(s(a__tail(s(mark(_x141))))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(a__nats)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x232))), a__incr(mark(cons(head(s(_x271)), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(mark(_x271))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(s(_x111))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(s(mark(_x111)))))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(_x121, _x122)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(tail(head(a__incr(cons(mark(_x121), _x122)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(tail(a__head(cons(0, incr(nats)))))))mark#(incr(head(head(cons(head(cons(nats, _x72)), _x31))))) → a__incr#(a__head(mark(a__head(cons(a__nats, _x72)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(odds)))), _x232))), a__incr(mark(cons(head(s(s(incr(odds)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(a__odds)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(s(s(incr(incr(0)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(0)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(s(nil)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(s(nil)))))))), _x62), _x52))))mark#(incr(head(s(tail(incr(incr(_x71))))))) → a__incr#(a__head(s(a__tail(incr(a__incr(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(mark(_x91)))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(odds, _x232))), a__incr(mark(cons(odds, _x232)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__odds, _x232))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(head(tail(pairs)))))) → a__incr#(head(s(head(a__tail(a__pairs)))))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(cons(0, incr(odds))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(tail(_x251), _x232))), a__incr(mark(cons(tail(_x251), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__tail(mark(_x251)), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(0)), a__incr(mark(0))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(s(mark(a__incr(0)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(odds)), _x122)))))), _x32), incr(a__head(tail(head(incr(cons(a__tail(a__head(a__odds)), _x122))))))))))) → a__incr#(head(cons(mark(incr(a__head(tail(head(incr(cons(a__tail(a__head(a__odds)), _x122))))))), _x32)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(_x281))), _x232))), a__incr(mark(cons(head(s(s(_x281))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(s(mark(_x281)))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(s(_x141)))))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(s(s(a__tail(s(mark(_x141))))))))), _x62))))mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(a__head(a__odds)))))))))
mark#(incr(incr(incr(tail(head(incr(_x71))))))) → a__incr#(incr(a__incr(tail(a__head(a__incr(mark(_x71)))))))mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(head(s(a__tail(incr(incr(cons(0, incr(nats))))))))
mark#(incr(head(s(tail(incr(head(cons(_x81, _x82)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(cons(mark(_x81), _x82)))))))mark#(incr(incr(incr(tail(head(odds)))))) → a__incr#(a__incr(a__incr(tail(a__head(a__odds)))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(nil)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(nil)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(mark(_x141))), _x122)))))), _x62), _x52))))
mark#(incr(head(s(head(tail(s(_x71))))))) → a__incr#(head(s(a__head(a__tail(s(mark(_x71)))))))mark#(incr(incr(incr(tail(s(_x61)))))) → a__incr#(a__incr(incr(a__tail(s(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(head(_x321)))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(head(_x321)))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(a__head(mark(_x321))))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(odds)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(a__odds)), _x122)))))), _x62), _x52))))
mark#(incr(head(s(tail(cons(_x61, _x62)))))) → a__incr#(head(s(a__tail(cons(mark(_x61), _x62)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(incr(_x311))))), _x221))), a__incr(mark(cons(head(s(s(incr(incr(_x311))))), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(cons(s(mark(head(s(s(a__incr(a__incr(mark(_x311)))))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(s(tail(_x61)))))) → a__incr#(head(s(s(a__tail(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(_x141)))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(tail(a__head(s(s(s(s(mark(_x141))))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(pairs), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(pairs)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__pairs), _x132))))), incr(_x91))))))), _x32)))mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))
mark#(incr(odds)) → a__incr#(incr(a__pairs))mark#(incr(incr(incr(tail(head(head(tail(_x81)))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(a__tail(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x232))), a__incr(mark(cons(head(s(_x271)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(mark(_x271))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(_x151)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(head(a__head(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(_x131, _x132))), _x122)))))), _x32), incr(head(tail(head(a__incr(cons(a__tail(a__head(cons(mark(_x131), _x132))), _x122))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(a__incr(cons(a__tail(a__head(cons(mark(_x131), _x132))), _x122))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(_x111))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(mark(_x111)))))), _x62), _x52))))mark#(incr(head(s(tail(incr(cons(incr(_x81), _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(a__incr(mark(_x81)), _x72))))))
mark#(incr(head(s(head(tail(cons(incr(_x81), _x72))))))) → a__incr#(head(s(head(a__tail(cons(a__incr(mark(_x81)), _x72))))))mark#(incr(head(s(tail(nats))))) → a__incr#(a__head(s(tail(cons(0, incr(nats))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(head(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(a__head(mark(_x141))))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(tail(cons(_x281, _x282)), _x242))), _x232))), a__incr(mark(cons(head(s(cons(tail(cons(_x281, _x282)), _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(a__tail(cons(mark(_x281), _x282)), _x242))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(a__nats)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(nats), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(a__nats), _x62), _x52))))
mark#(incr(head(head(cons(odds, _x52))))) → a__incr#(a__head(head(cons(a__odds, _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(nil), _x232))), a__incr(mark(cons(head(nil), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(nil), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(head(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(a__head(mark(_x141))))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(nil)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(s(s(nil)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(nil)), _x232))), a__incr(mark(cons(head(s(nil)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(nil)), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(a__incr(a__pairs))))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(0, _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(0, _x132))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(_x201, _x202))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(cons(mark(_x201), _x202))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(s(s(s(_x91))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(s(mark(_x91)))))))))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(incr(pairs)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(nats))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(s(s(a__tail(a__nats))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(nats), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__nats), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(cons(s(mark(_x151)), _x132))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(head(_x281))), _x232))), a__incr(mark(cons(head(s(head(_x281))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(a__head(mark(_x281)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(a__head(a__head(cons(cons(0, incr(nats)), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x221))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(cons(s(mark(a__head(s(s(a__incr(mark(_x291))))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(tail(incr(head(_x71))))))) → a__incr#(head(s(a__tail(a__incr(a__head(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(odds), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(s(a__odds), _x132))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(tail(a__head(mark(_x141))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(head(cons(incr(_x81), _x72)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(cons(a__incr(mark(_x81)), _x72)), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(_x211), _x191))), _x161))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(mark(s(mark(s(mark(_x211)))))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(mark(a__nats)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(head(cons(0, _x51)), 0))))) → a__incr#(a__head(a__head(cons(mark(0), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(_x201)), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(head(_x201))), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(mark(_x201))), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(s(_x151))))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(s(s(mark(_x151)))))))))), _x62), _x52))))mark#(incr(incr(incr(tail(pairs))))) → a__incr#(a__incr(a__incr(a__tail(a__pairs))))
mark#(incr(head(head(cons(cons(head(_x71), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__head(mark(_x71)), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(0, _x232))), a__incr(mark(cons(0, _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(0, _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(_x241, _x242))), _x232))), a__incr(mark(cons(head(s(cons(_x241, _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(mark(_x241), _x242))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(_x151), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(a__tail(mark(_x151)))), incr(_x101)))))), _x62), _x52))))
mark#(incr(head(s(head(nil))))) → a__incr#(head(s(a__head(nil))))mark#(incr(head(head(cons(head(cons(nats, _x72)), _x52))))) → a__incr#(head(a__head(cons(a__head(cons(a__nats, _x72)), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(tail(_x171)), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(s(a__tail(mark(_x171))), _x132))), _x122)))))), _x62))))mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(head(s(a__tail(a__incr(a__incr(cons(0, incr(nats))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(odds), _x232))), a__incr(mark(cons(head(odds), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(a__odds), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(s(odds)))))) → a__incr#(a__incr(a__incr(tail(s(a__odds)))))
mark#(incr(head(head(cons(head(cons(nats, _x72)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(cons(nats, _x72)), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(nats))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(a__nats))), _x122)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(_x231, _x221))), a__incr(mark(cons(_x231, _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(cons(s(mark(mark(_x231))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(pairs)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(a__pairs)), _x122)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(tail(_x81)))))))) → a__incr#(incr(incr(tail(a__head(s(a__tail(mark(_x81))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(_x311))))), _x221))), a__incr(mark(cons(head(s(s(incr(tail(_x311))))), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(cons(s(mark(head(s(s(a__incr(a__tail(mark(_x311)))))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(head(cons(s(mark(s(a__incr(mark(_x221))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(tail(_x221), _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(a__tail(mark(_x221)), _x212))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(head(s(cons(_x91, _x92))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(cons(mark(_x91), _x92))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(cons(_x141, _x142)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(cons(mark(_x141), _x142)))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x232))), a__incr(mark(cons(head(s(_x271)), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(incr(cons(a__head(s(mark(_x271))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(tail(a__head(cons(0, incr(nats)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(0), _x132))), _x122)))))), _x32), incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(s(0), _x132))), _x122))))))))))) → a__incr#(head(cons(mark(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(s(0), _x132))), _x122))))))), _x32)))mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(a__incr(a__incr(tail(head(mark(_x61))))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(cons(_x111, _x112))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(cons(mark(_x111), _x112))))))))))mark#(incr(incr(incr(tail(head(s(odds))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__odds))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(tail(_x141)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__tail(mark(_x141))), _x122)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(incr(nats))))))) → a__incr#(a__incr(a__incr(tail(head(a__incr(a__nats))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(incr(_x231))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(s(a__incr(a__incr(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(s(tail(incr(head(incr(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(a__incr(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(nil)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(a__tail(a__head(nil)), _x122)))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(s(s(incr(incr(odds)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(a__odds)))))))))
mark#(incr(incr(incr(tail(head(s(tail(_x81)))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__tail(mark(_x81))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(odds)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(s(s(a__odds)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(s(_x81)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(s(mark(_x81))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(tail(tail(_x281)), _x242))), _x232))), a__incr(mark(cons(head(s(cons(tail(tail(_x281)), _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(a__tail(a__tail(mark(_x281))), _x242))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(tail(incr(odds)))))) → a__incr#(a__head(s(a__tail(a__incr(a__odds)))))mark#(incr(incr(incr(tail(head(s(s(incr(s(_x101)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(s(mark(_x101))))))))))
mark#(incr(odds)) → a__incr#(cons(s(mark(0)), incr(incr(odds))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nil)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(nil)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(0)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(head(0)), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(cons(_x111, _x112))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(mark(_x111), _x112))))), _x62), _x52))))
mark#(incr(head(s(tail(nats))))) → a__incr#(head(s(tail(a__nats))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(head(_x221), _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(cons(a__head(mark(_x221)), _x202))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(_x281))), _x232))), a__incr(mark(cons(head(s(s(_x281))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(mark(_x281)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(nats), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__nats))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(tail(_x241))), _x232))), a__incr(mark(cons(head(s(tail(_x241))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(a__tail(mark(_x241)))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(head(cons(_x71, _x72)), _x52))))) → a__incr#(a__head(head(cons(a__head(cons(mark(_x71), _x72)), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(s(_x221)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(s(mark(_x221))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(0), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(0), _x122)))))), _x62), _x52))))
mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(s(incr(_x151))))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(s(a__incr(mark(_x151)))))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(odds), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__odds), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(incr(_x81)), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(a__incr(mark(_x81))), _x62), _x52))))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(pairs, _x191))), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(a__pairs)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(a__pairs)), _x132))))), incr(_x91))))))), _x32)))
mark#(incr(head(head(cons(cons(_x61, _x62), _x52))))) → a__incr#(a__head(head(cons(cons(mark(_x61), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(incr(cons(0, incr(odds))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(mark(_x101))))), _x62))))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(incr(incr(tail(head(a__head(nil))))))
mark#(incr(head(head(cons(cons(incr(head(head(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__head(mark(_x91)))), _x62), _x52))))mark#(incr(incr(incr(tail(head(pairs)))))) → a__incr#(a__incr(incr(tail(a__head(a__pairs)))))
mark#(incr(head(s(tail(incr(0)))))) → a__incr#(head(s(tail(a__incr(0)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(odds))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(a__odds))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(0), _x32), incr(0)))))) → a__incr#(a__head(cons(mark(incr(0)), _x32)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(pairs)), a__incr(mark(pairs))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(pairs)))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(head(tail(0)))))) → a__incr#(head(s(a__head(a__tail(0)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(_x121, _x101)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(tail(head(cons(s(mark(mark(_x121))), incr(_x101)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(cons(_x301, _x302))))), _x232))), a__incr(mark(cons(head(s(s(incr(cons(_x301, _x302))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(cons(mark(_x301), _x302))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(pairs, _x232))), a__incr(mark(cons(pairs, _x232)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__pairs, _x232))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(head(cons(nats, _x51)), a__nats))))) → a__incr#(a__head(a__head(cons(mark(a__nats), _x52))))mark#(incr(head(s(tail(s(head(_x71))))))) → a__incr#(a__head(s(tail(s(a__head(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(nats))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(a__tail(a__nats))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(_x231, _x232))), a__incr(mark(cons(_x231, _x232)))))), _x161))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(mark(_x231), _x232))))))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(odds))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(a__odds))))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(pairs)))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(pairs)))))))mark#(incr(head(s(tail(incr(incr(tail(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(a__tail(mark(_x81))))))))
mark#(incr(head(s(tail(incr(cons(pairs, _x72))))))) → a__incr#(head(s(a__tail(incr(cons(a__pairs, _x72))))))mark#(incr(head(head(cons(cons(incr(head(0)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(0)), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(nil))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(nil))))), _x62))))mark#(incr(incr(odds))) → a__incr#(a__incr(a__odds))
mark#(incr(head(head(cons(cons(incr(s(_x81)), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(s(mark(_x81))), _x62), _x52))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(tail(a__head(a__nats)))))
mark#(incr(head(s(head(incr(odds)))))) → a__incr#(head(s(a__head(a__incr(a__odds)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(incr(_x141)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__incr(mark(_x141))), _x122)))))), _x62), _x52))))
mark#(incr(incr(nats))) → a__incr#(a__incr(cons(0, incr(nats))))mark#(incr(incr(incr(tail(head(s(s(incr(head(pairs)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(a__pairs)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(incr(cons(tail(a__head(mark(_x141))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(head(_x231))), a__incr(mark(head(_x231)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(s(mark(a__incr(a__head(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(incr(nats))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(nats))))))mark#(incr(head(s(tail(incr(s(_x71))))))) → a__incr#(head(s(a__tail(a__incr(s(mark(_x71)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(nil), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(nil), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(nats, _x52))))) → a__incr#(head(a__head(cons(a__nats, _x52))))
mark#(incr(incr(incr(tail(head(head(pairs))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__pairs))))))mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(head(s(head(a__incr(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(incr(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(head(a__incr(mark(_x91)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(tail(nats), _x242))), _x232))), a__incr(mark(cons(head(s(cons(tail(nats), _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(a__tail(a__nats), _x242))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(head(odds)))))))))
mark#(incr(incr(incr(tail(head(s(_x71))))))) → a__incr#(a__incr(incr(a__tail(a__head(s(mark(_x71)))))))mark#(incr(head(s(tail(incr(cons(_x71, _x72))))))) → a__incr#(a__head(s(a__tail(incr(cons(mark(_x71), _x72))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x232))), a__incr(mark(cons(head(s(_x271)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(incr(cons(a__head(s(mark(_x271))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(s(tail(incr(cons(pairs, _x72))))))) → a__incr#(head(s(tail(a__incr(cons(a__pairs, _x72))))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(_x101)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(incr(a__incr(mark(_x101))))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(cons(_x271, _x272)), _x232))), a__incr(mark(cons(head(cons(_x271, _x272)), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(cons(mark(_x271), _x272)), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(head(tail(cons(s(_x81), _x72))))))) → a__incr#(head(s(head(a__tail(cons(s(mark(_x81)), _x72))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), a__incr(mark(_x221))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(head(cons(s(s(mark(a__incr(mark(_x221))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(tail(incr(pairs)))))) → a__incr#(a__head(s(a__tail(a__incr(a__pairs)))))mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x31))))) → a__incr#(head(mark(cons(a__incr(a__pairs), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(_x131, _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(a__incr(cons(a__tail(head(cons(mark(_x131), _x132))), _x122)))))), _x62))))mark#(incr(head(s(tail(incr(cons(0, _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(0, _x72))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(head(_x161)), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(s(a__head(mark(_x161))))), incr(_x101)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(pairs, _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(a__pairs, _x132))), _x122)))))), _x62))))
mark#(incr(incr(incr(tail(head(_x61)))))) → a__incr#(a__incr(a__incr(a__tail(head(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(pairs)), _x232))), a__incr(mark(cons(head(s(pairs)), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(a__pairs)), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(a__tail(incr(a__incr(nats))))))mark#(incr(head(s(tail(incr(cons(pairs, _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(pairs, _x72))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(s(_x141)))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(s(mark(_x141))))), _x122)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(a__tail(head(mark(_x101))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(_x231, _x232))), a__incr(mark(cons(_x231, _x232)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(s(mark(a__incr(cons(mark(_x231), _x232))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(s(_x311))))), _x221))), a__incr(mark(cons(head(s(s(incr(s(_x311))))), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(cons(s(mark(head(s(s(a__incr(s(mark(_x311)))))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(0, _x232))), a__incr(mark(cons(0, _x232)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(0, _x232))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(_x131))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(s(s(s(mark(_x131)))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(_x241, _x242))), _x232))), a__incr(mark(cons(head(s(cons(_x241, _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(incr(cons(a__head(s(cons(mark(_x241), _x242))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(incr(tail(_x241)))), a__incr(mark(incr(tail(_x241))))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(s(mark(a__incr(a__incr(a__tail(mark(_x241))))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(tail(incr(cons(pairs, _x51))))))) → a__incr#(a__head(s(a__tail(cons(s(mark(a__pairs)), incr(_x51))))))mark#(incr(incr(incr(tail(head(s(s(incr(pairs))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__pairs))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(head(_x241)))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__tail(a__head(mark(_x241))))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(_x241, _x242))), a__incr(mark(cons(_x241, _x242)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(mark(_x241), _x242))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(a__incr(cons(tail(a__head(mark(_x141))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(nats)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(a__nats)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(incr(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(incr(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__incr(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(nats, _x232))), a__incr(mark(cons(nats, _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__nats, _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(_x231, _x232))), a__incr(mark(cons(_x231, _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(mark(_x231), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(0)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(0)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(incr(_x151), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(a__incr(mark(_x151)))), incr(_x101)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x201))), a__incr(mark(cons(head(s(_x271)), _x201)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(cons(s(mark(a__head(s(mark(_x271))))), incr(_x201))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(head(incr(_x71)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(a__incr(mark(_x71))), _x52))))mark#(incr(incr(incr(tail(head(head(s(tail(_x91))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(a__tail(mark(_x91)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(_x131, _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(incr(cons(a__tail(a__head(cons(mark(_x131), _x132))), _x122)))))), _x62))))mark#(incr(head(s(head(tail(cons(odds, _x72))))))) → a__incr#(head(s(head(a__tail(cons(a__odds, _x72))))))
mark#(incr(incr(incr(tail(head(head(s(incr(_x91))))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(s(a__incr(mark(_x91)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nil)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__head(nil)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(0)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(0)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(nats, _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(a__nats)), incr(_x101)))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(_x131))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(s(s(a__tail(mark(_x131)))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(_x211, _x212), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(cons(mark(_x211), _x212))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))mark#(incr(head(head(cons(head(_x61), _x52))))) → a__incr#(head(a__head(cons(a__head(mark(_x61)), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(_x121)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(tail(head(s(s(mark(_x121))))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(head(mark(_x71)))))))
mark#(incr(head(head(cons(head(cons(0, _x51)), 0))))) → a__incr#(a__head(head(cons(mark(0), _x52))))mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(a__head(mark(_x81))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(nats))))))) → a__incr#(incr(a__incr(a__tail(a__head(head(a__nats))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(0)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(0)), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(mark(_x101))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(incr(_x231))), a__incr(mark(incr(_x231)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(s(mark(a__incr(a__incr(mark(_x231)))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(tail(s(_x141)))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(a__tail(s(mark(_x141))))))))), _x62), _x52))))mark#(incr(head(head(cons(pairs, _x52))))) → a__incr#(a__head(a__head(cons(a__pairs, _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(_x101)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(a__incr(mark(_x101))))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(incr(_x121)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(a__incr(mark(_x121))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(0)), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(s(a__incr(0)))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(pairs))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__pairs))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(nil), _x62), _x31))))) → a__incr#(a__head(mark(cons(a__incr(nil), _x62))))mark#(incr(head(s(tail(head(_x61)))))) → a__incr#(a__head(s(a__tail(a__head(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(pairs)), a__incr(mark(pairs))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(a__pairs)))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(_x221)), a__incr(mark(_x221))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(mark(_x221))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(head(_x261), _x242))), _x232))), a__incr(mark(cons(head(s(cons(head(_x261), _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(a__head(mark(_x261)), _x242))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(tail(_x241))), _x232))), a__incr(mark(cons(head(s(tail(_x241))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(a__tail(mark(_x241)))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(incr(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(incr(mark(_x91)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(nats)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(head(s(s(a__nats)))))), _x62), _x52))))
mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(a__tail(mark(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(_x241))), _x232))), a__incr(mark(cons(head(s(s(_x241))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(s(mark(_x241)))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(nil))))))
mark#(incr(head(head(pairs)))) → a__incr#(a__head(a__head(pairs)))mark#(incr(head(nats))) → a__incr#(head(a__nats))
mark#(incr(head(head(cons(cons(incr(head(tail(head(tail(_x111))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(a__tail(mark(_x111)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(_x241))), _x232))), a__incr(mark(cons(head(s(s(_x241))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(s(mark(_x241)))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(nats)))), _x62))))mark#(incr(incr(incr(tail(head(incr(pairs))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(a__pairs))))))
mark#(incr(incr(incr(tail(head(pairs)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__pairs)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(nil, _x232))), a__incr(mark(cons(nil, _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(nil, _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x151))), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(s(mark(_x151)))))), incr(_x101)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(cons(_x81, _x82)), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(cons(mark(_x81), _x82)), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nil)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(nil)))), _x62), _x52))))mark#(incr(head(head(cons(head(cons(cons(_x81, _x82), _x72)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(cons(cons(mark(_x81), _x82), _x72)), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(mark(_x141))), _x122)))))), _x62), _x52))))mark#(incr(head(head(cons(head(cons(0, _x72)), _x52))))) → a__incr#(head(head(cons(a__head(cons(0, _x72)), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(_x121, _x101)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(mark(_x121))), incr(_x101)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(head(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(head(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__head(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(nats)), a__incr(mark(nats))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(a__incr(a__nats)))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(s(s(incr(incr(tail(_x111))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(a__tail(mark(_x111)))))))))))
mark#(incr(incr(incr(tail(head(s(head(_x81)))))))) → a__incr#(incr(incr(tail(a__head(s(a__head(mark(_x81))))))))mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(tail(odds))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(a__odds))), _x62), _x52))))mark#(incr(head(s(head(s(nil)))))) → a__incr#(a__head(s(a__head(s(nil)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(_x131, _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(mark(_x131), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(incr(a__incr(tail(a__head(a__head(a__odds))))))
mark#(incr(head(head(cons(cons(0, _x62), _x52))))) → a__incr#(head(a__head(cons(cons(0, _x62), _x52))))mark#(incr(head(s(s(odds))))) → a__incr#(head(s(s(a__odds))))
mark#(incr(head(head(_x41)))) → a__incr#(head(a__head(mark(_x41))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(0)), _x151))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(mark(s(head(0)))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(nats, _x232))), a__incr(mark(cons(nats, _x232)))))), _x161))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__nats, _x232))))))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(s(s(incr(head(nil)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(incr(a__head(nil)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(mark(_x91)))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(_x101)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(a__head(mark(_x101))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(s(_x261), _x242))), _x232))), a__incr(mark(cons(head(s(cons(s(_x261), _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(s(mark(_x261)), _x242))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(a__tail(mark(_x91)))), _x62))))
mark#(incr(head(s(pairs)))) → a__incr#(head(s(cons(0, incr(odds)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(head(s(s(a__incr(mark(_x291))))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(incr(incr(tail(head(head(pairs))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(a__head(a__pairs))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(pairs)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(a__pairs)), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(odds)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(a__incr(a__pairs))))))))), _x62), _x52))))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(a__incr(cons(0, incr(odds)))))))))
mark#(incr(incr(incr(tail(head(s(s(cons(_x91, _x92))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(cons(mark(_x91), _x92))))))))mark#(incr(incr(incr(tail(head(head(0))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(0))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(0))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__tail(0))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(head(tail(_x71)), _x52))))) → a__incr#(a__head(a__head(cons(a__head(a__tail(mark(_x71))), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(tail(mark(head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(_x251), _x232))), a__incr(mark(cons(head(_x251), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(mark(_x251)), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(head(tail(s(_x71))))))) → a__incr#(head(s(head(a__tail(s(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(nats))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(cons(0, incr(nats))))))))), _x62), _x52))))
mark#(incr(head(head(incr(_x51))))) → a__incr#(a__head(head(a__incr(mark(_x51)))))mark#(incr(head(s(tail(incr(tail(_x71))))))) → a__incr#(a__head(s(a__tail(a__incr(a__tail(mark(_x71)))))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(cons(_x111, _x112))))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(cons(mark(_x111), _x112))))))))))mark#(incr(incr(incr(tail(head(s(s(incr(head(s(_x111))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(s(mark(_x111)))))))))))
mark#(incr(head(s(head(s(s(_x71))))))) → a__incr#(a__head(s(a__head(s(s(mark(_x71)))))))mark#(incr(head(s(tail(nats))))) → a__incr#(a__head(s(a__tail(nats))))
mark#(incr(head(head(cons(odds, _x31))))) → a__incr#(a__head(mark(a__odds)))mark#(incr(head(head(cons(cons(incr(0), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(0), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(odds))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(a__odds))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x232))), a__incr(mark(cons(head(s(_x271)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(mark(_x271))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(cons(_x191, _x192)), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(cons(s(mark(a__tail(a__head(cons(s(cons(mark(_x191), _x192)), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(mark(_x81))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(_x131, _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(mark(_x131), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(nil))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(nil))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(tail(_x201))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(a__tail(mark(_x201)))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(_x81)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(head(mark(_x81))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__pairs), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(cons(_x81, _x82)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(cons(mark(_x81), _x82)), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(_x151), _x132))), _x91)))))), _x32), incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(_x151)), _x132))))), incr(_x91))))))))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(_x151)), _x132))))), incr(_x91))))))), _x32)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(odds, _x202))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__head(cons(a__odds, _x202))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(head(_x211), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(a__head(mark(_x211)))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x221))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(a__head(mark(cons(s(s(mark(cons(s(mark(head(s(s(a__incr(mark(_x291))))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(head(odds), _x52))))) → a__incr#(a__head(a__head(cons(a__head(a__odds), _x52))))mark#(incr(head(s(tail(incr(cons(_x71, _x51))))))) → a__incr#(a__head(s(a__tail(cons(s(mark(mark(_x71))), incr(_x51))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(cons(_x161, _x162)))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(s(cons(mark(_x161), _x162)))), _x122)))))), _x62), _x52))))mark#(incr(head(s(tail(incr(nil)))))) → a__incr#(head(s(a__tail(a__incr(nil)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(pairs), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(a__pairs), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(tail(_x131))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(incr(cons(a__tail(a__head(a__tail(mark(_x131)))), _x122)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(a__tail(a__head(a__nats)))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x232))), a__incr(mark(cons(head(s(_x271)), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(mark(_x271))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(s(incr(_x61)))))) → a__incr#(head(s(s(a__incr(mark(_x61))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x232))), a__incr(mark(cons(head(s(_x271)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(s(mark(s(mark(a__incr(cons(a__head(s(mark(_x271))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(incr(incr(tail(head(s(s(incr(tail(_x101)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__tail(mark(_x101))))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(0), _x232))), a__incr(mark(cons(head(0), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(0), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(head(tail(nil)))))) → a__incr#(head(s(head(a__tail(nil)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(odds)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(head(s(s(s(a__incr(a__odds)))))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(a__incr(incr(tail(a__head(head(nil))))))mark#(incr(head(head(cons(cons(incr(head(incr(nats))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(a__incr(a__head(a__incr(a__nats))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__tail(head(nats)))), _x62), _x52))))mark#(incr(head(s(tail(incr(_x61)))))) → a__incr#(head(s(a__tail(incr(mark(_x61))))))
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(_x131))))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(s(mark(_x131)))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(nats)))), _x232))), a__incr(mark(cons(head(s(s(incr(nats)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(a__nats)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(nats, _x232))), a__incr(mark(cons(nats, _x232)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__nats, _x232))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(incr(_x321)))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(incr(_x321)))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(a__incr(mark(_x321))))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(a__head(s(s(s(a__incr(mark(_x141))))))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(incr(_x71))))))) → a__incr#(a__incr(a__incr(tail(head(a__incr(mark(_x71)))))))mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(incr(a__incr(a__tail(a__head(s(a__nats))))))
mark#(incr(head(s(head(tail(head(_x71))))))) → a__incr#(head(s(head(a__tail(a__head(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(head(_x141)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__head(mark(_x141))))))))), _x62), _x52))))
mark#(incr(head(s(tail(s(nil)))))) → a__incr#(a__head(s(a__tail(s(nil)))))mark#(incr(head(head(cons(nats, _x31))))) → a__incr#(a__head(mark(a__nats)))
mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(incr(cons(0, incr(odds))))), _x62), _x52))))mark#(incr(head(pairs))) → a__incr#(a__head(a__pairs))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(_x131))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(s(s(s(mark(_x131)))))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(cons(_x211, _x212), _x191))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(cons(mark(_x211), _x212))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(0))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(a__tail(head(s(s(s(0))))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(head(tail(_x81)))))))) → a__incr#(a__incr(a__incr(tail(head(a__head(a__tail(mark(_x81))))))))mark#(incr(head(s(head(tail(odds)))))) → a__incr#(head(s(head(a__tail(a__odds)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(tail(_x211), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(a__tail(mark(_x211)))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(s(s(incr(odds))))))))) → a__incr#(incr(incr(tail(a__head(s(s(a__incr(a__odds))))))))
mark#(incr(head(s(head(incr(tail(_x71))))))) → a__incr#(head(s(a__head(a__incr(a__tail(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(incr(0))), a__incr(mark(incr(0)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(s(mark(a__incr(a__incr(0))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(pairs)))) → a__incr#(head(s(pairs)))mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(head(_x111))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(a__head(mark(_x111)))))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x221))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(cons(s(mark(a__head(s(s(a__incr(mark(_x291))))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(odds)))), _x232))), a__incr(mark(cons(head(s(s(incr(odds)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(a__odds)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(pairs)))), _x232))), a__incr(mark(cons(head(s(s(incr(pairs)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(a__pairs)))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(s(pairs))))) → a__incr#(head(s(s(a__pairs))))mark#(incr(head(head(cons(cons(incr(head(incr(_x91))), _x62), _x31))))) → a__incr#(head(mark(cons(a__incr(a__head(a__incr(mark(_x91)))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(_x271)), _x232))), a__incr(mark(cons(head(s(_x271)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(head(s(mark(_x271))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(s(s(incr(incr(incr(_x111))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__incr(a__incr(mark(_x111)))))))))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(incr(a__tail(head(a__nats)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(tail(_x261), _x242))), _x232))), a__incr(mark(cons(head(s(cons(tail(_x261), _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(a__tail(mark(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(a__tail(mark(_x261)), _x242))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(tail(incr(head(0))))))) → a__incr#(a__head(s(a__tail(a__incr(a__head(0))))))mark#(incr(head(s(tail(incr(cons(nats, _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(a__nats, _x72))))))
mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(head(s(a__head(cons(mark(_x61), _x62)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(_x251), _x232))), a__incr(mark(cons(head(_x251), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(mark(_x251)), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(s(tail(s(s(_x71))))))) → a__incr#(a__head(s(tail(s(s(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(cons(_x241, _x242), _x232))), a__incr(mark(cons(cons(_x241, _x242), _x232)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(cons(mark(_x241), _x242), _x232))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(s(tail(nats))))) → a__incr#(head(s(mark(incr(nats)))))mark#(incr(incr(incr(tail(head(0)))))) → a__incr#(a__incr(a__incr(a__tail(a__head(0)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(incr(cons(a__tail(a__head(mark(_x141))), _x122)))))), _x62))))mark#(incr(incr(incr(tail(head(s(cons(_x81, _x82)))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(cons(mark(_x81), _x82)))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(cons(_x251, _x252), _x232))), a__incr(mark(cons(cons(_x251, _x252), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(mark(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(cons(mark(_x251), _x252), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(incr(a__incr(a__tail(head(a__nats)))))
mark#(incr(incr(incr(tail(odds))))) → a__incr#(a__incr(a__incr(a__tail(a__odds))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(head(_x231))), a__incr(mark(head(_x231)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(a__head(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(s(odds), _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(s(a__odds))), incr(_x101)))))), _x62), _x52))))mark#(incr(head(s(tail(incr(incr(head(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(a__head(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(pairs), _x132))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__head(cons(s(a__pairs), _x132))), _x122)))))), _x62))))mark#(incr(incr(incr(tail(head(tail(_x71))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__tail(mark(_x71)))))))
mark#(incr(incr(incr(tail(head(s(s(incr(head(head(_x111))))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__head(a__head(mark(_x111)))))))))))mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(head(s(a__head(incr(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(incr(_x241), _x232))), a__incr(mark(cons(incr(_x241), _x232)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__incr(mark(_x241)), _x232))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(head(tail(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(tail(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(_x121)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(tail(a__head(s(s(mark(_x121))))))), _x62), _x52))))mark#(incr(head(s(tail(incr(incr(nats))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(cons(0, incr(nats))))))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(tail(head(cons(0, incr(nats)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x131))), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(tail(a__head(s(mark(_x131)))), _x122)))))), _x62))))
mark#(incr(incr(incr(tail(s(s(_x71))))))) → a__incr#(a__incr(a__incr(a__tail(s(s(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(_x231, _x232))), a__incr(mark(cons(_x231, _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(mark(_x231), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(pairs)), a__incr(mark(pairs))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(incr(a__pairs)))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(_x91))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(mark(_x91)))), _x62), _x52))))
mark#(incr(head(0))) → a__incr#(head(0))mark#(incr(incr(incr(tail(head(s(s(incr(head(odds)))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(head(a__odds)))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(incr(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(incr(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(a__incr(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(s(nats)))))) → a__incr#(a__incr(a__incr(tail(s(a__nats)))))
mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(a__tail(head(cons(0, incr(nats)))))))mark#(incr(head(s(tail(incr(cons(pairs, _x72))))))) → a__incr#(a__head(s(tail(a__incr(cons(a__pairs, _x72))))))
mark#(incr(incr(incr(tail(head(head(nil))))))) → a__incr#(incr(a__incr(tail(a__head(head(nil))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(s(_x151))), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(head(s(mark(_x151)))), _x122)))))), _x62), _x52))))
mark#(incr(head(head(pairs)))) → a__incr#(head(a__head(a__pairs)))mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(incr(tail(a__head(a__head(a__incr(a__pairs)))))))
mark#(incr(head(s(head(s(0)))))) → a__incr#(a__head(s(a__head(s(0)))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(nats)))), _x221))), a__incr(mark(cons(head(s(s(incr(nats)))), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(cons(s(mark(head(s(s(a__incr(a__nats)))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(s(_x51))))) → a__incr#(a__head(head(s(mark(_x51)))))mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))
mark#(incr(head(head(cons(cons(incr(head(odds)), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(a__odds)), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(_x231, _x232))), a__incr(mark(cons(_x231, _x232)))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(mark(_x231), _x232))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(nil)), _x232))), a__incr(mark(cons(head(s(nil)), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(nil)), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(0, _x242))), _x232))), a__incr(mark(cons(head(s(cons(0, _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(0, _x242))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(pairs)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(a__pairs)))))), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(nats)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__nats)), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(odds)), _x232))), a__incr(mark(cons(head(s(odds)), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(a__odds)), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(pairs)), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(a__head(a__pairs)), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(a__tail(mark(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(incr(incr(tail(head(s(head(_x81)))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__head(mark(_x81))))))))
mark#(incr(head(s(tail(incr(cons(s(_x81), _x72))))))) → a__incr#(a__head(s(a__tail(a__incr(cons(s(mark(_x81)), _x72))))))mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(incr(tail(a__head(s(a__nats))))))
mark#(incr(head(head(cons(cons(incr(pairs), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(a__incr(pairs), _x62), _x52))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(head(_x241))), _x232))), a__incr(mark(cons(head(s(head(_x241))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(a__head(mark(_x241)))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(_x291)))), _x232))), a__incr(mark(cons(head(s(s(incr(_x291)))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(mark(_x291))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(head(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(head(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__head(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(incr(incr(tail(head(head(odds))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__head(odds))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(_x251), _x232))), a__incr(mark(cons(head(_x251), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(a__tail(mark(head(cons(s(s(mark(a__incr(cons(a__head(mark(_x251)), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(incr(incr(tail(head(s(nats))))))) → a__incr#(a__incr(a__incr(a__tail(a__head(s(nats))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(_x241, _x242))), _x232))), a__incr(mark(cons(head(s(cons(_x241, _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(s(mark(s(mark(a__incr(cons(a__head(s(cons(mark(_x241), _x242))), _x232))))))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(cons(nil, _x242))), _x232))), a__incr(mark(cons(head(s(cons(nil, _x242))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(a__head(mark(tail(head(cons(s(a__tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(cons(nil, _x242))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(pairs), _x122)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(a__incr(cons(a__tail(a__pairs), _x122)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(s(incr(nats))))))))) → a__incr#(a__incr(incr(tail(a__head(s(s(a__incr(a__nats))))))))mark#(incr(head(odds))) → a__incr#(head(a__incr(a__pairs)))
mark#(incr(incr(incr(tail(s(_x61)))))) → a__incr#(a__incr(incr(tail(s(mark(_x61))))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(incr(a__tail(head(nats)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(tail(_x241)))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__tail(a__tail(mark(_x241))))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(s(tail(tail(_x61)))))) → a__incr#(a__head(s(a__tail(a__tail(mark(_x61))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(_x141)), _x122)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(a__head(tail(head(a__incr(cons(a__tail(head(mark(_x141))), _x122)))))), _x62))))mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))
mark#(incr(head(s(tail(incr(s(_x71))))))) → a__incr#(a__head(s(a__tail(a__incr(s(mark(_x71)))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(s(_x231))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(tail(a__head(cons(s(mark(s(a__incr(s(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(incr(incr(tail(head(s(s(incr(incr(odds)))))))))) → a__incr#(a__incr(incr(tail(head(s(s(a__incr(a__incr(a__odds)))))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(nats)))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(mark(0)))), _x62), _x52))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(nil, _x101)))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(a__head(tail(head(cons(s(mark(nil)), incr(_x101)))))), _x62), _x52))))mark#(incr(head(s(tail(incr(incr(incr(_x81)))))))) → a__incr#(a__head(s(a__tail(a__incr(a__incr(a__incr(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(head(_x231))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(a__head(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(incr(incr(tail(head(incr(tail(_x81)))))))) → a__incr#(a__incr(a__incr(tail(a__head(a__incr(a__tail(mark(_x81))))))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(s(_x301))))), _x232))), a__incr(mark(cons(head(s(s(incr(s(_x301))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(s(mark(_x301)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(s(tail(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__tail(cons(mark(_x61), _x62)))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(nats, _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(nats)), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(0)))))), _x62), _x52))))) → a__incr#(head(head(cons(cons(incr(head(a__tail(a__head(s(s(0)))))), _x62), _x52))))
mark#(incr(incr(incr(tail(head(s(nil))))))) → a__incr#(incr(incr(tail(a__head(s(nil))))))mark#(incr(head(head(cons(cons(incr(pairs), _x32), a__incr(a__pairs)))))) → a__incr#(a__head(cons(mark(a__incr(a__pairs)), _x32)))
mark#(incr(incr(incr(tail(head(head(nats))))))) → a__incr#(a__incr(incr(a__tail(a__head(a__head(a__nats))))))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(pairs)), a__incr(mark(pairs))))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(a__tail(mark(a__head(cons(s(s(mark(a__incr(cons(0, incr(odds)))))), _x132))))), incr(_x91)))))), _x62))))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(tail(_x231))), _x191))), _x132))), _x91)))))), _x62), _x31))))) → a__incr#(head(mark(cons(incr(head(tail(head(cons(s(mark(a__tail(a__head(cons(s(mark(s(a__incr(tail(mark(_x231)))))), _x132))))), incr(_x91)))))), _x62))))mark#(incr(head(head(cons(cons(incr(head(tail(head(s(s(s(incr(odds)))))))), _x62), _x52))))) → a__incr#(head(a__head(cons(cons(incr(head(tail(a__head(s(s(s(a__incr(odds)))))))), _x62), _x52))))
mark#(incr(head(head(cons(cons(cons(_x71, _x72), _x62), _x52))))) → a__incr#(a__head(a__head(cons(cons(cons(mark(_x71), _x72), _x62), _x52))))mark#(incr(incr(incr(tail(head(nats)))))) → a__incr#(a__incr(a__incr(tail(a__head(a__nats)))))

Rewrite Rules

a__nats → cons(0, incr(nats))a__pairs → cons(0, incr(odds))
a__odds → a__incr(a__pairs)a__incr(cons(X, XS)) → cons(s(mark(X)), incr(XS))
a__head(cons(X, XS)) → mark(X)a__tail(cons(X, XS)) → mark(XS)
mark(nats) → a__natsmark(pairs) → a__pairs
mark(odds) → a__oddsmark(incr(X)) → a__incr(mark(X))
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(0) → 0mark(s(X)) → s(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
a__nats → natsa__pairs → pairs
a__odds → oddsa__incr(X) → incr(X)
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: pairs, mark, tail, odds, a__nats, a__tail, a__odds, nats, 0, a__incr, s, a__pairs, incr, head, a__head, nil, cons

Strategy

The right-hand side of the rule mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(odds))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(odds))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(a__odds))))), _x232))))), _x132))))), incr(_x91))))))), _x42))) 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
a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(cons(s(mark(a__head(s(s(a__incr(a__tail(a__odds))))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42))) 
a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(a__odds))))), _x232))))), _x132))))), incr(_x91))))))), _x42))) 
a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(incr(a__tail(a__odds))))), _x232))))), _x132))))), incr(_x91))))))), _x42))) 
a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(tail(a__odds))))), _x232))))), _x132))))), incr(_x91))))))), _x42))) 
a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(a__odds))))), _x232))))), _x132))))), incr(_x91))))))), _x42))) 
a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(incr(cons(a__head(s(s(a__incr(a__tail(a__odds))))), _x232))))), _x132))))), incr(_x91))))))), _x42))) 
a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(a__tail(a__odds))))), _x232))))), _x132))))), incr(_x91))))))), _x42))) 
a__incr#(head(cons(incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(a__odds))))), _x232))))), _x132))))), incr(_x91))))))), _x42))) 
a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(a__odds))))), _x232))))))))), incr(_x91))))))), _x42))) 
a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(odds))))), _x232))))), _x132))))), incr(_x91))))))), _x42))) 
a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(a__incr(a__pairs)))))), _x232))))), _x132))))), incr(_x91))))))), _x42))) 
Thus, the rule mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(odds))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(odds))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(a__odds))))), _x232))))), _x132))))), incr(_x91))))))), _x42))) is replaced by the following rules:
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(odds))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(odds))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(a__odds))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(odds))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(odds))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(tail(a__odds))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(odds))))), _x221))), a__incr(mark(cons(head(s(s(incr(tail(odds))))), _x221)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(cons(s(mark(a__head(s(s(a__incr(a__tail(a__odds))))))), incr(_x221))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(odds))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(odds))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(incr(cons(a__head(s(s(a__incr(a__tail(a__odds))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(odds))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(odds))))), _x232)))))), _x171))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(mark(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(a__odds))))), _x232))))))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(odds))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(odds))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(odds))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(odds))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(odds))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(a__odds))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(odds))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(odds))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(head(s(s(a__incr(a__tail(a__odds))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(odds))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(odds))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(a__incr(a__pairs)))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(odds))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(odds))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(a__head(mark(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(a__incr(a__tail(a__odds))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))
mark#(incr(head(head(cons(cons(incr(head(tail(head(incr(cons(tail(head(cons(s(head(cons(s(incr(cons(head(s(s(incr(tail(odds))))), _x232))), a__incr(mark(cons(head(s(s(incr(tail(odds))))), _x232)))))), _x132))), _x91)))))), _x42), _x31))))) → a__incr#(head(cons(a__incr(mark(head(tail(head(cons(s(tail(mark(a__head(cons(s(s(mark(a__incr(cons(a__head(s(s(incr(a__tail(a__odds))))), _x232))))), _x132))))), incr(_x91))))))), _x42)))