Runtime Complexity (innermost) proof of /tmp/tmpSJvk2j/PALINDROME_nosorts_noand

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

0 CpxTRS

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

↳2 CdtProblem

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

    ↳4 CdtProblem

    ↳5 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))), 1225 ms)

    ↳6 CdtProblem

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

    ↳8 CdtProblem

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

    ↳10 CdtProblem

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

    ↳12 CdtProblem

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

    ↳14 CdtProblem

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

    ↳16 CdtProblem

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

    ↳18 CdtProblem

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

    ↳20 CdtProblem

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

    ↳22 CdtProblem

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

    ↳24 CdtProblem

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

    ↳26 CdtProblem

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

    ↳28 CdtProblem

    ↳29 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID), 0 ms)

    ↳30 CdtProblem

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

    ↳32 CdtProblem

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

    ↳34 CdtProblem

    ↳35 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID), 0 ms)

    ↳36 CdtProblem

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

    ↳38 CdtProblem

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

    ↳40 CdtProblem

    ↳41 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID), 0 ms)

    ↳42 CdtProblem

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

    ↳44 CdtProblem

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

    ↳46 CdtProblem

    ↳47 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID), 0 ms)

    ↳48 CdtProblem

↳49 CpxTrsMatchBoundsTAProof (⇔, 707 ms)

↳50 BOUNDS(O(1), O(n^1))

(0) Obligation:

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

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

Rewrite Strategy: INNERMOST

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

Converted CpxTRS to CDT

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

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

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(U11(tt)) → c3(U12'(tt))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c5(U11'(tt))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(U11(z0)) → c8(U11'(active(z0)), ACTIVE(z0))
ACTIVE(U12(z0)) → c9(U12'(active(z0)), ACTIVE(z0))
ACTIVE(isNePal(z0)) → c10(ISNEPAL(active(z0)), ACTIVE(z0))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(U11(tt)) → c3(U12'(tt))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c5(U11'(tt))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(U11(z0)) → c8(U11'(active(z0)), ACTIVE(z0))
ACTIVE(U12(z0)) → c9(U12'(active(z0)), ACTIVE(z0))
ACTIVE(isNePal(z0)) → c10(ISNEPAL(active(z0)), ACTIVE(z0))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))

K tuples:none
Defined Rule Symbols:

active, __, U11, U12, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, PROPER, TOP

Compound Symbols:

c, c3, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c22, c24, c25, c26, c27

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

Removed 2 trailing nodes:

ACTIVE(isNePal(__(z0, __(z1, z0)))) → c5(U11'(tt))
ACTIVE(U11(tt)) → c3(U12'(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(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
active(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(U11(z0)) → U11(active(z0))
active(U12(z0)) → U12(active(z0))
active(isNePal(z0)) → isNePal(active(z0))
__(mark(z0), z1) → mark(__(z0, z1))
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
U11(mark(z0)) → mark(U11(z0))
U11(ok(z0)) → ok(U11(z0))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNePal(mark(z0)) → mark(isNePal(z0))
isNePal(ok(z0)) → ok(isNePal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(U11(z0)) → U11(proper(z0))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(U11(z0)) → c8(U11'(active(z0)), ACTIVE(z0))
ACTIVE(U12(z0)) → c9(U12'(active(z0)), ACTIVE(z0))
ACTIVE(isNePal(z0)) → c10(ISNEPAL(active(z0)), ACTIVE(z0))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(U11(z0)) → c8(U11'(active(z0)), ACTIVE(z0))
ACTIVE(U12(z0)) → c9(U12'(active(z0)), ACTIVE(z0))
ACTIVE(isNePal(z0)) → c10(ISNEPAL(active(z0)), ACTIVE(z0))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))

K tuples:none
Defined Rule Symbols:

active, __, U11, U12, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, PROPER, TOP

Compound Symbols:

c, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c22, c24, c25, c26, c27

(5) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))

We considered the (Usable) Rules:

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

And the Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(U11(z0)) → c8(U11'(active(z0)), ACTIVE(z0))
ACTIVE(U12(z0)) → c9(U12'(active(z0)), ACTIVE(z0))
ACTIVE(isNePal(z0)) → c10(ISNEPAL(active(z0)), ACTIVE(z0))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ACTIVE(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(PROPER(x₁)) = 0
POL(TOP(x₁)) = [4]x₁
POL(U11(x₁)) = [5]x₁
POL(U11'(x₁)) = 0
POL(U12(x₁)) = [3]x₁
POL(U12'(x₁)) = 0
POL(__(x₁, x₂)) = [4] + [4]x₁ + x₂
POL(__'(x₁, x₂)) = 0
POL(active(x₁)) = x₁
POL(c(x₁, x₂)) = x₁ + x₂
POL(c10(x₁, x₂)) = x₁ + x₂
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁, x₂, x₃)) = x₁ + x₂ + x₃
POL(c22(x₁, x₂)) = x₁ + x₂
POL(c24(x₁, x₂)) = x₁ + x₂
POL(c25(x₁, x₂)) = x₁ + x₂
POL(c26(x₁, x₂)) = x₁ + x₂
POL(c27(x₁, x₂)) = x₁ + x₂
POL(c6(x₁, x₂)) = x₁ + x₂
POL(c7(x₁, x₂)) = x₁ + x₂
POL(c8(x₁, x₂)) = x₁ + x₂
POL(c9(x₁, x₂)) = x₁ + x₂
POL(isNePal(x₁)) = [2]x₁
POL(mark(x₁)) = [2] + x₁
POL(nil) = 0
POL(ok(x₁)) = x₁
POL(proper(x₁)) = x₁
POL(tt) = [1]

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

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

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(U11(z0)) → c8(U11'(active(z0)), ACTIVE(z0))
ACTIVE(U12(z0)) → c9(U12'(active(z0)), ACTIVE(z0))
ACTIVE(isNePal(z0)) → c10(ISNEPAL(active(z0)), ACTIVE(z0))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(U11(z0)) → c8(U11'(active(z0)), ACTIVE(z0))
ACTIVE(U12(z0)) → c9(U12'(active(z0)), ACTIVE(z0))
ACTIVE(isNePal(z0)) → c10(ISNEPAL(active(z0)), ACTIVE(z0))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))

K tuples:

TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, U11, U12, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, PROPER, TOP

Compound Symbols:

c, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c22, c24, c25, c26, c27

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

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

ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))), ACTIVE(U11(tt)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(x0)) → c8

(8) Obligation:

Complexity Dependency Tuples Problem
Rules:

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

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(U12(z0)) → c9(U12'(active(z0)), ACTIVE(z0))
ACTIVE(isNePal(z0)) → c10(ISNEPAL(active(z0)), ACTIVE(z0))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))), ACTIVE(U11(tt)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(x0)) → c8

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(U12(z0)) → c9(U12'(active(z0)), ACTIVE(z0))
ACTIVE(isNePal(z0)) → c10(ISNEPAL(active(z0)), ACTIVE(z0))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))), ACTIVE(U11(tt)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(x0)) → c8

K tuples:

TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, U11, U12, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, PROPER, TOP

Compound Symbols:

c, c6, c7, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c22, c24, c25, c26, c27, c8, c8

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

Removed 1 trailing nodes:

ACTIVE(U11(x0)) → c8

(10) Obligation:

Complexity Dependency Tuples Problem
Rules:

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

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(U12(z0)) → c9(U12'(active(z0)), ACTIVE(z0))
ACTIVE(isNePal(z0)) → c10(ISNEPAL(active(z0)), ACTIVE(z0))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))), ACTIVE(U11(tt)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(U12(z0)) → c9(U12'(active(z0)), ACTIVE(z0))
ACTIVE(isNePal(z0)) → c10(ISNEPAL(active(z0)), ACTIVE(z0))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))), ACTIVE(U11(tt)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))

K tuples:

TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, U11, U12, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, PROPER, TOP

Compound Symbols:

c, c6, c7, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c22, c24, c25, c26, c27, c8

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

Removed 1 trailing tuple parts

(12) Obligation:

Complexity Dependency Tuples Problem
Rules:

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

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(U12(z0)) → c9(U12'(active(z0)), ACTIVE(z0))
ACTIVE(isNePal(z0)) → c10(ISNEPAL(active(z0)), ACTIVE(z0))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(U12(z0)) → c9(U12'(active(z0)), ACTIVE(z0))
ACTIVE(isNePal(z0)) → c10(ISNEPAL(active(z0)), ACTIVE(z0))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))

K tuples:

TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, U11, U12, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, PROPER, TOP

Compound Symbols:

c, c6, c7, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c22, c24, c25, c26, c27, c8, c8

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

Use narrowing to replace ACTIVE(U12(z0)) → c9(U12'(active(z0)), ACTIVE(z0)) by

ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))), ACTIVE(U11(tt)))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U12(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(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
active(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(U11(z0)) → U11(active(z0))
active(U12(z0)) → U12(active(z0))
active(isNePal(z0)) → isNePal(active(z0))
__(mark(z0), z1) → mark(__(z0, z1))
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
U11(mark(z0)) → mark(U11(z0))
U11(ok(z0)) → ok(U11(z0))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNePal(mark(z0)) → mark(isNePal(z0))
isNePal(ok(z0)) → ok(isNePal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(U11(z0)) → U11(proper(z0))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(isNePal(z0)) → c10(ISNEPAL(active(z0)), ACTIVE(z0))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))), ACTIVE(U11(tt)))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U12(x0)) → c9

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(isNePal(z0)) → c10(ISNEPAL(active(z0)), ACTIVE(z0))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))), ACTIVE(U11(tt)))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U12(x0)) → c9

K tuples:

TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, U11, U12, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, PROPER, TOP

Compound Symbols:

c, c6, c7, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c22, c24, c25, c26, c27, c8, c8, c9, c9

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

Removed 1 trailing nodes:

ACTIVE(U12(x0)) → c9

(16) Obligation:

Complexity Dependency Tuples Problem
Rules:

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

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(isNePal(z0)) → c10(ISNEPAL(active(z0)), ACTIVE(z0))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))), ACTIVE(U11(tt)))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(isNePal(z0)) → c10(ISNEPAL(active(z0)), ACTIVE(z0))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))), ACTIVE(U11(tt)))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))

K tuples:

TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, U11, U12, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, PROPER, TOP

Compound Symbols:

c, c6, c7, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c22, c24, c25, c26, c27, c8, c8, c9

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

Removed 3 trailing tuple parts

(18) Obligation:

Complexity Dependency Tuples Problem
Rules:

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

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(isNePal(z0)) → c10(ISNEPAL(active(z0)), ACTIVE(z0))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(isNePal(z0)) → c10(ISNEPAL(active(z0)), ACTIVE(z0))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))

K tuples:

TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, U11, U12, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, PROPER, TOP

Compound Symbols:

c, c6, c7, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c22, c24, c25, c26, c27, c8, c8, c9, c9

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

Use narrowing to replace ACTIVE(isNePal(z0)) → c10(ISNEPAL(active(z0)), ACTIVE(z0)) by

ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))), ACTIVE(U11(tt)))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(x0)) → c10

(20) Obligation:

Complexity Dependency Tuples Problem
Rules:

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

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))), ACTIVE(U11(tt)))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(x0)) → c10

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))), ACTIVE(U11(tt)))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(x0)) → c10

K tuples:

TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, U11, U12, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, PROPER, TOP

Compound Symbols:

c, c6, c7, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c22, c24, c25, c26, c27, c8, c8, c9, c9, c10, c10

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

Removed 1 trailing nodes:

ACTIVE(isNePal(x0)) → c10

(22) Obligation:

Complexity Dependency Tuples Problem
Rules:

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

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))), ACTIVE(U11(tt)))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))), ACTIVE(U11(tt)))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))

K tuples:

TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, U11, U12, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, PROPER, TOP

Compound Symbols:

c, c6, c7, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c22, c24, c25, c26, c27, c8, c8, c9, c9, c10

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

Removed 2 trailing tuple parts

(24) Obligation:

Complexity Dependency Tuples Problem
Rules:

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

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))

K tuples:

TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, U11, U12, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, PROPER, TOP

Compound Symbols:

c, c6, c7, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c22, c24, c25, c26, c27, c8, c8, c9, c9, c10, c10

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

Use narrowing to replace PROPER(__(z0, z1)) → c20(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(__(x0, __(z0, z1))) → c20(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, nil)) → c20(__'(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(__(x0, U11(z0))) → c20(__'(proper(x0), U11(proper(z0))), PROPER(x0), PROPER(U11(z0)))
PROPER(__(x0, tt)) → c20(__'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(__(x0, U12(z0))) → c20(__'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(__(x0, isNePal(z0))) → c20(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(__(z0, z1), x1)) → c20(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(nil, x1)) → c20(__'(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(__(U11(z0), x1)) → c20(__'(U11(proper(z0)), proper(x1)), PROPER(U11(z0)), PROPER(x1))
PROPER(__(tt, x1)) → c20(__'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(__(U12(z0), x1)) → c20(__'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c20(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(x0, x1)) → c20

(26) Obligation:

Complexity Dependency Tuples Problem
Rules:

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

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))
PROPER(__(x0, __(z0, z1))) → c20(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, nil)) → c20(__'(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(__(x0, U11(z0))) → c20(__'(proper(x0), U11(proper(z0))), PROPER(x0), PROPER(U11(z0)))
PROPER(__(x0, tt)) → c20(__'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(__(x0, U12(z0))) → c20(__'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(__(x0, isNePal(z0))) → c20(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(__(z0, z1), x1)) → c20(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(nil, x1)) → c20(__'(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(__(U11(z0), x1)) → c20(__'(U11(proper(z0)), proper(x1)), PROPER(U11(z0)), PROPER(x1))
PROPER(__(tt, x1)) → c20(__'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(__(U12(z0), x1)) → c20(__'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c20(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(x0, x1)) → c20

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))
PROPER(__(x0, __(z0, z1))) → c20(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, nil)) → c20(__'(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(__(x0, U11(z0))) → c20(__'(proper(x0), U11(proper(z0))), PROPER(x0), PROPER(U11(z0)))
PROPER(__(x0, tt)) → c20(__'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(__(x0, U12(z0))) → c20(__'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(__(x0, isNePal(z0))) → c20(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(__(z0, z1), x1)) → c20(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(nil, x1)) → c20(__'(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(__(U11(z0), x1)) → c20(__'(U11(proper(z0)), proper(x1)), PROPER(U11(z0)), PROPER(x1))
PROPER(__(tt, x1)) → c20(__'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(__(U12(z0), x1)) → c20(__'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c20(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(x0, x1)) → c20

K tuples:

TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, U11, U12, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, PROPER, TOP

Compound Symbols:

c, c6, c7, c11, c12, c13, c14, c15, c16, c17, c18, c19, c22, c24, c25, c26, c27, c8, c8, c9, c9, c10, c10, c20, c20

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

Removed 1 trailing nodes:

PROPER(__(x0, x1)) → c20

(28) Obligation:

Complexity Dependency Tuples Problem
Rules:

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

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))
PROPER(__(x0, __(z0, z1))) → c20(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, nil)) → c20(__'(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(__(x0, U11(z0))) → c20(__'(proper(x0), U11(proper(z0))), PROPER(x0), PROPER(U11(z0)))
PROPER(__(x0, tt)) → c20(__'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(__(x0, U12(z0))) → c20(__'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(__(x0, isNePal(z0))) → c20(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(__(z0, z1), x1)) → c20(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(nil, x1)) → c20(__'(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(__(U11(z0), x1)) → c20(__'(U11(proper(z0)), proper(x1)), PROPER(U11(z0)), PROPER(x1))
PROPER(__(tt, x1)) → c20(__'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(__(U12(z0), x1)) → c20(__'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c20(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))
PROPER(__(x0, __(z0, z1))) → c20(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, nil)) → c20(__'(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(__(x0, U11(z0))) → c20(__'(proper(x0), U11(proper(z0))), PROPER(x0), PROPER(U11(z0)))
PROPER(__(x0, tt)) → c20(__'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(__(x0, U12(z0))) → c20(__'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(__(x0, isNePal(z0))) → c20(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(__(z0, z1), x1)) → c20(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(nil, x1)) → c20(__'(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(__(U11(z0), x1)) → c20(__'(U11(proper(z0)), proper(x1)), PROPER(U11(z0)), PROPER(x1))
PROPER(__(tt, x1)) → c20(__'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(__(U12(z0), x1)) → c20(__'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c20(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))

K tuples:

TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, U11, U12, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, PROPER, TOP

Compound Symbols:

c, c6, c7, c11, c12, c13, c14, c15, c16, c17, c18, c19, c22, c24, c25, c26, c27, c8, c8, c9, c9, c10, c10, c20

(29) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 4 trailing tuple parts

(30) Obligation:

Complexity Dependency Tuples Problem
Rules:

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

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))
PROPER(__(x0, __(z0, z1))) → c20(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, U11(z0))) → c20(__'(proper(x0), U11(proper(z0))), PROPER(x0), PROPER(U11(z0)))
PROPER(__(x0, U12(z0))) → c20(__'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(__(x0, isNePal(z0))) → c20(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(__(z0, z1), x1)) → c20(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(U11(z0), x1)) → c20(__'(U11(proper(z0)), proper(x1)), PROPER(U11(z0)), PROPER(x1))
PROPER(__(U12(z0), x1)) → c20(__'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c20(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c20(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c20(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(nil, x1)) → c20(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c20(__'(ok(tt), proper(x1)), PROPER(x1))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))
PROPER(__(x0, __(z0, z1))) → c20(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, U11(z0))) → c20(__'(proper(x0), U11(proper(z0))), PROPER(x0), PROPER(U11(z0)))
PROPER(__(x0, U12(z0))) → c20(__'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(__(x0, isNePal(z0))) → c20(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(__(z0, z1), x1)) → c20(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(U11(z0), x1)) → c20(__'(U11(proper(z0)), proper(x1)), PROPER(U11(z0)), PROPER(x1))
PROPER(__(U12(z0), x1)) → c20(__'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c20(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c20(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c20(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(nil, x1)) → c20(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c20(__'(ok(tt), proper(x1)), PROPER(x1))

K tuples:

TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, U11, U12, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, PROPER, TOP

Compound Symbols:

c, c6, c7, c11, c12, c13, c14, c15, c16, c17, c18, c19, c22, c24, c25, c26, c27, c8, c8, c9, c9, c10, c10, c20, c20

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

Use narrowing to replace PROPER(U11(z0)) → c22(U11'(proper(z0)), PROPER(z0)) by

PROPER(U11(__(z0, z1))) → c22(U11'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U11(nil)) → c22(U11'(ok(nil)), PROPER(nil))
PROPER(U11(U11(z0))) → c22(U11'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U11(tt)) → c22(U11'(ok(tt)), PROPER(tt))
PROPER(U11(U12(z0))) → c22(U11'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U11(isNePal(z0))) → c22(U11'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U11(x0)) → c22

(32) Obligation:

Complexity Dependency Tuples Problem
Rules:

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

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))
PROPER(__(x0, __(z0, z1))) → c20(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, U11(z0))) → c20(__'(proper(x0), U11(proper(z0))), PROPER(x0), PROPER(U11(z0)))
PROPER(__(x0, U12(z0))) → c20(__'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(__(x0, isNePal(z0))) → c20(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(__(z0, z1), x1)) → c20(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(U11(z0), x1)) → c20(__'(U11(proper(z0)), proper(x1)), PROPER(U11(z0)), PROPER(x1))
PROPER(__(U12(z0), x1)) → c20(__'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c20(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c20(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c20(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(nil, x1)) → c20(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c20(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(__(z0, z1))) → c22(U11'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U11(nil)) → c22(U11'(ok(nil)), PROPER(nil))
PROPER(U11(U11(z0))) → c22(U11'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U11(tt)) → c22(U11'(ok(tt)), PROPER(tt))
PROPER(U11(U12(z0))) → c22(U11'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U11(isNePal(z0))) → c22(U11'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U11(x0)) → c22

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))
PROPER(__(x0, __(z0, z1))) → c20(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, U11(z0))) → c20(__'(proper(x0), U11(proper(z0))), PROPER(x0), PROPER(U11(z0)))
PROPER(__(x0, U12(z0))) → c20(__'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(__(x0, isNePal(z0))) → c20(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(__(z0, z1), x1)) → c20(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(U11(z0), x1)) → c20(__'(U11(proper(z0)), proper(x1)), PROPER(U11(z0)), PROPER(x1))
PROPER(__(U12(z0), x1)) → c20(__'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c20(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c20(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c20(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(nil, x1)) → c20(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c20(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(__(z0, z1))) → c22(U11'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U11(nil)) → c22(U11'(ok(nil)), PROPER(nil))
PROPER(U11(U11(z0))) → c22(U11'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U11(tt)) → c22(U11'(ok(tt)), PROPER(tt))
PROPER(U11(U12(z0))) → c22(U11'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U11(isNePal(z0))) → c22(U11'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U11(x0)) → c22

K tuples:

TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, U11, U12, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, PROPER, TOP

Compound Symbols:

c, c6, c7, c11, c12, c13, c14, c15, c16, c17, c18, c19, c24, c25, c26, c27, c8, c8, c9, c9, c10, c10, c20, c20, c22, c22

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

Removed 1 trailing nodes:

PROPER(U11(x0)) → c22

(34) Obligation:

Complexity Dependency Tuples Problem
Rules:

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

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))
PROPER(__(x0, __(z0, z1))) → c20(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, U11(z0))) → c20(__'(proper(x0), U11(proper(z0))), PROPER(x0), PROPER(U11(z0)))
PROPER(__(x0, U12(z0))) → c20(__'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(__(x0, isNePal(z0))) → c20(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(__(z0, z1), x1)) → c20(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(U11(z0), x1)) → c20(__'(U11(proper(z0)), proper(x1)), PROPER(U11(z0)), PROPER(x1))
PROPER(__(U12(z0), x1)) → c20(__'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c20(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c20(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c20(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(nil, x1)) → c20(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c20(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(__(z0, z1))) → c22(U11'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U11(nil)) → c22(U11'(ok(nil)), PROPER(nil))
PROPER(U11(U11(z0))) → c22(U11'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U11(tt)) → c22(U11'(ok(tt)), PROPER(tt))
PROPER(U11(U12(z0))) → c22(U11'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U11(isNePal(z0))) → c22(U11'(isNePal(proper(z0))), PROPER(isNePal(z0)))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))
PROPER(__(x0, __(z0, z1))) → c20(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, U11(z0))) → c20(__'(proper(x0), U11(proper(z0))), PROPER(x0), PROPER(U11(z0)))
PROPER(__(x0, U12(z0))) → c20(__'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(__(x0, isNePal(z0))) → c20(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(__(z0, z1), x1)) → c20(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(U11(z0), x1)) → c20(__'(U11(proper(z0)), proper(x1)), PROPER(U11(z0)), PROPER(x1))
PROPER(__(U12(z0), x1)) → c20(__'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c20(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c20(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c20(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(nil, x1)) → c20(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c20(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(__(z0, z1))) → c22(U11'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U11(nil)) → c22(U11'(ok(nil)), PROPER(nil))
PROPER(U11(U11(z0))) → c22(U11'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U11(tt)) → c22(U11'(ok(tt)), PROPER(tt))
PROPER(U11(U12(z0))) → c22(U11'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U11(isNePal(z0))) → c22(U11'(isNePal(proper(z0))), PROPER(isNePal(z0)))

K tuples:

TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, U11, U12, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, PROPER, TOP

Compound Symbols:

c, c6, c7, c11, c12, c13, c14, c15, c16, c17, c18, c19, c24, c25, c26, c27, c8, c8, c9, c9, c10, c10, c20, c20, c22

(35) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 2 trailing tuple parts

(36) Obligation:

Complexity Dependency Tuples Problem
Rules:

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

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))
PROPER(__(x0, __(z0, z1))) → c20(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, U11(z0))) → c20(__'(proper(x0), U11(proper(z0))), PROPER(x0), PROPER(U11(z0)))
PROPER(__(x0, U12(z0))) → c20(__'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(__(x0, isNePal(z0))) → c20(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(__(z0, z1), x1)) → c20(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(U11(z0), x1)) → c20(__'(U11(proper(z0)), proper(x1)), PROPER(U11(z0)), PROPER(x1))
PROPER(__(U12(z0), x1)) → c20(__'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c20(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c20(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c20(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(nil, x1)) → c20(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c20(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(__(z0, z1))) → c22(U11'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U11(U11(z0))) → c22(U11'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U11(U12(z0))) → c22(U11'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U11(isNePal(z0))) → c22(U11'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U11(nil)) → c22(U11'(ok(nil)))
PROPER(U11(tt)) → c22(U11'(ok(tt)))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))
PROPER(__(x0, __(z0, z1))) → c20(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, U11(z0))) → c20(__'(proper(x0), U11(proper(z0))), PROPER(x0), PROPER(U11(z0)))
PROPER(__(x0, U12(z0))) → c20(__'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(__(x0, isNePal(z0))) → c20(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(__(z0, z1), x1)) → c20(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(U11(z0), x1)) → c20(__'(U11(proper(z0)), proper(x1)), PROPER(U11(z0)), PROPER(x1))
PROPER(__(U12(z0), x1)) → c20(__'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c20(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c20(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c20(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(nil, x1)) → c20(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c20(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(__(z0, z1))) → c22(U11'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U11(U11(z0))) → c22(U11'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U11(U12(z0))) → c22(U11'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U11(isNePal(z0))) → c22(U11'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U11(nil)) → c22(U11'(ok(nil)))
PROPER(U11(tt)) → c22(U11'(ok(tt)))

K tuples:

TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, U11, U12, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, PROPER, TOP

Compound Symbols:

c, c6, c7, c11, c12, c13, c14, c15, c16, c17, c18, c19, c24, c25, c26, c27, c8, c8, c9, c9, c10, c10, c20, c20, c22, c22

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

Use narrowing to replace PROPER(U12(z0)) → c24(U12'(proper(z0)), PROPER(z0)) by

PROPER(U12(__(z0, z1))) → c24(U12'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U12(nil)) → c24(U12'(ok(nil)), PROPER(nil))
PROPER(U12(U11(z0))) → c24(U12'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U12(tt)) → c24(U12'(ok(tt)), PROPER(tt))
PROPER(U12(U12(z0))) → c24(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNePal(z0))) → c24(U12'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U12(x0)) → c24

(38) Obligation:

Complexity Dependency Tuples Problem
Rules:

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

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))
PROPER(__(x0, __(z0, z1))) → c20(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, U11(z0))) → c20(__'(proper(x0), U11(proper(z0))), PROPER(x0), PROPER(U11(z0)))
PROPER(__(x0, U12(z0))) → c20(__'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(__(x0, isNePal(z0))) → c20(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(__(z0, z1), x1)) → c20(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(U11(z0), x1)) → c20(__'(U11(proper(z0)), proper(x1)), PROPER(U11(z0)), PROPER(x1))
PROPER(__(U12(z0), x1)) → c20(__'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c20(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c20(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c20(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(nil, x1)) → c20(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c20(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(__(z0, z1))) → c22(U11'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U11(U11(z0))) → c22(U11'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U11(U12(z0))) → c22(U11'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U11(isNePal(z0))) → c22(U11'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U11(nil)) → c22(U11'(ok(nil)))
PROPER(U11(tt)) → c22(U11'(ok(tt)))
PROPER(U12(__(z0, z1))) → c24(U12'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U12(nil)) → c24(U12'(ok(nil)), PROPER(nil))
PROPER(U12(U11(z0))) → c24(U12'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U12(tt)) → c24(U12'(ok(tt)), PROPER(tt))
PROPER(U12(U12(z0))) → c24(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNePal(z0))) → c24(U12'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U12(x0)) → c24

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))
PROPER(__(x0, __(z0, z1))) → c20(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, U11(z0))) → c20(__'(proper(x0), U11(proper(z0))), PROPER(x0), PROPER(U11(z0)))
PROPER(__(x0, U12(z0))) → c20(__'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(__(x0, isNePal(z0))) → c20(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(__(z0, z1), x1)) → c20(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(U11(z0), x1)) → c20(__'(U11(proper(z0)), proper(x1)), PROPER(U11(z0)), PROPER(x1))
PROPER(__(U12(z0), x1)) → c20(__'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c20(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c20(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c20(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(nil, x1)) → c20(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c20(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(__(z0, z1))) → c22(U11'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U11(U11(z0))) → c22(U11'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U11(U12(z0))) → c22(U11'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U11(isNePal(z0))) → c22(U11'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U11(nil)) → c22(U11'(ok(nil)))
PROPER(U11(tt)) → c22(U11'(ok(tt)))
PROPER(U12(__(z0, z1))) → c24(U12'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U12(nil)) → c24(U12'(ok(nil)), PROPER(nil))
PROPER(U12(U11(z0))) → c24(U12'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U12(tt)) → c24(U12'(ok(tt)), PROPER(tt))
PROPER(U12(U12(z0))) → c24(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNePal(z0))) → c24(U12'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U12(x0)) → c24

K tuples:

TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, U11, U12, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, PROPER, TOP

Compound Symbols:

c, c6, c7, c11, c12, c13, c14, c15, c16, c17, c18, c19, c25, c26, c27, c8, c8, c9, c9, c10, c10, c20, c20, c22, c22, c24, c24

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

Removed 1 trailing nodes:

PROPER(U12(x0)) → c24

(40) Obligation:

Complexity Dependency Tuples Problem
Rules:

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

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))
PROPER(__(x0, __(z0, z1))) → c20(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, U11(z0))) → c20(__'(proper(x0), U11(proper(z0))), PROPER(x0), PROPER(U11(z0)))
PROPER(__(x0, U12(z0))) → c20(__'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(__(x0, isNePal(z0))) → c20(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(__(z0, z1), x1)) → c20(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(U11(z0), x1)) → c20(__'(U11(proper(z0)), proper(x1)), PROPER(U11(z0)), PROPER(x1))
PROPER(__(U12(z0), x1)) → c20(__'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c20(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c20(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c20(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(nil, x1)) → c20(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c20(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(__(z0, z1))) → c22(U11'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U11(U11(z0))) → c22(U11'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U11(U12(z0))) → c22(U11'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U11(isNePal(z0))) → c22(U11'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U11(nil)) → c22(U11'(ok(nil)))
PROPER(U11(tt)) → c22(U11'(ok(tt)))
PROPER(U12(__(z0, z1))) → c24(U12'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U12(nil)) → c24(U12'(ok(nil)), PROPER(nil))
PROPER(U12(U11(z0))) → c24(U12'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U12(tt)) → c24(U12'(ok(tt)), PROPER(tt))
PROPER(U12(U12(z0))) → c24(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNePal(z0))) → c24(U12'(isNePal(proper(z0))), PROPER(isNePal(z0)))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))
PROPER(__(x0, __(z0, z1))) → c20(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, U11(z0))) → c20(__'(proper(x0), U11(proper(z0))), PROPER(x0), PROPER(U11(z0)))
PROPER(__(x0, U12(z0))) → c20(__'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(__(x0, isNePal(z0))) → c20(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(__(z0, z1), x1)) → c20(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(U11(z0), x1)) → c20(__'(U11(proper(z0)), proper(x1)), PROPER(U11(z0)), PROPER(x1))
PROPER(__(U12(z0), x1)) → c20(__'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c20(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c20(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c20(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(nil, x1)) → c20(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c20(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(__(z0, z1))) → c22(U11'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U11(U11(z0))) → c22(U11'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U11(U12(z0))) → c22(U11'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U11(isNePal(z0))) → c22(U11'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U11(nil)) → c22(U11'(ok(nil)))
PROPER(U11(tt)) → c22(U11'(ok(tt)))
PROPER(U12(__(z0, z1))) → c24(U12'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U12(nil)) → c24(U12'(ok(nil)), PROPER(nil))
PROPER(U12(U11(z0))) → c24(U12'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U12(tt)) → c24(U12'(ok(tt)), PROPER(tt))
PROPER(U12(U12(z0))) → c24(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNePal(z0))) → c24(U12'(isNePal(proper(z0))), PROPER(isNePal(z0)))

K tuples:

TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, U11, U12, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, PROPER, TOP

Compound Symbols:

c, c6, c7, c11, c12, c13, c14, c15, c16, c17, c18, c19, c25, c26, c27, c8, c8, c9, c9, c10, c10, c20, c20, c22, c22, c24

(41) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 2 trailing tuple parts

(42) Obligation:

Complexity Dependency Tuples Problem
Rules:

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

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))
PROPER(__(x0, __(z0, z1))) → c20(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, U11(z0))) → c20(__'(proper(x0), U11(proper(z0))), PROPER(x0), PROPER(U11(z0)))
PROPER(__(x0, U12(z0))) → c20(__'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(__(x0, isNePal(z0))) → c20(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(__(z0, z1), x1)) → c20(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(U11(z0), x1)) → c20(__'(U11(proper(z0)), proper(x1)), PROPER(U11(z0)), PROPER(x1))
PROPER(__(U12(z0), x1)) → c20(__'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c20(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c20(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c20(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(nil, x1)) → c20(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c20(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(__(z0, z1))) → c22(U11'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U11(U11(z0))) → c22(U11'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U11(U12(z0))) → c22(U11'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U11(isNePal(z0))) → c22(U11'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U11(nil)) → c22(U11'(ok(nil)))
PROPER(U11(tt)) → c22(U11'(ok(tt)))
PROPER(U12(__(z0, z1))) → c24(U12'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U12(U11(z0))) → c24(U12'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U12(U12(z0))) → c24(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNePal(z0))) → c24(U12'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U12(nil)) → c24(U12'(ok(nil)))
PROPER(U12(tt)) → c24(U12'(ok(tt)))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))
PROPER(__(x0, __(z0, z1))) → c20(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, U11(z0))) → c20(__'(proper(x0), U11(proper(z0))), PROPER(x0), PROPER(U11(z0)))
PROPER(__(x0, U12(z0))) → c20(__'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(__(x0, isNePal(z0))) → c20(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(__(z0, z1), x1)) → c20(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(U11(z0), x1)) → c20(__'(U11(proper(z0)), proper(x1)), PROPER(U11(z0)), PROPER(x1))
PROPER(__(U12(z0), x1)) → c20(__'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c20(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c20(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c20(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(nil, x1)) → c20(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c20(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(__(z0, z1))) → c22(U11'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U11(U11(z0))) → c22(U11'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U11(U12(z0))) → c22(U11'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U11(isNePal(z0))) → c22(U11'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U11(nil)) → c22(U11'(ok(nil)))
PROPER(U11(tt)) → c22(U11'(ok(tt)))
PROPER(U12(__(z0, z1))) → c24(U12'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U12(U11(z0))) → c24(U12'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U12(U12(z0))) → c24(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNePal(z0))) → c24(U12'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U12(nil)) → c24(U12'(ok(nil)))
PROPER(U12(tt)) → c24(U12'(ok(tt)))

K tuples:

TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, U11, U12, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, PROPER, TOP

Compound Symbols:

c, c6, c7, c11, c12, c13, c14, c15, c16, c17, c18, c19, c25, c26, c27, c8, c8, c9, c9, c10, c10, c20, c20, c22, c22, c24, c24

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

Use narrowing to replace PROPER(isNePal(z0)) → c25(ISNEPAL(proper(z0)), PROPER(z0)) by

PROPER(isNePal(__(z0, z1))) → c25(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNePal(nil)) → c25(ISNEPAL(ok(nil)), PROPER(nil))
PROPER(isNePal(U11(z0))) → c25(ISNEPAL(U11(proper(z0))), PROPER(U11(z0)))
PROPER(isNePal(tt)) → c25(ISNEPAL(ok(tt)), PROPER(tt))
PROPER(isNePal(U12(z0))) → c25(ISNEPAL(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNePal(isNePal(z0))) → c25(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNePal(x0)) → c25

(44) Obligation:

Complexity Dependency Tuples Problem
Rules:

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

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))
PROPER(__(x0, __(z0, z1))) → c20(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, U11(z0))) → c20(__'(proper(x0), U11(proper(z0))), PROPER(x0), PROPER(U11(z0)))
PROPER(__(x0, U12(z0))) → c20(__'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(__(x0, isNePal(z0))) → c20(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(__(z0, z1), x1)) → c20(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(U11(z0), x1)) → c20(__'(U11(proper(z0)), proper(x1)), PROPER(U11(z0)), PROPER(x1))
PROPER(__(U12(z0), x1)) → c20(__'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c20(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c20(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c20(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(nil, x1)) → c20(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c20(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(__(z0, z1))) → c22(U11'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U11(U11(z0))) → c22(U11'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U11(U12(z0))) → c22(U11'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U11(isNePal(z0))) → c22(U11'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U11(nil)) → c22(U11'(ok(nil)))
PROPER(U11(tt)) → c22(U11'(ok(tt)))
PROPER(U12(__(z0, z1))) → c24(U12'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U12(U11(z0))) → c24(U12'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U12(U12(z0))) → c24(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNePal(z0))) → c24(U12'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U12(nil)) → c24(U12'(ok(nil)))
PROPER(U12(tt)) → c24(U12'(ok(tt)))
PROPER(isNePal(__(z0, z1))) → c25(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNePal(nil)) → c25(ISNEPAL(ok(nil)), PROPER(nil))
PROPER(isNePal(U11(z0))) → c25(ISNEPAL(U11(proper(z0))), PROPER(U11(z0)))
PROPER(isNePal(tt)) → c25(ISNEPAL(ok(tt)), PROPER(tt))
PROPER(isNePal(U12(z0))) → c25(ISNEPAL(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNePal(isNePal(z0))) → c25(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNePal(x0)) → c25

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))
PROPER(__(x0, __(z0, z1))) → c20(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, U11(z0))) → c20(__'(proper(x0), U11(proper(z0))), PROPER(x0), PROPER(U11(z0)))
PROPER(__(x0, U12(z0))) → c20(__'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(__(x0, isNePal(z0))) → c20(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(__(z0, z1), x1)) → c20(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(U11(z0), x1)) → c20(__'(U11(proper(z0)), proper(x1)), PROPER(U11(z0)), PROPER(x1))
PROPER(__(U12(z0), x1)) → c20(__'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c20(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c20(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c20(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(nil, x1)) → c20(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c20(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(__(z0, z1))) → c22(U11'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U11(U11(z0))) → c22(U11'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U11(U12(z0))) → c22(U11'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U11(isNePal(z0))) → c22(U11'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U11(nil)) → c22(U11'(ok(nil)))
PROPER(U11(tt)) → c22(U11'(ok(tt)))
PROPER(U12(__(z0, z1))) → c24(U12'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U12(U11(z0))) → c24(U12'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U12(U12(z0))) → c24(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNePal(z0))) → c24(U12'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U12(nil)) → c24(U12'(ok(nil)))
PROPER(U12(tt)) → c24(U12'(ok(tt)))
PROPER(isNePal(__(z0, z1))) → c25(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNePal(nil)) → c25(ISNEPAL(ok(nil)), PROPER(nil))
PROPER(isNePal(U11(z0))) → c25(ISNEPAL(U11(proper(z0))), PROPER(U11(z0)))
PROPER(isNePal(tt)) → c25(ISNEPAL(ok(tt)), PROPER(tt))
PROPER(isNePal(U12(z0))) → c25(ISNEPAL(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNePal(isNePal(z0))) → c25(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNePal(x0)) → c25

K tuples:

TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, U11, U12, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, TOP, PROPER

Compound Symbols:

c, c6, c7, c11, c12, c13, c14, c15, c16, c17, c18, c19, c26, c27, c8, c8, c9, c9, c10, c10, c20, c20, c22, c22, c24, c24, c25, c25

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

Removed 1 trailing nodes:

PROPER(isNePal(x0)) → c25

(46) Obligation:

Complexity Dependency Tuples Problem
Rules:

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

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))
PROPER(__(x0, __(z0, z1))) → c20(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, U11(z0))) → c20(__'(proper(x0), U11(proper(z0))), PROPER(x0), PROPER(U11(z0)))
PROPER(__(x0, U12(z0))) → c20(__'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(__(x0, isNePal(z0))) → c20(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(__(z0, z1), x1)) → c20(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(U11(z0), x1)) → c20(__'(U11(proper(z0)), proper(x1)), PROPER(U11(z0)), PROPER(x1))
PROPER(__(U12(z0), x1)) → c20(__'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c20(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c20(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c20(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(nil, x1)) → c20(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c20(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(__(z0, z1))) → c22(U11'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U11(U11(z0))) → c22(U11'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U11(U12(z0))) → c22(U11'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U11(isNePal(z0))) → c22(U11'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U11(nil)) → c22(U11'(ok(nil)))
PROPER(U11(tt)) → c22(U11'(ok(tt)))
PROPER(U12(__(z0, z1))) → c24(U12'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U12(U11(z0))) → c24(U12'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U12(U12(z0))) → c24(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNePal(z0))) → c24(U12'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U12(nil)) → c24(U12'(ok(nil)))
PROPER(U12(tt)) → c24(U12'(ok(tt)))
PROPER(isNePal(__(z0, z1))) → c25(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNePal(nil)) → c25(ISNEPAL(ok(nil)), PROPER(nil))
PROPER(isNePal(U11(z0))) → c25(ISNEPAL(U11(proper(z0))), PROPER(U11(z0)))
PROPER(isNePal(tt)) → c25(ISNEPAL(ok(tt)), PROPER(tt))
PROPER(isNePal(U12(z0))) → c25(ISNEPAL(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNePal(isNePal(z0))) → c25(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))
PROPER(__(x0, __(z0, z1))) → c20(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, U11(z0))) → c20(__'(proper(x0), U11(proper(z0))), PROPER(x0), PROPER(U11(z0)))
PROPER(__(x0, U12(z0))) → c20(__'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(__(x0, isNePal(z0))) → c20(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(__(z0, z1), x1)) → c20(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(U11(z0), x1)) → c20(__'(U11(proper(z0)), proper(x1)), PROPER(U11(z0)), PROPER(x1))
PROPER(__(U12(z0), x1)) → c20(__'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c20(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c20(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c20(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(nil, x1)) → c20(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c20(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(__(z0, z1))) → c22(U11'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U11(U11(z0))) → c22(U11'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U11(U12(z0))) → c22(U11'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U11(isNePal(z0))) → c22(U11'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U11(nil)) → c22(U11'(ok(nil)))
PROPER(U11(tt)) → c22(U11'(ok(tt)))
PROPER(U12(__(z0, z1))) → c24(U12'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U12(U11(z0))) → c24(U12'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U12(U12(z0))) → c24(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNePal(z0))) → c24(U12'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U12(nil)) → c24(U12'(ok(nil)))
PROPER(U12(tt)) → c24(U12'(ok(tt)))
PROPER(isNePal(__(z0, z1))) → c25(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNePal(nil)) → c25(ISNEPAL(ok(nil)), PROPER(nil))
PROPER(isNePal(U11(z0))) → c25(ISNEPAL(U11(proper(z0))), PROPER(U11(z0)))
PROPER(isNePal(tt)) → c25(ISNEPAL(ok(tt)), PROPER(tt))
PROPER(isNePal(U12(z0))) → c25(ISNEPAL(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNePal(isNePal(z0))) → c25(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))

K tuples:

TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, U11, U12, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, TOP, PROPER

Compound Symbols:

c, c6, c7, c11, c12, c13, c14, c15, c16, c17, c18, c19, c26, c27, c8, c8, c9, c9, c10, c10, c20, c20, c22, c22, c24, c24, c25

(47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 2 trailing tuple parts

(48) Obligation:

Complexity Dependency Tuples Problem
Rules:

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

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))
PROPER(__(x0, __(z0, z1))) → c20(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, U11(z0))) → c20(__'(proper(x0), U11(proper(z0))), PROPER(x0), PROPER(U11(z0)))
PROPER(__(x0, U12(z0))) → c20(__'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(__(x0, isNePal(z0))) → c20(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(__(z0, z1), x1)) → c20(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(U11(z0), x1)) → c20(__'(U11(proper(z0)), proper(x1)), PROPER(U11(z0)), PROPER(x1))
PROPER(__(U12(z0), x1)) → c20(__'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c20(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c20(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c20(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(nil, x1)) → c20(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c20(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(__(z0, z1))) → c22(U11'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U11(U11(z0))) → c22(U11'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U11(U12(z0))) → c22(U11'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U11(isNePal(z0))) → c22(U11'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U11(nil)) → c22(U11'(ok(nil)))
PROPER(U11(tt)) → c22(U11'(ok(tt)))
PROPER(U12(__(z0, z1))) → c24(U12'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U12(U11(z0))) → c24(U12'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U12(U12(z0))) → c24(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNePal(z0))) → c24(U12'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U12(nil)) → c24(U12'(ok(nil)))
PROPER(U12(tt)) → c24(U12'(ok(tt)))
PROPER(isNePal(__(z0, z1))) → c25(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNePal(U11(z0))) → c25(ISNEPAL(U11(proper(z0))), PROPER(U11(z0)))
PROPER(isNePal(U12(z0))) → c25(ISNEPAL(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNePal(isNePal(z0))) → c25(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNePal(nil)) → c25(ISNEPAL(ok(nil)))
PROPER(isNePal(tt)) → c25(ISNEPAL(ok(tt)))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, z1)) → c6(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c7(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c11(__'(z0, z1))
__'(z0, mark(z1)) → c12(__'(z0, z1))
__'(ok(z0), ok(z1)) → c13(__'(z0, z1))
U11'(mark(z0)) → c14(U11'(z0))
U11'(ok(z0)) → c15(U11'(z0))
U12'(mark(z0)) → c16(U12'(z0))
U12'(ok(z0)) → c17(U12'(z0))
ISNEPAL(mark(z0)) → c18(ISNEPAL(z0))
ISNEPAL(ok(z0)) → c19(ISNEPAL(z0))
TOP(ok(z0)) → c27(TOP(active(z0)), ACTIVE(z0))
ACTIVE(U11(__(__(z0, z1), z2))) → c8(U11'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U11(__(z0, nil))) → c8(U11'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U11(__(nil, z0))) → c8(U11'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U11(isNePal(__(z0, __(z1, z0))))) → c8(U11'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U11(__(z0, z1))) → c8(U11'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U11(U11(z0))) → c8(U11'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U11(U12(z0))) → c8(U11'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U11(isNePal(z0))) → c8(U11'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U11(tt))) → c8(U11'(mark(U12(tt))))
ACTIVE(U12(__(__(z0, z1), z2))) → c9(U12'(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(U12(__(z0, nil))) → c9(U12'(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(U12(__(nil, z0))) → c9(U12'(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(U12(isNePal(__(z0, __(z1, z0))))) → c9(U12'(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(U12(__(z0, z1))) → c9(U12'(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(U12(U11(z0))) → c9(U12'(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(U12(U12(z0))) → c9(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(isNePal(z0))) → c9(U12'(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(U11(U12(tt))) → c8(U11'(mark(tt)))
ACTIVE(U12(U11(tt))) → c9(U12'(mark(U12(tt))))
ACTIVE(U12(U12(tt))) → c9(U12'(mark(tt)))
ACTIVE(isNePal(__(__(z0, z1), z2))) → c10(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(isNePal(__(z0, nil))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil)))
ACTIVE(isNePal(__(nil, z0))) → c10(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0)))
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c10(ISNEPAL(mark(U11(tt))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(__(z0, z1))) → c10(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1)))
ACTIVE(isNePal(U11(z0))) → c10(ISNEPAL(U11(active(z0))), ACTIVE(U11(z0)))
ACTIVE(isNePal(U12(z0))) → c10(ISNEPAL(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(isNePal(isNePal(z0))) → c10(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
ACTIVE(isNePal(U11(tt))) → c10(ISNEPAL(mark(U12(tt))))
ACTIVE(isNePal(U12(tt))) → c10(ISNEPAL(mark(tt)))
PROPER(__(x0, __(z0, z1))) → c20(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, U11(z0))) → c20(__'(proper(x0), U11(proper(z0))), PROPER(x0), PROPER(U11(z0)))
PROPER(__(x0, U12(z0))) → c20(__'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(__(x0, isNePal(z0))) → c20(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(__(z0, z1), x1)) → c20(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(U11(z0), x1)) → c20(__'(U11(proper(z0)), proper(x1)), PROPER(U11(z0)), PROPER(x1))
PROPER(__(U12(z0), x1)) → c20(__'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c20(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c20(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c20(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(nil, x1)) → c20(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c20(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(__(z0, z1))) → c22(U11'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U11(U11(z0))) → c22(U11'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U11(U12(z0))) → c22(U11'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U11(isNePal(z0))) → c22(U11'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U11(nil)) → c22(U11'(ok(nil)))
PROPER(U11(tt)) → c22(U11'(ok(tt)))
PROPER(U12(__(z0, z1))) → c24(U12'(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(U12(U11(z0))) → c24(U12'(U11(proper(z0))), PROPER(U11(z0)))
PROPER(U12(U12(z0))) → c24(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNePal(z0))) → c24(U12'(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(U12(nil)) → c24(U12'(ok(nil)))
PROPER(U12(tt)) → c24(U12'(ok(tt)))
PROPER(isNePal(__(z0, z1))) → c25(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNePal(U11(z0))) → c25(ISNEPAL(U11(proper(z0))), PROPER(U11(z0)))
PROPER(isNePal(U12(z0))) → c25(ISNEPAL(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNePal(isNePal(z0))) → c25(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNePal(nil)) → c25(ISNEPAL(ok(nil)))
PROPER(isNePal(tt)) → c25(ISNEPAL(ok(tt)))

K tuples:

TOP(mark(z0)) → c26(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, U11, U12, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', U11', U12', ISNEPAL, TOP, PROPER

Compound Symbols:

c, c6, c7, c11, c12, c13, c14, c15, c16, c17, c18, c19, c26, c27, c8, c8, c9, c9, c10, c10, c20, c20, c22, c22, c24, c24, c25, c25

(49) 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 2.

The compatible tree automaton used to show the Match(-raise)-Boundedness (for constructor-based start-terms) is represented by:
final states : [7, 2, 3, 4, 5, 6, 1, 20, 21, 22, 23, 26, 27, 30, 38, 39, 40, 41, 42, 43]
transitions:
mark0(0) → 0
ok0(0) → 0
top0(0) → 7
__1(0, 0) → 8
mark1(8) → 2
__1(0, 0) → 2
U111(0) → 9
mark1(9) → 3
U111(0) → 3
U121(0) → 10
mark1(10) → 4
U121(0) → 4
isNePal1(0) → 11
mark1(11) → 5
isNePal1(0) → 5
ok1(12) → 6
ok1(13) → 6
__1(0, 0) → 14
ok1(14) → 2
U111(0) → 15
ok1(15) → 3
U121(0) → 16
ok1(16) → 4
isNePal1(0) → 17
ok1(17) → 5
proper1(0) → 18
top1(18) → 7
proper1(0) → 6
active1(0) → 19
top1(19) → 7
active1(0) → 1
__1(0, 0) → 20
U111(0) → 21
U121(0) → 22
isNePal1(0) → 23
proper1(0) → 26
active1(0) → 27
mark0(24) → 0
mark0(25) → 0
ok0(24) → 0
ok0(25) → 0
top0(24) → 7
top0(25) → 7
mark1(20) → 2
mark1(21) → 3
mark1(22) → 4
mark1(23) → 5
__1(24, 0) → 20
__1(0, 24) → 20
__1(25, 0) → 20
__1(0, 25) → 20
__1(24, 24) → 20
__1(24, 25) → 20
__1(25, 24) → 20
__1(25, 25) → 20
U111(24) → 21
U111(25) → 21
U121(24) → 22
U121(25) → 22
isNePal1(24) → 23
isNePal1(25) → 23
ok1(20) → 2
ok1(21) → 3
ok1(22) → 4
ok1(23) → 5
ok1(24) → 6
ok1(25) → 6
top1(26) → 7
top1(27) → 7
proper1(24) → 26
proper1(25) → 26
active1(24) → 27
active1(25) → 27
ok1(24) → 0
ok1(25) → 0
mark1(8) → 20
__1(24, 0) → 8
__1(25, 0) → 8
__1(0, 24) → 8
__1(24, 24) → 8
__1(25, 24) → 8
__1(0, 25) → 8
__1(24, 25) → 8
__1(25, 25) → 8
mark1(9) → 21
U111(24) → 9
U111(25) → 9
mark1(10) → 22
U121(24) → 10
U121(25) → 10
mark1(11) → 23
isNePal1(24) → 11
isNePal1(25) → 11
nil2() → 28
ok2(28) → 26
nil2() → 12
nil2() → 0
nil2() → 24
tt2() → 29
ok2(29) → 26
tt2() → 13
tt2() → 0
tt2() → 25
ok1(14) → 20
__1(0, 24) → 14
__1(0, 25) → 14
__1(24, 0) → 14
__1(24, 24) → 14
__1(24, 25) → 14
__1(25, 0) → 14
__1(25, 24) → 14
__1(25, 25) → 14
ok1(15) → 21
U111(24) → 15
U111(25) → 15
ok1(16) → 22
U121(24) → 16
U121(25) → 16
ok1(17) → 23
isNePal1(24) → 17
isNePal1(25) → 17
ok1(24) → 30
ok1(25) → 30
nil2() → 31
tt2() → 32
mark0(30) → 0
mark0(31) → 0
mark0(32) → 0
ok0(30) → 0
ok0(31) → 0
ok0(32) → 0
top0(30) → 7
top0(31) → 7
top0(32) → 7
mark1(20) → 20
mark1(21) → 21
mark1(22) → 22
mark1(23) → 23
__1(30, 0) → 20
__1(30, 24) → 20
__1(30, 25) → 20
__1(0, 30) → 20
__1(24, 30) → 20
__1(25, 30) → 20
__1(31, 0) → 20
__1(31, 24) → 20
__1(31, 25) → 20
__1(0, 31) → 20
__1(24, 31) → 20
__1(25, 31) → 20
__1(32, 0) → 20
__1(32, 24) → 20
__1(32, 25) → 20
__1(0, 32) → 20
__1(24, 32) → 20
__1(25, 32) → 20
__1(30, 30) → 20
__1(30, 31) → 20
__1(30, 32) → 20
__1(31, 30) → 20
__1(32, 30) → 20
U111(30) → 21
U121(30) → 22
isNePal1(30) → 23
ok1(20) → 20
ok1(21) → 21
ok1(22) → 22
ok1(23) → 23
ok1(31) → 30
ok1(32) → 30
proper1(30) → 26
proper1(31) → 26
proper1(32) → 26
active1(30) → 27
ok2(31) → 26
ok2(32) → 26
ok1(31) → 0
ok2(31) → 0
ok1(32) → 0
ok2(32) → 0
ok2(31) → 30
ok2(32) → 30
__2(31, 31) → 33
ok2(33) → 20
__2(31, 31) → 20
__2(31, 32) → 33
__2(31, 32) → 20
__2(32, 31) → 33
__2(32, 31) → 20
__2(32, 32) → 33
__2(32, 32) → 20
U112(31) → 34
ok2(34) → 21
U112(31) → 21
U112(32) → 34
U112(32) → 21
U122(31) → 35
ok2(35) → 22
U122(31) → 22
U122(32) → 35
U122(32) → 22
isNePal2(31) → 36
ok2(36) → 23
isNePal2(31) → 23
isNePal2(32) → 36
isNePal2(32) → 23
active2(31) → 37
top2(37) → 7
active2(31) → 27
active2(32) → 37
active2(32) → 27
ok2(31) → 38
ok2(32) → 38
__2(31, 31) → 39
__2(31, 32) → 39
__2(32, 31) → 39
__2(32, 32) → 39
U112(31) → 40
U112(32) → 40
U122(31) → 41
U122(32) → 41
isNePal2(31) → 42
isNePal2(32) → 42
active2(31) → 43
active2(32) → 43
mark0(38) → 0
ok0(38) → 0
top0(38) → 7
mark1(39) → 20
mark1(40) → 21
mark1(41) → 22
mark1(42) → 23
__1(31, 31) → 20
__1(31, 32) → 20
__1(32, 31) → 20
__1(32, 32) → 20
__1(38, 0) → 20
__1(38, 24) → 20
__1(38, 25) → 20
__1(38, 30) → 20
__1(38, 31) → 20
__1(38, 32) → 20
__1(0, 38) → 20
__1(24, 38) → 20
__1(25, 38) → 20
__1(30, 38) → 20
__1(31, 38) → 20
__1(32, 38) → 20
__1(38, 38) → 20
U111(31) → 21
U111(32) → 21
U111(38) → 21
U121(31) → 22
U121(32) → 22
U121(38) → 22
isNePal1(31) → 23
isNePal1(32) → 23
isNePal1(38) → 23
ok1(39) → 20
ok1(40) → 21
ok1(41) → 22
ok1(42) → 23
top1(38) → 7
top1(43) → 7
proper1(38) → 26
active1(31) → 27
active1(32) → 27
active1(38) → 27
ok2(39) → 20
ok2(40) → 21
ok2(41) → 22
ok2(42) → 23
top2(43) → 7

(0) Obligation:

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

(2) Obligation:

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

(4) Obligation:

(5) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

(6) Obligation:

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

(8) Obligation:

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

(10) Obligation:

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

(12) Obligation:

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

(14) Obligation:

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

(16) Obligation:

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

(18) Obligation:

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

(20) Obligation:

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

(22) Obligation:

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

(24) Obligation:

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

(26) Obligation:

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

(28) Obligation:

(29) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

(30) Obligation:

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

(32) Obligation:

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

(34) Obligation:

(35) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

(36) Obligation:

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

(38) Obligation:

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

(40) Obligation:

(41) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

(42) Obligation:

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

(44) Obligation:

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

(46) Obligation:

(47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

(48) Obligation:

(49) CpxTrsMatchBoundsTAProof (EQUIVALENT transformation)

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