Runtime Complexity (innermost) proof of /tmp/tmp04Bddh/PALINDROME_nosorts

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), 46 ms)

    ↳6 CdtProblem

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

    ↳8 CdtProblem

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

    ↳10 CdtProblem

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

    ↳12 CdtProblem

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

    ↳14 CdtProblem

    ↳15 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 29 ms)

    ↳16 CdtProblem

    ↳17 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 6 ms)

    ↳18 CdtProblem

    ↳19 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 77 ms)

    ↳20 CdtProblem

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

    ↳22 CdtProblem

↳23 CpxTrsMatchBoundsTAProof (⇔, 0 ms)

↳24 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(and(tt, X)) → mark(X)
active(isNePal(__(I, __(P, I)))) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(and(X1, X2)) → active(and(mark(X1), X2))
mark(tt) → active(tt)
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)
and(mark(X1), X2) → and(X1, X2)
and(X1, mark(X2)) → and(X1, X2)
and(active(X1), X2) → and(X1, X2)
and(X1, active(X2)) → and(X1, X2)
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(and(tt, z0)) → mark(z0)
active(isNePal(__(z0, __(z1, z0)))) → mark(tt)
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(and(z0, z1)) → active(and(mark(z0), z1))
mark(tt) → active(tt)
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)
and(mark(z0), z1) → and(z0, z1)
and(z0, mark(z1)) → and(z0, z1)
and(active(z0), z1) → and(z0, z1)
and(z0, active(z1)) → and(z0, z1)
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(and(tt, z0)) → c3(MARK(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c4(MARK(tt))
MARK(__(z0, z1)) → c5(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(nil) → c6(ACTIVE(nil))
MARK(and(z0, z1)) → c7(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0))
MARK(tt) → c8(ACTIVE(tt))
MARK(isNePal(z0)) → c9(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c10(__'(z0, z1))
__'(z0, mark(z1)) → c11(__'(z0, z1))
__'(active(z0), z1) → c12(__'(z0, z1))
__'(z0, active(z1)) → c13(__'(z0, z1))
AND(mark(z0), z1) → c14(AND(z0, z1))
AND(z0, mark(z1)) → c15(AND(z0, z1))
AND(active(z0), z1) → c16(AND(z0, z1))
AND(z0, active(z1)) → c17(AND(z0, z1))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(active(z0)) → c19(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(and(tt, z0)) → c3(MARK(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c4(MARK(tt))
MARK(__(z0, z1)) → c5(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(nil) → c6(ACTIVE(nil))
MARK(and(z0, z1)) → c7(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0))
MARK(tt) → c8(ACTIVE(tt))
MARK(isNePal(z0)) → c9(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c10(__'(z0, z1))
__'(z0, mark(z1)) → c11(__'(z0, z1))
__'(active(z0), z1) → c12(__'(z0, z1))
__'(z0, active(z1)) → c13(__'(z0, z1))
AND(mark(z0), z1) → c14(AND(z0, z1))
AND(z0, mark(z1)) → c15(AND(z0, z1))
AND(active(z0), z1) → c16(AND(z0, z1))
AND(z0, active(z1)) → c17(AND(z0, z1))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(active(z0)) → c19(ISNEPAL(z0))

K tuples:none
Defined Rule Symbols:

active, mark, __, and, isNePal

Defined Pair Symbols:

ACTIVE, MARK, __', AND, ISNEPAL

Compound Symbols:

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

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

Removed 3 trailing nodes:

MARK(nil) → c6(ACTIVE(nil))
MARK(tt) → c8(ACTIVE(tt))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c4(MARK(tt))

(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(and(tt, z0)) → mark(z0)
active(isNePal(__(z0, __(z1, z0)))) → mark(tt)
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(and(z0, z1)) → active(and(mark(z0), z1))
mark(tt) → active(tt)
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)
and(mark(z0), z1) → and(z0, z1)
and(z0, mark(z1)) → and(z0, z1)
and(active(z0), z1) → and(z0, z1)
and(z0, active(z1)) → and(z0, z1)
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(and(tt, z0)) → c3(MARK(z0))
MARK(__(z0, z1)) → c5(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(and(z0, z1)) → c7(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0))
MARK(isNePal(z0)) → c9(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c10(__'(z0, z1))
__'(z0, mark(z1)) → c11(__'(z0, z1))
__'(active(z0), z1) → c12(__'(z0, z1))
__'(z0, active(z1)) → c13(__'(z0, z1))
AND(mark(z0), z1) → c14(AND(z0, z1))
AND(z0, mark(z1)) → c15(AND(z0, z1))
AND(active(z0), z1) → c16(AND(z0, z1))
AND(z0, active(z1)) → c17(AND(z0, z1))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(active(z0)) → c19(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(and(tt, z0)) → c3(MARK(z0))
MARK(__(z0, z1)) → c5(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(and(z0, z1)) → c7(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0))
MARK(isNePal(z0)) → c9(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c10(__'(z0, z1))
__'(z0, mark(z1)) → c11(__'(z0, z1))
__'(active(z0), z1) → c12(__'(z0, z1))
__'(z0, active(z1)) → c13(__'(z0, z1))
AND(mark(z0), z1) → c14(AND(z0, z1))
AND(z0, mark(z1)) → c15(AND(z0, z1))
AND(active(z0), z1) → c16(AND(z0, z1))
AND(z0, active(z1)) → c17(AND(z0, z1))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(active(z0)) → c19(ISNEPAL(z0))

K tuples:none
Defined Rule Symbols:

active, mark, __, and, isNePal

Defined Pair Symbols:

ACTIVE, MARK, __', AND, ISNEPAL

Compound Symbols:

c, c1, c2, c3, c5, c7, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19

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

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

MARK(__(z0, x1)) → c5(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c5(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c5(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c5(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(mark(x0), active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), mark(x1))), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(__(x0, x1)) → c5

(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(and(tt, z0)) → mark(z0)
active(isNePal(__(z0, __(z1, z0)))) → mark(tt)
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(and(z0, z1)) → active(and(mark(z0), z1))
mark(tt) → active(tt)
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)
and(mark(z0), z1) → and(z0, z1)
and(z0, mark(z1)) → and(z0, z1)
and(active(z0), z1) → and(z0, z1)
and(z0, active(z1)) → and(z0, z1)
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(and(tt, z0)) → c3(MARK(z0))
MARK(and(z0, z1)) → c7(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0))
MARK(isNePal(z0)) → c9(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c10(__'(z0, z1))
__'(z0, mark(z1)) → c11(__'(z0, z1))
__'(active(z0), z1) → c12(__'(z0, z1))
__'(z0, active(z1)) → c13(__'(z0, z1))
AND(mark(z0), z1) → c14(AND(z0, z1))
AND(z0, mark(z1)) → c15(AND(z0, z1))
AND(active(z0), z1) → c16(AND(z0, z1))
AND(z0, active(z1)) → c17(AND(z0, z1))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(active(z0)) → c19(ISNEPAL(z0))
MARK(__(z0, x1)) → c5(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c5(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c5(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c5(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(mark(x0), active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), mark(x1))), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(__(x0, x1)) → c5

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(and(tt, z0)) → c3(MARK(z0))
MARK(and(z0, z1)) → c7(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0))
MARK(isNePal(z0)) → c9(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c10(__'(z0, z1))
__'(z0, mark(z1)) → c11(__'(z0, z1))
__'(active(z0), z1) → c12(__'(z0, z1))
__'(z0, active(z1)) → c13(__'(z0, z1))
AND(mark(z0), z1) → c14(AND(z0, z1))
AND(z0, mark(z1)) → c15(AND(z0, z1))
AND(active(z0), z1) → c16(AND(z0, z1))
AND(z0, active(z1)) → c17(AND(z0, z1))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(active(z0)) → c19(ISNEPAL(z0))
MARK(__(z0, x1)) → c5(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c5(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c5(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c5(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(mark(x0), active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), mark(x1))), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(__(x0, x1)) → c5

K tuples:none
Defined Rule Symbols:

active, mark, __, and, isNePal

Defined Pair Symbols:

ACTIVE, MARK, __', AND, ISNEPAL

Compound Symbols:

c, c1, c2, c3, c7, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c5, c5

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

Removed 1 trailing nodes:

MARK(__(x0, x1)) → c5

(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(and(tt, z0)) → mark(z0)
active(isNePal(__(z0, __(z1, z0)))) → mark(tt)
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(and(z0, z1)) → active(and(mark(z0), z1))
mark(tt) → active(tt)
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)
and(mark(z0), z1) → and(z0, z1)
and(z0, mark(z1)) → and(z0, z1)
and(active(z0), z1) → and(z0, z1)
and(z0, active(z1)) → and(z0, z1)
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(and(tt, z0)) → c3(MARK(z0))
MARK(and(z0, z1)) → c7(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0))
MARK(isNePal(z0)) → c9(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c10(__'(z0, z1))
__'(z0, mark(z1)) → c11(__'(z0, z1))
__'(active(z0), z1) → c12(__'(z0, z1))
__'(z0, active(z1)) → c13(__'(z0, z1))
AND(mark(z0), z1) → c14(AND(z0, z1))
AND(z0, mark(z1)) → c15(AND(z0, z1))
AND(active(z0), z1) → c16(AND(z0, z1))
AND(z0, active(z1)) → c17(AND(z0, z1))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(active(z0)) → c19(ISNEPAL(z0))
MARK(__(z0, x1)) → c5(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c5(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c5(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c5(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(mark(x0), active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), mark(x1))), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(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))
ACTIVE(and(tt, z0)) → c3(MARK(z0))
MARK(and(z0, z1)) → c7(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0))
MARK(isNePal(z0)) → c9(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c10(__'(z0, z1))
__'(z0, mark(z1)) → c11(__'(z0, z1))
__'(active(z0), z1) → c12(__'(z0, z1))
__'(z0, active(z1)) → c13(__'(z0, z1))
AND(mark(z0), z1) → c14(AND(z0, z1))
AND(z0, mark(z1)) → c15(AND(z0, z1))
AND(active(z0), z1) → c16(AND(z0, z1))
AND(z0, active(z1)) → c17(AND(z0, z1))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(active(z0)) → c19(ISNEPAL(z0))
MARK(__(z0, x1)) → c5(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c5(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c5(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c5(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(mark(x0), active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), mark(x1))), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(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, __, and, isNePal

Defined Pair Symbols:

ACTIVE, MARK, __', AND, ISNEPAL

Compound Symbols:

c, c1, c2, c3, c7, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c5

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

Use narrowing to replace MARK(and(z0, z1)) → c7(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) by

MARK(and(z0, z1)) → c7(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0))
MARK(and(__(z0, z1), x1)) → c7(ACTIVE(and(active(__(mark(z0), mark(z1))), x1)), AND(mark(__(z0, z1)), x1), MARK(__(z0, z1)))
MARK(and(nil, x1)) → c7(ACTIVE(and(active(nil), x1)), AND(mark(nil), x1), MARK(nil))
MARK(and(and(z0, z1), x1)) → c7(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1)))
MARK(and(tt, x1)) → c7(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt))
MARK(and(isNePal(z0), x1)) → c7(ACTIVE(and(active(isNePal(mark(z0))), x1)), AND(mark(isNePal(z0)), x1), MARK(isNePal(z0)))
MARK(and(x0, x1)) → c7(AND(mark(x0), x1))

(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(and(tt, z0)) → mark(z0)
active(isNePal(__(z0, __(z1, z0)))) → mark(tt)
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(and(z0, z1)) → active(and(mark(z0), z1))
mark(tt) → active(tt)
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)
and(mark(z0), z1) → and(z0, z1)
and(z0, mark(z1)) → and(z0, z1)
and(active(z0), z1) → and(z0, z1)
and(z0, active(z1)) → and(z0, z1)
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(and(tt, z0)) → c3(MARK(z0))
MARK(isNePal(z0)) → c9(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c10(__'(z0, z1))
__'(z0, mark(z1)) → c11(__'(z0, z1))
__'(active(z0), z1) → c12(__'(z0, z1))
__'(z0, active(z1)) → c13(__'(z0, z1))
AND(mark(z0), z1) → c14(AND(z0, z1))
AND(z0, mark(z1)) → c15(AND(z0, z1))
AND(active(z0), z1) → c16(AND(z0, z1))
AND(z0, active(z1)) → c17(AND(z0, z1))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(active(z0)) → c19(ISNEPAL(z0))
MARK(__(z0, x1)) → c5(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c5(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c5(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c5(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(mark(x0), active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), mark(x1))), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(and(z0, z1)) → c7(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0))
MARK(and(__(z0, z1), x1)) → c7(ACTIVE(and(active(__(mark(z0), mark(z1))), x1)), AND(mark(__(z0, z1)), x1), MARK(__(z0, z1)))
MARK(and(nil, x1)) → c7(ACTIVE(and(active(nil), x1)), AND(mark(nil), x1), MARK(nil))
MARK(and(and(z0, z1), x1)) → c7(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1)))
MARK(and(tt, x1)) → c7(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt))
MARK(and(isNePal(z0), x1)) → c7(ACTIVE(and(active(isNePal(mark(z0))), x1)), AND(mark(isNePal(z0)), x1), MARK(isNePal(z0)))
MARK(and(x0, x1)) → c7(AND(mark(x0), 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))
ACTIVE(and(tt, z0)) → c3(MARK(z0))
MARK(isNePal(z0)) → c9(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c10(__'(z0, z1))
__'(z0, mark(z1)) → c11(__'(z0, z1))
__'(active(z0), z1) → c12(__'(z0, z1))
__'(z0, active(z1)) → c13(__'(z0, z1))
AND(mark(z0), z1) → c14(AND(z0, z1))
AND(z0, mark(z1)) → c15(AND(z0, z1))
AND(active(z0), z1) → c16(AND(z0, z1))
AND(z0, active(z1)) → c17(AND(z0, z1))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(active(z0)) → c19(ISNEPAL(z0))
MARK(__(z0, x1)) → c5(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c5(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c5(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c5(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(mark(x0), active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), mark(x1))), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(and(z0, z1)) → c7(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0))
MARK(and(__(z0, z1), x1)) → c7(ACTIVE(and(active(__(mark(z0), mark(z1))), x1)), AND(mark(__(z0, z1)), x1), MARK(__(z0, z1)))
MARK(and(nil, x1)) → c7(ACTIVE(and(active(nil), x1)), AND(mark(nil), x1), MARK(nil))
MARK(and(and(z0, z1), x1)) → c7(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1)))
MARK(and(tt, x1)) → c7(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt))
MARK(and(isNePal(z0), x1)) → c7(ACTIVE(and(active(isNePal(mark(z0))), x1)), AND(mark(isNePal(z0)), x1), MARK(isNePal(z0)))
MARK(and(x0, x1)) → c7(AND(mark(x0), x1))

K tuples:none
Defined Rule Symbols:

active, mark, __, and, isNePal

Defined Pair Symbols:

ACTIVE, MARK, __', AND, ISNEPAL

Compound Symbols:

c, c1, c2, c3, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c5, c7, c7

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

Use narrowing to replace MARK(isNePal(z0)) → c9(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0)) by

MARK(isNePal(z0)) → c9(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c9(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c9(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(and(z0, z1))) → c9(ACTIVE(isNePal(active(and(mark(z0), z1)))), ISNEPAL(mark(and(z0, z1))), MARK(and(z0, z1)))
MARK(isNePal(tt)) → c9(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(isNePal(z0))) → c9(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(isNePal(x0)) → c9

(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(and(tt, z0)) → mark(z0)
active(isNePal(__(z0, __(z1, z0)))) → mark(tt)
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(and(z0, z1)) → active(and(mark(z0), z1))
mark(tt) → active(tt)
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)
and(mark(z0), z1) → and(z0, z1)
and(z0, mark(z1)) → and(z0, z1)
and(active(z0), z1) → and(z0, z1)
and(z0, active(z1)) → and(z0, z1)
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(and(tt, z0)) → c3(MARK(z0))
__'(mark(z0), z1) → c10(__'(z0, z1))
__'(z0, mark(z1)) → c11(__'(z0, z1))
__'(active(z0), z1) → c12(__'(z0, z1))
__'(z0, active(z1)) → c13(__'(z0, z1))
AND(mark(z0), z1) → c14(AND(z0, z1))
AND(z0, mark(z1)) → c15(AND(z0, z1))
AND(active(z0), z1) → c16(AND(z0, z1))
AND(z0, active(z1)) → c17(AND(z0, z1))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(active(z0)) → c19(ISNEPAL(z0))
MARK(__(z0, x1)) → c5(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c5(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c5(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c5(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(mark(x0), active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), mark(x1))), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(and(z0, z1)) → c7(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0))
MARK(and(__(z0, z1), x1)) → c7(ACTIVE(and(active(__(mark(z0), mark(z1))), x1)), AND(mark(__(z0, z1)), x1), MARK(__(z0, z1)))
MARK(and(nil, x1)) → c7(ACTIVE(and(active(nil), x1)), AND(mark(nil), x1), MARK(nil))
MARK(and(and(z0, z1), x1)) → c7(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1)))
MARK(and(tt, x1)) → c7(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt))
MARK(and(isNePal(z0), x1)) → c7(ACTIVE(and(active(isNePal(mark(z0))), x1)), AND(mark(isNePal(z0)), x1), MARK(isNePal(z0)))
MARK(and(x0, x1)) → c7(AND(mark(x0), x1))
MARK(isNePal(z0)) → c9(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c9(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c9(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(and(z0, z1))) → c9(ACTIVE(isNePal(active(and(mark(z0), z1)))), ISNEPAL(mark(and(z0, z1))), MARK(and(z0, z1)))
MARK(isNePal(tt)) → c9(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(isNePal(z0))) → c9(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(isNePal(x0)) → c9

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(and(tt, z0)) → c3(MARK(z0))
__'(mark(z0), z1) → c10(__'(z0, z1))
__'(z0, mark(z1)) → c11(__'(z0, z1))
__'(active(z0), z1) → c12(__'(z0, z1))
__'(z0, active(z1)) → c13(__'(z0, z1))
AND(mark(z0), z1) → c14(AND(z0, z1))
AND(z0, mark(z1)) → c15(AND(z0, z1))
AND(active(z0), z1) → c16(AND(z0, z1))
AND(z0, active(z1)) → c17(AND(z0, z1))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(active(z0)) → c19(ISNEPAL(z0))
MARK(__(z0, x1)) → c5(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c5(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c5(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c5(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(mark(x0), active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), mark(x1))), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(and(z0, z1)) → c7(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0))
MARK(and(__(z0, z1), x1)) → c7(ACTIVE(and(active(__(mark(z0), mark(z1))), x1)), AND(mark(__(z0, z1)), x1), MARK(__(z0, z1)))
MARK(and(nil, x1)) → c7(ACTIVE(and(active(nil), x1)), AND(mark(nil), x1), MARK(nil))
MARK(and(and(z0, z1), x1)) → c7(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1)))
MARK(and(tt, x1)) → c7(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt))
MARK(and(isNePal(z0), x1)) → c7(ACTIVE(and(active(isNePal(mark(z0))), x1)), AND(mark(isNePal(z0)), x1), MARK(isNePal(z0)))
MARK(and(x0, x1)) → c7(AND(mark(x0), x1))
MARK(isNePal(z0)) → c9(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c9(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c9(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(and(z0, z1))) → c9(ACTIVE(isNePal(active(and(mark(z0), z1)))), ISNEPAL(mark(and(z0, z1))), MARK(and(z0, z1)))
MARK(isNePal(tt)) → c9(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(isNePal(z0))) → c9(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(isNePal(x0)) → c9

K tuples:none
Defined Rule Symbols:

active, mark, __, and, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, ISNEPAL, MARK

Compound Symbols:

c, c1, c2, c3, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c5, c7, c7, c9, c9

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

Removed 1 trailing nodes:

MARK(isNePal(x0)) → c9

(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(and(tt, z0)) → mark(z0)
active(isNePal(__(z0, __(z1, z0)))) → mark(tt)
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(and(z0, z1)) → active(and(mark(z0), z1))
mark(tt) → active(tt)
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)
and(mark(z0), z1) → and(z0, z1)
and(z0, mark(z1)) → and(z0, z1)
and(active(z0), z1) → and(z0, z1)
and(z0, active(z1)) → and(z0, z1)
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(and(tt, z0)) → c3(MARK(z0))
__'(mark(z0), z1) → c10(__'(z0, z1))
__'(z0, mark(z1)) → c11(__'(z0, z1))
__'(active(z0), z1) → c12(__'(z0, z1))
__'(z0, active(z1)) → c13(__'(z0, z1))
AND(mark(z0), z1) → c14(AND(z0, z1))
AND(z0, mark(z1)) → c15(AND(z0, z1))
AND(active(z0), z1) → c16(AND(z0, z1))
AND(z0, active(z1)) → c17(AND(z0, z1))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(active(z0)) → c19(ISNEPAL(z0))
MARK(__(z0, x1)) → c5(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c5(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c5(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c5(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(mark(x0), active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), mark(x1))), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(and(z0, z1)) → c7(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0))
MARK(and(__(z0, z1), x1)) → c7(ACTIVE(and(active(__(mark(z0), mark(z1))), x1)), AND(mark(__(z0, z1)), x1), MARK(__(z0, z1)))
MARK(and(nil, x1)) → c7(ACTIVE(and(active(nil), x1)), AND(mark(nil), x1), MARK(nil))
MARK(and(and(z0, z1), x1)) → c7(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1)))
MARK(and(tt, x1)) → c7(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt))
MARK(and(isNePal(z0), x1)) → c7(ACTIVE(and(active(isNePal(mark(z0))), x1)), AND(mark(isNePal(z0)), x1), MARK(isNePal(z0)))
MARK(and(x0, x1)) → c7(AND(mark(x0), x1))
MARK(isNePal(z0)) → c9(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c9(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c9(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(and(z0, z1))) → c9(ACTIVE(isNePal(active(and(mark(z0), z1)))), ISNEPAL(mark(and(z0, z1))), MARK(and(z0, z1)))
MARK(isNePal(tt)) → c9(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(isNePal(z0))) → c9(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))
ACTIVE(and(tt, z0)) → c3(MARK(z0))
__'(mark(z0), z1) → c10(__'(z0, z1))
__'(z0, mark(z1)) → c11(__'(z0, z1))
__'(active(z0), z1) → c12(__'(z0, z1))
__'(z0, active(z1)) → c13(__'(z0, z1))
AND(mark(z0), z1) → c14(AND(z0, z1))
AND(z0, mark(z1)) → c15(AND(z0, z1))
AND(active(z0), z1) → c16(AND(z0, z1))
AND(z0, active(z1)) → c17(AND(z0, z1))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(active(z0)) → c19(ISNEPAL(z0))
MARK(__(z0, x1)) → c5(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c5(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c5(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c5(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(mark(x0), active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), mark(x1))), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(and(z0, z1)) → c7(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0))
MARK(and(__(z0, z1), x1)) → c7(ACTIVE(and(active(__(mark(z0), mark(z1))), x1)), AND(mark(__(z0, z1)), x1), MARK(__(z0, z1)))
MARK(and(nil, x1)) → c7(ACTIVE(and(active(nil), x1)), AND(mark(nil), x1), MARK(nil))
MARK(and(and(z0, z1), x1)) → c7(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1)))
MARK(and(tt, x1)) → c7(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt))
MARK(and(isNePal(z0), x1)) → c7(ACTIVE(and(active(isNePal(mark(z0))), x1)), AND(mark(isNePal(z0)), x1), MARK(isNePal(z0)))
MARK(and(x0, x1)) → c7(AND(mark(x0), x1))
MARK(isNePal(z0)) → c9(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c9(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c9(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(and(z0, z1))) → c9(ACTIVE(isNePal(active(and(mark(z0), z1)))), ISNEPAL(mark(and(z0, z1))), MARK(and(z0, z1)))
MARK(isNePal(tt)) → c9(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(isNePal(z0))) → c9(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))

K tuples:none
Defined Rule Symbols:

active, mark, __, and, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, ISNEPAL, MARK

Compound Symbols:

c, c1, c2, c3, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c5, c7, c7, c9

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

Use narrowing to replace MARK(__(z0, x1)) → c5(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1)) by

MARK(__(z0, z1)) → c5(ACTIVE(__(z0, z1)), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c5(ACTIVE(__(x0, active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c5(ACTIVE(__(x0, active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(x0, active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(x0, active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(x0, active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(x0, x1)) → c5(__'(mark(x0), mark(x1)))

(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(and(tt, z0)) → mark(z0)
active(isNePal(__(z0, __(z1, z0)))) → mark(tt)
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(and(z0, z1)) → active(and(mark(z0), z1))
mark(tt) → active(tt)
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)
and(mark(z0), z1) → and(z0, z1)
and(z0, mark(z1)) → and(z0, z1)
and(active(z0), z1) → and(z0, z1)
and(z0, active(z1)) → and(z0, z1)
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(and(tt, z0)) → c3(MARK(z0))
__'(mark(z0), z1) → c10(__'(z0, z1))
__'(z0, mark(z1)) → c11(__'(z0, z1))
__'(active(z0), z1) → c12(__'(z0, z1))
__'(z0, active(z1)) → c13(__'(z0, z1))
AND(mark(z0), z1) → c14(AND(z0, z1))
AND(z0, mark(z1)) → c15(AND(z0, z1))
AND(active(z0), z1) → c16(AND(z0, z1))
AND(z0, active(z1)) → c17(AND(z0, z1))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(active(z0)) → c19(ISNEPAL(z0))
MARK(__(x0, z1)) → c5(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c5(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c5(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(mark(x0), active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), mark(x1))), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(and(z0, z1)) → c7(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0))
MARK(and(__(z0, z1), x1)) → c7(ACTIVE(and(active(__(mark(z0), mark(z1))), x1)), AND(mark(__(z0, z1)), x1), MARK(__(z0, z1)))
MARK(and(nil, x1)) → c7(ACTIVE(and(active(nil), x1)), AND(mark(nil), x1), MARK(nil))
MARK(and(and(z0, z1), x1)) → c7(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1)))
MARK(and(tt, x1)) → c7(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt))
MARK(and(isNePal(z0), x1)) → c7(ACTIVE(and(active(isNePal(mark(z0))), x1)), AND(mark(isNePal(z0)), x1), MARK(isNePal(z0)))
MARK(and(x0, x1)) → c7(AND(mark(x0), x1))
MARK(isNePal(z0)) → c9(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c9(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c9(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(and(z0, z1))) → c9(ACTIVE(isNePal(active(and(mark(z0), z1)))), ISNEPAL(mark(and(z0, z1))), MARK(and(z0, z1)))
MARK(isNePal(tt)) → c9(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(isNePal(z0))) → c9(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(__(z0, z1)) → c5(ACTIVE(__(z0, z1)), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c5(ACTIVE(__(x0, active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c5(ACTIVE(__(x0, active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(x0, active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(x0, active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(x0, active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(x0, x1)) → c5(__'(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))
ACTIVE(and(tt, z0)) → c3(MARK(z0))
__'(mark(z0), z1) → c10(__'(z0, z1))
__'(z0, mark(z1)) → c11(__'(z0, z1))
__'(active(z0), z1) → c12(__'(z0, z1))
__'(z0, active(z1)) → c13(__'(z0, z1))
AND(mark(z0), z1) → c14(AND(z0, z1))
AND(z0, mark(z1)) → c15(AND(z0, z1))
AND(active(z0), z1) → c16(AND(z0, z1))
AND(z0, active(z1)) → c17(AND(z0, z1))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(active(z0)) → c19(ISNEPAL(z0))
MARK(__(x0, z1)) → c5(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c5(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c5(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(mark(x0), active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), mark(x1))), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(and(z0, z1)) → c7(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0))
MARK(and(__(z0, z1), x1)) → c7(ACTIVE(and(active(__(mark(z0), mark(z1))), x1)), AND(mark(__(z0, z1)), x1), MARK(__(z0, z1)))
MARK(and(nil, x1)) → c7(ACTIVE(and(active(nil), x1)), AND(mark(nil), x1), MARK(nil))
MARK(and(and(z0, z1), x1)) → c7(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1)))
MARK(and(tt, x1)) → c7(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt))
MARK(and(isNePal(z0), x1)) → c7(ACTIVE(and(active(isNePal(mark(z0))), x1)), AND(mark(isNePal(z0)), x1), MARK(isNePal(z0)))
MARK(and(x0, x1)) → c7(AND(mark(x0), x1))
MARK(isNePal(z0)) → c9(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c9(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c9(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(and(z0, z1))) → c9(ACTIVE(isNePal(active(and(mark(z0), z1)))), ISNEPAL(mark(and(z0, z1))), MARK(and(z0, z1)))
MARK(isNePal(tt)) → c9(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(isNePal(z0))) → c9(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(__(z0, z1)) → c5(ACTIVE(__(z0, z1)), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c5(ACTIVE(__(x0, active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c5(ACTIVE(__(x0, active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(x0, active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(x0, active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(x0, active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(x0, x1)) → c5(__'(mark(x0), mark(x1)))

K tuples:none
Defined Rule Symbols:

active, mark, __, and, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, ISNEPAL, MARK

Compound Symbols:

c, c1, c2, c3, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c5, c7, c7, c9, c5

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

Use narrowing to replace MARK(__(x0, z1)) → c5(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1)) by

MARK(__(z0, z1)) → c5(ACTIVE(__(z0, z1)), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), x1)), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), x1)), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), x1)), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), x1)), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(ACTIVE(__(active(isNePal(mark(z0))), x1)), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(__(x0, x1)) → c5(__'(mark(x0), mark(x1)))

(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(and(tt, z0)) → mark(z0)
active(isNePal(__(z0, __(z1, z0)))) → mark(tt)
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(and(z0, z1)) → active(and(mark(z0), z1))
mark(tt) → active(tt)
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)
and(mark(z0), z1) → and(z0, z1)
and(z0, mark(z1)) → and(z0, z1)
and(active(z0), z1) → and(z0, z1)
and(z0, active(z1)) → and(z0, z1)
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(and(tt, z0)) → c3(MARK(z0))
__'(mark(z0), z1) → c10(__'(z0, z1))
__'(z0, mark(z1)) → c11(__'(z0, z1))
__'(active(z0), z1) → c12(__'(z0, z1))
__'(z0, active(z1)) → c13(__'(z0, z1))
AND(mark(z0), z1) → c14(AND(z0, z1))
AND(z0, mark(z1)) → c15(AND(z0, z1))
AND(active(z0), z1) → c16(AND(z0, z1))
AND(z0, active(z1)) → c17(AND(z0, z1))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(active(z0)) → c19(ISNEPAL(z0))
MARK(__(x0, __(z0, z1))) → c5(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c5(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(mark(x0), active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), mark(x1))), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(and(z0, z1)) → c7(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0))
MARK(and(__(z0, z1), x1)) → c7(ACTIVE(and(active(__(mark(z0), mark(z1))), x1)), AND(mark(__(z0, z1)), x1), MARK(__(z0, z1)))
MARK(and(nil, x1)) → c7(ACTIVE(and(active(nil), x1)), AND(mark(nil), x1), MARK(nil))
MARK(and(and(z0, z1), x1)) → c7(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1)))
MARK(and(tt, x1)) → c7(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt))
MARK(and(isNePal(z0), x1)) → c7(ACTIVE(and(active(isNePal(mark(z0))), x1)), AND(mark(isNePal(z0)), x1), MARK(isNePal(z0)))
MARK(and(x0, x1)) → c7(AND(mark(x0), x1))
MARK(isNePal(z0)) → c9(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c9(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c9(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(and(z0, z1))) → c9(ACTIVE(isNePal(active(and(mark(z0), z1)))), ISNEPAL(mark(and(z0, z1))), MARK(and(z0, z1)))
MARK(isNePal(tt)) → c9(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(isNePal(z0))) → c9(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(__(z0, z1)) → c5(ACTIVE(__(z0, z1)), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c5(ACTIVE(__(x0, active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c5(ACTIVE(__(x0, active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(x0, active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(x0, active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(x0, active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(x0, x1)) → c5(__'(mark(x0), mark(x1)))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), x1)), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), x1)), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), x1)), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), x1)), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(ACTIVE(__(active(isNePal(mark(z0))), 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))
ACTIVE(and(tt, z0)) → c3(MARK(z0))
__'(mark(z0), z1) → c10(__'(z0, z1))
__'(z0, mark(z1)) → c11(__'(z0, z1))
__'(active(z0), z1) → c12(__'(z0, z1))
__'(z0, active(z1)) → c13(__'(z0, z1))
AND(mark(z0), z1) → c14(AND(z0, z1))
AND(z0, mark(z1)) → c15(AND(z0, z1))
AND(active(z0), z1) → c16(AND(z0, z1))
AND(z0, active(z1)) → c17(AND(z0, z1))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(active(z0)) → c19(ISNEPAL(z0))
MARK(__(x0, __(z0, z1))) → c5(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c5(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(mark(x0), active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), mark(x1))), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(and(z0, z1)) → c7(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0))
MARK(and(__(z0, z1), x1)) → c7(ACTIVE(and(active(__(mark(z0), mark(z1))), x1)), AND(mark(__(z0, z1)), x1), MARK(__(z0, z1)))
MARK(and(nil, x1)) → c7(ACTIVE(and(active(nil), x1)), AND(mark(nil), x1), MARK(nil))
MARK(and(and(z0, z1), x1)) → c7(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1)))
MARK(and(tt, x1)) → c7(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt))
MARK(and(isNePal(z0), x1)) → c7(ACTIVE(and(active(isNePal(mark(z0))), x1)), AND(mark(isNePal(z0)), x1), MARK(isNePal(z0)))
MARK(and(x0, x1)) → c7(AND(mark(x0), x1))
MARK(isNePal(z0)) → c9(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c9(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c9(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(and(z0, z1))) → c9(ACTIVE(isNePal(active(and(mark(z0), z1)))), ISNEPAL(mark(and(z0, z1))), MARK(and(z0, z1)))
MARK(isNePal(tt)) → c9(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(isNePal(z0))) → c9(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(__(z0, z1)) → c5(ACTIVE(__(z0, z1)), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c5(ACTIVE(__(x0, active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c5(ACTIVE(__(x0, active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(x0, active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(x0, active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(x0, active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(x0, x1)) → c5(__'(mark(x0), mark(x1)))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), x1)), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), x1)), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), x1)), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), x1)), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(ACTIVE(__(active(isNePal(mark(z0))), x1)), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))

K tuples:none
Defined Rule Symbols:

active, mark, __, and, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, ISNEPAL, MARK

Compound Symbols:

c, c1, c2, c3, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c5, c7, c7, c9, c5

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

Use narrowing to replace MARK(__(x0, __(z0, z1))) → c5(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1))) by

MARK(__(z0, __(x1, x2))) → c5(ACTIVE(__(z0, active(__(mark(x1), mark(x2))))), __'(mark(z0), mark(__(x1, x2))), MARK(z0), MARK(__(x1, x2)))
MARK(__(x0, __(x1, x2))) → c5(ACTIVE(__(mark(x0), __(mark(x1), mark(x2)))), __'(mark(x0), mark(__(x1, x2))), MARK(x0), MARK(__(x1, x2)))
MARK(__(x0, __(z0, x2))) → c5(ACTIVE(__(mark(x0), active(__(z0, mark(x2))))), __'(mark(x0), mark(__(z0, x2))), MARK(x0), MARK(__(z0, x2)))
MARK(__(x0, __(x1, z1))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), z1)))), __'(mark(x0), mark(__(x1, z1))), MARK(x0), MARK(__(x1, z1)))
MARK(__(x0, __(x1, __(z0, z1)))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), active(__(mark(z0), mark(z1))))))), __'(mark(x0), mark(__(x1, __(z0, z1)))), MARK(x0), MARK(__(x1, __(z0, z1))))
MARK(__(x0, __(x1, nil))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), active(nil))))), __'(mark(x0), mark(__(x1, nil))), MARK(x0), MARK(__(x1, nil)))
MARK(__(x0, __(x1, and(z0, z1)))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), active(and(mark(z0), z1)))))), __'(mark(x0), mark(__(x1, and(z0, z1)))), MARK(x0), MARK(__(x1, and(z0, z1))))
MARK(__(x0, __(x1, tt))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), active(tt))))), __'(mark(x0), mark(__(x1, tt))), MARK(x0), MARK(__(x1, tt)))
MARK(__(x0, __(x1, isNePal(z0)))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), active(isNePal(mark(z0))))))), __'(mark(x0), mark(__(x1, isNePal(z0)))), MARK(x0), MARK(__(x1, isNePal(z0))))
MARK(__(x0, __(__(z0, z1), x2))) → c5(ACTIVE(__(mark(x0), active(__(active(__(mark(z0), mark(z1))), mark(x2))))), __'(mark(x0), mark(__(__(z0, z1), x2))), MARK(x0), MARK(__(__(z0, z1), x2)))
MARK(__(x0, __(nil, x2))) → c5(ACTIVE(__(mark(x0), active(__(active(nil), mark(x2))))), __'(mark(x0), mark(__(nil, x2))), MARK(x0), MARK(__(nil, x2)))
MARK(__(x0, __(and(z0, z1), x2))) → c5(ACTIVE(__(mark(x0), active(__(active(and(mark(z0), z1)), mark(x2))))), __'(mark(x0), mark(__(and(z0, z1), x2))), MARK(x0), MARK(__(and(z0, z1), x2)))
MARK(__(x0, __(tt, x2))) → c5(ACTIVE(__(mark(x0), active(__(active(tt), mark(x2))))), __'(mark(x0), mark(__(tt, x2))), MARK(x0), MARK(__(tt, x2)))
MARK(__(x0, __(isNePal(z0), x2))) → c5(ACTIVE(__(mark(x0), active(__(active(isNePal(mark(z0))), mark(x2))))), __'(mark(x0), mark(__(isNePal(z0), x2))), MARK(x0), MARK(__(isNePal(z0), x2)))
MARK(__(__(z0, z1), __(x1, x2))) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), active(__(mark(x1), mark(x2))))), __'(mark(__(z0, z1)), mark(__(x1, x2))), MARK(__(z0, z1)), MARK(__(x1, x2)))
MARK(__(nil, __(x1, x2))) → c5(ACTIVE(__(active(nil), active(__(mark(x1), mark(x2))))), __'(mark(nil), mark(__(x1, x2))), MARK(nil), MARK(__(x1, x2)))
MARK(__(and(z0, z1), __(x1, x2))) → c5(ACTIVE(__(active(and(mark(z0), z1)), active(__(mark(x1), mark(x2))))), __'(mark(and(z0, z1)), mark(__(x1, x2))), MARK(and(z0, z1)), MARK(__(x1, x2)))
MARK(__(tt, __(x1, x2))) → c5(ACTIVE(__(active(tt), active(__(mark(x1), mark(x2))))), __'(mark(tt), mark(__(x1, x2))), MARK(tt), MARK(__(x1, x2)))
MARK(__(isNePal(z0), __(x1, x2))) → c5(ACTIVE(__(active(isNePal(mark(z0))), active(__(mark(x1), mark(x2))))), __'(mark(isNePal(z0)), mark(__(x1, x2))), MARK(isNePal(z0)), MARK(__(x1, x2)))
MARK(__(x0, __(x1, x2))) → c5(__'(mark(x0), mark(__(x1, x2))), MARK(__(x1, x2)))

(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(and(tt, z0)) → mark(z0)
active(isNePal(__(z0, __(z1, z0)))) → mark(tt)
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(and(z0, z1)) → active(and(mark(z0), z1))
mark(tt) → active(tt)
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)
and(mark(z0), z1) → and(z0, z1)
and(z0, mark(z1)) → and(z0, z1)
and(active(z0), z1) → and(z0, z1)
and(z0, active(z1)) → and(z0, z1)
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(and(tt, z0)) → c3(MARK(z0))
__'(mark(z0), z1) → c10(__'(z0, z1))
__'(z0, mark(z1)) → c11(__'(z0, z1))
__'(active(z0), z1) → c12(__'(z0, z1))
__'(z0, active(z1)) → c13(__'(z0, z1))
AND(mark(z0), z1) → c14(AND(z0, z1))
AND(z0, mark(z1)) → c15(AND(z0, z1))
AND(active(z0), z1) → c16(AND(z0, z1))
AND(z0, active(z1)) → c17(AND(z0, z1))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(active(z0)) → c19(ISNEPAL(z0))
MARK(__(x0, nil)) → c5(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(mark(x0), active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), mark(x1))), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(and(z0, z1)) → c7(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0))
MARK(and(__(z0, z1), x1)) → c7(ACTIVE(and(active(__(mark(z0), mark(z1))), x1)), AND(mark(__(z0, z1)), x1), MARK(__(z0, z1)))
MARK(and(nil, x1)) → c7(ACTIVE(and(active(nil), x1)), AND(mark(nil), x1), MARK(nil))
MARK(and(and(z0, z1), x1)) → c7(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1)))
MARK(and(tt, x1)) → c7(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt))
MARK(and(isNePal(z0), x1)) → c7(ACTIVE(and(active(isNePal(mark(z0))), x1)), AND(mark(isNePal(z0)), x1), MARK(isNePal(z0)))
MARK(and(x0, x1)) → c7(AND(mark(x0), x1))
MARK(isNePal(z0)) → c9(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c9(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c9(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(and(z0, z1))) → c9(ACTIVE(isNePal(active(and(mark(z0), z1)))), ISNEPAL(mark(and(z0, z1))), MARK(and(z0, z1)))
MARK(isNePal(tt)) → c9(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(isNePal(z0))) → c9(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(__(z0, z1)) → c5(ACTIVE(__(z0, z1)), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c5(ACTIVE(__(x0, active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c5(ACTIVE(__(x0, active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(x0, active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(x0, active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(x0, active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(x0, x1)) → c5(__'(mark(x0), mark(x1)))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), x1)), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), x1)), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), x1)), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), x1)), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(ACTIVE(__(active(isNePal(mark(z0))), x1)), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(__(x0, __(x1, x2))) → c5(ACTIVE(__(mark(x0), __(mark(x1), mark(x2)))), __'(mark(x0), mark(__(x1, x2))), MARK(x0), MARK(__(x1, x2)))
MARK(__(x0, __(z0, x2))) → c5(ACTIVE(__(mark(x0), active(__(z0, mark(x2))))), __'(mark(x0), mark(__(z0, x2))), MARK(x0), MARK(__(z0, x2)))
MARK(__(x0, __(x1, z1))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), z1)))), __'(mark(x0), mark(__(x1, z1))), MARK(x0), MARK(__(x1, z1)))
MARK(__(x0, __(x1, __(z0, z1)))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), active(__(mark(z0), mark(z1))))))), __'(mark(x0), mark(__(x1, __(z0, z1)))), MARK(x0), MARK(__(x1, __(z0, z1))))
MARK(__(x0, __(x1, nil))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), active(nil))))), __'(mark(x0), mark(__(x1, nil))), MARK(x0), MARK(__(x1, nil)))
MARK(__(x0, __(x1, and(z0, z1)))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), active(and(mark(z0), z1)))))), __'(mark(x0), mark(__(x1, and(z0, z1)))), MARK(x0), MARK(__(x1, and(z0, z1))))
MARK(__(x0, __(x1, tt))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), active(tt))))), __'(mark(x0), mark(__(x1, tt))), MARK(x0), MARK(__(x1, tt)))
MARK(__(x0, __(x1, isNePal(z0)))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), active(isNePal(mark(z0))))))), __'(mark(x0), mark(__(x1, isNePal(z0)))), MARK(x0), MARK(__(x1, isNePal(z0))))
MARK(__(x0, __(__(z0, z1), x2))) → c5(ACTIVE(__(mark(x0), active(__(active(__(mark(z0), mark(z1))), mark(x2))))), __'(mark(x0), mark(__(__(z0, z1), x2))), MARK(x0), MARK(__(__(z0, z1), x2)))
MARK(__(x0, __(nil, x2))) → c5(ACTIVE(__(mark(x0), active(__(active(nil), mark(x2))))), __'(mark(x0), mark(__(nil, x2))), MARK(x0), MARK(__(nil, x2)))
MARK(__(x0, __(and(z0, z1), x2))) → c5(ACTIVE(__(mark(x0), active(__(active(and(mark(z0), z1)), mark(x2))))), __'(mark(x0), mark(__(and(z0, z1), x2))), MARK(x0), MARK(__(and(z0, z1), x2)))
MARK(__(x0, __(tt, x2))) → c5(ACTIVE(__(mark(x0), active(__(active(tt), mark(x2))))), __'(mark(x0), mark(__(tt, x2))), MARK(x0), MARK(__(tt, x2)))
MARK(__(x0, __(isNePal(z0), x2))) → c5(ACTIVE(__(mark(x0), active(__(active(isNePal(mark(z0))), mark(x2))))), __'(mark(x0), mark(__(isNePal(z0), x2))), MARK(x0), MARK(__(isNePal(z0), x2)))
MARK(__(__(z0, z1), __(x1, x2))) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), active(__(mark(x1), mark(x2))))), __'(mark(__(z0, z1)), mark(__(x1, x2))), MARK(__(z0, z1)), MARK(__(x1, x2)))
MARK(__(nil, __(x1, x2))) → c5(ACTIVE(__(active(nil), active(__(mark(x1), mark(x2))))), __'(mark(nil), mark(__(x1, x2))), MARK(nil), MARK(__(x1, x2)))
MARK(__(and(z0, z1), __(x1, x2))) → c5(ACTIVE(__(active(and(mark(z0), z1)), active(__(mark(x1), mark(x2))))), __'(mark(and(z0, z1)), mark(__(x1, x2))), MARK(and(z0, z1)), MARK(__(x1, x2)))
MARK(__(tt, __(x1, x2))) → c5(ACTIVE(__(active(tt), active(__(mark(x1), mark(x2))))), __'(mark(tt), mark(__(x1, x2))), MARK(tt), MARK(__(x1, x2)))
MARK(__(isNePal(z0), __(x1, x2))) → c5(ACTIVE(__(active(isNePal(mark(z0))), active(__(mark(x1), mark(x2))))), __'(mark(isNePal(z0)), mark(__(x1, x2))), MARK(isNePal(z0)), MARK(__(x1, x2)))
MARK(__(x0, __(x1, x2))) → c5(__'(mark(x0), mark(__(x1, x2))), MARK(__(x1, x2)))

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(and(tt, z0)) → c3(MARK(z0))
__'(mark(z0), z1) → c10(__'(z0, z1))
__'(z0, mark(z1)) → c11(__'(z0, z1))
__'(active(z0), z1) → c12(__'(z0, z1))
__'(z0, active(z1)) → c13(__'(z0, z1))
AND(mark(z0), z1) → c14(AND(z0, z1))
AND(z0, mark(z1)) → c15(AND(z0, z1))
AND(active(z0), z1) → c16(AND(z0, z1))
AND(z0, active(z1)) → c17(AND(z0, z1))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(active(z0)) → c19(ISNEPAL(z0))
MARK(__(x0, nil)) → c5(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(mark(x0), active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), mark(x1))), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(and(z0, z1)) → c7(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0))
MARK(and(__(z0, z1), x1)) → c7(ACTIVE(and(active(__(mark(z0), mark(z1))), x1)), AND(mark(__(z0, z1)), x1), MARK(__(z0, z1)))
MARK(and(nil, x1)) → c7(ACTIVE(and(active(nil), x1)), AND(mark(nil), x1), MARK(nil))
MARK(and(and(z0, z1), x1)) → c7(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1)))
MARK(and(tt, x1)) → c7(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt))
MARK(and(isNePal(z0), x1)) → c7(ACTIVE(and(active(isNePal(mark(z0))), x1)), AND(mark(isNePal(z0)), x1), MARK(isNePal(z0)))
MARK(and(x0, x1)) → c7(AND(mark(x0), x1))
MARK(isNePal(z0)) → c9(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c9(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c9(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(and(z0, z1))) → c9(ACTIVE(isNePal(active(and(mark(z0), z1)))), ISNEPAL(mark(and(z0, z1))), MARK(and(z0, z1)))
MARK(isNePal(tt)) → c9(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(isNePal(z0))) → c9(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(__(z0, z1)) → c5(ACTIVE(__(z0, z1)), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c5(ACTIVE(__(x0, active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c5(ACTIVE(__(x0, active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(x0, active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(x0, active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(x0, active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(x0, x1)) → c5(__'(mark(x0), mark(x1)))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), x1)), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), x1)), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), x1)), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), x1)), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(ACTIVE(__(active(isNePal(mark(z0))), x1)), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(__(x0, __(x1, x2))) → c5(ACTIVE(__(mark(x0), __(mark(x1), mark(x2)))), __'(mark(x0), mark(__(x1, x2))), MARK(x0), MARK(__(x1, x2)))
MARK(__(x0, __(z0, x2))) → c5(ACTIVE(__(mark(x0), active(__(z0, mark(x2))))), __'(mark(x0), mark(__(z0, x2))), MARK(x0), MARK(__(z0, x2)))
MARK(__(x0, __(x1, z1))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), z1)))), __'(mark(x0), mark(__(x1, z1))), MARK(x0), MARK(__(x1, z1)))
MARK(__(x0, __(x1, __(z0, z1)))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), active(__(mark(z0), mark(z1))))))), __'(mark(x0), mark(__(x1, __(z0, z1)))), MARK(x0), MARK(__(x1, __(z0, z1))))
MARK(__(x0, __(x1, nil))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), active(nil))))), __'(mark(x0), mark(__(x1, nil))), MARK(x0), MARK(__(x1, nil)))
MARK(__(x0, __(x1, and(z0, z1)))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), active(and(mark(z0), z1)))))), __'(mark(x0), mark(__(x1, and(z0, z1)))), MARK(x0), MARK(__(x1, and(z0, z1))))
MARK(__(x0, __(x1, tt))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), active(tt))))), __'(mark(x0), mark(__(x1, tt))), MARK(x0), MARK(__(x1, tt)))
MARK(__(x0, __(x1, isNePal(z0)))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), active(isNePal(mark(z0))))))), __'(mark(x0), mark(__(x1, isNePal(z0)))), MARK(x0), MARK(__(x1, isNePal(z0))))
MARK(__(x0, __(__(z0, z1), x2))) → c5(ACTIVE(__(mark(x0), active(__(active(__(mark(z0), mark(z1))), mark(x2))))), __'(mark(x0), mark(__(__(z0, z1), x2))), MARK(x0), MARK(__(__(z0, z1), x2)))
MARK(__(x0, __(nil, x2))) → c5(ACTIVE(__(mark(x0), active(__(active(nil), mark(x2))))), __'(mark(x0), mark(__(nil, x2))), MARK(x0), MARK(__(nil, x2)))
MARK(__(x0, __(and(z0, z1), x2))) → c5(ACTIVE(__(mark(x0), active(__(active(and(mark(z0), z1)), mark(x2))))), __'(mark(x0), mark(__(and(z0, z1), x2))), MARK(x0), MARK(__(and(z0, z1), x2)))
MARK(__(x0, __(tt, x2))) → c5(ACTIVE(__(mark(x0), active(__(active(tt), mark(x2))))), __'(mark(x0), mark(__(tt, x2))), MARK(x0), MARK(__(tt, x2)))
MARK(__(x0, __(isNePal(z0), x2))) → c5(ACTIVE(__(mark(x0), active(__(active(isNePal(mark(z0))), mark(x2))))), __'(mark(x0), mark(__(isNePal(z0), x2))), MARK(x0), MARK(__(isNePal(z0), x2)))
MARK(__(__(z0, z1), __(x1, x2))) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), active(__(mark(x1), mark(x2))))), __'(mark(__(z0, z1)), mark(__(x1, x2))), MARK(__(z0, z1)), MARK(__(x1, x2)))
MARK(__(nil, __(x1, x2))) → c5(ACTIVE(__(active(nil), active(__(mark(x1), mark(x2))))), __'(mark(nil), mark(__(x1, x2))), MARK(nil), MARK(__(x1, x2)))
MARK(__(and(z0, z1), __(x1, x2))) → c5(ACTIVE(__(active(and(mark(z0), z1)), active(__(mark(x1), mark(x2))))), __'(mark(and(z0, z1)), mark(__(x1, x2))), MARK(and(z0, z1)), MARK(__(x1, x2)))
MARK(__(tt, __(x1, x2))) → c5(ACTIVE(__(active(tt), active(__(mark(x1), mark(x2))))), __'(mark(tt), mark(__(x1, x2))), MARK(tt), MARK(__(x1, x2)))
MARK(__(isNePal(z0), __(x1, x2))) → c5(ACTIVE(__(active(isNePal(mark(z0))), active(__(mark(x1), mark(x2))))), __'(mark(isNePal(z0)), mark(__(x1, x2))), MARK(isNePal(z0)), MARK(__(x1, x2)))
MARK(__(x0, __(x1, x2))) → c5(__'(mark(x0), mark(__(x1, x2))), MARK(__(x1, x2)))

K tuples:none
Defined Rule Symbols:

active, mark, __, and, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, ISNEPAL, MARK

Compound Symbols:

c, c1, c2, c3, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c5, c7, c7, c9, c5, c5

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

Use narrowing to replace MARK(__(x0, nil)) → c5(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil)) by

MARK(__(z0, nil)) → c5(ACTIVE(__(z0, active(nil))), __'(mark(z0), mark(nil)), MARK(z0), MARK(nil))
MARK(__(x0, nil)) → c5(ACTIVE(__(mark(x0), nil)), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(__(z0, z1), nil)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), active(nil))), __'(mark(__(z0, z1)), mark(nil)), MARK(__(z0, z1)), MARK(nil))
MARK(__(nil, nil)) → c5(ACTIVE(__(active(nil), active(nil))), __'(mark(nil), mark(nil)), MARK(nil), MARK(nil))
MARK(__(and(z0, z1), nil)) → c5(ACTIVE(__(active(and(mark(z0), z1)), active(nil))), __'(mark(and(z0, z1)), mark(nil)), MARK(and(z0, z1)), MARK(nil))
MARK(__(tt, nil)) → c5(ACTIVE(__(active(tt), active(nil))), __'(mark(tt), mark(nil)), MARK(tt), MARK(nil))
MARK(__(isNePal(z0), nil)) → c5(ACTIVE(__(active(isNePal(mark(z0))), active(nil))), __'(mark(isNePal(z0)), mark(nil)), MARK(isNePal(z0)), MARK(nil))
MARK(__(x0, nil)) → c5(__'(mark(x0), mark(nil)))

(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(and(tt, z0)) → mark(z0)
active(isNePal(__(z0, __(z1, z0)))) → mark(tt)
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(and(z0, z1)) → active(and(mark(z0), z1))
mark(tt) → active(tt)
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)
and(mark(z0), z1) → and(z0, z1)
and(z0, mark(z1)) → and(z0, z1)
and(active(z0), z1) → and(z0, z1)
and(z0, active(z1)) → and(z0, z1)
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(and(tt, z0)) → c3(MARK(z0))
__'(mark(z0), z1) → c10(__'(z0, z1))
__'(z0, mark(z1)) → c11(__'(z0, z1))
__'(active(z0), z1) → c12(__'(z0, z1))
__'(z0, active(z1)) → c13(__'(z0, z1))
AND(mark(z0), z1) → c14(AND(z0, z1))
AND(z0, mark(z1)) → c15(AND(z0, z1))
AND(active(z0), z1) → c16(AND(z0, z1))
AND(z0, active(z1)) → c17(AND(z0, z1))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(active(z0)) → c19(ISNEPAL(z0))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(mark(x0), active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), mark(x1))), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(and(z0, z1)) → c7(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0))
MARK(and(__(z0, z1), x1)) → c7(ACTIVE(and(active(__(mark(z0), mark(z1))), x1)), AND(mark(__(z0, z1)), x1), MARK(__(z0, z1)))
MARK(and(nil, x1)) → c7(ACTIVE(and(active(nil), x1)), AND(mark(nil), x1), MARK(nil))
MARK(and(and(z0, z1), x1)) → c7(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1)))
MARK(and(tt, x1)) → c7(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt))
MARK(and(isNePal(z0), x1)) → c7(ACTIVE(and(active(isNePal(mark(z0))), x1)), AND(mark(isNePal(z0)), x1), MARK(isNePal(z0)))
MARK(and(x0, x1)) → c7(AND(mark(x0), x1))
MARK(isNePal(z0)) → c9(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c9(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c9(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(and(z0, z1))) → c9(ACTIVE(isNePal(active(and(mark(z0), z1)))), ISNEPAL(mark(and(z0, z1))), MARK(and(z0, z1)))
MARK(isNePal(tt)) → c9(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(isNePal(z0))) → c9(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(__(z0, z1)) → c5(ACTIVE(__(z0, z1)), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c5(ACTIVE(__(x0, active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c5(ACTIVE(__(x0, active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(x0, active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(x0, active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(x0, active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(x0, x1)) → c5(__'(mark(x0), mark(x1)))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), x1)), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), x1)), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), x1)), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), x1)), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(ACTIVE(__(active(isNePal(mark(z0))), x1)), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(__(x0, __(x1, x2))) → c5(ACTIVE(__(mark(x0), __(mark(x1), mark(x2)))), __'(mark(x0), mark(__(x1, x2))), MARK(x0), MARK(__(x1, x2)))
MARK(__(x0, __(z0, x2))) → c5(ACTIVE(__(mark(x0), active(__(z0, mark(x2))))), __'(mark(x0), mark(__(z0, x2))), MARK(x0), MARK(__(z0, x2)))
MARK(__(x0, __(x1, z1))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), z1)))), __'(mark(x0), mark(__(x1, z1))), MARK(x0), MARK(__(x1, z1)))
MARK(__(x0, __(x1, __(z0, z1)))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), active(__(mark(z0), mark(z1))))))), __'(mark(x0), mark(__(x1, __(z0, z1)))), MARK(x0), MARK(__(x1, __(z0, z1))))
MARK(__(x0, __(x1, nil))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), active(nil))))), __'(mark(x0), mark(__(x1, nil))), MARK(x0), MARK(__(x1, nil)))
MARK(__(x0, __(x1, and(z0, z1)))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), active(and(mark(z0), z1)))))), __'(mark(x0), mark(__(x1, and(z0, z1)))), MARK(x0), MARK(__(x1, and(z0, z1))))
MARK(__(x0, __(x1, tt))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), active(tt))))), __'(mark(x0), mark(__(x1, tt))), MARK(x0), MARK(__(x1, tt)))
MARK(__(x0, __(x1, isNePal(z0)))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), active(isNePal(mark(z0))))))), __'(mark(x0), mark(__(x1, isNePal(z0)))), MARK(x0), MARK(__(x1, isNePal(z0))))
MARK(__(x0, __(__(z0, z1), x2))) → c5(ACTIVE(__(mark(x0), active(__(active(__(mark(z0), mark(z1))), mark(x2))))), __'(mark(x0), mark(__(__(z0, z1), x2))), MARK(x0), MARK(__(__(z0, z1), x2)))
MARK(__(x0, __(nil, x2))) → c5(ACTIVE(__(mark(x0), active(__(active(nil), mark(x2))))), __'(mark(x0), mark(__(nil, x2))), MARK(x0), MARK(__(nil, x2)))
MARK(__(x0, __(and(z0, z1), x2))) → c5(ACTIVE(__(mark(x0), active(__(active(and(mark(z0), z1)), mark(x2))))), __'(mark(x0), mark(__(and(z0, z1), x2))), MARK(x0), MARK(__(and(z0, z1), x2)))
MARK(__(x0, __(tt, x2))) → c5(ACTIVE(__(mark(x0), active(__(active(tt), mark(x2))))), __'(mark(x0), mark(__(tt, x2))), MARK(x0), MARK(__(tt, x2)))
MARK(__(x0, __(isNePal(z0), x2))) → c5(ACTIVE(__(mark(x0), active(__(active(isNePal(mark(z0))), mark(x2))))), __'(mark(x0), mark(__(isNePal(z0), x2))), MARK(x0), MARK(__(isNePal(z0), x2)))
MARK(__(__(z0, z1), __(x1, x2))) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), active(__(mark(x1), mark(x2))))), __'(mark(__(z0, z1)), mark(__(x1, x2))), MARK(__(z0, z1)), MARK(__(x1, x2)))
MARK(__(nil, __(x1, x2))) → c5(ACTIVE(__(active(nil), active(__(mark(x1), mark(x2))))), __'(mark(nil), mark(__(x1, x2))), MARK(nil), MARK(__(x1, x2)))
MARK(__(and(z0, z1), __(x1, x2))) → c5(ACTIVE(__(active(and(mark(z0), z1)), active(__(mark(x1), mark(x2))))), __'(mark(and(z0, z1)), mark(__(x1, x2))), MARK(and(z0, z1)), MARK(__(x1, x2)))
MARK(__(tt, __(x1, x2))) → c5(ACTIVE(__(active(tt), active(__(mark(x1), mark(x2))))), __'(mark(tt), mark(__(x1, x2))), MARK(tt), MARK(__(x1, x2)))
MARK(__(isNePal(z0), __(x1, x2))) → c5(ACTIVE(__(active(isNePal(mark(z0))), active(__(mark(x1), mark(x2))))), __'(mark(isNePal(z0)), mark(__(x1, x2))), MARK(isNePal(z0)), MARK(__(x1, x2)))
MARK(__(x0, __(x1, x2))) → c5(__'(mark(x0), mark(__(x1, x2))), MARK(__(x1, x2)))
MARK(__(x0, nil)) → c5(ACTIVE(__(mark(x0), nil)), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(__(z0, z1), nil)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), active(nil))), __'(mark(__(z0, z1)), mark(nil)), MARK(__(z0, z1)), MARK(nil))
MARK(__(nil, nil)) → c5(ACTIVE(__(active(nil), active(nil))), __'(mark(nil), mark(nil)), MARK(nil), MARK(nil))
MARK(__(and(z0, z1), nil)) → c5(ACTIVE(__(active(and(mark(z0), z1)), active(nil))), __'(mark(and(z0, z1)), mark(nil)), MARK(and(z0, z1)), MARK(nil))
MARK(__(tt, nil)) → c5(ACTIVE(__(active(tt), active(nil))), __'(mark(tt), mark(nil)), MARK(tt), MARK(nil))
MARK(__(isNePal(z0), nil)) → c5(ACTIVE(__(active(isNePal(mark(z0))), active(nil))), __'(mark(isNePal(z0)), mark(nil)), MARK(isNePal(z0)), MARK(nil))
MARK(__(x0, nil)) → c5(__'(mark(x0), mark(nil)))

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(and(tt, z0)) → c3(MARK(z0))
__'(mark(z0), z1) → c10(__'(z0, z1))
__'(z0, mark(z1)) → c11(__'(z0, z1))
__'(active(z0), z1) → c12(__'(z0, z1))
__'(z0, active(z1)) → c13(__'(z0, z1))
AND(mark(z0), z1) → c14(AND(z0, z1))
AND(z0, mark(z1)) → c15(AND(z0, z1))
AND(active(z0), z1) → c16(AND(z0, z1))
AND(z0, active(z1)) → c17(AND(z0, z1))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(active(z0)) → c19(ISNEPAL(z0))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(mark(x0), active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), mark(x1))), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(and(z0, z1)) → c7(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0))
MARK(and(__(z0, z1), x1)) → c7(ACTIVE(and(active(__(mark(z0), mark(z1))), x1)), AND(mark(__(z0, z1)), x1), MARK(__(z0, z1)))
MARK(and(nil, x1)) → c7(ACTIVE(and(active(nil), x1)), AND(mark(nil), x1), MARK(nil))
MARK(and(and(z0, z1), x1)) → c7(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1)))
MARK(and(tt, x1)) → c7(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt))
MARK(and(isNePal(z0), x1)) → c7(ACTIVE(and(active(isNePal(mark(z0))), x1)), AND(mark(isNePal(z0)), x1), MARK(isNePal(z0)))
MARK(and(x0, x1)) → c7(AND(mark(x0), x1))
MARK(isNePal(z0)) → c9(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c9(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c9(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(and(z0, z1))) → c9(ACTIVE(isNePal(active(and(mark(z0), z1)))), ISNEPAL(mark(and(z0, z1))), MARK(and(z0, z1)))
MARK(isNePal(tt)) → c9(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(isNePal(z0))) → c9(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(__(z0, z1)) → c5(ACTIVE(__(z0, z1)), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c5(ACTIVE(__(x0, active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c5(ACTIVE(__(x0, active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, and(z0, z1))) → c5(ACTIVE(__(x0, active(and(mark(z0), z1)))), __'(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1)))
MARK(__(x0, tt)) → c5(ACTIVE(__(x0, active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, isNePal(z0))) → c5(ACTIVE(__(x0, active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(x0, x1)) → c5(__'(mark(x0), mark(x1)))
MARK(__(__(z0, z1), x1)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), x1)), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c5(ACTIVE(__(active(nil), x1)), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(and(z0, z1), x1)) → c5(ACTIVE(__(active(and(mark(z0), z1)), x1)), __'(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1))
MARK(__(tt, x1)) → c5(ACTIVE(__(active(tt), x1)), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(isNePal(z0), x1)) → c5(ACTIVE(__(active(isNePal(mark(z0))), x1)), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(__(x0, __(x1, x2))) → c5(ACTIVE(__(mark(x0), __(mark(x1), mark(x2)))), __'(mark(x0), mark(__(x1, x2))), MARK(x0), MARK(__(x1, x2)))
MARK(__(x0, __(z0, x2))) → c5(ACTIVE(__(mark(x0), active(__(z0, mark(x2))))), __'(mark(x0), mark(__(z0, x2))), MARK(x0), MARK(__(z0, x2)))
MARK(__(x0, __(x1, z1))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), z1)))), __'(mark(x0), mark(__(x1, z1))), MARK(x0), MARK(__(x1, z1)))
MARK(__(x0, __(x1, __(z0, z1)))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), active(__(mark(z0), mark(z1))))))), __'(mark(x0), mark(__(x1, __(z0, z1)))), MARK(x0), MARK(__(x1, __(z0, z1))))
MARK(__(x0, __(x1, nil))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), active(nil))))), __'(mark(x0), mark(__(x1, nil))), MARK(x0), MARK(__(x1, nil)))
MARK(__(x0, __(x1, and(z0, z1)))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), active(and(mark(z0), z1)))))), __'(mark(x0), mark(__(x1, and(z0, z1)))), MARK(x0), MARK(__(x1, and(z0, z1))))
MARK(__(x0, __(x1, tt))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), active(tt))))), __'(mark(x0), mark(__(x1, tt))), MARK(x0), MARK(__(x1, tt)))
MARK(__(x0, __(x1, isNePal(z0)))) → c5(ACTIVE(__(mark(x0), active(__(mark(x1), active(isNePal(mark(z0))))))), __'(mark(x0), mark(__(x1, isNePal(z0)))), MARK(x0), MARK(__(x1, isNePal(z0))))
MARK(__(x0, __(__(z0, z1), x2))) → c5(ACTIVE(__(mark(x0), active(__(active(__(mark(z0), mark(z1))), mark(x2))))), __'(mark(x0), mark(__(__(z0, z1), x2))), MARK(x0), MARK(__(__(z0, z1), x2)))
MARK(__(x0, __(nil, x2))) → c5(ACTIVE(__(mark(x0), active(__(active(nil), mark(x2))))), __'(mark(x0), mark(__(nil, x2))), MARK(x0), MARK(__(nil, x2)))
MARK(__(x0, __(and(z0, z1), x2))) → c5(ACTIVE(__(mark(x0), active(__(active(and(mark(z0), z1)), mark(x2))))), __'(mark(x0), mark(__(and(z0, z1), x2))), MARK(x0), MARK(__(and(z0, z1), x2)))
MARK(__(x0, __(tt, x2))) → c5(ACTIVE(__(mark(x0), active(__(active(tt), mark(x2))))), __'(mark(x0), mark(__(tt, x2))), MARK(x0), MARK(__(tt, x2)))
MARK(__(x0, __(isNePal(z0), x2))) → c5(ACTIVE(__(mark(x0), active(__(active(isNePal(mark(z0))), mark(x2))))), __'(mark(x0), mark(__(isNePal(z0), x2))), MARK(x0), MARK(__(isNePal(z0), x2)))
MARK(__(__(z0, z1), __(x1, x2))) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), active(__(mark(x1), mark(x2))))), __'(mark(__(z0, z1)), mark(__(x1, x2))), MARK(__(z0, z1)), MARK(__(x1, x2)))
MARK(__(nil, __(x1, x2))) → c5(ACTIVE(__(active(nil), active(__(mark(x1), mark(x2))))), __'(mark(nil), mark(__(x1, x2))), MARK(nil), MARK(__(x1, x2)))
MARK(__(and(z0, z1), __(x1, x2))) → c5(ACTIVE(__(active(and(mark(z0), z1)), active(__(mark(x1), mark(x2))))), __'(mark(and(z0, z1)), mark(__(x1, x2))), MARK(and(z0, z1)), MARK(__(x1, x2)))
MARK(__(tt, __(x1, x2))) → c5(ACTIVE(__(active(tt), active(__(mark(x1), mark(x2))))), __'(mark(tt), mark(__(x1, x2))), MARK(tt), MARK(__(x1, x2)))
MARK(__(isNePal(z0), __(x1, x2))) → c5(ACTIVE(__(active(isNePal(mark(z0))), active(__(mark(x1), mark(x2))))), __'(mark(isNePal(z0)), mark(__(x1, x2))), MARK(isNePal(z0)), MARK(__(x1, x2)))
MARK(__(x0, __(x1, x2))) → c5(__'(mark(x0), mark(__(x1, x2))), MARK(__(x1, x2)))
MARK(__(x0, nil)) → c5(ACTIVE(__(mark(x0), nil)), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(__(z0, z1), nil)) → c5(ACTIVE(__(active(__(mark(z0), mark(z1))), active(nil))), __'(mark(__(z0, z1)), mark(nil)), MARK(__(z0, z1)), MARK(nil))
MARK(__(nil, nil)) → c5(ACTIVE(__(active(nil), active(nil))), __'(mark(nil), mark(nil)), MARK(nil), MARK(nil))
MARK(__(and(z0, z1), nil)) → c5(ACTIVE(__(active(and(mark(z0), z1)), active(nil))), __'(mark(and(z0, z1)), mark(nil)), MARK(and(z0, z1)), MARK(nil))
MARK(__(tt, nil)) → c5(ACTIVE(__(active(tt), active(nil))), __'(mark(tt), mark(nil)), MARK(tt), MARK(nil))
MARK(__(isNePal(z0), nil)) → c5(ACTIVE(__(active(isNePal(mark(z0))), active(nil))), __'(mark(isNePal(z0)), mark(nil)), MARK(isNePal(z0)), MARK(nil))
MARK(__(x0, nil)) → c5(__'(mark(x0), mark(nil)))

K tuples:none
Defined Rule Symbols:

active, mark, __, and, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, ISNEPAL, MARK

Compound Symbols:

c, c1, c2, c3, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c5, c7, c7, c9, c5, c5

(23) 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]
transitions:
active0(0) → 1
mark0(0) → 2
__0(0, 0) → 3
and0(0, 0) → 4
isNePal0(0) → 5
nil1() → 6
active1(6) → 2
nil1() → 0
tt1() → 7
active1(7) → 2
tt1() → 0
nil1() → 8
tt1() → 9
active0(8) → 1
active0(9) → 1
mark0(8) → 2
mark0(9) → 2
__0(8, 0) → 3
__0(0, 8) → 3
__0(9, 0) → 3
__0(0, 9) → 3
__0(8, 8) → 3
__0(8, 9) → 3
__0(9, 8) → 3
__0(9, 9) → 3
and0(8, 0) → 4
and0(0, 8) → 4
and0(9, 0) → 4
and0(0, 9) → 4
and0(8, 8) → 4
and0(8, 9) → 4
and0(9, 8) → 4
and0(9, 9) → 4
isNePal0(8) → 5
isNePal0(9) → 5
active1(8) → 2
active1(9) → 2
active1(8) → 1
active1(9) → 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) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

(8) Obligation:

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

(10) Obligation:

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

(12) Obligation:

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

(14) Obligation:

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

(16) Obligation:

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

(18) Obligation:

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

(20) Obligation:

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

(22) Obligation:

(23) CpxTrsMatchBoundsTAProof (EQUIVALENT transformation)

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