YES(O(1), O(n^3)) 117.51/44.14 YES(O(1), O(n^3)) 117.84/44.20 117.84/44.20 117.84/44.20 117.84/44.20 117.84/44.20 117.84/44.20 Runtime Complexity (innermost) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml.xml 117.84/44.20 117.84/44.20 117.84/44.20
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117.84/44.20
117.84/44.20
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(O(1), O(n^3)).

0 CpxTRS
117.84/44.20 
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))
117.84/44.20 
↳2 CdtProblem
117.84/44.20 
↳3 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
117.84/44.20 
↳4 CdtProblem
117.84/44.20 
↳5 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
117.84/44.20 
↳6 CdtProblem
117.84/44.20 
↳7 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
117.84/44.20 
↳8 CdtProblem
117.84/44.20 
↳9 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
117.84/44.20 
↳10 CdtProblem
117.84/44.20 
↳11 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
117.84/44.20 
↳12 CdtProblem
117.84/44.20 
↳13 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
117.84/44.20 
↳14 CdtProblem
117.84/44.20 
↳15 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
117.84/44.20 
↳16 CdtProblem
117.84/44.20 
↳17 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
117.84/44.20 
↳18 CdtProblem
117.84/44.20 
↳19 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
117.84/44.20 
↳20 CdtProblem
117.84/44.20 
↳21 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
117.84/44.20 
↳22 CdtProblem
117.84/44.20 
↳23 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
117.84/44.20 
↳24 CdtProblem
117.84/44.20 
↳25 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
117.84/44.20 
↳26 CdtProblem
117.84/44.20 
↳27 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
117.84/44.20 
↳28 CdtProblem
117.84/44.20 
↳29 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
117.84/44.20 
↳30 CdtProblem
117.84/44.20 
↳31 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
117.84/44.20 
↳32 CdtProblem
117.84/44.20 
↳33 CdtUnreachableProof (⇔)
117.84/44.20 
↳34 CdtProblem
117.84/44.20 
↳35 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
117.84/44.20 
↳36 CdtProblem
117.84/44.20 
↳37 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
117.84/44.20 
↳38 CdtProblem
117.84/44.20 
↳39 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^3))))
117.84/44.20 
↳40 CdtProblem
117.84/44.20 
↳41 SIsEmptyProof (BOTH BOUNDS(ID, ID))
117.84/44.20 
↳42 BOUNDS(O(1), O(1))
117.84/44.20
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117.84/44.20

(0) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z))) 117.84/44.20
active(__(X, nil)) → mark(X) 117.84/44.20
active(__(nil, X)) → mark(X) 117.84/44.20
active(and(tt, X)) → mark(X) 117.84/44.20
active(isNePal(__(I, __(P, I)))) → mark(tt) 117.84/44.20
active(__(X1, X2)) → __(active(X1), X2) 117.84/44.20
active(__(X1, X2)) → __(X1, active(X2)) 117.84/44.20
active(and(X1, X2)) → and(active(X1), X2) 117.84/44.20
active(isNePal(X)) → isNePal(active(X)) 117.84/44.20
__(mark(X1), X2) → mark(__(X1, X2)) 117.84/44.20
__(X1, mark(X2)) → mark(__(X1, X2)) 117.84/44.20
and(mark(X1), X2) → mark(and(X1, X2)) 117.84/44.20
isNePal(mark(X)) → mark(isNePal(X)) 117.84/44.20
proper(__(X1, X2)) → __(proper(X1), proper(X2)) 117.84/44.20
proper(nil) → ok(nil) 117.84/44.20
proper(and(X1, X2)) → and(proper(X1), proper(X2)) 117.84/44.20
proper(tt) → ok(tt) 117.84/44.20
proper(isNePal(X)) → isNePal(proper(X)) 117.84/44.20
__(ok(X1), ok(X2)) → ok(__(X1, X2)) 117.84/44.20
and(ok(X1), ok(X2)) → ok(and(X1, X2)) 117.84/44.20
isNePal(ok(X)) → ok(isNePal(X)) 117.84/44.20
top(mark(X)) → top(proper(X)) 117.84/44.20
top(ok(X)) → top(active(X))

Rewrite Strategy: INNERMOST
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117.84/44.20

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

Converted CpxTRS to CDT
117.84/44.20
117.84/44.20

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2))) 117.84/44.20
active(__(z0, nil)) → mark(z0) 117.84/44.20
active(__(nil, z0)) → mark(z0) 117.84/44.20
active(and(tt, z0)) → mark(z0) 117.84/44.20
active(isNePal(__(z0, __(z1, z0)))) → mark(tt) 117.84/44.20
active(__(z0, z1)) → __(active(z0), z1) 117.84/44.20
active(__(z0, z1)) → __(z0, active(z1)) 117.84/44.20
active(and(z0, z1)) → and(active(z0), z1) 117.84/44.20
active(isNePal(z0)) → isNePal(active(z0)) 117.84/44.20
__(mark(z0), z1) → mark(__(z0, z1)) 117.84/44.20
__(z0, mark(z1)) → mark(__(z0, z1)) 117.84/44.20
__(ok(z0), ok(z1)) → ok(__(z0, z1)) 117.84/44.20
and(mark(z0), z1) → mark(and(z0, z1)) 117.84/44.20
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 117.84/44.20
isNePal(mark(z0)) → mark(isNePal(z0)) 117.84/44.20
isNePal(ok(z0)) → ok(isNePal(z0)) 117.84/44.20
proper(__(z0, z1)) → __(proper(z0), proper(z1)) 117.84/44.20
proper(nil) → ok(nil) 117.84/44.20
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 117.84/44.20
proper(tt) → ok(tt) 117.84/44.20
proper(isNePal(z0)) → isNePal(proper(z0)) 117.84/44.20
top(mark(z0)) → top(proper(z0)) 117.84/44.20
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2)) 117.84/44.20
ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 117.84/44.20
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 117.84/44.20
ACTIVE(and(z0, z1)) → c7(AND(active(z0), z1), ACTIVE(z0)) 117.84/44.20
ACTIVE(isNePal(z0)) → c8(ISNEPAL(active(z0)), ACTIVE(z0)) 117.84/44.20
__'(mark(z0), z1) → c9(__'(z0, z1)) 117.84/44.20
__'(z0, mark(z1)) → c10(__'(z0, z1)) 117.84/44.20
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 117.84/44.20
AND(mark(z0), z1) → c12(AND(z0, z1)) 117.84/44.20
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 117.84/44.20
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 117.84/44.20
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 117.84/44.20
PROPER(__(z0, z1)) → c16(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.20
PROPER(and(z0, z1)) → c18(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.20
PROPER(isNePal(z0)) → c20(ISNEPAL(proper(z0)), PROPER(z0)) 117.84/44.20
TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0)) 117.84/44.20
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0))
S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2)) 117.84/44.20
ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 117.84/44.20
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 117.84/44.20
ACTIVE(and(z0, z1)) → c7(AND(active(z0), z1), ACTIVE(z0)) 117.84/44.20
ACTIVE(isNePal(z0)) → c8(ISNEPAL(active(z0)), ACTIVE(z0)) 117.84/44.20
__'(mark(z0), z1) → c9(__'(z0, z1)) 117.84/44.20
__'(z0, mark(z1)) → c10(__'(z0, z1)) 117.84/44.20
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 117.84/44.20
AND(mark(z0), z1) → c12(AND(z0, z1)) 117.84/44.20
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 117.84/44.20
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 117.84/44.20
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 117.84/44.20
PROPER(__(z0, z1)) → c16(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.20
PROPER(and(z0, z1)) → c18(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.20
PROPER(isNePal(z0)) → c20(ISNEPAL(proper(z0)), PROPER(z0)) 117.84/44.20
TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0)) 117.84/44.20
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0))
K tuples:none
Defined Rule Symbols:

active, __, and, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', AND, ISNEPAL, PROPER, TOP

Compound Symbols:

c, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c18, c20, c21, c22

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117.84/44.20

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

Split RHS of tuples not part of any SCC
117.84/44.20
117.84/44.20

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2))) 117.84/44.20
active(__(z0, nil)) → mark(z0) 117.84/44.20
active(__(nil, z0)) → mark(z0) 117.84/44.20
active(and(tt, z0)) → mark(z0) 117.84/44.20
active(isNePal(__(z0, __(z1, z0)))) → mark(tt) 117.84/44.20
active(__(z0, z1)) → __(active(z0), z1) 117.84/44.20
active(__(z0, z1)) → __(z0, active(z1)) 117.84/44.20
active(and(z0, z1)) → and(active(z0), z1) 117.84/44.20
active(isNePal(z0)) → isNePal(active(z0)) 117.84/44.20
__(mark(z0), z1) → mark(__(z0, z1)) 117.84/44.20
__(z0, mark(z1)) → mark(__(z0, z1)) 117.84/44.20
__(ok(z0), ok(z1)) → ok(__(z0, z1)) 117.84/44.20
and(mark(z0), z1) → mark(and(z0, z1)) 117.84/44.20
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 117.84/44.20
isNePal(mark(z0)) → mark(isNePal(z0)) 117.84/44.20
isNePal(ok(z0)) → ok(isNePal(z0)) 117.84/44.20
proper(__(z0, z1)) → __(proper(z0), proper(z1)) 117.84/44.20
proper(nil) → ok(nil) 117.84/44.20
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 117.84/44.20
proper(tt) → ok(tt) 117.84/44.20
proper(isNePal(z0)) → isNePal(proper(z0)) 117.84/44.20
top(mark(z0)) → top(proper(z0)) 117.84/44.20
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 117.84/44.20
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 117.84/44.20
ACTIVE(and(z0, z1)) → c7(AND(active(z0), z1), ACTIVE(z0)) 117.84/44.20
ACTIVE(isNePal(z0)) → c8(ISNEPAL(active(z0)), ACTIVE(z0)) 117.84/44.20
__'(mark(z0), z1) → c9(__'(z0, z1)) 117.84/44.20
__'(z0, mark(z1)) → c10(__'(z0, z1)) 117.84/44.20
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 117.84/44.20
AND(mark(z0), z1) → c12(AND(z0, z1)) 117.84/44.20
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 117.84/44.20
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 117.84/44.20
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 117.84/44.20
PROPER(__(z0, z1)) → c16(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.23
PROPER(and(z0, z1)) → c18(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.23
PROPER(isNePal(z0)) → c20(ISNEPAL(proper(z0)), PROPER(z0)) 117.84/44.23
TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0)) 117.84/44.23
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 117.84/44.23
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 117.84/44.23
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
S tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 117.84/44.23
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 117.84/44.23
ACTIVE(and(z0, z1)) → c7(AND(active(z0), z1), ACTIVE(z0)) 117.84/44.23
ACTIVE(isNePal(z0)) → c8(ISNEPAL(active(z0)), ACTIVE(z0)) 117.84/44.23
__'(mark(z0), z1) → c9(__'(z0, z1)) 117.84/44.23
__'(z0, mark(z1)) → c10(__'(z0, z1)) 117.84/44.23
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 117.84/44.23
AND(mark(z0), z1) → c12(AND(z0, z1)) 117.84/44.23
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 117.84/44.23
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 117.84/44.23
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 117.84/44.23
PROPER(__(z0, z1)) → c16(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.23
PROPER(and(z0, z1)) → c18(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.23
PROPER(isNePal(z0)) → c20(ISNEPAL(proper(z0)), PROPER(z0)) 117.84/44.23
TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0)) 117.84/44.23
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 117.84/44.23
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 117.84/44.23
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
K tuples:none
Defined Rule Symbols:

active, __, and, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', AND, ISNEPAL, PROPER, TOP

Compound Symbols:

c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c18, c20, c21, c22, c1

117.84/44.23
117.84/44.23

(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)) → c21(TOP(proper(z0)), PROPER(z0))
We considered the (Usable) Rules:

__(ok(z0), ok(z1)) → ok(__(z0, z1)) 117.84/44.23
__(mark(z0), z1) → mark(__(z0, z1)) 117.84/44.23
__(z0, mark(z1)) → mark(__(z0, z1)) 117.84/44.23
active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2))) 117.84/44.23
active(__(z0, nil)) → mark(z0) 117.84/44.23
active(__(nil, z0)) → mark(z0) 117.84/44.23
active(and(tt, z0)) → mark(z0) 117.84/44.23
active(isNePal(__(z0, __(z1, z0)))) → mark(tt) 117.84/44.23
active(__(z0, z1)) → __(active(z0), z1) 117.84/44.23
active(__(z0, z1)) → __(z0, active(z1)) 117.84/44.23
active(and(z0, z1)) → and(active(z0), z1) 117.84/44.23
active(isNePal(z0)) → isNePal(active(z0)) 117.84/44.23
isNePal(mark(z0)) → mark(isNePal(z0)) 117.84/44.23
isNePal(ok(z0)) → ok(isNePal(z0)) 117.84/44.23
and(mark(z0), z1) → mark(and(z0, z1)) 117.84/44.23
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 117.84/44.23
proper(__(z0, z1)) → __(proper(z0), proper(z1)) 117.84/44.23
proper(nil) → ok(nil) 117.84/44.23
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 117.84/44.23
proper(tt) → ok(tt) 117.84/44.23
proper(isNePal(z0)) → isNePal(proper(z0))
And the Tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 117.84/44.23
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 117.84/44.23
ACTIVE(and(z0, z1)) → c7(AND(active(z0), z1), ACTIVE(z0)) 117.84/44.23
ACTIVE(isNePal(z0)) → c8(ISNEPAL(active(z0)), ACTIVE(z0)) 117.84/44.23
__'(mark(z0), z1) → c9(__'(z0, z1)) 117.84/44.23
__'(z0, mark(z1)) → c10(__'(z0, z1)) 117.84/44.23
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 117.84/44.23
AND(mark(z0), z1) → c12(AND(z0, z1)) 117.84/44.23
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 117.84/44.23
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 117.84/44.23
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 117.84/44.23
PROPER(__(z0, z1)) → c16(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.23
PROPER(and(z0, z1)) → c18(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.23
PROPER(isNePal(z0)) → c20(ISNEPAL(proper(z0)), PROPER(z0)) 117.84/44.23
TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0)) 117.84/44.23
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 117.84/44.23
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 117.84/44.23
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
The order we found is given by the following interpretation:
Polynomial interpretation : 117.84/44.23

POL(ACTIVE(x1)) = 0    117.84/44.23
POL(AND(x1, x2)) = 0    117.84/44.23
POL(ISNEPAL(x1)) = 0    117.84/44.23
POL(PROPER(x1)) = 0    117.84/44.23
POL(TOP(x1)) = x1    117.84/44.23
POL(__(x1, x2)) = [2] + [2]x1 + x2    117.84/44.23
POL(__'(x1, x2)) = 0    117.84/44.23
POL(active(x1)) = x1    117.84/44.23
POL(and(x1, x2)) = [1] + x1 + x2    117.84/44.23
POL(c1(x1)) = x1    117.84/44.23
POL(c10(x1)) = x1    117.84/44.23
POL(c11(x1)) = x1    117.84/44.23
POL(c12(x1)) = x1    117.84/44.23
POL(c13(x1)) = x1    117.84/44.23
POL(c14(x1)) = x1    117.84/44.23
POL(c15(x1)) = x1    117.84/44.23
POL(c16(x1, x2, x3)) = x1 + x2 + x3    117.84/44.23
POL(c18(x1, x2, x3)) = x1 + x2 + x3    117.84/44.23
POL(c20(x1, x2)) = x1 + x2    117.84/44.23
POL(c21(x1, x2)) = x1 + x2    117.84/44.23
POL(c22(x1, x2)) = x1 + x2    117.84/44.23
POL(c5(x1, x2)) = x1 + x2    117.84/44.23
POL(c6(x1, x2)) = x1 + x2    117.84/44.23
POL(c7(x1, x2)) = x1 + x2    117.84/44.23
POL(c8(x1, x2)) = x1 + x2    117.84/44.23
POL(c9(x1)) = x1    117.84/44.23
POL(isNePal(x1)) = [2]x1    117.84/44.23
POL(mark(x1)) = [1] + x1    117.84/44.23
POL(nil) = 0    117.84/44.23
POL(ok(x1)) = x1    117.84/44.23
POL(proper(x1)) = x1    117.84/44.23
POL(tt) = 0   
117.84/44.23
117.84/44.23

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2))) 117.84/44.23
active(__(z0, nil)) → mark(z0) 117.84/44.23
active(__(nil, z0)) → mark(z0) 117.84/44.23
active(and(tt, z0)) → mark(z0) 117.84/44.23
active(isNePal(__(z0, __(z1, z0)))) → mark(tt) 117.84/44.23
active(__(z0, z1)) → __(active(z0), z1) 117.84/44.23
active(__(z0, z1)) → __(z0, active(z1)) 117.84/44.23
active(and(z0, z1)) → and(active(z0), z1) 117.84/44.23
active(isNePal(z0)) → isNePal(active(z0)) 117.84/44.23
__(mark(z0), z1) → mark(__(z0, z1)) 117.84/44.23
__(z0, mark(z1)) → mark(__(z0, z1)) 117.84/44.23
__(ok(z0), ok(z1)) → ok(__(z0, z1)) 117.84/44.23
and(mark(z0), z1) → mark(and(z0, z1)) 117.84/44.23
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 117.84/44.23
isNePal(mark(z0)) → mark(isNePal(z0)) 117.84/44.23
isNePal(ok(z0)) → ok(isNePal(z0)) 117.84/44.23
proper(__(z0, z1)) → __(proper(z0), proper(z1)) 117.84/44.23
proper(nil) → ok(nil) 117.84/44.23
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 117.84/44.23
proper(tt) → ok(tt) 117.84/44.23
proper(isNePal(z0)) → isNePal(proper(z0)) 117.84/44.23
top(mark(z0)) → top(proper(z0)) 117.84/44.23
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 117.84/44.23
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 117.84/44.23
ACTIVE(and(z0, z1)) → c7(AND(active(z0), z1), ACTIVE(z0)) 117.84/44.23
ACTIVE(isNePal(z0)) → c8(ISNEPAL(active(z0)), ACTIVE(z0)) 117.84/44.23
__'(mark(z0), z1) → c9(__'(z0, z1)) 117.84/44.23
__'(z0, mark(z1)) → c10(__'(z0, z1)) 117.84/44.23
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 117.84/44.23
AND(mark(z0), z1) → c12(AND(z0, z1)) 117.84/44.23
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 117.84/44.23
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 117.84/44.23
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 117.84/44.23
PROPER(__(z0, z1)) → c16(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.23
PROPER(and(z0, z1)) → c18(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.23
PROPER(isNePal(z0)) → c20(ISNEPAL(proper(z0)), PROPER(z0)) 117.84/44.23
TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0)) 117.84/44.23
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 117.84/44.23
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 117.84/44.23
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
S tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 117.84/44.23
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 117.84/44.23
ACTIVE(and(z0, z1)) → c7(AND(active(z0), z1), ACTIVE(z0)) 117.84/44.23
ACTIVE(isNePal(z0)) → c8(ISNEPAL(active(z0)), ACTIVE(z0)) 117.84/44.23
__'(mark(z0), z1) → c9(__'(z0, z1)) 117.84/44.23
__'(z0, mark(z1)) → c10(__'(z0, z1)) 117.84/44.23
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 117.84/44.23
AND(mark(z0), z1) → c12(AND(z0, z1)) 117.84/44.23
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 117.84/44.23
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 117.84/44.23
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 117.84/44.23
PROPER(__(z0, z1)) → c16(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.23
PROPER(and(z0, z1)) → c18(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.23
PROPER(isNePal(z0)) → c20(ISNEPAL(proper(z0)), PROPER(z0)) 117.84/44.23
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 117.84/44.23
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 117.84/44.23
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
K tuples:

TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, __, and, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', AND, ISNEPAL, PROPER, TOP

Compound Symbols:

c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c18, c20, c21, c22, c1

117.84/44.23
117.84/44.23

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

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

ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 117.84/44.23
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 117.84/44.23
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 117.84/44.23
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(and(tt, z0))) 117.84/44.23
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 117.84/44.23
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 117.84/44.23
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 117.84/44.23
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 117.84/44.23
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0)))
117.84/44.23
117.84/44.23

(8) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2))) 117.84/44.23
active(__(z0, nil)) → mark(z0) 117.84/44.23
active(__(nil, z0)) → mark(z0) 117.84/44.23
active(and(tt, z0)) → mark(z0) 117.84/44.23
active(isNePal(__(z0, __(z1, z0)))) → mark(tt) 117.84/44.23
active(__(z0, z1)) → __(active(z0), z1) 117.84/44.23
active(__(z0, z1)) → __(z0, active(z1)) 117.84/44.23
active(and(z0, z1)) → and(active(z0), z1) 117.84/44.23
active(isNePal(z0)) → isNePal(active(z0)) 117.84/44.23
__(mark(z0), z1) → mark(__(z0, z1)) 117.84/44.23
__(z0, mark(z1)) → mark(__(z0, z1)) 117.84/44.23
__(ok(z0), ok(z1)) → ok(__(z0, z1)) 117.84/44.23
and(mark(z0), z1) → mark(and(z0, z1)) 117.84/44.23
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 117.84/44.23
isNePal(mark(z0)) → mark(isNePal(z0)) 117.84/44.23
isNePal(ok(z0)) → ok(isNePal(z0)) 117.84/44.23
proper(__(z0, z1)) → __(proper(z0), proper(z1)) 117.84/44.23
proper(nil) → ok(nil) 117.84/44.23
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 117.84/44.23
proper(tt) → ok(tt) 117.84/44.23
proper(isNePal(z0)) → isNePal(proper(z0)) 117.84/44.23
top(mark(z0)) → top(proper(z0)) 117.84/44.23
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 117.84/44.23
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 117.84/44.23
ACTIVE(isNePal(z0)) → c8(ISNEPAL(active(z0)), ACTIVE(z0)) 117.84/44.23
__'(mark(z0), z1) → c9(__'(z0, z1)) 117.84/44.23
__'(z0, mark(z1)) → c10(__'(z0, z1)) 117.84/44.23
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 117.84/44.23
AND(mark(z0), z1) → c12(AND(z0, z1)) 117.84/44.23
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 117.84/44.23
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 117.84/44.23
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 117.84/44.23
PROPER(__(z0, z1)) → c16(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.23
PROPER(and(z0, z1)) → c18(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.23
PROPER(isNePal(z0)) → c20(ISNEPAL(proper(z0)), PROPER(z0)) 117.84/44.23
TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0)) 117.84/44.23
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 117.84/44.23
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 117.84/44.23
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 117.84/44.23
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 117.84/44.23
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 117.84/44.23
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 117.84/44.23
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(and(tt, z0))) 117.84/44.23
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 117.84/44.23
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 117.84/44.23
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 117.84/44.23
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 117.84/44.23
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0)))
S tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 117.84/44.23
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 117.84/44.23
ACTIVE(isNePal(z0)) → c8(ISNEPAL(active(z0)), ACTIVE(z0)) 117.84/44.23
__'(mark(z0), z1) → c9(__'(z0, z1)) 117.84/44.23
__'(z0, mark(z1)) → c10(__'(z0, z1)) 117.84/44.23
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 117.84/44.23
AND(mark(z0), z1) → c12(AND(z0, z1)) 117.84/44.23
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 117.84/44.23
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 117.84/44.23
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 117.84/44.23
PROPER(__(z0, z1)) → c16(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.23
PROPER(and(z0, z1)) → c18(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.23
PROPER(isNePal(z0)) → c20(ISNEPAL(proper(z0)), PROPER(z0)) 117.84/44.23
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 117.84/44.23
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 117.84/44.23
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 117.84/44.23
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 117.84/44.23
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 117.84/44.23
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 117.84/44.23
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(and(tt, z0))) 117.84/44.23
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 117.84/44.23
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 117.84/44.23
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 117.84/44.25
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 117.84/44.25
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0)))
K tuples:

TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, __, and, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', AND, ISNEPAL, PROPER, TOP

Compound Symbols:

c5, c6, c8, c9, c10, c11, c12, c13, c14, c15, c16, c18, c20, c21, c22, c1, c7

117.84/44.25
117.84/44.25

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

Removed 1 trailing tuple parts
117.84/44.25
117.84/44.25

(10) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2))) 117.84/44.25
active(__(z0, nil)) → mark(z0) 117.84/44.25
active(__(nil, z0)) → mark(z0) 117.84/44.25
active(and(tt, z0)) → mark(z0) 117.84/44.25
active(isNePal(__(z0, __(z1, z0)))) → mark(tt) 117.84/44.25
active(__(z0, z1)) → __(active(z0), z1) 117.84/44.25
active(__(z0, z1)) → __(z0, active(z1)) 117.84/44.25
active(and(z0, z1)) → and(active(z0), z1) 117.84/44.25
active(isNePal(z0)) → isNePal(active(z0)) 117.84/44.25
__(mark(z0), z1) → mark(__(z0, z1)) 117.84/44.25
__(z0, mark(z1)) → mark(__(z0, z1)) 117.84/44.25
__(ok(z0), ok(z1)) → ok(__(z0, z1)) 117.84/44.25
and(mark(z0), z1) → mark(and(z0, z1)) 117.84/44.25
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 117.84/44.25
isNePal(mark(z0)) → mark(isNePal(z0)) 117.84/44.25
isNePal(ok(z0)) → ok(isNePal(z0)) 117.84/44.25
proper(__(z0, z1)) → __(proper(z0), proper(z1)) 117.84/44.25
proper(nil) → ok(nil) 117.84/44.25
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 117.84/44.25
proper(tt) → ok(tt) 117.84/44.25
proper(isNePal(z0)) → isNePal(proper(z0)) 117.84/44.25
top(mark(z0)) → top(proper(z0)) 117.84/44.25
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 117.84/44.25
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 117.84/44.25
ACTIVE(isNePal(z0)) → c8(ISNEPAL(active(z0)), ACTIVE(z0)) 117.84/44.25
__'(mark(z0), z1) → c9(__'(z0, z1)) 117.84/44.25
__'(z0, mark(z1)) → c10(__'(z0, z1)) 117.84/44.25
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 117.84/44.25
AND(mark(z0), z1) → c12(AND(z0, z1)) 117.84/44.25
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 117.84/44.25
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 117.84/44.25
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 117.84/44.25
PROPER(__(z0, z1)) → c16(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.25
PROPER(and(z0, z1)) → c18(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.25
PROPER(isNePal(z0)) → c20(ISNEPAL(proper(z0)), PROPER(z0)) 117.84/44.25
TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0)) 117.84/44.25
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 117.84/44.25
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 117.84/44.25
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 117.84/44.25
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 117.84/44.25
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 117.84/44.25
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 117.84/44.25
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 117.84/44.25
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 117.84/44.25
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 117.84/44.25
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 117.84/44.25
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0))) 117.84/44.25
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1))
S tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 117.84/44.25
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 117.84/44.25
ACTIVE(isNePal(z0)) → c8(ISNEPAL(active(z0)), ACTIVE(z0)) 117.84/44.25
__'(mark(z0), z1) → c9(__'(z0, z1)) 117.84/44.25
__'(z0, mark(z1)) → c10(__'(z0, z1)) 117.84/44.25
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 117.84/44.25
AND(mark(z0), z1) → c12(AND(z0, z1)) 117.84/44.25
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 117.84/44.25
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 117.84/44.25
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 117.84/44.25
PROPER(__(z0, z1)) → c16(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.25
PROPER(and(z0, z1)) → c18(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.25
PROPER(isNePal(z0)) → c20(ISNEPAL(proper(z0)), PROPER(z0)) 117.84/44.25
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 117.84/44.25
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 117.84/44.25
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 117.84/44.25
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 117.84/44.25
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 117.84/44.25
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 117.84/44.25
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 117.84/44.25
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 117.84/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 117.84/44.31
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 117.84/44.31
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0))) 117.84/44.31
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1))
K tuples:

TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, __, and, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', AND, ISNEPAL, PROPER, TOP

Compound Symbols:

c5, c6, c8, c9, c10, c11, c12, c13, c14, c15, c16, c18, c20, c21, c22, c1, c7, c7

117.84/44.31
117.84/44.31

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

Use narrowing to replace ACTIVE(isNePal(z0)) → c8(ISNEPAL(active(z0)), ACTIVE(z0)) by

ACTIVE(isNePal(__(__(z0, z1), z2))) → c8(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 117.84/44.31
ACTIVE(isNePal(__(z0, nil))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil))) 117.84/44.31
ACTIVE(isNePal(__(nil, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0))) 117.84/44.31
ACTIVE(isNePal(and(tt, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(and(tt, z0))) 117.84/44.31
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c8(ISNEPAL(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 117.84/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1))) 117.84/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1))) 117.84/44.31
ACTIVE(isNePal(and(z0, z1))) → c8(ISNEPAL(and(active(z0), z1)), ACTIVE(and(z0, z1))) 117.84/44.31
ACTIVE(isNePal(isNePal(z0))) → c8(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
117.84/44.31
117.84/44.31

(12) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2))) 117.84/44.31
active(__(z0, nil)) → mark(z0) 117.84/44.31
active(__(nil, z0)) → mark(z0) 117.84/44.31
active(and(tt, z0)) → mark(z0) 117.84/44.31
active(isNePal(__(z0, __(z1, z0)))) → mark(tt) 117.84/44.31
active(__(z0, z1)) → __(active(z0), z1) 117.84/44.31
active(__(z0, z1)) → __(z0, active(z1)) 117.84/44.31
active(and(z0, z1)) → and(active(z0), z1) 117.84/44.31
active(isNePal(z0)) → isNePal(active(z0)) 117.84/44.31
__(mark(z0), z1) → mark(__(z0, z1)) 117.84/44.31
__(z0, mark(z1)) → mark(__(z0, z1)) 117.84/44.31
__(ok(z0), ok(z1)) → ok(__(z0, z1)) 117.84/44.31
and(mark(z0), z1) → mark(and(z0, z1)) 117.84/44.31
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 117.84/44.31
isNePal(mark(z0)) → mark(isNePal(z0)) 117.84/44.31
isNePal(ok(z0)) → ok(isNePal(z0)) 117.84/44.31
proper(__(z0, z1)) → __(proper(z0), proper(z1)) 117.84/44.31
proper(nil) → ok(nil) 117.84/44.31
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 117.84/44.31
proper(tt) → ok(tt) 117.84/44.31
proper(isNePal(z0)) → isNePal(proper(z0)) 117.84/44.31
top(mark(z0)) → top(proper(z0)) 117.84/44.31
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 117.84/44.31
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 117.84/44.31
__'(mark(z0), z1) → c9(__'(z0, z1)) 117.84/44.31
__'(z0, mark(z1)) → c10(__'(z0, z1)) 117.84/44.31
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 117.84/44.31
AND(mark(z0), z1) → c12(AND(z0, z1)) 117.84/44.31
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 117.84/44.31
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 117.84/44.31
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 117.84/44.31
PROPER(__(z0, z1)) → c16(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.31
PROPER(and(z0, z1)) → c18(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.31
PROPER(isNePal(z0)) → c20(ISNEPAL(proper(z0)), PROPER(z0)) 117.84/44.31
TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0)) 117.84/44.31
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 117.84/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 117.84/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 117.84/44.31
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 117.84/44.31
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 117.84/44.31
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 117.84/44.31
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 117.84/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 117.84/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 117.84/44.31
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 117.84/44.31
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0))) 117.84/44.31
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1)) 117.84/44.31
ACTIVE(isNePal(__(__(z0, z1), z2))) → c8(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 117.84/44.31
ACTIVE(isNePal(__(z0, nil))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil))) 117.84/44.31
ACTIVE(isNePal(__(nil, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0))) 117.84/44.31
ACTIVE(isNePal(and(tt, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(and(tt, z0))) 117.84/44.31
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c8(ISNEPAL(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 117.84/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1))) 117.84/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1))) 117.84/44.31
ACTIVE(isNePal(and(z0, z1))) → c8(ISNEPAL(and(active(z0), z1)), ACTIVE(and(z0, z1))) 117.84/44.31
ACTIVE(isNePal(isNePal(z0))) → c8(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
S tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 117.84/44.31
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 117.84/44.31
__'(mark(z0), z1) → c9(__'(z0, z1)) 117.84/44.31
__'(z0, mark(z1)) → c10(__'(z0, z1)) 117.84/44.31
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 117.84/44.31
AND(mark(z0), z1) → c12(AND(z0, z1)) 117.84/44.31
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 117.84/44.31
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 117.84/44.31
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 117.84/44.31
PROPER(__(z0, z1)) → c16(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.31
PROPER(and(z0, z1)) → c18(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.31
PROPER(isNePal(z0)) → c20(ISNEPAL(proper(z0)), PROPER(z0)) 117.84/44.31
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 117.84/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 117.84/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 117.84/44.31
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 117.84/44.31
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 117.84/44.31
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 117.84/44.31
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 117.84/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 117.84/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 117.84/44.31
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 117.84/44.31
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0))) 117.84/44.31
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1)) 117.84/44.31
ACTIVE(isNePal(__(__(z0, z1), z2))) → c8(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 117.84/44.31
ACTIVE(isNePal(__(z0, nil))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil))) 117.84/44.31
ACTIVE(isNePal(__(nil, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0))) 117.84/44.31
ACTIVE(isNePal(and(tt, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(and(tt, z0))) 117.84/44.31
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c8(ISNEPAL(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 117.84/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1))) 117.84/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1))) 117.84/44.31
ACTIVE(isNePal(and(z0, z1))) → c8(ISNEPAL(and(active(z0), z1)), ACTIVE(and(z0, z1))) 117.84/44.31
ACTIVE(isNePal(isNePal(z0))) → c8(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0)))
K tuples:

TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, __, and, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', AND, ISNEPAL, PROPER, TOP

Compound Symbols:

c5, c6, c9, c10, c11, c12, c13, c14, c15, c16, c18, c20, c21, c22, c1, c7, c7, c8

117.84/44.31
117.84/44.31

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

Removed 1 trailing tuple parts
117.84/44.31
117.84/44.31

(14) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2))) 117.84/44.31
active(__(z0, nil)) → mark(z0) 117.84/44.31
active(__(nil, z0)) → mark(z0) 117.84/44.31
active(and(tt, z0)) → mark(z0) 117.84/44.31
active(isNePal(__(z0, __(z1, z0)))) → mark(tt) 117.84/44.31
active(__(z0, z1)) → __(active(z0), z1) 117.84/44.31
active(__(z0, z1)) → __(z0, active(z1)) 117.84/44.31
active(and(z0, z1)) → and(active(z0), z1) 117.84/44.31
active(isNePal(z0)) → isNePal(active(z0)) 117.84/44.31
__(mark(z0), z1) → mark(__(z0, z1)) 117.84/44.31
__(z0, mark(z1)) → mark(__(z0, z1)) 117.84/44.31
__(ok(z0), ok(z1)) → ok(__(z0, z1)) 117.84/44.31
and(mark(z0), z1) → mark(and(z0, z1)) 117.84/44.31
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 117.84/44.31
isNePal(mark(z0)) → mark(isNePal(z0)) 117.84/44.31
isNePal(ok(z0)) → ok(isNePal(z0)) 117.84/44.31
proper(__(z0, z1)) → __(proper(z0), proper(z1)) 117.84/44.31
proper(nil) → ok(nil) 117.84/44.31
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 117.84/44.31
proper(tt) → ok(tt) 117.84/44.31
proper(isNePal(z0)) → isNePal(proper(z0)) 117.84/44.31
top(mark(z0)) → top(proper(z0)) 117.84/44.31
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 117.84/44.31
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 117.84/44.31
__'(mark(z0), z1) → c9(__'(z0, z1)) 117.84/44.31
__'(z0, mark(z1)) → c10(__'(z0, z1)) 117.84/44.31
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 117.84/44.31
AND(mark(z0), z1) → c12(AND(z0, z1)) 117.84/44.31
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 117.84/44.31
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 117.84/44.31
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 117.84/44.31
PROPER(__(z0, z1)) → c16(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.31
PROPER(and(z0, z1)) → c18(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 117.84/44.31
PROPER(isNePal(z0)) → c20(ISNEPAL(proper(z0)), PROPER(z0)) 117.84/44.31
TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0)) 117.84/44.31
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 117.84/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 117.84/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 117.84/44.31
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 117.84/44.31
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 117.84/44.31
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 117.84/44.31
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 117.84/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 117.84/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 117.84/44.31
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 117.84/44.31
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0))) 117.84/44.31
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1)) 117.84/44.31
ACTIVE(isNePal(__(__(z0, z1), z2))) → c8(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 117.84/44.31
ACTIVE(isNePal(__(z0, nil))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil))) 117.84/44.31
ACTIVE(isNePal(__(nil, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0))) 117.84/44.31
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c8(ISNEPAL(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 117.84/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1))) 117.84/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1))) 117.84/44.31
ACTIVE(isNePal(and(z0, z1))) → c8(ISNEPAL(and(active(z0), z1)), ACTIVE(and(z0, z1))) 117.84/44.31
ACTIVE(isNePal(isNePal(z0))) → c8(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0))) 117.84/44.31
ACTIVE(isNePal(and(tt, z0))) → c8(ISNEPAL(mark(z0)))
S tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 117.84/44.31
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 117.84/44.31
__'(mark(z0), z1) → c9(__'(z0, z1)) 117.84/44.31
__'(z0, mark(z1)) → c10(__'(z0, z1)) 117.84/44.31
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 117.84/44.31
AND(mark(z0), z1) → c12(AND(z0, z1)) 117.84/44.31
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 117.84/44.31
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 117.84/44.31
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 117.84/44.31
PROPER(__(z0, z1)) → c16(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 118.27/44.31
PROPER(and(z0, z1)) → c18(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 118.27/44.31
PROPER(isNePal(z0)) → c20(ISNEPAL(proper(z0)), PROPER(z0)) 118.27/44.31
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 118.27/44.31
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1)) 118.27/44.31
ACTIVE(isNePal(__(__(z0, z1), z2))) → c8(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(isNePal(__(z0, nil))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(isNePal(__(nil, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c8(ISNEPAL(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(and(z0, z1))) → c8(ISNEPAL(and(active(z0), z1)), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(isNePal(isNePal(z0))) → c8(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(isNePal(and(tt, z0))) → c8(ISNEPAL(mark(z0)))
K tuples:

TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, __, and, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', AND, ISNEPAL, PROPER, TOP

Compound Symbols:

c5, c6, c9, c10, c11, c12, c13, c14, c15, c16, c18, c20, c21, c22, c1, c7, c7, c8, c8

118.27/44.31
118.27/44.31

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

Use narrowing to replace PROPER(__(z0, z1)) → c16(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(__(x0, __(z0, z1))) → c16(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(__(x0, nil)) → c16(__'(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 118.27/44.31
PROPER(__(x0, and(z0, z1))) → c16(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(__(x0, tt)) → c16(__'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 118.27/44.31
PROPER(__(x0, isNePal(z0))) → c16(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(__(__(z0, z1), x1)) → c16(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(nil, x1)) → c16(__'(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 118.27/44.31
PROPER(__(and(z0, z1), x1)) → c16(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(tt, x1)) → c16(__'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 118.27/44.31
PROPER(__(isNePal(z0), x1)) → c16(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
118.27/44.31
118.27/44.31

(16) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2))) 118.27/44.31
active(__(z0, nil)) → mark(z0) 118.27/44.31
active(__(nil, z0)) → mark(z0) 118.27/44.31
active(and(tt, z0)) → mark(z0) 118.27/44.31
active(isNePal(__(z0, __(z1, z0)))) → mark(tt) 118.27/44.31
active(__(z0, z1)) → __(active(z0), z1) 118.27/44.31
active(__(z0, z1)) → __(z0, active(z1)) 118.27/44.31
active(and(z0, z1)) → and(active(z0), z1) 118.27/44.31
active(isNePal(z0)) → isNePal(active(z0)) 118.27/44.31
__(mark(z0), z1) → mark(__(z0, z1)) 118.27/44.31
__(z0, mark(z1)) → mark(__(z0, z1)) 118.27/44.31
__(ok(z0), ok(z1)) → ok(__(z0, z1)) 118.27/44.31
and(mark(z0), z1) → mark(and(z0, z1)) 118.27/44.31
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 118.27/44.31
isNePal(mark(z0)) → mark(isNePal(z0)) 118.27/44.31
isNePal(ok(z0)) → ok(isNePal(z0)) 118.27/44.31
proper(__(z0, z1)) → __(proper(z0), proper(z1)) 118.27/44.31
proper(nil) → ok(nil) 118.27/44.31
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 118.27/44.31
proper(tt) → ok(tt) 118.27/44.31
proper(isNePal(z0)) → isNePal(proper(z0)) 118.27/44.31
top(mark(z0)) → top(proper(z0)) 118.27/44.31
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 118.27/44.31
__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.31
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.31
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.31
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.31
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.31
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.31
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 118.27/44.31
PROPER(and(z0, z1)) → c18(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 118.27/44.31
PROPER(isNePal(z0)) → c20(ISNEPAL(proper(z0)), PROPER(z0)) 118.27/44.31
TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0)) 118.27/44.31
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 118.27/44.31
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1)) 118.27/44.31
ACTIVE(isNePal(__(__(z0, z1), z2))) → c8(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(isNePal(__(z0, nil))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(isNePal(__(nil, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c8(ISNEPAL(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(and(z0, z1))) → c8(ISNEPAL(and(active(z0), z1)), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(isNePal(isNePal(z0))) → c8(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(isNePal(and(tt, z0))) → c8(ISNEPAL(mark(z0))) 118.27/44.31
PROPER(__(x0, __(z0, z1))) → c16(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(__(x0, nil)) → c16(__'(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 118.27/44.31
PROPER(__(x0, and(z0, z1))) → c16(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(__(x0, tt)) → c16(__'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 118.27/44.31
PROPER(__(x0, isNePal(z0))) → c16(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(__(__(z0, z1), x1)) → c16(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(nil, x1)) → c16(__'(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 118.27/44.31
PROPER(__(and(z0, z1), x1)) → c16(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(tt, x1)) → c16(__'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 118.27/44.31
PROPER(__(isNePal(z0), x1)) → c16(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
S tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 118.27/44.31
__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.31
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.31
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.31
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.31
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.31
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.31
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 118.27/44.31
PROPER(and(z0, z1)) → c18(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 118.27/44.31
PROPER(isNePal(z0)) → c20(ISNEPAL(proper(z0)), PROPER(z0)) 118.27/44.31
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 118.27/44.31
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1)) 118.27/44.31
ACTIVE(isNePal(__(__(z0, z1), z2))) → c8(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(isNePal(__(z0, nil))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(isNePal(__(nil, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c8(ISNEPAL(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(and(z0, z1))) → c8(ISNEPAL(and(active(z0), z1)), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(isNePal(isNePal(z0))) → c8(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(isNePal(and(tt, z0))) → c8(ISNEPAL(mark(z0))) 118.27/44.31
PROPER(__(x0, __(z0, z1))) → c16(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(__(x0, nil)) → c16(__'(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 118.27/44.31
PROPER(__(x0, and(z0, z1))) → c16(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(__(x0, tt)) → c16(__'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 118.27/44.31
PROPER(__(x0, isNePal(z0))) → c16(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(__(__(z0, z1), x1)) → c16(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(nil, x1)) → c16(__'(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 118.27/44.31
PROPER(__(and(z0, z1), x1)) → c16(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(tt, x1)) → c16(__'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 118.27/44.31
PROPER(__(isNePal(z0), x1)) → c16(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
K tuples:

TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, __, and, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', AND, ISNEPAL, PROPER, TOP

Compound Symbols:

c5, c6, c9, c10, c11, c12, c13, c14, c15, c18, c20, c21, c22, c1, c7, c7, c8, c8, c16

118.27/44.31
118.27/44.31

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

Removed 4 trailing tuple parts
118.27/44.31
118.27/44.31

(18) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2))) 118.27/44.31
active(__(z0, nil)) → mark(z0) 118.27/44.31
active(__(nil, z0)) → mark(z0) 118.27/44.31
active(and(tt, z0)) → mark(z0) 118.27/44.31
active(isNePal(__(z0, __(z1, z0)))) → mark(tt) 118.27/44.31
active(__(z0, z1)) → __(active(z0), z1) 118.27/44.31
active(__(z0, z1)) → __(z0, active(z1)) 118.27/44.31
active(and(z0, z1)) → and(active(z0), z1) 118.27/44.31
active(isNePal(z0)) → isNePal(active(z0)) 118.27/44.31
__(mark(z0), z1) → mark(__(z0, z1)) 118.27/44.31
__(z0, mark(z1)) → mark(__(z0, z1)) 118.27/44.31
__(ok(z0), ok(z1)) → ok(__(z0, z1)) 118.27/44.31
and(mark(z0), z1) → mark(and(z0, z1)) 118.27/44.31
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 118.27/44.31
isNePal(mark(z0)) → mark(isNePal(z0)) 118.27/44.31
isNePal(ok(z0)) → ok(isNePal(z0)) 118.27/44.31
proper(__(z0, z1)) → __(proper(z0), proper(z1)) 118.27/44.31
proper(nil) → ok(nil) 118.27/44.31
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 118.27/44.31
proper(tt) → ok(tt) 118.27/44.31
proper(isNePal(z0)) → isNePal(proper(z0)) 118.27/44.31
top(mark(z0)) → top(proper(z0)) 118.27/44.31
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 118.27/44.31
__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.31
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.31
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.31
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.31
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.31
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.31
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 118.27/44.31
PROPER(and(z0, z1)) → c18(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 118.27/44.31
PROPER(isNePal(z0)) → c20(ISNEPAL(proper(z0)), PROPER(z0)) 118.27/44.31
TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0)) 118.27/44.31
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 118.27/44.31
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1)) 118.27/44.31
ACTIVE(isNePal(__(__(z0, z1), z2))) → c8(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(isNePal(__(z0, nil))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(isNePal(__(nil, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c8(ISNEPAL(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(and(z0, z1))) → c8(ISNEPAL(and(active(z0), z1)), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(isNePal(isNePal(z0))) → c8(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(isNePal(and(tt, z0))) → c8(ISNEPAL(mark(z0))) 118.27/44.31
PROPER(__(x0, __(z0, z1))) → c16(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(__(x0, and(z0, z1))) → c16(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(__(x0, isNePal(z0))) → c16(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(__(__(z0, z1), x1)) → c16(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(and(z0, z1), x1)) → c16(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(isNePal(z0), x1)) → c16(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.31
PROPER(__(x0, nil)) → c16(__'(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.31
PROPER(__(x0, tt)) → c16(__'(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.31
PROPER(__(nil, x1)) → c16(__'(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(__(tt, x1)) → c16(__'(ok(tt), proper(x1)), PROPER(x1))
S tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 118.27/44.31
__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.31
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.31
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.31
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.31
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.31
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.31
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 118.27/44.31
PROPER(and(z0, z1)) → c18(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 118.27/44.31
PROPER(isNePal(z0)) → c20(ISNEPAL(proper(z0)), PROPER(z0)) 118.27/44.31
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 118.27/44.31
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1)) 118.27/44.31
ACTIVE(isNePal(__(__(z0, z1), z2))) → c8(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(isNePal(__(z0, nil))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(isNePal(__(nil, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c8(ISNEPAL(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(and(z0, z1))) → c8(ISNEPAL(and(active(z0), z1)), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(isNePal(isNePal(z0))) → c8(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(isNePal(and(tt, z0))) → c8(ISNEPAL(mark(z0))) 118.27/44.31
PROPER(__(x0, __(z0, z1))) → c16(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(__(x0, and(z0, z1))) → c16(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(__(x0, isNePal(z0))) → c16(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(__(__(z0, z1), x1)) → c16(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(and(z0, z1), x1)) → c16(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(isNePal(z0), x1)) → c16(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.31
PROPER(__(x0, nil)) → c16(__'(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.31
PROPER(__(x0, tt)) → c16(__'(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.31
PROPER(__(nil, x1)) → c16(__'(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(__(tt, x1)) → c16(__'(ok(tt), proper(x1)), PROPER(x1))
K tuples:

TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, __, and, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', AND, ISNEPAL, PROPER, TOP

Compound Symbols:

c5, c6, c9, c10, c11, c12, c13, c14, c15, c18, c20, c21, c22, c1, c7, c7, c8, c8, c16, c16

118.27/44.31
118.27/44.31

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

Use narrowing to replace PROPER(and(z0, z1)) → c18(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(and(x0, __(z0, z1))) → c18(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(and(x0, nil)) → c18(AND(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 118.27/44.31
PROPER(and(x0, and(z0, z1))) → c18(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(and(x0, tt)) → c18(AND(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 118.27/44.31
PROPER(and(x0, isNePal(z0))) → c18(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(and(__(z0, z1), x1)) → c18(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(and(nil, x1)) → c18(AND(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 118.27/44.31
PROPER(and(and(z0, z1), x1)) → c18(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(and(tt, x1)) → c18(AND(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 118.27/44.31
PROPER(and(isNePal(z0), x1)) → c18(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
118.27/44.31
118.27/44.31

(20) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2))) 118.27/44.31
active(__(z0, nil)) → mark(z0) 118.27/44.31
active(__(nil, z0)) → mark(z0) 118.27/44.31
active(and(tt, z0)) → mark(z0) 118.27/44.31
active(isNePal(__(z0, __(z1, z0)))) → mark(tt) 118.27/44.31
active(__(z0, z1)) → __(active(z0), z1) 118.27/44.31
active(__(z0, z1)) → __(z0, active(z1)) 118.27/44.31
active(and(z0, z1)) → and(active(z0), z1) 118.27/44.31
active(isNePal(z0)) → isNePal(active(z0)) 118.27/44.31
__(mark(z0), z1) → mark(__(z0, z1)) 118.27/44.31
__(z0, mark(z1)) → mark(__(z0, z1)) 118.27/44.31
__(ok(z0), ok(z1)) → ok(__(z0, z1)) 118.27/44.31
and(mark(z0), z1) → mark(and(z0, z1)) 118.27/44.31
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 118.27/44.31
isNePal(mark(z0)) → mark(isNePal(z0)) 118.27/44.31
isNePal(ok(z0)) → ok(isNePal(z0)) 118.27/44.31
proper(__(z0, z1)) → __(proper(z0), proper(z1)) 118.27/44.31
proper(nil) → ok(nil) 118.27/44.31
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 118.27/44.31
proper(tt) → ok(tt) 118.27/44.31
proper(isNePal(z0)) → isNePal(proper(z0)) 118.27/44.31
top(mark(z0)) → top(proper(z0)) 118.27/44.31
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 118.27/44.31
__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.31
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.31
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.31
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.31
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.31
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.31
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 118.27/44.31
PROPER(isNePal(z0)) → c20(ISNEPAL(proper(z0)), PROPER(z0)) 118.27/44.31
TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0)) 118.27/44.31
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 118.27/44.31
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1)) 118.27/44.31
ACTIVE(isNePal(__(__(z0, z1), z2))) → c8(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(isNePal(__(z0, nil))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(isNePal(__(nil, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c8(ISNEPAL(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(and(z0, z1))) → c8(ISNEPAL(and(active(z0), z1)), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(isNePal(isNePal(z0))) → c8(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(isNePal(and(tt, z0))) → c8(ISNEPAL(mark(z0))) 118.27/44.31
PROPER(__(x0, __(z0, z1))) → c16(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(__(x0, and(z0, z1))) → c16(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(__(x0, isNePal(z0))) → c16(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(__(__(z0, z1), x1)) → c16(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(and(z0, z1), x1)) → c16(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(isNePal(z0), x1)) → c16(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.31
PROPER(__(x0, nil)) → c16(__'(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.31
PROPER(__(x0, tt)) → c16(__'(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.31
PROPER(__(nil, x1)) → c16(__'(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(__(tt, x1)) → c16(__'(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(and(x0, __(z0, z1))) → c18(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(and(x0, nil)) → c18(AND(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 118.27/44.31
PROPER(and(x0, and(z0, z1))) → c18(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(and(x0, tt)) → c18(AND(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 118.27/44.31
PROPER(and(x0, isNePal(z0))) → c18(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(and(__(z0, z1), x1)) → c18(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(and(nil, x1)) → c18(AND(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 118.27/44.31
PROPER(and(and(z0, z1), x1)) → c18(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(and(tt, x1)) → c18(AND(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 118.27/44.31
PROPER(and(isNePal(z0), x1)) → c18(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
S tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 118.27/44.31
__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.31
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.31
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.31
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.31
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.31
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.31
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 118.27/44.31
PROPER(isNePal(z0)) → c20(ISNEPAL(proper(z0)), PROPER(z0)) 118.27/44.31
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 118.27/44.31
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1)) 118.27/44.31
ACTIVE(isNePal(__(__(z0, z1), z2))) → c8(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(isNePal(__(z0, nil))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(isNePal(__(nil, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c8(ISNEPAL(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(and(z0, z1))) → c8(ISNEPAL(and(active(z0), z1)), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(isNePal(isNePal(z0))) → c8(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(isNePal(and(tt, z0))) → c8(ISNEPAL(mark(z0))) 118.27/44.31
PROPER(__(x0, __(z0, z1))) → c16(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(__(x0, and(z0, z1))) → c16(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(__(x0, isNePal(z0))) → c16(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(__(__(z0, z1), x1)) → c16(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(and(z0, z1), x1)) → c16(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(isNePal(z0), x1)) → c16(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.31
PROPER(__(x0, nil)) → c16(__'(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.31
PROPER(__(x0, tt)) → c16(__'(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.31
PROPER(__(nil, x1)) → c16(__'(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(__(tt, x1)) → c16(__'(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(and(x0, __(z0, z1))) → c18(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(and(x0, nil)) → c18(AND(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 118.27/44.31
PROPER(and(x0, and(z0, z1))) → c18(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(and(x0, tt)) → c18(AND(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 118.27/44.31
PROPER(and(x0, isNePal(z0))) → c18(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(and(__(z0, z1), x1)) → c18(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(and(nil, x1)) → c18(AND(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 118.27/44.31
PROPER(and(and(z0, z1), x1)) → c18(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(and(tt, x1)) → c18(AND(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 118.27/44.31
PROPER(and(isNePal(z0), x1)) → c18(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
K tuples:

TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, __, and, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', AND, ISNEPAL, PROPER, TOP

Compound Symbols:

c5, c6, c9, c10, c11, c12, c13, c14, c15, c20, c21, c22, c1, c7, c7, c8, c8, c16, c16, c18

118.27/44.31
118.27/44.31

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

Removed 4 trailing tuple parts
118.27/44.31
118.27/44.31

(22) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2))) 118.27/44.31
active(__(z0, nil)) → mark(z0) 118.27/44.31
active(__(nil, z0)) → mark(z0) 118.27/44.31
active(and(tt, z0)) → mark(z0) 118.27/44.31
active(isNePal(__(z0, __(z1, z0)))) → mark(tt) 118.27/44.31
active(__(z0, z1)) → __(active(z0), z1) 118.27/44.31
active(__(z0, z1)) → __(z0, active(z1)) 118.27/44.31
active(and(z0, z1)) → and(active(z0), z1) 118.27/44.31
active(isNePal(z0)) → isNePal(active(z0)) 118.27/44.31
__(mark(z0), z1) → mark(__(z0, z1)) 118.27/44.31
__(z0, mark(z1)) → mark(__(z0, z1)) 118.27/44.31
__(ok(z0), ok(z1)) → ok(__(z0, z1)) 118.27/44.31
and(mark(z0), z1) → mark(and(z0, z1)) 118.27/44.31
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 118.27/44.31
isNePal(mark(z0)) → mark(isNePal(z0)) 118.27/44.31
isNePal(ok(z0)) → ok(isNePal(z0)) 118.27/44.31
proper(__(z0, z1)) → __(proper(z0), proper(z1)) 118.27/44.31
proper(nil) → ok(nil) 118.27/44.31
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 118.27/44.31
proper(tt) → ok(tt) 118.27/44.31
proper(isNePal(z0)) → isNePal(proper(z0)) 118.27/44.31
top(mark(z0)) → top(proper(z0)) 118.27/44.31
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 118.27/44.31
__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.31
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.31
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.31
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.31
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.31
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.31
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 118.27/44.31
PROPER(isNePal(z0)) → c20(ISNEPAL(proper(z0)), PROPER(z0)) 118.27/44.31
TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0)) 118.27/44.31
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 118.27/44.31
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1)) 118.27/44.31
ACTIVE(isNePal(__(__(z0, z1), z2))) → c8(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(isNePal(__(z0, nil))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(isNePal(__(nil, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c8(ISNEPAL(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(and(z0, z1))) → c8(ISNEPAL(and(active(z0), z1)), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(isNePal(isNePal(z0))) → c8(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(isNePal(and(tt, z0))) → c8(ISNEPAL(mark(z0))) 118.27/44.31
PROPER(__(x0, __(z0, z1))) → c16(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(__(x0, and(z0, z1))) → c16(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(__(x0, isNePal(z0))) → c16(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(__(__(z0, z1), x1)) → c16(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(and(z0, z1), x1)) → c16(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(isNePal(z0), x1)) → c16(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.31
PROPER(__(x0, nil)) → c16(__'(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.31
PROPER(__(x0, tt)) → c16(__'(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.31
PROPER(__(nil, x1)) → c16(__'(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(__(tt, x1)) → c16(__'(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(and(x0, __(z0, z1))) → c18(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(and(x0, and(z0, z1))) → c18(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(and(x0, isNePal(z0))) → c18(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(and(__(z0, z1), x1)) → c18(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(and(and(z0, z1), x1)) → c18(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(and(isNePal(z0), x1)) → c18(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.31
PROPER(and(x0, nil)) → c18(AND(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.31
PROPER(and(x0, tt)) → c18(AND(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.31
PROPER(and(nil, x1)) → c18(AND(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(and(tt, x1)) → c18(AND(ok(tt), proper(x1)), PROPER(x1))
S tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 118.27/44.31
__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.31
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.31
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.31
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.31
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.31
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.31
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 118.27/44.31
PROPER(isNePal(z0)) → c20(ISNEPAL(proper(z0)), PROPER(z0)) 118.27/44.31
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 118.27/44.31
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1)) 118.27/44.31
ACTIVE(isNePal(__(__(z0, z1), z2))) → c8(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(isNePal(__(z0, nil))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(isNePal(__(nil, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c8(ISNEPAL(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(and(z0, z1))) → c8(ISNEPAL(and(active(z0), z1)), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(isNePal(isNePal(z0))) → c8(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(isNePal(and(tt, z0))) → c8(ISNEPAL(mark(z0))) 118.27/44.31
PROPER(__(x0, __(z0, z1))) → c16(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(__(x0, and(z0, z1))) → c16(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(__(x0, isNePal(z0))) → c16(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(__(__(z0, z1), x1)) → c16(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(and(z0, z1), x1)) → c16(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(isNePal(z0), x1)) → c16(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.31
PROPER(__(x0, nil)) → c16(__'(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.31
PROPER(__(x0, tt)) → c16(__'(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.31
PROPER(__(nil, x1)) → c16(__'(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(__(tt, x1)) → c16(__'(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(and(x0, __(z0, z1))) → c18(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(and(x0, and(z0, z1))) → c18(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(and(x0, isNePal(z0))) → c18(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(and(__(z0, z1), x1)) → c18(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(and(and(z0, z1), x1)) → c18(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(and(isNePal(z0), x1)) → c18(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.31
PROPER(and(x0, nil)) → c18(AND(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.31
PROPER(and(x0, tt)) → c18(AND(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.31
PROPER(and(nil, x1)) → c18(AND(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(and(tt, x1)) → c18(AND(ok(tt), proper(x1)), PROPER(x1))
K tuples:

TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, __, and, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', AND, ISNEPAL, PROPER, TOP

Compound Symbols:

c5, c6, c9, c10, c11, c12, c13, c14, c15, c20, c21, c22, c1, c7, c7, c8, c8, c16, c16, c18, c18

118.27/44.31
118.27/44.31

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

Use narrowing to replace PROPER(isNePal(z0)) → c20(ISNEPAL(proper(z0)), PROPER(z0)) by

PROPER(isNePal(__(z0, z1))) → c20(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1))) 118.27/44.31
PROPER(isNePal(nil)) → c20(ISNEPAL(ok(nil)), PROPER(nil)) 118.27/44.31
PROPER(isNePal(and(z0, z1))) → c20(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 118.27/44.31
PROPER(isNePal(tt)) → c20(ISNEPAL(ok(tt)), PROPER(tt)) 118.27/44.31
PROPER(isNePal(isNePal(z0))) → c20(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
118.27/44.31
118.27/44.31

(24) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2))) 118.27/44.31
active(__(z0, nil)) → mark(z0) 118.27/44.31
active(__(nil, z0)) → mark(z0) 118.27/44.31
active(and(tt, z0)) → mark(z0) 118.27/44.31
active(isNePal(__(z0, __(z1, z0)))) → mark(tt) 118.27/44.31
active(__(z0, z1)) → __(active(z0), z1) 118.27/44.31
active(__(z0, z1)) → __(z0, active(z1)) 118.27/44.31
active(and(z0, z1)) → and(active(z0), z1) 118.27/44.31
active(isNePal(z0)) → isNePal(active(z0)) 118.27/44.31
__(mark(z0), z1) → mark(__(z0, z1)) 118.27/44.31
__(z0, mark(z1)) → mark(__(z0, z1)) 118.27/44.31
__(ok(z0), ok(z1)) → ok(__(z0, z1)) 118.27/44.31
and(mark(z0), z1) → mark(and(z0, z1)) 118.27/44.31
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 118.27/44.31
isNePal(mark(z0)) → mark(isNePal(z0)) 118.27/44.31
isNePal(ok(z0)) → ok(isNePal(z0)) 118.27/44.31
proper(__(z0, z1)) → __(proper(z0), proper(z1)) 118.27/44.31
proper(nil) → ok(nil) 118.27/44.31
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 118.27/44.31
proper(tt) → ok(tt) 118.27/44.31
proper(isNePal(z0)) → isNePal(proper(z0)) 118.27/44.31
top(mark(z0)) → top(proper(z0)) 118.27/44.31
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 118.27/44.31
__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.31
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.31
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.31
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.31
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.31
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.31
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 118.27/44.31
TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0)) 118.27/44.31
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 118.27/44.31
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1)) 118.27/44.31
ACTIVE(isNePal(__(__(z0, z1), z2))) → c8(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(isNePal(__(z0, nil))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(isNePal(__(nil, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c8(ISNEPAL(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(and(z0, z1))) → c8(ISNEPAL(and(active(z0), z1)), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(isNePal(isNePal(z0))) → c8(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(isNePal(and(tt, z0))) → c8(ISNEPAL(mark(z0))) 118.27/44.31
PROPER(__(x0, __(z0, z1))) → c16(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(__(x0, and(z0, z1))) → c16(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(__(x0, isNePal(z0))) → c16(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(__(__(z0, z1), x1)) → c16(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(and(z0, z1), x1)) → c16(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(isNePal(z0), x1)) → c16(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.31
PROPER(__(x0, nil)) → c16(__'(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.31
PROPER(__(x0, tt)) → c16(__'(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.31
PROPER(__(nil, x1)) → c16(__'(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(__(tt, x1)) → c16(__'(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(and(x0, __(z0, z1))) → c18(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(and(x0, and(z0, z1))) → c18(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(and(x0, isNePal(z0))) → c18(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(and(__(z0, z1), x1)) → c18(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(and(and(z0, z1), x1)) → c18(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(and(isNePal(z0), x1)) → c18(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.31
PROPER(and(x0, nil)) → c18(AND(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.31
PROPER(and(x0, tt)) → c18(AND(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.31
PROPER(and(nil, x1)) → c18(AND(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(and(tt, x1)) → c18(AND(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(isNePal(__(z0, z1))) → c20(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1))) 118.27/44.31
PROPER(isNePal(nil)) → c20(ISNEPAL(ok(nil)), PROPER(nil)) 118.27/44.31
PROPER(isNePal(and(z0, z1))) → c20(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 118.27/44.31
PROPER(isNePal(tt)) → c20(ISNEPAL(ok(tt)), PROPER(tt)) 118.27/44.31
PROPER(isNePal(isNePal(z0))) → c20(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
S tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 118.27/44.31
__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.31
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.31
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.31
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.31
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.31
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.31
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 118.27/44.31
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 118.27/44.31
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1)) 118.27/44.31
ACTIVE(isNePal(__(__(z0, z1), z2))) → c8(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(isNePal(__(z0, nil))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(isNePal(__(nil, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c8(ISNEPAL(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(and(z0, z1))) → c8(ISNEPAL(and(active(z0), z1)), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(isNePal(isNePal(z0))) → c8(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(isNePal(and(tt, z0))) → c8(ISNEPAL(mark(z0))) 118.27/44.31
PROPER(__(x0, __(z0, z1))) → c16(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(__(x0, and(z0, z1))) → c16(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(__(x0, isNePal(z0))) → c16(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(__(__(z0, z1), x1)) → c16(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(and(z0, z1), x1)) → c16(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(isNePal(z0), x1)) → c16(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.31
PROPER(__(x0, nil)) → c16(__'(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.31
PROPER(__(x0, tt)) → c16(__'(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.31
PROPER(__(nil, x1)) → c16(__'(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(__(tt, x1)) → c16(__'(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(and(x0, __(z0, z1))) → c18(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(and(x0, and(z0, z1))) → c18(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(and(x0, isNePal(z0))) → c18(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(and(__(z0, z1), x1)) → c18(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(and(and(z0, z1), x1)) → c18(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(and(isNePal(z0), x1)) → c18(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.31
PROPER(and(x0, nil)) → c18(AND(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.31
PROPER(and(x0, tt)) → c18(AND(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.31
PROPER(and(nil, x1)) → c18(AND(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(and(tt, x1)) → c18(AND(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(isNePal(__(z0, z1))) → c20(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1))) 118.27/44.31
PROPER(isNePal(nil)) → c20(ISNEPAL(ok(nil)), PROPER(nil)) 118.27/44.31
PROPER(isNePal(and(z0, z1))) → c20(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 118.27/44.31
PROPER(isNePal(tt)) → c20(ISNEPAL(ok(tt)), PROPER(tt)) 118.27/44.31
PROPER(isNePal(isNePal(z0))) → c20(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
K tuples:

TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, __, and, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', AND, ISNEPAL, TOP, PROPER

Compound Symbols:

c5, c6, c9, c10, c11, c12, c13, c14, c15, c21, c22, c1, c7, c7, c8, c8, c16, c16, c18, c18, c20

118.27/44.31
118.27/44.31

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

Removed 2 trailing tuple parts
118.27/44.31
118.27/44.31

(26) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2))) 118.27/44.31
active(__(z0, nil)) → mark(z0) 118.27/44.31
active(__(nil, z0)) → mark(z0) 118.27/44.31
active(and(tt, z0)) → mark(z0) 118.27/44.31
active(isNePal(__(z0, __(z1, z0)))) → mark(tt) 118.27/44.31
active(__(z0, z1)) → __(active(z0), z1) 118.27/44.31
active(__(z0, z1)) → __(z0, active(z1)) 118.27/44.31
active(and(z0, z1)) → and(active(z0), z1) 118.27/44.31
active(isNePal(z0)) → isNePal(active(z0)) 118.27/44.31
__(mark(z0), z1) → mark(__(z0, z1)) 118.27/44.31
__(z0, mark(z1)) → mark(__(z0, z1)) 118.27/44.31
__(ok(z0), ok(z1)) → ok(__(z0, z1)) 118.27/44.31
and(mark(z0), z1) → mark(and(z0, z1)) 118.27/44.31
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 118.27/44.31
isNePal(mark(z0)) → mark(isNePal(z0)) 118.27/44.31
isNePal(ok(z0)) → ok(isNePal(z0)) 118.27/44.31
proper(__(z0, z1)) → __(proper(z0), proper(z1)) 118.27/44.31
proper(nil) → ok(nil) 118.27/44.31
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 118.27/44.31
proper(tt) → ok(tt) 118.27/44.31
proper(isNePal(z0)) → isNePal(proper(z0)) 118.27/44.31
top(mark(z0)) → top(proper(z0)) 118.27/44.31
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 118.27/44.31
__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.31
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.31
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.31
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.31
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.31
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.31
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 118.27/44.31
TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0)) 118.27/44.31
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 118.27/44.31
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1)) 118.27/44.31
ACTIVE(isNePal(__(__(z0, z1), z2))) → c8(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(isNePal(__(z0, nil))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(isNePal(__(nil, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c8(ISNEPAL(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(and(z0, z1))) → c8(ISNEPAL(and(active(z0), z1)), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(isNePal(isNePal(z0))) → c8(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(isNePal(and(tt, z0))) → c8(ISNEPAL(mark(z0))) 118.27/44.31
PROPER(__(x0, __(z0, z1))) → c16(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(__(x0, and(z0, z1))) → c16(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(__(x0, isNePal(z0))) → c16(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(__(__(z0, z1), x1)) → c16(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(and(z0, z1), x1)) → c16(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(isNePal(z0), x1)) → c16(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.31
PROPER(__(x0, nil)) → c16(__'(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.31
PROPER(__(x0, tt)) → c16(__'(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.31
PROPER(__(nil, x1)) → c16(__'(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(__(tt, x1)) → c16(__'(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(and(x0, __(z0, z1))) → c18(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(and(x0, and(z0, z1))) → c18(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(and(x0, isNePal(z0))) → c18(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(and(__(z0, z1), x1)) → c18(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(and(and(z0, z1), x1)) → c18(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(and(isNePal(z0), x1)) → c18(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.31
PROPER(and(x0, nil)) → c18(AND(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.31
PROPER(and(x0, tt)) → c18(AND(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.31
PROPER(and(nil, x1)) → c18(AND(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(and(tt, x1)) → c18(AND(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(isNePal(__(z0, z1))) → c20(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1))) 118.27/44.31
PROPER(isNePal(and(z0, z1))) → c20(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 118.27/44.31
PROPER(isNePal(isNePal(z0))) → c20(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0))) 118.27/44.31
PROPER(isNePal(nil)) → c20(ISNEPAL(ok(nil))) 118.27/44.31
PROPER(isNePal(tt)) → c20(ISNEPAL(ok(tt)))
S tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 118.27/44.31
__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.31
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.31
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.31
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.31
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.31
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.31
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 118.27/44.31
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 118.27/44.31
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1)) 118.27/44.31
ACTIVE(isNePal(__(__(z0, z1), z2))) → c8(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(isNePal(__(z0, nil))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(isNePal(__(nil, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c8(ISNEPAL(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(and(z0, z1))) → c8(ISNEPAL(and(active(z0), z1)), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(isNePal(isNePal(z0))) → c8(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(isNePal(and(tt, z0))) → c8(ISNEPAL(mark(z0))) 118.27/44.31
PROPER(__(x0, __(z0, z1))) → c16(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(__(x0, and(z0, z1))) → c16(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(__(x0, isNePal(z0))) → c16(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(__(__(z0, z1), x1)) → c16(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(and(z0, z1), x1)) → c16(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(isNePal(z0), x1)) → c16(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.31
PROPER(__(x0, nil)) → c16(__'(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.31
PROPER(__(x0, tt)) → c16(__'(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.31
PROPER(__(nil, x1)) → c16(__'(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(__(tt, x1)) → c16(__'(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(and(x0, __(z0, z1))) → c18(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(and(x0, and(z0, z1))) → c18(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(and(x0, isNePal(z0))) → c18(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(and(__(z0, z1), x1)) → c18(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(and(and(z0, z1), x1)) → c18(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(and(isNePal(z0), x1)) → c18(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.31
PROPER(and(x0, nil)) → c18(AND(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.31
PROPER(and(x0, tt)) → c18(AND(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.31
PROPER(and(nil, x1)) → c18(AND(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(and(tt, x1)) → c18(AND(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(isNePal(__(z0, z1))) → c20(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1))) 118.27/44.31
PROPER(isNePal(and(z0, z1))) → c20(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 118.27/44.31
PROPER(isNePal(isNePal(z0))) → c20(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0))) 118.27/44.31
PROPER(isNePal(nil)) → c20(ISNEPAL(ok(nil))) 118.27/44.31
PROPER(isNePal(tt)) → c20(ISNEPAL(ok(tt)))
K tuples:

TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, __, and, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', AND, ISNEPAL, TOP, PROPER

Compound Symbols:

c5, c6, c9, c10, c11, c12, c13, c14, c15, c21, c22, c1, c7, c7, c8, c8, c16, c16, c18, c18, c20, c20

118.27/44.31
118.27/44.31

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

Use narrowing to replace TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0)) by

TOP(mark(__(z0, z1))) → c21(TOP(__(proper(z0), proper(z1))), PROPER(__(z0, z1))) 118.27/44.31
TOP(mark(nil)) → c21(TOP(ok(nil)), PROPER(nil)) 118.27/44.31
TOP(mark(and(z0, z1))) → c21(TOP(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 118.27/44.31
TOP(mark(tt)) → c21(TOP(ok(tt)), PROPER(tt)) 118.27/44.31
TOP(mark(isNePal(z0))) → c21(TOP(isNePal(proper(z0))), PROPER(isNePal(z0)))
118.27/44.31
118.27/44.31

(28) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2))) 118.27/44.31
active(__(z0, nil)) → mark(z0) 118.27/44.31
active(__(nil, z0)) → mark(z0) 118.27/44.31
active(and(tt, z0)) → mark(z0) 118.27/44.31
active(isNePal(__(z0, __(z1, z0)))) → mark(tt) 118.27/44.31
active(__(z0, z1)) → __(active(z0), z1) 118.27/44.31
active(__(z0, z1)) → __(z0, active(z1)) 118.27/44.31
active(and(z0, z1)) → and(active(z0), z1) 118.27/44.31
active(isNePal(z0)) → isNePal(active(z0)) 118.27/44.31
__(mark(z0), z1) → mark(__(z0, z1)) 118.27/44.31
__(z0, mark(z1)) → mark(__(z0, z1)) 118.27/44.31
__(ok(z0), ok(z1)) → ok(__(z0, z1)) 118.27/44.31
and(mark(z0), z1) → mark(and(z0, z1)) 118.27/44.31
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 118.27/44.31
isNePal(mark(z0)) → mark(isNePal(z0)) 118.27/44.31
isNePal(ok(z0)) → ok(isNePal(z0)) 118.27/44.31
proper(__(z0, z1)) → __(proper(z0), proper(z1)) 118.27/44.31
proper(nil) → ok(nil) 118.27/44.31
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 118.27/44.31
proper(tt) → ok(tt) 118.27/44.31
proper(isNePal(z0)) → isNePal(proper(z0)) 118.27/44.31
top(mark(z0)) → top(proper(z0)) 118.27/44.31
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 118.27/44.31
__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.31
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.31
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.31
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.31
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.31
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.31
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 118.27/44.31
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 118.27/44.31
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1)) 118.27/44.31
ACTIVE(isNePal(__(__(z0, z1), z2))) → c8(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(isNePal(__(z0, nil))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(isNePal(__(nil, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c8(ISNEPAL(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(and(z0, z1))) → c8(ISNEPAL(and(active(z0), z1)), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(isNePal(isNePal(z0))) → c8(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(isNePal(and(tt, z0))) → c8(ISNEPAL(mark(z0))) 118.27/44.31
PROPER(__(x0, __(z0, z1))) → c16(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(__(x0, and(z0, z1))) → c16(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(__(x0, isNePal(z0))) → c16(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(__(__(z0, z1), x1)) → c16(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(and(z0, z1), x1)) → c16(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(isNePal(z0), x1)) → c16(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.31
PROPER(__(x0, nil)) → c16(__'(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.31
PROPER(__(x0, tt)) → c16(__'(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.31
PROPER(__(nil, x1)) → c16(__'(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(__(tt, x1)) → c16(__'(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(and(x0, __(z0, z1))) → c18(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(and(x0, and(z0, z1))) → c18(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(and(x0, isNePal(z0))) → c18(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(and(__(z0, z1), x1)) → c18(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(and(and(z0, z1), x1)) → c18(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(and(isNePal(z0), x1)) → c18(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.31
PROPER(and(x0, nil)) → c18(AND(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.31
PROPER(and(x0, tt)) → c18(AND(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.31
PROPER(and(nil, x1)) → c18(AND(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(and(tt, x1)) → c18(AND(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(isNePal(__(z0, z1))) → c20(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1))) 118.27/44.31
PROPER(isNePal(and(z0, z1))) → c20(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 118.27/44.31
PROPER(isNePal(isNePal(z0))) → c20(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0))) 118.27/44.31
PROPER(isNePal(nil)) → c20(ISNEPAL(ok(nil))) 118.27/44.31
PROPER(isNePal(tt)) → c20(ISNEPAL(ok(tt))) 118.27/44.31
TOP(mark(__(z0, z1))) → c21(TOP(__(proper(z0), proper(z1))), PROPER(__(z0, z1))) 118.27/44.31
TOP(mark(nil)) → c21(TOP(ok(nil)), PROPER(nil)) 118.27/44.31
TOP(mark(and(z0, z1))) → c21(TOP(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 118.27/44.31
TOP(mark(tt)) → c21(TOP(ok(tt)), PROPER(tt)) 118.27/44.31
TOP(mark(isNePal(z0))) → c21(TOP(isNePal(proper(z0))), PROPER(isNePal(z0)))
S tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 118.27/44.31
__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.31
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.31
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.31
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.31
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.31
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.31
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 118.27/44.31
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 118.27/44.31
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1)) 118.27/44.31
ACTIVE(isNePal(__(__(z0, z1), z2))) → c8(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(isNePal(__(z0, nil))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(isNePal(__(nil, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c8(ISNEPAL(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(and(z0, z1))) → c8(ISNEPAL(and(active(z0), z1)), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(isNePal(isNePal(z0))) → c8(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(isNePal(and(tt, z0))) → c8(ISNEPAL(mark(z0))) 118.27/44.31
PROPER(__(x0, __(z0, z1))) → c16(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(__(x0, and(z0, z1))) → c16(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(__(x0, isNePal(z0))) → c16(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(__(__(z0, z1), x1)) → c16(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(and(z0, z1), x1)) → c16(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(isNePal(z0), x1)) → c16(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.31
PROPER(__(x0, nil)) → c16(__'(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.31
PROPER(__(x0, tt)) → c16(__'(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.31
PROPER(__(nil, x1)) → c16(__'(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(__(tt, x1)) → c16(__'(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(and(x0, __(z0, z1))) → c18(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(and(x0, and(z0, z1))) → c18(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(and(x0, isNePal(z0))) → c18(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(and(__(z0, z1), x1)) → c18(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(and(and(z0, z1), x1)) → c18(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(and(isNePal(z0), x1)) → c18(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.31
PROPER(and(x0, nil)) → c18(AND(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.31
PROPER(and(x0, tt)) → c18(AND(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.31
PROPER(and(nil, x1)) → c18(AND(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(and(tt, x1)) → c18(AND(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(isNePal(__(z0, z1))) → c20(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1))) 118.27/44.31
PROPER(isNePal(and(z0, z1))) → c20(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 118.27/44.31
PROPER(isNePal(isNePal(z0))) → c20(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0))) 118.27/44.31
PROPER(isNePal(nil)) → c20(ISNEPAL(ok(nil))) 118.27/44.31
PROPER(isNePal(tt)) → c20(ISNEPAL(ok(tt)))
K tuples:

TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, __, and, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', AND, ISNEPAL, TOP, PROPER

Compound Symbols:

c5, c6, c9, c10, c11, c12, c13, c14, c15, c22, c1, c7, c7, c8, c8, c16, c16, c18, c18, c20, c20, c21

118.27/44.31
118.27/44.31

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

Removed 2 trailing tuple parts
118.27/44.31
118.27/44.31

(30) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2))) 118.27/44.31
active(__(z0, nil)) → mark(z0) 118.27/44.31
active(__(nil, z0)) → mark(z0) 118.27/44.31
active(and(tt, z0)) → mark(z0) 118.27/44.31
active(isNePal(__(z0, __(z1, z0)))) → mark(tt) 118.27/44.31
active(__(z0, z1)) → __(active(z0), z1) 118.27/44.31
active(__(z0, z1)) → __(z0, active(z1)) 118.27/44.31
active(and(z0, z1)) → and(active(z0), z1) 118.27/44.31
active(isNePal(z0)) → isNePal(active(z0)) 118.27/44.31
__(mark(z0), z1) → mark(__(z0, z1)) 118.27/44.31
__(z0, mark(z1)) → mark(__(z0, z1)) 118.27/44.31
__(ok(z0), ok(z1)) → ok(__(z0, z1)) 118.27/44.31
and(mark(z0), z1) → mark(and(z0, z1)) 118.27/44.31
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 118.27/44.31
isNePal(mark(z0)) → mark(isNePal(z0)) 118.27/44.31
isNePal(ok(z0)) → ok(isNePal(z0)) 118.27/44.31
proper(__(z0, z1)) → __(proper(z0), proper(z1)) 118.27/44.31
proper(nil) → ok(nil) 118.27/44.31
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 118.27/44.31
proper(tt) → ok(tt) 118.27/44.31
proper(isNePal(z0)) → isNePal(proper(z0)) 118.27/44.31
top(mark(z0)) → top(proper(z0)) 118.27/44.31
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 118.27/44.31
__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.31
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.31
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.31
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.31
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.31
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.31
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 118.27/44.31
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 118.27/44.31
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 118.27/44.31
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1)) 118.27/44.31
ACTIVE(isNePal(__(__(z0, z1), z2))) → c8(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 118.27/44.31
ACTIVE(isNePal(__(z0, nil))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil))) 118.27/44.31
ACTIVE(isNePal(__(nil, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0))) 118.27/44.31
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c8(ISNEPAL(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1))) 118.27/44.31
ACTIVE(isNePal(and(z0, z1))) → c8(ISNEPAL(and(active(z0), z1)), ACTIVE(and(z0, z1))) 118.27/44.31
ACTIVE(isNePal(isNePal(z0))) → c8(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0))) 118.27/44.31
ACTIVE(isNePal(and(tt, z0))) → c8(ISNEPAL(mark(z0))) 118.27/44.31
PROPER(__(x0, __(z0, z1))) → c16(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(__(x0, and(z0, z1))) → c16(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(__(x0, isNePal(z0))) → c16(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(__(__(z0, z1), x1)) → c16(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(and(z0, z1), x1)) → c16(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(__(isNePal(z0), x1)) → c16(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.31
PROPER(__(x0, nil)) → c16(__'(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.31
PROPER(__(x0, tt)) → c16(__'(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.31
PROPER(__(nil, x1)) → c16(__'(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(__(tt, x1)) → c16(__'(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(and(x0, __(z0, z1))) → c18(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.31
PROPER(and(x0, and(z0, z1))) → c18(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.31
PROPER(and(x0, isNePal(z0))) → c18(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.31
PROPER(and(__(z0, z1), x1)) → c18(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(and(and(z0, z1), x1)) → c18(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.31
PROPER(and(isNePal(z0), x1)) → c18(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.31
PROPER(and(x0, nil)) → c18(AND(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.31
PROPER(and(x0, tt)) → c18(AND(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.31
PROPER(and(nil, x1)) → c18(AND(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(and(tt, x1)) → c18(AND(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.31
PROPER(isNePal(__(z0, z1))) → c20(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1))) 118.27/44.31
PROPER(isNePal(and(z0, z1))) → c20(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 118.27/44.31
PROPER(isNePal(isNePal(z0))) → c20(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0))) 118.27/44.31
PROPER(isNePal(nil)) → c20(ISNEPAL(ok(nil))) 118.27/44.31
PROPER(isNePal(tt)) → c20(ISNEPAL(ok(tt))) 118.27/44.31
TOP(mark(__(z0, z1))) → c21(TOP(__(proper(z0), proper(z1))), PROPER(__(z0, z1))) 118.27/44.31
TOP(mark(and(z0, z1))) → c21(TOP(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 118.27/44.31
TOP(mark(isNePal(z0))) → c21(TOP(isNePal(proper(z0))), PROPER(isNePal(z0))) 118.27/44.31
TOP(mark(nil)) → c21(TOP(ok(nil))) 118.27/44.31
TOP(mark(tt)) → c21(TOP(ok(tt)))
S tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 118.27/44.31
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 118.27/44.31
__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.31
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.31
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.31
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.31
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.31
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.32
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 118.27/44.32
TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) 118.27/44.32
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 118.27/44.32
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 118.27/44.32
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 118.27/44.32
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 118.27/44.32
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 118.27/44.32
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.32
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 118.27/44.32
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 118.27/44.32
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 118.27/44.32
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0))) 118.27/44.32
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1)) 118.27/44.32
ACTIVE(isNePal(__(__(z0, z1), z2))) → c8(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 118.27/44.32
ACTIVE(isNePal(__(z0, nil))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil))) 118.27/44.32
ACTIVE(isNePal(__(nil, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0))) 118.27/44.32
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c8(ISNEPAL(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.32
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1))) 118.27/44.32
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1))) 118.27/44.32
ACTIVE(isNePal(and(z0, z1))) → c8(ISNEPAL(and(active(z0), z1)), ACTIVE(and(z0, z1))) 118.27/44.32
ACTIVE(isNePal(isNePal(z0))) → c8(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0))) 118.27/44.32
ACTIVE(isNePal(and(tt, z0))) → c8(ISNEPAL(mark(z0))) 118.27/44.32
PROPER(__(x0, __(z0, z1))) → c16(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.32
PROPER(__(x0, and(z0, z1))) → c16(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.32
PROPER(__(x0, isNePal(z0))) → c16(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.32
PROPER(__(__(z0, z1), x1)) → c16(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.32
PROPER(__(and(z0, z1), x1)) → c16(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.32
PROPER(__(isNePal(z0), x1)) → c16(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.32
PROPER(__(x0, nil)) → c16(__'(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.32
PROPER(__(x0, tt)) → c16(__'(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.32
PROPER(__(nil, x1)) → c16(__'(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.32
PROPER(__(tt, x1)) → c16(__'(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.32
PROPER(and(x0, __(z0, z1))) → c18(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.32
PROPER(and(x0, and(z0, z1))) → c18(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.32
PROPER(and(x0, isNePal(z0))) → c18(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.32
PROPER(and(__(z0, z1), x1)) → c18(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.32
PROPER(and(and(z0, z1), x1)) → c18(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.32
PROPER(and(isNePal(z0), x1)) → c18(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.32
PROPER(and(x0, nil)) → c18(AND(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.32
PROPER(and(x0, tt)) → c18(AND(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.32
PROPER(and(nil, x1)) → c18(AND(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.32
PROPER(and(tt, x1)) → c18(AND(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.32
PROPER(isNePal(__(z0, z1))) → c20(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1))) 118.27/44.32
PROPER(isNePal(and(z0, z1))) → c20(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 118.27/44.32
PROPER(isNePal(isNePal(z0))) → c20(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0))) 118.27/44.32
PROPER(isNePal(nil)) → c20(ISNEPAL(ok(nil))) 118.27/44.32
PROPER(isNePal(tt)) → c20(ISNEPAL(ok(tt)))
K tuples:

TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, __, and, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', AND, ISNEPAL, TOP, PROPER

Compound Symbols:

c5, c6, c9, c10, c11, c12, c13, c14, c15, c22, c1, c7, c7, c8, c8, c16, c16, c18, c18, c20, c20, c21, c21

118.27/44.32
118.27/44.32

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

Use narrowing to replace TOP(ok(z0)) → c22(TOP(active(z0)), ACTIVE(z0)) by

TOP(ok(__(__(z0, z1), z2))) → c22(TOP(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 118.27/44.32
TOP(ok(__(z0, nil))) → c22(TOP(mark(z0)), ACTIVE(__(z0, nil))) 118.27/44.32
TOP(ok(__(nil, z0))) → c22(TOP(mark(z0)), ACTIVE(__(nil, z0))) 118.27/44.32
TOP(ok(and(tt, z0))) → c22(TOP(mark(z0)), ACTIVE(and(tt, z0))) 118.27/44.32
TOP(ok(isNePal(__(z0, __(z1, z0))))) → c22(TOP(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.32
TOP(ok(__(z0, z1))) → c22(TOP(__(active(z0), z1)), ACTIVE(__(z0, z1))) 118.27/44.32
TOP(ok(__(z0, z1))) → c22(TOP(__(z0, active(z1))), ACTIVE(__(z0, z1))) 118.27/44.32
TOP(ok(and(z0, z1))) → c22(TOP(and(active(z0), z1)), ACTIVE(and(z0, z1))) 118.27/44.32
TOP(ok(isNePal(z0))) → c22(TOP(isNePal(active(z0))), ACTIVE(isNePal(z0)))
118.27/44.32
118.27/44.32

(32) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2))) 118.27/44.32
active(__(z0, nil)) → mark(z0) 118.27/44.32
active(__(nil, z0)) → mark(z0) 118.27/44.32
active(and(tt, z0)) → mark(z0) 118.27/44.32
active(isNePal(__(z0, __(z1, z0)))) → mark(tt) 118.27/44.32
active(__(z0, z1)) → __(active(z0), z1) 118.27/44.32
active(__(z0, z1)) → __(z0, active(z1)) 118.27/44.32
active(and(z0, z1)) → and(active(z0), z1) 118.27/44.32
active(isNePal(z0)) → isNePal(active(z0)) 118.27/44.32
__(mark(z0), z1) → mark(__(z0, z1)) 118.27/44.32
__(z0, mark(z1)) → mark(__(z0, z1)) 118.27/44.32
__(ok(z0), ok(z1)) → ok(__(z0, z1)) 118.27/44.32
and(mark(z0), z1) → mark(and(z0, z1)) 118.27/44.32
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 118.27/44.32
isNePal(mark(z0)) → mark(isNePal(z0)) 118.27/44.32
isNePal(ok(z0)) → ok(isNePal(z0)) 118.27/44.32
proper(__(z0, z1)) → __(proper(z0), proper(z1)) 118.27/44.32
proper(nil) → ok(nil) 118.27/44.32
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 118.27/44.32
proper(tt) → ok(tt) 118.27/44.32
proper(isNePal(z0)) → isNePal(proper(z0)) 118.27/44.32
top(mark(z0)) → top(proper(z0)) 118.27/44.32
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 118.27/44.32
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 118.27/44.32
__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.32
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.32
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.32
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.32
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.32
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.32
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 118.27/44.32
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 118.27/44.32
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 118.27/44.32
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 118.27/44.32
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 118.27/44.32
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 118.27/44.32
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.32
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 118.27/44.32
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 118.27/44.32
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 118.27/44.32
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0))) 118.27/44.32
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1)) 118.27/44.32
ACTIVE(isNePal(__(__(z0, z1), z2))) → c8(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 118.27/44.32
ACTIVE(isNePal(__(z0, nil))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil))) 118.27/44.32
ACTIVE(isNePal(__(nil, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0))) 118.27/44.32
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c8(ISNEPAL(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.32
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1))) 118.27/44.32
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1))) 118.27/44.32
ACTIVE(isNePal(and(z0, z1))) → c8(ISNEPAL(and(active(z0), z1)), ACTIVE(and(z0, z1))) 118.27/44.32
ACTIVE(isNePal(isNePal(z0))) → c8(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0))) 118.27/44.32
ACTIVE(isNePal(and(tt, z0))) → c8(ISNEPAL(mark(z0))) 118.27/44.32
PROPER(__(x0, __(z0, z1))) → c16(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.32
PROPER(__(x0, and(z0, z1))) → c16(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.32
PROPER(__(x0, isNePal(z0))) → c16(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.32
PROPER(__(__(z0, z1), x1)) → c16(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.32
PROPER(__(and(z0, z1), x1)) → c16(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.32
PROPER(__(isNePal(z0), x1)) → c16(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.32
PROPER(__(x0, nil)) → c16(__'(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.32
PROPER(__(x0, tt)) → c16(__'(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.32
PROPER(__(nil, x1)) → c16(__'(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.32
PROPER(__(tt, x1)) → c16(__'(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.32
PROPER(and(x0, __(z0, z1))) → c18(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.32
PROPER(and(x0, and(z0, z1))) → c18(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.32
PROPER(and(x0, isNePal(z0))) → c18(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.32
PROPER(and(__(z0, z1), x1)) → c18(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.32
PROPER(and(and(z0, z1), x1)) → c18(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.32
PROPER(and(isNePal(z0), x1)) → c18(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.32
PROPER(and(x0, nil)) → c18(AND(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.32
PROPER(and(x0, tt)) → c18(AND(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.32
PROPER(and(nil, x1)) → c18(AND(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.32
PROPER(and(tt, x1)) → c18(AND(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.32
PROPER(isNePal(__(z0, z1))) → c20(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1))) 118.27/44.32
PROPER(isNePal(and(z0, z1))) → c20(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 118.27/44.32
PROPER(isNePal(isNePal(z0))) → c20(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0))) 118.27/44.32
PROPER(isNePal(nil)) → c20(ISNEPAL(ok(nil))) 118.27/44.32
PROPER(isNePal(tt)) → c20(ISNEPAL(ok(tt))) 118.27/44.32
TOP(mark(__(z0, z1))) → c21(TOP(__(proper(z0), proper(z1))), PROPER(__(z0, z1))) 118.27/44.32
TOP(mark(and(z0, z1))) → c21(TOP(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 118.27/44.32
TOP(mark(isNePal(z0))) → c21(TOP(isNePal(proper(z0))), PROPER(isNePal(z0))) 118.27/44.32
TOP(mark(nil)) → c21(TOP(ok(nil))) 118.27/44.32
TOP(mark(tt)) → c21(TOP(ok(tt))) 118.27/44.32
TOP(ok(__(__(z0, z1), z2))) → c22(TOP(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 118.27/44.32
TOP(ok(__(z0, nil))) → c22(TOP(mark(z0)), ACTIVE(__(z0, nil))) 118.27/44.32
TOP(ok(__(nil, z0))) → c22(TOP(mark(z0)), ACTIVE(__(nil, z0))) 118.27/44.32
TOP(ok(and(tt, z0))) → c22(TOP(mark(z0)), ACTIVE(and(tt, z0))) 118.27/44.32
TOP(ok(isNePal(__(z0, __(z1, z0))))) → c22(TOP(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.32
TOP(ok(__(z0, z1))) → c22(TOP(__(active(z0), z1)), ACTIVE(__(z0, z1))) 118.27/44.32
TOP(ok(__(z0, z1))) → c22(TOP(__(z0, active(z1))), ACTIVE(__(z0, z1))) 118.27/44.32
TOP(ok(and(z0, z1))) → c22(TOP(and(active(z0), z1)), ACTIVE(and(z0, z1))) 118.27/44.32
TOP(ok(isNePal(z0))) → c22(TOP(isNePal(active(z0))), ACTIVE(isNePal(z0)))
S tuples:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 118.27/44.32
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 118.27/44.32
__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.32
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.32
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.32
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.32
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.32
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.32
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 118.27/44.32
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 118.27/44.32
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 118.27/44.32
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 118.27/44.32
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 118.27/44.32
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 118.27/44.32
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.32
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 118.27/44.32
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 118.27/44.32
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 118.27/44.32
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0))) 118.27/44.32
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1)) 118.27/44.32
ACTIVE(isNePal(__(__(z0, z1), z2))) → c8(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 118.27/44.32
ACTIVE(isNePal(__(z0, nil))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil))) 118.27/44.32
ACTIVE(isNePal(__(nil, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0))) 118.27/44.32
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c8(ISNEPAL(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.32
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1))) 118.27/44.32
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1))) 118.27/44.32
ACTIVE(isNePal(and(z0, z1))) → c8(ISNEPAL(and(active(z0), z1)), ACTIVE(and(z0, z1))) 118.27/44.32
ACTIVE(isNePal(isNePal(z0))) → c8(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0))) 118.27/44.32
ACTIVE(isNePal(and(tt, z0))) → c8(ISNEPAL(mark(z0))) 118.27/44.32
PROPER(__(x0, __(z0, z1))) → c16(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.32
PROPER(__(x0, and(z0, z1))) → c16(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.32
PROPER(__(x0, isNePal(z0))) → c16(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.32
PROPER(__(__(z0, z1), x1)) → c16(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.32
PROPER(__(and(z0, z1), x1)) → c16(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.32
PROPER(__(isNePal(z0), x1)) → c16(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.32
PROPER(__(x0, nil)) → c16(__'(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.32
PROPER(__(x0, tt)) → c16(__'(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.32
PROPER(__(nil, x1)) → c16(__'(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.32
PROPER(__(tt, x1)) → c16(__'(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.32
PROPER(and(x0, __(z0, z1))) → c18(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.32
PROPER(and(x0, and(z0, z1))) → c18(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.32
PROPER(and(x0, isNePal(z0))) → c18(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.32
PROPER(and(__(z0, z1), x1)) → c18(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.32
PROPER(and(and(z0, z1), x1)) → c18(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.32
PROPER(and(isNePal(z0), x1)) → c18(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.32
PROPER(and(x0, nil)) → c18(AND(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.32
PROPER(and(x0, tt)) → c18(AND(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.32
PROPER(and(nil, x1)) → c18(AND(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.32
PROPER(and(tt, x1)) → c18(AND(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.32
PROPER(isNePal(__(z0, z1))) → c20(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1))) 118.27/44.32
PROPER(isNePal(and(z0, z1))) → c20(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 118.27/44.32
PROPER(isNePal(isNePal(z0))) → c20(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0))) 118.27/44.32
PROPER(isNePal(nil)) → c20(ISNEPAL(ok(nil))) 118.27/44.32
PROPER(isNePal(tt)) → c20(ISNEPAL(ok(tt))) 118.27/44.32
TOP(ok(__(__(z0, z1), z2))) → c22(TOP(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 118.27/44.32
TOP(ok(__(z0, nil))) → c22(TOP(mark(z0)), ACTIVE(__(z0, nil))) 118.27/44.32
TOP(ok(__(nil, z0))) → c22(TOP(mark(z0)), ACTIVE(__(nil, z0))) 118.27/44.32
TOP(ok(and(tt, z0))) → c22(TOP(mark(z0)), ACTIVE(and(tt, z0))) 118.27/44.32
TOP(ok(isNePal(__(z0, __(z1, z0))))) → c22(TOP(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.32
TOP(ok(__(z0, z1))) → c22(TOP(__(active(z0), z1)), ACTIVE(__(z0, z1))) 118.27/44.32
TOP(ok(__(z0, z1))) → c22(TOP(__(z0, active(z1))), ACTIVE(__(z0, z1))) 118.27/44.32
TOP(ok(and(z0, z1))) → c22(TOP(and(active(z0), z1)), ACTIVE(and(z0, z1))) 118.27/44.32
TOP(ok(isNePal(z0))) → c22(TOP(isNePal(active(z0))), ACTIVE(isNePal(z0)))
K tuples:

TOP(mark(z0)) → c21(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, __, and, isNePal, proper, top

Defined Pair Symbols:

ACTIVE, __', AND, ISNEPAL, PROPER, TOP

Compound Symbols:

c5, c6, c9, c10, c11, c12, c13, c14, c15, c1, c7, c7, c8, c8, c16, c16, c18, c18, c20, c20, c21, c21, c22

118.27/44.32
118.27/44.32

(33) CdtUnreachableProof (EQUIVALENT transformation)

The following tuples could be removed as they are not reachable from basic start terms:

ACTIVE(__(z0, z1)) → c5(__'(active(z0), z1), ACTIVE(z0)) 118.27/44.32
ACTIVE(__(z0, z1)) → c6(__'(z0, active(z1)), ACTIVE(z1)) 118.27/44.32
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2))) 118.27/44.32
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2)) 118.27/44.32
ACTIVE(and(__(__(z0, z1), z2), x1)) → c7(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2))) 118.27/44.32
ACTIVE(and(__(z0, nil), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(z0, nil))) 118.27/44.32
ACTIVE(and(__(nil, z0), x1)) → c7(AND(mark(z0), x1), ACTIVE(__(nil, z0))) 118.27/44.32
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c7(AND(mark(tt), x1), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.32
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1))) 118.27/44.32
ACTIVE(and(__(z0, z1), x1)) → c7(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1))) 118.27/44.32
ACTIVE(and(and(z0, z1), x1)) → c7(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 118.27/44.32
ACTIVE(and(isNePal(z0), x1)) → c7(AND(isNePal(active(z0)), x1), ACTIVE(isNePal(z0))) 118.27/44.32
ACTIVE(and(and(tt, z0), x1)) → c7(AND(mark(z0), x1)) 118.27/44.32
ACTIVE(isNePal(__(__(z0, z1), z2))) → c8(ISNEPAL(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 118.27/44.32
ACTIVE(isNePal(__(z0, nil))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(z0, nil))) 118.27/44.32
ACTIVE(isNePal(__(nil, z0))) → c8(ISNEPAL(mark(z0)), ACTIVE(__(nil, z0))) 118.27/44.32
ACTIVE(isNePal(isNePal(__(z0, __(z1, z0))))) → c8(ISNEPAL(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.32
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(active(z0), z1)), ACTIVE(__(z0, z1))) 118.27/44.32
ACTIVE(isNePal(__(z0, z1))) → c8(ISNEPAL(__(z0, active(z1))), ACTIVE(__(z0, z1))) 118.27/44.32
ACTIVE(isNePal(and(z0, z1))) → c8(ISNEPAL(and(active(z0), z1)), ACTIVE(and(z0, z1))) 118.27/44.32
ACTIVE(isNePal(isNePal(z0))) → c8(ISNEPAL(isNePal(active(z0))), ACTIVE(isNePal(z0))) 118.27/44.32
ACTIVE(isNePal(and(tt, z0))) → c8(ISNEPAL(mark(z0))) 118.27/44.32
PROPER(__(x0, __(z0, z1))) → c16(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.32
PROPER(__(x0, and(z0, z1))) → c16(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.32
PROPER(__(x0, isNePal(z0))) → c16(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.32
PROPER(__(__(z0, z1), x1)) → c16(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.32
PROPER(__(and(z0, z1), x1)) → c16(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.32
PROPER(__(isNePal(z0), x1)) → c16(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.32
PROPER(__(x0, nil)) → c16(__'(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.32
PROPER(__(x0, tt)) → c16(__'(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.32
PROPER(__(nil, x1)) → c16(__'(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.32
PROPER(__(tt, x1)) → c16(__'(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.32
PROPER(and(x0, __(z0, z1))) → c18(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1))) 118.27/44.32
PROPER(and(x0, and(z0, z1))) → c18(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 118.27/44.32
PROPER(and(x0, isNePal(z0))) → c18(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0))) 118.27/44.32
PROPER(and(__(z0, z1), x1)) → c18(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1)) 118.27/44.32
PROPER(and(and(z0, z1), x1)) → c18(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 118.27/44.32
PROPER(and(isNePal(z0), x1)) → c18(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1)) 118.27/44.32
PROPER(and(x0, nil)) → c18(AND(proper(x0), ok(nil)), PROPER(x0)) 118.27/44.32
PROPER(and(x0, tt)) → c18(AND(proper(x0), ok(tt)), PROPER(x0)) 118.27/44.32
PROPER(and(nil, x1)) → c18(AND(ok(nil), proper(x1)), PROPER(x1)) 118.27/44.32
PROPER(and(tt, x1)) → c18(AND(ok(tt), proper(x1)), PROPER(x1)) 118.27/44.32
PROPER(isNePal(__(z0, z1))) → c20(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1))) 118.27/44.32
PROPER(isNePal(and(z0, z1))) → c20(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 118.27/44.32
PROPER(isNePal(isNePal(z0))) → c20(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0))) 118.27/44.32
PROPER(isNePal(nil)) → c20(ISNEPAL(ok(nil))) 118.27/44.32
PROPER(isNePal(tt)) → c20(ISNEPAL(ok(tt))) 118.27/44.32
TOP(mark(__(z0, z1))) → c21(TOP(__(proper(z0), proper(z1))), PROPER(__(z0, z1))) 118.27/44.32
TOP(mark(and(z0, z1))) → c21(TOP(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 118.27/44.32
TOP(mark(isNePal(z0))) → c21(TOP(isNePal(proper(z0))), PROPER(isNePal(z0))) 118.27/44.32
TOP(ok(__(__(z0, z1), z2))) → c22(TOP(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2))) 118.27/44.32
TOP(ok(__(z0, nil))) → c22(TOP(mark(z0)), ACTIVE(__(z0, nil))) 118.27/44.32
TOP(ok(__(nil, z0))) → c22(TOP(mark(z0)), ACTIVE(__(nil, z0))) 118.27/44.32
TOP(ok(and(tt, z0))) → c22(TOP(mark(z0)), ACTIVE(and(tt, z0))) 118.27/44.32
TOP(ok(isNePal(__(z0, __(z1, z0))))) → c22(TOP(mark(tt)), ACTIVE(isNePal(__(z0, __(z1, z0))))) 118.27/44.32
TOP(ok(__(z0, z1))) → c22(TOP(__(active(z0), z1)), ACTIVE(__(z0, z1))) 118.27/44.32
TOP(ok(__(z0, z1))) → c22(TOP(__(z0, active(z1))), ACTIVE(__(z0, z1))) 118.27/44.32
TOP(ok(and(z0, z1))) → c22(TOP(and(active(z0), z1)), ACTIVE(and(z0, z1))) 118.27/44.32
TOP(ok(isNePal(z0))) → c22(TOP(isNePal(active(z0))), ACTIVE(isNePal(z0)))
118.27/44.32
118.27/44.32

(34) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2))) 118.27/44.32
active(__(z0, nil)) → mark(z0) 118.27/44.32
active(__(nil, z0)) → mark(z0) 118.27/44.32
active(and(tt, z0)) → mark(z0) 118.27/44.32
active(isNePal(__(z0, __(z1, z0)))) → mark(tt) 118.27/44.32
active(__(z0, z1)) → __(active(z0), z1) 118.27/44.32
active(__(z0, z1)) → __(z0, active(z1)) 118.27/44.32
active(and(z0, z1)) → and(active(z0), z1) 118.27/44.32
active(isNePal(z0)) → isNePal(active(z0)) 118.27/44.32
__(mark(z0), z1) → mark(__(z0, z1)) 118.27/44.32
__(z0, mark(z1)) → mark(__(z0, z1)) 118.27/44.32
__(ok(z0), ok(z1)) → ok(__(z0, z1)) 118.27/44.32
and(mark(z0), z1) → mark(and(z0, z1)) 118.27/44.32
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 118.27/44.32
isNePal(mark(z0)) → mark(isNePal(z0)) 118.27/44.32
isNePal(ok(z0)) → ok(isNePal(z0)) 118.27/44.32
proper(__(z0, z1)) → __(proper(z0), proper(z1)) 118.27/44.32
proper(nil) → ok(nil) 118.27/44.32
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 118.27/44.32
proper(tt) → ok(tt) 118.27/44.32
proper(isNePal(z0)) → isNePal(proper(z0)) 118.27/44.32
top(mark(z0)) → top(proper(z0)) 118.27/44.32
top(ok(z0)) → top(active(z0))
Tuples:

__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.32
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.32
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.32
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.32
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.32
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.32
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 118.27/44.32
TOP(mark(nil)) → c21(TOP(ok(nil))) 118.27/44.32
TOP(mark(tt)) → c21(TOP(ok(tt)))
S tuples:

__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.32
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.32
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.32
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.32
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.32
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.32
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0))
K tuples:none
Defined Rule Symbols:

active, __, and, isNePal, proper, top

Defined Pair Symbols:

__', AND, ISNEPAL, TOP

Compound Symbols:

c9, c10, c11, c12, c13, c14, c15, c21

118.27/44.32
118.27/44.32

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

Removed 2 trailing tuple parts
118.27/44.32
118.27/44.32

(36) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2))) 118.27/44.32
active(__(z0, nil)) → mark(z0) 118.27/44.32
active(__(nil, z0)) → mark(z0) 118.27/44.32
active(and(tt, z0)) → mark(z0) 118.27/44.32
active(isNePal(__(z0, __(z1, z0)))) → mark(tt) 118.27/44.32
active(__(z0, z1)) → __(active(z0), z1) 118.27/44.32
active(__(z0, z1)) → __(z0, active(z1)) 118.27/44.32
active(and(z0, z1)) → and(active(z0), z1) 118.27/44.32
active(isNePal(z0)) → isNePal(active(z0)) 118.27/44.32
__(mark(z0), z1) → mark(__(z0, z1)) 118.27/44.32
__(z0, mark(z1)) → mark(__(z0, z1)) 118.27/44.32
__(ok(z0), ok(z1)) → ok(__(z0, z1)) 118.27/44.32
and(mark(z0), z1) → mark(and(z0, z1)) 118.27/44.32
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 118.27/44.32
isNePal(mark(z0)) → mark(isNePal(z0)) 118.27/44.32
isNePal(ok(z0)) → ok(isNePal(z0)) 118.27/44.32
proper(__(z0, z1)) → __(proper(z0), proper(z1)) 118.27/44.32
proper(nil) → ok(nil) 118.27/44.32
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 118.27/44.32
proper(tt) → ok(tt) 118.27/44.32
proper(isNePal(z0)) → isNePal(proper(z0)) 118.27/44.32
top(mark(z0)) → top(proper(z0)) 118.27/44.32
top(ok(z0)) → top(active(z0))
Tuples:

__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.32
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.32
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.32
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.32
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.32
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.32
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0)) 118.27/44.32
TOP(mark(nil)) → c21 118.27/44.32
TOP(mark(tt)) → c21
S tuples:

__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.32
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.32
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.32
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.32
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.32
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.32
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0))
K tuples:none
Defined Rule Symbols:

active, __, and, isNePal, proper, top

Defined Pair Symbols:

__', AND, ISNEPAL, TOP

Compound Symbols:

c9, c10, c11, c12, c13, c14, c15, c21

118.27/44.32
118.27/44.32

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

Removed 2 trailing nodes:

TOP(mark(tt)) → c21 118.27/44.32
TOP(mark(nil)) → c21
118.27/44.32
118.27/44.32

(38) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2))) 118.27/44.32
active(__(z0, nil)) → mark(z0) 118.27/44.32
active(__(nil, z0)) → mark(z0) 118.27/44.32
active(and(tt, z0)) → mark(z0) 118.27/44.32
active(isNePal(__(z0, __(z1, z0)))) → mark(tt) 118.27/44.32
active(__(z0, z1)) → __(active(z0), z1) 118.27/44.32
active(__(z0, z1)) → __(z0, active(z1)) 118.27/44.32
active(and(z0, z1)) → and(active(z0), z1) 118.27/44.32
active(isNePal(z0)) → isNePal(active(z0)) 118.27/44.32
__(mark(z0), z1) → mark(__(z0, z1)) 118.27/44.32
__(z0, mark(z1)) → mark(__(z0, z1)) 118.27/44.32
__(ok(z0), ok(z1)) → ok(__(z0, z1)) 118.27/44.32
and(mark(z0), z1) → mark(and(z0, z1)) 118.27/44.32
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 118.27/44.32
isNePal(mark(z0)) → mark(isNePal(z0)) 118.27/44.32
isNePal(ok(z0)) → ok(isNePal(z0)) 118.27/44.32
proper(__(z0, z1)) → __(proper(z0), proper(z1)) 118.27/44.32
proper(nil) → ok(nil) 118.27/44.32
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 118.27/44.32
proper(tt) → ok(tt) 118.27/44.32
proper(isNePal(z0)) → isNePal(proper(z0)) 118.27/44.32
top(mark(z0)) → top(proper(z0)) 118.27/44.32
top(ok(z0)) → top(active(z0))
Tuples:

__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.32
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.32
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.32
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.32
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.32
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.32
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0))
S tuples:

__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.32
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.32
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.32
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.32
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.32
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.32
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0))
K tuples:none
Defined Rule Symbols:

active, __, and, isNePal, proper, top

Defined Pair Symbols:

__', AND, ISNEPAL

Compound Symbols:

c9, c10, c11, c12, c13, c14, c15

118.27/44.32
118.27/44.32

(39) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^3))) transformation)

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

__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.32
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.32
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.32
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.32
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.32
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.32
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0))
We considered the (Usable) Rules:none
And the Tuples:

__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.32
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.32
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.32
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.32
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.32
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.32
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 118.27/44.32

POL(AND(x1, x2)) = x1 + x2 + x1·x2 + x12 + x1·x22 + x23    118.27/44.32
POL(ISNEPAL(x1)) = x1 + x12 + x13    118.27/44.32
POL(__'(x1, x2)) = x1 + x12 + x13 + x12·x2 + x1·x22 + x23    118.27/44.32
POL(c10(x1)) = x1    118.27/44.32
POL(c11(x1)) = x1    118.27/44.32
POL(c12(x1)) = x1    118.27/44.32
POL(c13(x1)) = x1    118.27/44.32
POL(c14(x1)) = x1    118.27/44.32
POL(c15(x1)) = x1    118.27/44.32
POL(c9(x1)) = x1    118.27/44.32
POL(mark(x1)) = [1] + x1    118.27/44.32
POL(ok(x1)) = [1] + x1   
118.27/44.32
118.27/44.32

(40) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2))) 118.27/44.32
active(__(z0, nil)) → mark(z0) 118.27/44.32
active(__(nil, z0)) → mark(z0) 118.27/44.32
active(and(tt, z0)) → mark(z0) 118.27/44.32
active(isNePal(__(z0, __(z1, z0)))) → mark(tt) 118.27/44.32
active(__(z0, z1)) → __(active(z0), z1) 118.27/44.32
active(__(z0, z1)) → __(z0, active(z1)) 118.27/44.32
active(and(z0, z1)) → and(active(z0), z1) 118.27/44.32
active(isNePal(z0)) → isNePal(active(z0)) 118.27/44.32
__(mark(z0), z1) → mark(__(z0, z1)) 118.27/44.32
__(z0, mark(z1)) → mark(__(z0, z1)) 118.27/44.32
__(ok(z0), ok(z1)) → ok(__(z0, z1)) 118.27/44.32
and(mark(z0), z1) → mark(and(z0, z1)) 118.27/44.32
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 118.27/44.32
isNePal(mark(z0)) → mark(isNePal(z0)) 118.27/44.32
isNePal(ok(z0)) → ok(isNePal(z0)) 118.27/44.32
proper(__(z0, z1)) → __(proper(z0), proper(z1)) 118.27/44.32
proper(nil) → ok(nil) 118.27/44.32
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 118.27/44.32
proper(tt) → ok(tt) 118.27/44.32
proper(isNePal(z0)) → isNePal(proper(z0)) 118.27/44.32
top(mark(z0)) → top(proper(z0)) 118.27/44.32
top(ok(z0)) → top(active(z0))
Tuples:

__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.32
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.32
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.32
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.32
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.32
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.32
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0))
S tuples:none
K tuples:

__'(mark(z0), z1) → c9(__'(z0, z1)) 118.27/44.32
__'(z0, mark(z1)) → c10(__'(z0, z1)) 118.27/44.32
__'(ok(z0), ok(z1)) → c11(__'(z0, z1)) 118.27/44.32
AND(mark(z0), z1) → c12(AND(z0, z1)) 118.27/44.32
AND(ok(z0), ok(z1)) → c13(AND(z0, z1)) 118.27/44.32
ISNEPAL(mark(z0)) → c14(ISNEPAL(z0)) 118.27/44.32
ISNEPAL(ok(z0)) → c15(ISNEPAL(z0))
Defined Rule Symbols:

active, __, and, isNePal, proper, top

Defined Pair Symbols:

__', AND, ISNEPAL

Compound Symbols:

c9, c10, c11, c12, c13, c14, c15

118.27/44.32
118.27/44.32

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

The set S is empty
118.27/44.32
118.27/44.32

(42) BOUNDS(O(1), O(1))

118.27/44.32
118.27/44.32
118.49/44.41 EOF