(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(I, __(P, I)))) → mark(U11(tt))
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U12(X)) → active(U12(mark(X)))
mark(isNePal(X)) → active(isNePal(mark(X)))
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U12(mark(X)) → U12(X)
U12(active(X)) → U12(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
Rewrite Strategy: INNERMOST
(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)
Converted CpxTRS to CDT
(2) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)
Tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)), U12'(tt))
ACTIVE(U12(tt)) → c4(MARK(tt))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c5(MARK(U11(tt)), U11'(tt))
MARK(__(z0, z1)) → c6(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(nil) → c7(ACTIVE(nil))
MARK(U11(z0)) → c8(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(tt) → c9(ACTIVE(tt))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
S tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)), U12'(tt))
ACTIVE(U12(tt)) → c4(MARK(tt))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c5(MARK(U11(tt)), U11'(tt))
MARK(__(z0, z1)) → c6(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(nil) → c7(ACTIVE(nil))
MARK(U11(z0)) → c8(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(tt) → c9(ACTIVE(tt))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
K tuples:none
Defined Rule Symbols:
active, mark, __, U11, U12, isNePal
Defined Pair Symbols:
ACTIVE, MARK, __', U11', U12', ISNEPAL
Compound Symbols:
c, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21
(3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing nodes:
MARK(tt) → c9(ACTIVE(tt))
ACTIVE(U12(tt)) → c4(MARK(tt))
MARK(nil) → c7(ACTIVE(nil))
(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)
Tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)), U12'(tt))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c5(MARK(U11(tt)), U11'(tt))
MARK(__(z0, z1)) → c6(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U11(z0)) → c8(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
S tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)), U12'(tt))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c5(MARK(U11(tt)), U11'(tt))
MARK(__(z0, z1)) → c6(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U11(z0)) → c8(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
K tuples:none
Defined Rule Symbols:
active, mark, __, U11, U12, isNePal
Defined Pair Symbols:
ACTIVE, MARK, __', U11', U12', ISNEPAL
Compound Symbols:
c, c1, c2, c3, c5, c6, c8, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21
(5) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
U11(
tt)) →
c3(
MARK(
U12(
tt)),
U12'(
tt)) by
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
(6) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)
Tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c5(MARK(U11(tt)), U11'(tt))
MARK(__(z0, z1)) → c6(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U11(z0)) → c8(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
S tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c5(MARK(U11(tt)), U11'(tt))
MARK(__(z0, z1)) → c6(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U11(z0)) → c8(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
K tuples:none
Defined Rule Symbols:
active, mark, __, U11, U12, isNePal
Defined Pair Symbols:
ACTIVE, MARK, __', U11', U12', ISNEPAL
Compound Symbols:
c, c1, c2, c5, c6, c8, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c3
(7) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
isNePal(
__(
z0,
__(
z1,
z0)))) →
c5(
MARK(
U11(
tt)),
U11'(
tt)) by
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
(8) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)
Tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(__(z0, z1)) → c6(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U11(z0)) → c8(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
S tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(__(z0, z1)) → c6(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U11(z0)) → c8(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
K tuples:none
Defined Rule Symbols:
active, mark, __, U11, U12, isNePal
Defined Pair Symbols:
ACTIVE, MARK, __', U11', U12', ISNEPAL
Compound Symbols:
c, c1, c2, c6, c8, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c3, c5
(9) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
MARK(
__(
z0,
z1)) →
c6(
ACTIVE(
__(
mark(
z0),
mark(
z1))),
__'(
mark(
z0),
mark(
z1)),
MARK(
z0),
MARK(
z1)) by
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(__(x0, x1)) → c6
(10) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)
Tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(U11(z0)) → c8(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(__(x0, x1)) → c6
S tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(U11(z0)) → c8(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(__(x0, x1)) → c6
K tuples:none
Defined Rule Symbols:
active, mark, __, U11, U12, isNePal
Defined Pair Symbols:
ACTIVE, MARK, __', U11', U12', ISNEPAL
Compound Symbols:
c, c1, c2, c8, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c3, c5, c6, c6
(11) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)
Removed 1 trailing nodes:
MARK(__(x0, x1)) → c6
(12) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)
Tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(U11(z0)) → c8(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
S tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(U11(z0)) → c8(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
K tuples:none
Defined Rule Symbols:
active, mark, __, U11, U12, isNePal
Defined Pair Symbols:
ACTIVE, MARK, __', U11', U12', ISNEPAL
Compound Symbols:
c, c1, c2, c8, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c3, c5, c6
(13) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
MARK(
U11(
z0)) →
c8(
ACTIVE(
U11(
mark(
z0))),
U11'(
mark(
z0)),
MARK(
z0)) by
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U11(x0)) → c8
(14) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)
Tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U11(x0)) → c8
S tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U11(x0)) → c8
K tuples:none
Defined Rule Symbols:
active, mark, __, U11, U12, isNePal
Defined Pair Symbols:
ACTIVE, MARK, __', U11', U12', ISNEPAL
Compound Symbols:
c, c1, c2, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c3, c5, c6, c8, c8
(15) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)
Removed 1 trailing nodes:
MARK(U11(x0)) → c8
(16) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)
Tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
S tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(U12(z0)) → c10(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
K tuples:none
Defined Rule Symbols:
active, mark, __, U11, U12, isNePal
Defined Pair Symbols:
ACTIVE, MARK, __', U11', U12', ISNEPAL
Compound Symbols:
c, c1, c2, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c3, c5, c6, c8
(17) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
MARK(
U12(
z0)) →
c10(
ACTIVE(
U12(
mark(
z0))),
U12'(
mark(
z0)),
MARK(
z0)) by
MARK(U12(z0)) → c10(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0))
MARK(U12(__(z0, z1))) → c10(ACTIVE(U12(active(__(mark(z0), mark(z1))))), U12'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U12(nil)) → c10(ACTIVE(U12(active(nil))), U12'(mark(nil)), MARK(nil))
MARK(U12(U11(z0))) → c10(ACTIVE(U12(active(U11(mark(z0))))), U12'(mark(U11(z0))), MARK(U11(z0)))
MARK(U12(tt)) → c10(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt))
MARK(U12(U12(z0))) → c10(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0)))
MARK(U12(isNePal(z0))) → c10(ACTIVE(U12(active(isNePal(mark(z0))))), U12'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(x0)) → c10
(18) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)
Tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(z0)) → c10(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0))
MARK(U12(__(z0, z1))) → c10(ACTIVE(U12(active(__(mark(z0), mark(z1))))), U12'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U12(nil)) → c10(ACTIVE(U12(active(nil))), U12'(mark(nil)), MARK(nil))
MARK(U12(U11(z0))) → c10(ACTIVE(U12(active(U11(mark(z0))))), U12'(mark(U11(z0))), MARK(U11(z0)))
MARK(U12(tt)) → c10(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt))
MARK(U12(U12(z0))) → c10(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0)))
MARK(U12(isNePal(z0))) → c10(ACTIVE(U12(active(isNePal(mark(z0))))), U12'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(x0)) → c10
S tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(z0)) → c10(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0))
MARK(U12(__(z0, z1))) → c10(ACTIVE(U12(active(__(mark(z0), mark(z1))))), U12'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U12(nil)) → c10(ACTIVE(U12(active(nil))), U12'(mark(nil)), MARK(nil))
MARK(U12(U11(z0))) → c10(ACTIVE(U12(active(U11(mark(z0))))), U12'(mark(U11(z0))), MARK(U11(z0)))
MARK(U12(tt)) → c10(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt))
MARK(U12(U12(z0))) → c10(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0)))
MARK(U12(isNePal(z0))) → c10(ACTIVE(U12(active(isNePal(mark(z0))))), U12'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(x0)) → c10
K tuples:none
Defined Rule Symbols:
active, mark, __, U11, U12, isNePal
Defined Pair Symbols:
ACTIVE, MARK, __', U11', U12', ISNEPAL
Compound Symbols:
c, c1, c2, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c3, c5, c6, c8, c10, c10
(19) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)
Removed 1 trailing nodes:
MARK(U12(x0)) → c10
(20) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)
Tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(z0)) → c10(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0))
MARK(U12(__(z0, z1))) → c10(ACTIVE(U12(active(__(mark(z0), mark(z1))))), U12'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U12(nil)) → c10(ACTIVE(U12(active(nil))), U12'(mark(nil)), MARK(nil))
MARK(U12(U11(z0))) → c10(ACTIVE(U12(active(U11(mark(z0))))), U12'(mark(U11(z0))), MARK(U11(z0)))
MARK(U12(tt)) → c10(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt))
MARK(U12(U12(z0))) → c10(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0)))
MARK(U12(isNePal(z0))) → c10(ACTIVE(U12(active(isNePal(mark(z0))))), U12'(mark(isNePal(z0))), MARK(isNePal(z0)))
S tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(mark(z0))), ISNEPAL(mark(z0)), MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(z0)) → c10(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0))
MARK(U12(__(z0, z1))) → c10(ACTIVE(U12(active(__(mark(z0), mark(z1))))), U12'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U12(nil)) → c10(ACTIVE(U12(active(nil))), U12'(mark(nil)), MARK(nil))
MARK(U12(U11(z0))) → c10(ACTIVE(U12(active(U11(mark(z0))))), U12'(mark(U11(z0))), MARK(U11(z0)))
MARK(U12(tt)) → c10(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt))
MARK(U12(U12(z0))) → c10(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0)))
MARK(U12(isNePal(z0))) → c10(ACTIVE(U12(active(isNePal(mark(z0))))), U12'(mark(isNePal(z0))), MARK(isNePal(z0)))
K tuples:none
Defined Rule Symbols:
active, mark, __, U11, U12, isNePal
Defined Pair Symbols:
ACTIVE, MARK, __', U11', U12', ISNEPAL
Compound Symbols:
c, c1, c2, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c3, c5, c6, c8, c10
(21) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
MARK(
isNePal(
z0)) →
c11(
ACTIVE(
isNePal(
mark(
z0))),
ISNEPAL(
mark(
z0)),
MARK(
z0)) by
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c11(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c11(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(U11(z0))) → c11(ACTIVE(isNePal(active(U11(mark(z0))))), ISNEPAL(mark(U11(z0))), MARK(U11(z0)))
MARK(isNePal(tt)) → c11(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(U12(z0))) → c11(ACTIVE(isNePal(active(U12(mark(z0))))), ISNEPAL(mark(U12(z0))), MARK(U12(z0)))
MARK(isNePal(isNePal(z0))) → c11(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(isNePal(x0)) → c11
(22) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)
Tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(z0)) → c10(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0))
MARK(U12(__(z0, z1))) → c10(ACTIVE(U12(active(__(mark(z0), mark(z1))))), U12'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U12(nil)) → c10(ACTIVE(U12(active(nil))), U12'(mark(nil)), MARK(nil))
MARK(U12(U11(z0))) → c10(ACTIVE(U12(active(U11(mark(z0))))), U12'(mark(U11(z0))), MARK(U11(z0)))
MARK(U12(tt)) → c10(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt))
MARK(U12(U12(z0))) → c10(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0)))
MARK(U12(isNePal(z0))) → c10(ACTIVE(U12(active(isNePal(mark(z0))))), U12'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c11(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c11(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(U11(z0))) → c11(ACTIVE(isNePal(active(U11(mark(z0))))), ISNEPAL(mark(U11(z0))), MARK(U11(z0)))
MARK(isNePal(tt)) → c11(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(U12(z0))) → c11(ACTIVE(isNePal(active(U12(mark(z0))))), ISNEPAL(mark(U12(z0))), MARK(U12(z0)))
MARK(isNePal(isNePal(z0))) → c11(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(isNePal(x0)) → c11
S tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(z0)) → c10(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0))
MARK(U12(__(z0, z1))) → c10(ACTIVE(U12(active(__(mark(z0), mark(z1))))), U12'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U12(nil)) → c10(ACTIVE(U12(active(nil))), U12'(mark(nil)), MARK(nil))
MARK(U12(U11(z0))) → c10(ACTIVE(U12(active(U11(mark(z0))))), U12'(mark(U11(z0))), MARK(U11(z0)))
MARK(U12(tt)) → c10(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt))
MARK(U12(U12(z0))) → c10(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0)))
MARK(U12(isNePal(z0))) → c10(ACTIVE(U12(active(isNePal(mark(z0))))), U12'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c11(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c11(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(U11(z0))) → c11(ACTIVE(isNePal(active(U11(mark(z0))))), ISNEPAL(mark(U11(z0))), MARK(U11(z0)))
MARK(isNePal(tt)) → c11(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(U12(z0))) → c11(ACTIVE(isNePal(active(U12(mark(z0))))), ISNEPAL(mark(U12(z0))), MARK(U12(z0)))
MARK(isNePal(isNePal(z0))) → c11(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(isNePal(x0)) → c11
K tuples:none
Defined Rule Symbols:
active, mark, __, U11, U12, isNePal
Defined Pair Symbols:
ACTIVE, __', U11', U12', ISNEPAL, MARK
Compound Symbols:
c, c1, c2, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c3, c5, c6, c8, c10, c11, c11
(23) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)
Removed 1 trailing nodes:
MARK(isNePal(x0)) → c11
(24) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)
Tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(z0)) → c10(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0))
MARK(U12(__(z0, z1))) → c10(ACTIVE(U12(active(__(mark(z0), mark(z1))))), U12'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U12(nil)) → c10(ACTIVE(U12(active(nil))), U12'(mark(nil)), MARK(nil))
MARK(U12(U11(z0))) → c10(ACTIVE(U12(active(U11(mark(z0))))), U12'(mark(U11(z0))), MARK(U11(z0)))
MARK(U12(tt)) → c10(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt))
MARK(U12(U12(z0))) → c10(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0)))
MARK(U12(isNePal(z0))) → c10(ACTIVE(U12(active(isNePal(mark(z0))))), U12'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c11(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c11(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(U11(z0))) → c11(ACTIVE(isNePal(active(U11(mark(z0))))), ISNEPAL(mark(U11(z0))), MARK(U11(z0)))
MARK(isNePal(tt)) → c11(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(U12(z0))) → c11(ACTIVE(isNePal(active(U12(mark(z0))))), ISNEPAL(mark(U12(z0))), MARK(U12(z0)))
MARK(isNePal(isNePal(z0))) → c11(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))
S tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(z0, x1)) → c6(ACTIVE(__(z0, mark(x1))), __'(mark(z0), mark(x1)), MARK(z0), MARK(x1))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(z0)) → c10(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0))
MARK(U12(__(z0, z1))) → c10(ACTIVE(U12(active(__(mark(z0), mark(z1))))), U12'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U12(nil)) → c10(ACTIVE(U12(active(nil))), U12'(mark(nil)), MARK(nil))
MARK(U12(U11(z0))) → c10(ACTIVE(U12(active(U11(mark(z0))))), U12'(mark(U11(z0))), MARK(U11(z0)))
MARK(U12(tt)) → c10(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt))
MARK(U12(U12(z0))) → c10(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0)))
MARK(U12(isNePal(z0))) → c10(ACTIVE(U12(active(isNePal(mark(z0))))), U12'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c11(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c11(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(U11(z0))) → c11(ACTIVE(isNePal(active(U11(mark(z0))))), ISNEPAL(mark(U11(z0))), MARK(U11(z0)))
MARK(isNePal(tt)) → c11(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(U12(z0))) → c11(ACTIVE(isNePal(active(U12(mark(z0))))), ISNEPAL(mark(U12(z0))), MARK(U12(z0)))
MARK(isNePal(isNePal(z0))) → c11(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))
K tuples:none
Defined Rule Symbols:
active, mark, __, U11, U12, isNePal
Defined Pair Symbols:
ACTIVE, __', U11', U12', ISNEPAL, MARK
Compound Symbols:
c, c1, c2, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c3, c5, c6, c8, c10, c11
(25) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
MARK(
__(
z0,
x1)) →
c6(
ACTIVE(
__(
z0,
mark(
x1))),
__'(
mark(
z0),
mark(
x1)),
MARK(
z0),
MARK(
x1)) by
MARK(__(z0, z1)) → c6(ACTIVE(__(z0, z1)), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(x0, active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(x0, active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(x0, active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(x0, active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(x0, active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(x0, active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(x0, x1)) → c6(__'(mark(x0), mark(x1)))
(26) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(U11(tt)) → mark(U12(tt))
active(U12(tt)) → mark(tt)
active(isNePal(__(z0, __(z1, z0)))) → mark(U11(tt))
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNePal(z0)) → active(isNePal(mark(z0)))
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0)) → U11(z0)
U11(active(z0)) → U11(z0)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)
Tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(z0)) → c10(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0))
MARK(U12(__(z0, z1))) → c10(ACTIVE(U12(active(__(mark(z0), mark(z1))))), U12'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U12(nil)) → c10(ACTIVE(U12(active(nil))), U12'(mark(nil)), MARK(nil))
MARK(U12(U11(z0))) → c10(ACTIVE(U12(active(U11(mark(z0))))), U12'(mark(U11(z0))), MARK(U11(z0)))
MARK(U12(tt)) → c10(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt))
MARK(U12(U12(z0))) → c10(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0)))
MARK(U12(isNePal(z0))) → c10(ACTIVE(U12(active(isNePal(mark(z0))))), U12'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c11(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c11(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(U11(z0))) → c11(ACTIVE(isNePal(active(U11(mark(z0))))), ISNEPAL(mark(U11(z0))), MARK(U11(z0)))
MARK(isNePal(tt)) → c11(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(U12(z0))) → c11(ACTIVE(isNePal(active(U12(mark(z0))))), ISNEPAL(mark(U12(z0))), MARK(U12(z0)))
MARK(isNePal(isNePal(z0))) → c11(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(__(z0, z1)) → c6(ACTIVE(__(z0, z1)), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(x0, active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(x0, active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(x0, active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(x0, active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(x0, active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(x0, active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(x0, x1)) → c6(__'(mark(x0), mark(x1)))
S tuples:
ACTIVE(__(__(z0, z1), z2)) → c(MARK(__(z0, __(z1, z2))), __'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1(MARK(z0))
ACTIVE(__(nil, z0)) → c2(MARK(z0))
__'(mark(z0), z1) → c12(__'(z0, z1))
__'(z0, mark(z1)) → c13(__'(z0, z1))
__'(active(z0), z1) → c14(__'(z0, z1))
__'(z0, active(z1)) → c15(__'(z0, z1))
U11'(mark(z0)) → c16(U11'(z0))
U11'(active(z0)) → c17(U11'(z0))
U12'(mark(z0)) → c18(U12'(z0))
U12'(active(z0)) → c19(U12'(z0))
ISNEPAL(mark(z0)) → c20(ISNEPAL(z0))
ISNEPAL(active(z0)) → c21(ISNEPAL(z0))
ACTIVE(U11(tt)) → c3(MARK(U12(tt)))
ACTIVE(isNePal(__(x0, __(x1, x0)))) → c5(MARK(U11(tt)))
MARK(__(x0, z1)) → c6(ACTIVE(__(mark(x0), z1)), __'(mark(x0), mark(z1)), MARK(x0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(mark(x0), active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(mark(x0), active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(mark(x0), active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(mark(x0), active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(mark(x0), active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(mark(x0), active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(__(z0, z1), x1)) → c6(ACTIVE(__(active(__(mark(z0), mark(z1))), mark(x1))), __'(mark(__(z0, z1)), mark(x1)), MARK(__(z0, z1)), MARK(x1))
MARK(__(nil, x1)) → c6(ACTIVE(__(active(nil), mark(x1))), __'(mark(nil), mark(x1)), MARK(nil), MARK(x1))
MARK(__(U11(z0), x1)) → c6(ACTIVE(__(active(U11(mark(z0))), mark(x1))), __'(mark(U11(z0)), mark(x1)), MARK(U11(z0)), MARK(x1))
MARK(__(tt, x1)) → c6(ACTIVE(__(active(tt), mark(x1))), __'(mark(tt), mark(x1)), MARK(tt), MARK(x1))
MARK(__(U12(z0), x1)) → c6(ACTIVE(__(active(U12(mark(z0))), mark(x1))), __'(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1))
MARK(__(isNePal(z0), x1)) → c6(ACTIVE(__(active(isNePal(mark(z0))), mark(x1))), __'(mark(isNePal(z0)), mark(x1)), MARK(isNePal(z0)), MARK(x1))
MARK(U11(z0)) → c8(ACTIVE(U11(z0)), U11'(mark(z0)), MARK(z0))
MARK(U11(__(z0, z1))) → c8(ACTIVE(U11(active(__(mark(z0), mark(z1))))), U11'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U11(nil)) → c8(ACTIVE(U11(active(nil))), U11'(mark(nil)), MARK(nil))
MARK(U11(U11(z0))) → c8(ACTIVE(U11(active(U11(mark(z0))))), U11'(mark(U11(z0))), MARK(U11(z0)))
MARK(U11(tt)) → c8(ACTIVE(U11(active(tt))), U11'(mark(tt)), MARK(tt))
MARK(U11(U12(z0))) → c8(ACTIVE(U11(active(U12(mark(z0))))), U11'(mark(U12(z0))), MARK(U12(z0)))
MARK(U11(isNePal(z0))) → c8(ACTIVE(U11(active(isNePal(mark(z0))))), U11'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(U12(z0)) → c10(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0))
MARK(U12(__(z0, z1))) → c10(ACTIVE(U12(active(__(mark(z0), mark(z1))))), U12'(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(U12(nil)) → c10(ACTIVE(U12(active(nil))), U12'(mark(nil)), MARK(nil))
MARK(U12(U11(z0))) → c10(ACTIVE(U12(active(U11(mark(z0))))), U12'(mark(U11(z0))), MARK(U11(z0)))
MARK(U12(tt)) → c10(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt))
MARK(U12(U12(z0))) → c10(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0)))
MARK(U12(isNePal(z0))) → c10(ACTIVE(U12(active(isNePal(mark(z0))))), U12'(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(isNePal(z0)) → c11(ACTIVE(isNePal(z0)), ISNEPAL(mark(z0)), MARK(z0))
MARK(isNePal(__(z0, z1))) → c11(ACTIVE(isNePal(active(__(mark(z0), mark(z1))))), ISNEPAL(mark(__(z0, z1))), MARK(__(z0, z1)))
MARK(isNePal(nil)) → c11(ACTIVE(isNePal(active(nil))), ISNEPAL(mark(nil)), MARK(nil))
MARK(isNePal(U11(z0))) → c11(ACTIVE(isNePal(active(U11(mark(z0))))), ISNEPAL(mark(U11(z0))), MARK(U11(z0)))
MARK(isNePal(tt)) → c11(ACTIVE(isNePal(active(tt))), ISNEPAL(mark(tt)), MARK(tt))
MARK(isNePal(U12(z0))) → c11(ACTIVE(isNePal(active(U12(mark(z0))))), ISNEPAL(mark(U12(z0))), MARK(U12(z0)))
MARK(isNePal(isNePal(z0))) → c11(ACTIVE(isNePal(active(isNePal(mark(z0))))), ISNEPAL(mark(isNePal(z0))), MARK(isNePal(z0)))
MARK(__(z0, z1)) → c6(ACTIVE(__(z0, z1)), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(__(x0, __(z0, z1))) → c6(ACTIVE(__(x0, active(__(mark(z0), mark(z1))))), __'(mark(x0), mark(__(z0, z1))), MARK(x0), MARK(__(z0, z1)))
MARK(__(x0, nil)) → c6(ACTIVE(__(x0, active(nil))), __'(mark(x0), mark(nil)), MARK(x0), MARK(nil))
MARK(__(x0, U11(z0))) → c6(ACTIVE(__(x0, active(U11(mark(z0))))), __'(mark(x0), mark(U11(z0))), MARK(x0), MARK(U11(z0)))
MARK(__(x0, tt)) → c6(ACTIVE(__(x0, active(tt))), __'(mark(x0), mark(tt)), MARK(x0), MARK(tt))
MARK(__(x0, U12(z0))) → c6(ACTIVE(__(x0, active(U12(mark(z0))))), __'(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0)))
MARK(__(x0, isNePal(z0))) → c6(ACTIVE(__(x0, active(isNePal(mark(z0))))), __'(mark(x0), mark(isNePal(z0))), MARK(x0), MARK(isNePal(z0)))
MARK(__(x0, x1)) → c6(__'(mark(x0), mark(x1)))
K tuples:none
Defined Rule Symbols:
active, mark, __, U11, U12, isNePal
Defined Pair Symbols:
ACTIVE, __', U11', U12', ISNEPAL, MARK
Compound Symbols:
c, c1, c2, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c3, c5, c6, c8, c10, c11, c6
(27) CpxTrsMatchBoundsTAProof (EQUIVALENT transformation)
A linear upper bound on the runtime complexity of the TRS R could be shown with a Match(-raise)-Bound[TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] (for contructor-based start-terms) of 1.
The compatible tree automaton used to show the Match(-raise)-Boundedness (for constructor-based start-terms) is represented by:
final states : [1, 2, 3, 4, 5, 6]
transitions:
active0(0) → 1
mark0(0) → 2
__0(0, 0) → 3
U110(0) → 4
U120(0) → 5
isNePal0(0) → 6
nil1() → 7
active1(7) → 2
nil1() → 0
tt1() → 8
active1(8) → 2
tt1() → 0
nil1() → 9
tt1() → 10
active0(9) → 1
active0(10) → 1
mark0(9) → 2
mark0(10) → 2
__0(9, 0) → 3
__0(0, 9) → 3
__0(10, 0) → 3
__0(0, 10) → 3
__0(9, 9) → 3
__0(9, 10) → 3
__0(10, 9) → 3
__0(10, 10) → 3
U110(9) → 4
U110(10) → 4
U120(9) → 5
U120(10) → 5
isNePal0(9) → 6
isNePal0(10) → 6
active1(9) → 2
active1(10) → 2
active1(9) → 1
active1(10) → 1
(28) BOUNDS(O(1), O(n^1))