Runtime Complexity (innermost) proof of /tmp/tmp2lYS5j/PALINDROME_nosorts_noand

The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(O(1), O(n^1)).

0 CpxTRS

↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID), 0 ms)

↳2 CdtProblem

    ↳3 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID), 0 ms)

    ↳4 CdtProblem

    ↳5 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 0 ms)

    ↳6 CdtProblem

    ↳7 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 0 ms)

    ↳8 CdtProblem

    ↳9 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 36 ms)

    ↳10 CdtProblem

    ↳11 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID), 0 ms)

    ↳12 CdtProblem

    ↳13 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 0 ms)

    ↳14 CdtProblem

    ↳15 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID), 0 ms)

    ↳16 CdtProblem

    ↳17 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 0 ms)

    ↳18 CdtProblem

    ↳19 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID), 0 ms)

    ↳20 CdtProblem

    ↳21 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 0 ms)

    ↳22 CdtProblem

    ↳23 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID), 0 ms)

    ↳24 CdtProblem

    ↳25 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 33 ms)

    ↳26 CdtProblem

↳27 CpxTrsMatchBoundsTAProof (⇔, 0 ms)

↳28 BOUNDS(O(1), O(n^1))

(0) Obligation:

Runtime Complexity TRS:
The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(I, __(P, I)))) → mark(U11(tt))
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U12(X)) → active(U12(mark(X)))
mark(isNePal(X)) → active(isNePal(mark(X)))
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U12(mark(X)) → U12(X)
U12(active(X)) → U12(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)

Rewrite Strategy: INNERMOST

(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)

Converted CpxTRS to CDT

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)), U12'(tt))
ACTIVE(U12(tt)) → c4(MARK(tt))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c5(MARK(U11(tt)), U11'(tt))
MARK(__(z0, z1)) → c6(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(nil) → c7(ACTIVE(nil))
MARK(U11(z0)) → c8(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(tt) → c9(ACTIVE(tt))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)), U12'(tt))
ACTIVE(U12(tt)) → c4(MARK(tt))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c5(MARK(U11(tt)), U11'(tt))
MARK(__(z0, z1)) → c6(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(nil) → c7(ACTIVE(nil))
MARK(U11(z0)) → c8(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(tt) → c9(ACTIVE(tt))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))

K tuples:none
Defined Rule Symbols:

active, mark, __, U11, U12, isNePal

Defined Pair Symbols:

ACTIVE, MARK, __', U11', U12', ISNEPAL

Compound Symbols:

c, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21

(3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 3 trailing nodes:

MARK(tt) → c9(ACTIVE(tt))
ACTIVE(U12(tt)) → c4(MARK(tt))
MARK(nil) → c7(ACTIVE(nil))

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)), U12'(tt))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c5(MARK(U11(tt)), U11'(tt))
MARK(__(z0, z1)) → c6(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U11(z0)) → c8(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)), U12'(tt))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c5(MARK(U11(tt)), U11'(tt))
MARK(__(z0, z1)) → c6(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U11(z0)) → c8(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))

K tuples:none
Defined Rule Symbols:

active, mark, __, U11, U12, isNePal

Defined Pair Symbols:

ACTIVE, MARK, __', U11', U12', ISNEPAL

Compound Symbols:

c, c1, c2, c3, c5, c6, c8, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21

(5) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace ACTIVE(U11(tt)) → c3(MARK(U12(tt)), U12'(tt)) by

ACTIVE(U11(tt)) → c3(MARK(U12(tt)))

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c5(MARK(U11(tt)), U11'(tt))
MARK(__(z0, z1)) → c6(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U11(z0)) → c8(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c5(MARK(U11(tt)), U11'(tt))
MARK(__(z0, z1)) → c6(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U11(z0)) → c8(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))

K tuples:none
Defined Rule Symbols:

active, mark, __, U11, U12, isNePal

Defined Pair Symbols:

ACTIVE, MARK, __', U11', U12', ISNEPAL

Compound Symbols:

c, c1, c2, c5, c6, c8, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c3

(7) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace ACTIVE(isNePal(__(z0, __(z1, z0)))) → c5(MARK(U11(tt)), U11'(tt)) by

ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))

(8) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(__(z0, z1)) → c6(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U11(z0)) → c8(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(__(z0, z1)) → c6(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U11(z0)) → c8(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))

K tuples:none
Defined Rule Symbols:

active, mark, __, U11, U12, isNePal

Defined Pair Symbols:

ACTIVE, MARK, __', U11', U12', ISNEPAL

Compound Symbols:

c, c1, c2, c6, c8, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c3, c5

(9) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace MARK(__(z0, z1)) → c6(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1)) by

MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(__(x0, x1)) → c6

(10) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(U11(z0)) → c8(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(__(x0, x1)) → c6

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(U11(z0)) → c8(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(__(x0, x1)) → c6

K tuples:none
Defined Rule Symbols:

active, mark, __, U11, U12, isNePal

Defined Pair Symbols:

ACTIVE, MARK, __', U11', U12', ISNEPAL

Compound Symbols:

c, c1, c2, c8, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c3, c5, c6, c6

(11) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 1 trailing nodes:

MARK(__(x0, x1)) → c6

(12) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(U11(z0)) → c8(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(U11(z0)) → c8(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))

K tuples:none
Defined Rule Symbols:

active, mark, __, U11, U12, isNePal

Defined Pair Symbols:

ACTIVE, MARK, __', U11', U12', ISNEPAL

Compound Symbols:

c, c1, c2, c8, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c3, c5, c6

(13) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace MARK(U11(z0)) → c8(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0)) by

MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U11(x0)) → c8

(14) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U11(x0)) → c8

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U11(x0)) → c8

K tuples:none
Defined Rule Symbols:

active, mark, __, U11, U12, isNePal

Defined Pair Symbols:

ACTIVE, MARK, __', U11', U12', ISNEPAL

Compound Symbols:

c, c1, c2, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c3, c5, c6, c8, c8

(15) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 1 trailing nodes:

MARK(U11(x0)) → c8

(16) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))

K tuples:none
Defined Rule Symbols:

active, mark, __, U11, U12, isNePal

Defined Pair Symbols:

ACTIVE, MARK, __', U11', U12', ISNEPAL

Compound Symbols:

c, c1, c2, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c3, c5, c6, c8

(17) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) by

MARK(U12(z0)) → c10(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0))
MARK(U12(__(z0, z1))) → c10(ACTIVE(U12(active(__(mark(z0), mark(z1))))), U12'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U12(nil)) → c10(ACTIVE(U12(active(nil))), U12'(mark(nil)), MARK(nil))
MARK(U12(U11(z0))) → c10(ACTIVE(U12(active(U11(mark(z0))))), U12'(mark(U11(z0))), MARK(U11(z0)))
MARK(U12(tt)) → c10(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt))
MARK(U12(U12(z0))) → c10(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0)))
MARK(U12(isNePal(z0))) → c10(ACTIVE(U12(active(isNePal(mark(z0))))), U12'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(x0)) → c10

(18) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(z0)) → c10(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0))
MARK(U12(__(z0, z1))) → c10(ACTIVE(U12(active(__(mark(z0), mark(z1))))), U12'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U12(nil)) → c10(ACTIVE(U12(active(nil))), U12'(mark(nil)), MARK(nil))
MARK(U12(U11(z0))) → c10(ACTIVE(U12(active(U11(mark(z0))))), U12'(mark(U11(z0))), MARK(U11(z0)))
MARK(U12(tt)) → c10(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt))
MARK(U12(U12(z0))) → c10(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0)))
MARK(U12(isNePal(z0))) → c10(ACTIVE(U12(active(isNePal(mark(z0))))), U12'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(x0)) → c10

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(z0)) → c10(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0))
MARK(U12(__(z0, z1))) → c10(ACTIVE(U12(active(__(mark(z0), mark(z1))))), U12'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U12(nil)) → c10(ACTIVE(U12(active(nil))), U12'(mark(nil)), MARK(nil))
MARK(U12(U11(z0))) → c10(ACTIVE(U12(active(U11(mark(z0))))), U12'(mark(U11(z0))), MARK(U11(z0)))
MARK(U12(tt)) → c10(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt))
MARK(U12(U12(z0))) → c10(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0)))
MARK(U12(isNePal(z0))) → c10(ACTIVE(U12(active(isNePal(mark(z0))))), U12'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(x0)) → c10

K tuples:none
Defined Rule Symbols:

active, mark, __, U11, U12, isNePal

Defined Pair Symbols:

ACTIVE, MARK, __', U11', U12', ISNEPAL

Compound Symbols:

c, c1, c2, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c3, c5, c6, c8, c10, c10

(19) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 1 trailing nodes:

MARK(U12(x0)) → c10

(20) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(z0)) → c10(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0))
MARK(U12(__(z0, z1))) → c10(ACTIVE(U12(active(__(mark(z0), mark(z1))))), U12'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U12(nil)) → c10(ACTIVE(U12(active(nil))), U12'(mark(nil)), MARK(nil))
MARK(U12(U11(z0))) → c10(ACTIVE(U12(active(U11(mark(z0))))), U12'(mark(U11(z0))), MARK(U11(z0)))
MARK(U12(tt)) → c10(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt))
MARK(U12(U12(z0))) → c10(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0)))
MARK(U12(isNePal(z0))) → c10(ACTIVE(U12(active(isNePal(mark(z0))))), U12'(mark(isNePal(z0))), MARK(isNePal(z0)))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(z0)) → c10(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0))
MARK(U12(__(z0, z1))) → c10(ACTIVE(U12(active(__(mark(z0), mark(z1))))), U12'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U12(nil)) → c10(ACTIVE(U12(active(nil))), U12'(mark(nil)), MARK(nil))
MARK(U12(U11(z0))) → c10(ACTIVE(U12(active(U11(mark(z0))))), U12'(mark(U11(z0))), MARK(U11(z0)))
MARK(U12(tt)) → c10(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt))
MARK(U12(U12(z0))) → c10(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0)))
MARK(U12(isNePal(z0))) → c10(ACTIVE(U12(active(isNePal(mark(z0))))), U12'(mark(isNePal(z0))), MARK(isNePal(z0)))

K tuples:none
Defined Rule Symbols:

active, mark, __, U11, U12, isNePal

Defined Pair Symbols:

ACTIVE, MARK, __', U11', U12', ISNEPAL

Compound Symbols:

c, c1, c2, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c3, c5, c6, c8, c10

(21) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0)) by

MARK(isNePal(z0)) → c11(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c11(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c11(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(U11(z0))) → c11(ACTIVE(isNePal(active(U11(mark(z0))))), ISNEPAL(mark(U11(z0))), MARK(U11(z0)))
MARK(isNePal(tt)) → c11(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(U12(z0))) → c11(ACTIVE(isNePal(active(U12(mark(z0))))), ISNEPAL(mark(U12(z0))), MARK(U12(z0)))
MARK(isNePal(isNePal(z0))) → c11(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(isNePal(x0)) → c11

(22) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(z0)) → c10(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0))
MARK(U12(__(z0, z1))) → c10(ACTIVE(U12(active(__(mark(z0), mark(z1))))), U12'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U12(nil)) → c10(ACTIVE(U12(active(nil))), U12'(mark(nil)), MARK(nil))
MARK(U12(U11(z0))) → c10(ACTIVE(U12(active(U11(mark(z0))))), U12'(mark(U11(z0))), MARK(U11(z0)))
MARK(U12(tt)) → c10(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt))
MARK(U12(U12(z0))) → c10(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0)))
MARK(U12(isNePal(z0))) → c10(ACTIVE(U12(active(isNePal(mark(z0))))), U12'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c11(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c11(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(U11(z0))) → c11(ACTIVE(isNePal(active(U11(mark(z0))))), ISNEPAL(mark(U11(z0))), MARK(U11(z0)))
MARK(isNePal(tt)) → c11(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(U12(z0))) → c11(ACTIVE(isNePal(active(U12(mark(z0))))), ISNEPAL(mark(U12(z0))), MARK(U12(z0)))
MARK(isNePal(isNePal(z0))) → c11(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(isNePal(x0)) → c11

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(z0)) → c10(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0))
MARK(U12(__(z0, z1))) → c10(ACTIVE(U12(active(__(mark(z0), mark(z1))))), U12'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U12(nil)) → c10(ACTIVE(U12(active(nil))), U12'(mark(nil)), MARK(nil))
MARK(U12(U11(z0))) → c10(ACTIVE(U12(active(U11(mark(z0))))), U12'(mark(U11(z0))), MARK(U11(z0)))
MARK(U12(tt)) → c10(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt))
MARK(U12(U12(z0))) → c10(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0)))
MARK(U12(isNePal(z0))) → c10(ACTIVE(U12(active(isNePal(mark(z0))))), U12'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c11(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c11(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(U11(z0))) → c11(ACTIVE(isNePal(active(U11(mark(z0))))), ISNEPAL(mark(U11(z0))), MARK(U11(z0)))
MARK(isNePal(tt)) → c11(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(U12(z0))) → c11(ACTIVE(isNePal(active(U12(mark(z0))))), ISNEPAL(mark(U12(z0))), MARK(U12(z0)))
MARK(isNePal(isNePal(z0))) → c11(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(isNePal(x0)) → c11

K tuples:none
Defined Rule Symbols:

active, mark, __, U11, U12, isNePal

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, MARK

Compound Symbols:

c, c1, c2, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c3, c5, c6, c8, c10, c11, c11

(23) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 1 trailing nodes:

MARK(isNePal(x0)) → c11

(24) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(z0)) → c10(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0))
MARK(U12(__(z0, z1))) → c10(ACTIVE(U12(active(__(mark(z0), mark(z1))))), U12'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U12(nil)) → c10(ACTIVE(U12(active(nil))), U12'(mark(nil)), MARK(nil))
MARK(U12(U11(z0))) → c10(ACTIVE(U12(active(U11(mark(z0))))), U12'(mark(U11(z0))), MARK(U11(z0)))
MARK(U12(tt)) → c10(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt))
MARK(U12(U12(z0))) → c10(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0)))
MARK(U12(isNePal(z0))) → c10(ACTIVE(U12(active(isNePal(mark(z0))))), U12'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c11(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c11(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(U11(z0))) → c11(ACTIVE(isNePal(active(U11(mark(z0))))), ISNEPAL(mark(U11(z0))), MARK(U11(z0)))
MARK(isNePal(tt)) → c11(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(U12(z0))) → c11(ACTIVE(isNePal(active(U12(mark(z0))))), ISNEPAL(mark(U12(z0))), MARK(U12(z0)))
MARK(isNePal(isNePal(z0))) → c11(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(z0)) → c10(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0))
MARK(U12(__(z0, z1))) → c10(ACTIVE(U12(active(__(mark(z0), mark(z1))))), U12'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U12(nil)) → c10(ACTIVE(U12(active(nil))), U12'(mark(nil)), MARK(nil))
MARK(U12(U11(z0))) → c10(ACTIVE(U12(active(U11(mark(z0))))), U12'(mark(U11(z0))), MARK(U11(z0)))
MARK(U12(tt)) → c10(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt))
MARK(U12(U12(z0))) → c10(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0)))
MARK(U12(isNePal(z0))) → c10(ACTIVE(U12(active(isNePal(mark(z0))))), U12'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c11(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c11(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(U11(z0))) → c11(ACTIVE(isNePal(active(U11(mark(z0))))), ISNEPAL(mark(U11(z0))), MARK(U11(z0)))
MARK(isNePal(tt)) → c11(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(U12(z0))) → c11(ACTIVE(isNePal(active(U12(mark(z0))))), ISNEPAL(mark(U12(z0))), MARK(U12(z0)))
MARK(isNePal(isNePal(z0))) → c11(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))

K tuples:none
Defined Rule Symbols:

active, mark, __, U11, U12, isNePal

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, MARK

Compound Symbols:

c, c1, c2, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c3, c5, c6, c8, c10, c11

(25) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1)) by

MARK(__(z0, z1)) → c6(ACTIVE(__(z0, z1)), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(x0, active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(x0, active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(x0, active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(x0, active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(x0, active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(x0, active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(x0, x1)) → c6(__'(mark(x0), mark(x1)))

(26) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(z0)) → c10(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0))
MARK(U12(__(z0, z1))) → c10(ACTIVE(U12(active(__(mark(z0), mark(z1))))), U12'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U12(nil)) → c10(ACTIVE(U12(active(nil))), U12'(mark(nil)), MARK(nil))
MARK(U12(U11(z0))) → c10(ACTIVE(U12(active(U11(mark(z0))))), U12'(mark(U11(z0))), MARK(U11(z0)))
MARK(U12(tt)) → c10(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt))
MARK(U12(U12(z0))) → c10(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0)))
MARK(U12(isNePal(z0))) → c10(ACTIVE(U12(active(isNePal(mark(z0))))), U12'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c11(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c11(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(U11(z0))) → c11(ACTIVE(isNePal(active(U11(mark(z0))))), ISNEPAL(mark(U11(z0))), MARK(U11(z0)))
MARK(isNePal(tt)) → c11(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(U12(z0))) → c11(ACTIVE(isNePal(active(U12(mark(z0))))), ISNEPAL(mark(U12(z0))), MARK(U12(z0)))
MARK(isNePal(isNePal(z0))) → c11(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(__(z0, z1)) → c6(ACTIVE(__(z0, z1)), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(x0, active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(x0, active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(x0, active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(x0, active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(x0, active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(x0, active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(x0, x1)) → c6(__'(mark(x0), mark(x1)))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(z0)) → c10(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0))
MARK(U12(__(z0, z1))) → c10(ACTIVE(U12(active(__(mark(z0), mark(z1))))), U12'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U12(nil)) → c10(ACTIVE(U12(active(nil))), U12'(mark(nil)), MARK(nil))
MARK(U12(U11(z0))) → c10(ACTIVE(U12(active(U11(mark(z0))))), U12'(mark(U11(z0))), MARK(U11(z0)))
MARK(U12(tt)) → c10(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt))
MARK(U12(U12(z0))) → c10(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0)))
MARK(U12(isNePal(z0))) → c10(ACTIVE(U12(active(isNePal(mark(z0))))), U12'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c11(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c11(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(U11(z0))) → c11(ACTIVE(isNePal(active(U11(mark(z0))))), ISNEPAL(mark(U11(z0))), MARK(U11(z0)))
MARK(isNePal(tt)) → c11(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(U12(z0))) → c11(ACTIVE(isNePal(active(U12(mark(z0))))), ISNEPAL(mark(U12(z0))), MARK(U12(z0)))
MARK(isNePal(isNePal(z0))) → c11(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(__(z0, z1)) → c6(ACTIVE(__(z0, z1)), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(x0, active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(x0, active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(x0, active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(x0, active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(x0, active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(x0, active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(x0, x1)) → c6(__'(mark(x0), mark(x1)))

K tuples:none
Defined Rule Symbols:

active, mark, __, U11, U12, isNePal

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, MARK

Compound Symbols:

c, c1, c2, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c3, c5, c6, c8, c10, c11, c6

(27) CpxTrsMatchBoundsTAProof (EQUIVALENT transformation)

A linear upper bound on the runtime complexity of the TRS R could be shown with a Match(-raise)-Bound[TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] (for contructor-based start-terms) of 1.

The compatible tree automaton used to show the Match(-raise)-Boundedness (for constructor-based start-terms) is represented by:
final states : [1, 2, 3, 4, 5, 6]
transitions:
active0(0) → 1
mark0(0) → 2
__0(0, 0) → 3
U110(0) → 4
U120(0) → 5
isNePal0(0) → 6
nil1() → 7
active1(7) → 2
nil1() → 0
tt1() → 8
active1(8) → 2
tt1() → 0
nil1() → 9
tt1() → 10
active0(9) → 1
active0(10) → 1
mark0(9) → 2
mark0(10) → 2
__0(9, 0) → 3
__0(0, 9) → 3
__0(10, 0) → 3
__0(0, 10) → 3
__0(9, 9) → 3
__0(9, 10) → 3
__0(10, 9) → 3
__0(10, 10) → 3
U110(9) → 4
U110(10) → 4
U120(9) → 5
U120(10) → 5
isNePal0(9) → 6
isNePal0(10) → 6
active1(9) → 2
active1(10) → 2
active1(9) → 1
active1(10) → 1

(0) Obligation:

(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)

(2) Obligation:

(3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

(4) Obligation:

(5) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

(6) Obligation:

(7) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

(8) Obligation:

(9) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

(10) Obligation:

(11) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

(12) Obligation:

(13) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

(14) Obligation:

(15) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

(16) Obligation:

(17) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

(18) Obligation:

(19) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

(20) Obligation:

(21) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

(22) Obligation:

(23) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

(24) Obligation:

(25) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

(26) Obligation:

(27) CpxTrsMatchBoundsTAProof (EQUIVALENT transformation)

(28) BOUNDS(O(1), O(n^1))