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

(0) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isNeList(V)))
active(U12(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isList(V1), V2))
active(U22(tt, V2)) → mark(U23(isList(V2)))
active(U23(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isQid(V)))
active(U32(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isList(V1), V2))
active(U42(tt, V2)) → mark(U43(isNeList(V2)))
active(U43(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isNeList(V1), V2))
active(U52(tt, V2)) → mark(U53(isList(V2)))
active(U53(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isQid(V)))
active(U62(tt)) → mark(tt)
active(U71(tt, V)) → mark(U72(isNePal(V)))
active(U72(tt)) → mark(tt)
active(and(tt, X)) → mark(X)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(and(and(isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P))))
active(isPal(V)) → mark(U71(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(and(isPalListKind(V1), isPalListKind(V2)))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X)) → active(U12(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2)) → active(U42(mark(X1), X2))
mark(U43(X)) → active(U43(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U53(X)) → active(U53(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2)) → active(U71(mark(X1), X2))
mark(U72(X)) → active(U72(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(and(X1, X2)) → active(and(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(isPal(X)) → active(isPal(X))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X)) → U12(X)
U12(active(X)) → U12(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2) → U42(X1, X2)
U42(X1, mark(X2)) → U42(X1, X2)
U42(active(X1), X2) → U42(X1, X2)
U42(X1, active(X2)) → U42(X1, X2)
U43(mark(X)) → U43(X)
U43(active(X)) → U43(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U53(mark(X)) → U53(X)
U53(active(X)) → U53(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X)) → U62(X)
U62(active(X)) → U62(X)
U71(mark(X1), X2) → U71(X1, X2)
U71(X1, mark(X2)) → U71(X1, X2)
U71(active(X1), X2) → U71(X1, X2)
U71(X1, active(X2)) → U71(X1, X2)
U72(mark(X)) → U72(X)
U72(active(X)) → U72(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
and(mark(X1), X2) → and(X1, X2)
and(X1, mark(X2)) → and(X1, X2)
and(active(X1), X2) → and(X1, X2)
and(X1, active(X2)) → and(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(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, z0)) → mark(U12(isNeList(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt, z0, z1)) → mark(U22(isList(z0), z1))
active(U22(tt, z0)) → mark(U23(isList(z0)))
active(U23(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isQid(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0, z1)) → mark(U42(isList(z0), z1))
active(U42(tt, z0)) → mark(U43(isNeList(z0)))
active(U43(tt)) → mark(tt)
active(U51(tt, z0, z1)) → mark(U52(isNeList(z0), z1))
active(U52(tt, z0)) → mark(U53(isList(z0)))
active(U53(tt)) → mark(tt)
active(U61(tt, z0)) → mark(U62(isQid(z0)))
active(U62(tt)) → mark(tt)
active(U71(tt, z0)) → mark(U72(isNePal(z0)))
active(U72(tt)) → mark(tt)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(U11(isPalListKind(z0), z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(U21(and(isPalListKind(z0), isPalListKind(z1)), z0, z1))
active(isNeList(z0)) → mark(U31(isPalListKind(z0), z0))
active(isNeList(__(z0, z1))) → mark(U41(and(isPalListKind(z0), isPalListKind(z1)), z0, z1))
active(isNeList(__(z0, z1))) → mark(U51(and(isPalListKind(z0), isPalListKind(z1)), z0, z1))
active(isNePal(z0)) → mark(U61(isPalListKind(z0), z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(and(isQid(z0), isPalListKind(z0)), and(isPal(z1), isPalListKind(z1))))
active(isPal(z0)) → mark(U71(isPalListKind(z0), z0))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(z0, z1))) → mark(and(isPalListKind(z0), isPalListKind(z1)))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0, z1)) → active(U11(mark(z0), z1))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNeList(z0)) → active(isNeList(z0))
mark(U21(z0, z1, z2)) → active(U21(mark(z0), z1, z2))
mark(U22(z0, z1)) → active(U22(mark(z0), z1))
mark(isList(z0)) → active(isList(z0))
mark(U23(z0)) → active(U23(mark(z0)))
mark(U31(z0, z1)) → active(U31(mark(z0), z1))
mark(U32(z0)) → active(U32(mark(z0)))
mark(isQid(z0)) → active(isQid(z0))
mark(U41(z0, z1, z2)) → active(U41(mark(z0), z1, z2))
mark(U42(z0, z1)) → active(U42(mark(z0), z1))
mark(U43(z0)) → active(U43(mark(z0)))
mark(U51(z0, z1, z2)) → active(U51(mark(z0), z1, z2))
mark(U52(z0, z1)) → active(U52(mark(z0), z1))
mark(U53(z0)) → active(U53(mark(z0)))
mark(U61(z0, z1)) → active(U61(mark(z0), z1))
mark(U62(z0)) → active(U62(mark(z0)))
mark(U71(z0, z1)) → active(U71(mark(z0), z1))
mark(U72(z0)) → active(U72(mark(z0)))
mark(isNePal(z0)) → active(isNePal(z0))
mark(and(z0, z1)) → active(and(mark(z0), z1))
mark(isPalListKind(z0)) → active(isPalListKind(z0))
mark(isPal(z0)) → active(isPal(z0))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0), z1) → U11(z0, z1)
U11(z0, mark(z1)) → U11(z0, z1)
U11(active(z0), z1) → U11(z0, z1)
U11(z0, active(z1)) → U11(z0, z1)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNeList(mark(z0)) → isNeList(z0)
isNeList(active(z0)) → isNeList(z0)
U21(mark(z0), z1, z2) → U21(z0, z1, z2)
U21(z0, mark(z1), z2) → U21(z0, z1, z2)
U21(z0, z1, mark(z2)) → U21(z0, z1, z2)
U21(active(z0), z1, z2) → U21(z0, z1, z2)
U21(z0, active(z1), z2) → U21(z0, z1, z2)
U21(z0, z1, active(z2)) → U21(z0, z1, z2)
U22(mark(z0), z1) → U22(z0, z1)
U22(z0, mark(z1)) → U22(z0, z1)
U22(active(z0), z1) → U22(z0, z1)
U22(z0, active(z1)) → U22(z0, z1)
isList(mark(z0)) → isList(z0)
isList(active(z0)) → isList(z0)
U23(mark(z0)) → U23(z0)
U23(active(z0)) → U23(z0)
U31(mark(z0), z1) → U31(z0, z1)
U31(z0, mark(z1)) → U31(z0, z1)
U31(active(z0), z1) → U31(z0, z1)
U31(z0, active(z1)) → U31(z0, z1)
U32(mark(z0)) → U32(z0)
U32(active(z0)) → U32(z0)
isQid(mark(z0)) → isQid(z0)
isQid(active(z0)) → isQid(z0)
U41(mark(z0), z1, z2) → U41(z0, z1, z2)
U41(z0, mark(z1), z2) → U41(z0, z1, z2)
U41(z0, z1, mark(z2)) → U41(z0, z1, z2)
U41(active(z0), z1, z2) → U41(z0, z1, z2)
U41(z0, active(z1), z2) → U41(z0, z1, z2)
U41(z0, z1, active(z2)) → U41(z0, z1, z2)
U42(mark(z0), z1) → U42(z0, z1)
U42(z0, mark(z1)) → U42(z0, z1)
U42(active(z0), z1) → U42(z0, z1)
U42(z0, active(z1)) → U42(z0, z1)
U43(mark(z0)) → U43(z0)
U43(active(z0)) → U43(z0)
U51(mark(z0), z1, z2) → U51(z0, z1, z2)
U51(z0, mark(z1), z2) → U51(z0, z1, z2)
U51(z0, z1, mark(z2)) → U51(z0, z1, z2)
U51(active(z0), z1, z2) → U51(z0, z1, z2)
U51(z0, active(z1), z2) → U51(z0, z1, z2)
U51(z0, z1, active(z2)) → U51(z0, z1, z2)
U52(mark(z0), z1) → U52(z0, z1)
U52(z0, mark(z1)) → U52(z0, z1)
U52(active(z0), z1) → U52(z0, z1)
U52(z0, active(z1)) → U52(z0, z1)
U53(mark(z0)) → U53(z0)
U53(active(z0)) → U53(z0)
U61(mark(z0), z1) → U61(z0, z1)
U61(z0, mark(z1)) → U61(z0, z1)
U61(active(z0), z1) → U61(z0, z1)
U61(z0, active(z1)) → U61(z0, z1)
U62(mark(z0)) → U62(z0)
U62(active(z0)) → U62(z0)
U71(mark(z0), z1) → U71(z0, z1)
U71(z0, mark(z1)) → U71(z0, z1)
U71(active(z0), z1) → U71(z0, z1)
U71(z0, active(z1)) → U71(z0, z1)
U72(mark(z0)) → U72(z0)
U72(active(z0)) → U72(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)
and(mark(z0), z1) → and(z0, z1)
and(z0, mark(z1)) → and(z0, z1)
and(active(z0), z1) → and(z0, z1)
and(z0, active(z1)) → and(z0, z1)
isPalListKind(mark(z0)) → isPalListKind(z0)
isPalListKind(active(z0)) → isPalListKind(z0)
isPal(mark(z0)) → isPal(z0)
isPal(active(z0)) → isPal(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, z0)) → c3(MARK(U12(isNeList(z0))), U12'(isNeList(z0)), ISNELIST(z0))
ACTIVE(U12(tt)) → c4(MARK(tt))
ACTIVE(U21(tt, z0, z1)) → c5(MARK(U22(isList(z0), z1)), U22'(isList(z0), z1), ISLIST(z0))
ACTIVE(U22(tt, z0)) → c6(MARK(U23(isList(z0))), U23'(isList(z0)), ISLIST(z0))
ACTIVE(U23(tt)) → c7(MARK(tt))
ACTIVE(U31(tt, z0)) → c8(MARK(U32(isQid(z0))), U32'(isQid(z0)), ISQID(z0))
ACTIVE(U32(tt)) → c9(MARK(tt))
ACTIVE(U41(tt, z0, z1)) → c10(MARK(U42(isList(z0), z1)), U42'(isList(z0), z1), ISLIST(z0))
ACTIVE(U42(tt, z0)) → c11(MARK(U43(isNeList(z0))), U43'(isNeList(z0)), ISNELIST(z0))
ACTIVE(U43(tt)) → c12(MARK(tt))
ACTIVE(U51(tt, z0, z1)) → c13(MARK(U52(isNeList(z0), z1)), U52'(isNeList(z0), z1), ISNELIST(z0))
ACTIVE(U52(tt, z0)) → c14(MARK(U53(isList(z0))), U53'(isList(z0)), ISLIST(z0))
ACTIVE(U53(tt)) → c15(MARK(tt))
ACTIVE(U61(tt, z0)) → c16(MARK(U62(isQid(z0))), U62'(isQid(z0)), ISQID(z0))
ACTIVE(U62(tt)) → c17(MARK(tt))
ACTIVE(U71(tt, z0)) → c18(MARK(U72(isNePal(z0))), U72'(isNePal(z0)), ISNEPAL(z0))
ACTIVE(U72(tt)) → c19(MARK(tt))
ACTIVE(and(tt, z0)) → c20(MARK(z0))
ACTIVE(isList(z0)) → c21(MARK(U11(isPalListKind(z0), z0)), U11'(isPalListKind(z0), z0), ISPALLISTKIND(z0))
ACTIVE(isList(nil)) → c22(MARK(tt))
ACTIVE(isList(__(z0, z1))) → c23(MARK(U21(and(isPalListKind(z0), isPalListKind(z1)), z0, z1)), U21'(and(isPalListKind(z0), isPalListKind(z1)), z0, z1), AND(isPalListKind(z0), isPalListKind(z1)), ISPALLISTKIND(z0), ISPALLISTKIND(z1))
ACTIVE(isNeList(z0)) → c24(MARK(U31(isPalListKind(z0), z0)), U31'(isPalListKind(z0), z0), ISPALLISTKIND(z0))
ACTIVE(isNeList(__(z0, z1))) → c25(MARK(U41(and(isPalListKind(z0), isPalListKind(z1)), z0, z1)), U41'(and(isPalListKind(z0), isPalListKind(z1)), z0, z1), AND(isPalListKind(z0), isPalListKind(z1)), ISPALLISTKIND(z0), ISPALLISTKIND(z1))
ACTIVE(isNeList(__(z0, z1))) → c26(MARK(U51(and(isPalListKind(z0), isPalListKind(z1)), z0, z1)), U51'(and(isPalListKind(z0), isPalListKind(z1)), z0, z1), AND(isPalListKind(z0), isPalListKind(z1)), ISPALLISTKIND(z0), ISPALLISTKIND(z1))
ACTIVE(isNePal(z0)) → c27(MARK(U61(isPalListKind(z0), z0)), U61'(isPalListKind(z0), z0), ISPALLISTKIND(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c28(MARK(and(and(isQid(z0), isPalListKind(z0)), and(isPal(z1), isPalListKind(z1)))), AND(and(isQid(z0), isPalListKind(z0)), and(isPal(z1), isPalListKind(z1))), AND(isQid(z0), isPalListKind(z0)), ISQID(z0), ISPALLISTKIND(z0), AND(isPal(z1), isPalListKind(z1)), ISPAL(z1), ISPALLISTKIND(z1))
ACTIVE(isPal(z0)) → c29(MARK(U71(isPalListKind(z0), z0)), U71'(isPalListKind(z0), z0), ISPALLISTKIND(z0))
ACTIVE(isPal(nil)) → c30(MARK(tt))
ACTIVE(isPalListKind(a)) → c31(MARK(tt))
ACTIVE(isPalListKind(e)) → c32(MARK(tt))
ACTIVE(isPalListKind(i)) → c33(MARK(tt))
ACTIVE(isPalListKind(nil)) → c34(MARK(tt))
ACTIVE(isPalListKind(o)) → c35(MARK(tt))
ACTIVE(isPalListKind(u)) → c36(MARK(tt))
ACTIVE(isPalListKind(__(z0, z1))) → c37(MARK(and(isPalListKind(z0), isPalListKind(z1))), AND(isPalListKind(z0), isPalListKind(z1)), ISPALLISTKIND(z0), ISPALLISTKIND(z1))
ACTIVE(isQid(a)) → c38(MARK(tt))
ACTIVE(isQid(e)) → c39(MARK(tt))
ACTIVE(isQid(i)) → c40(MARK(tt))
ACTIVE(isQid(o)) → c41(MARK(tt))
ACTIVE(isQid(u)) → c42(MARK(tt))
MARK(__(z0, z1)) → c43(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(nil) → c44(ACTIVE(nil))
MARK(U11(z0, z1)) → c45(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0))
MARK(tt) → c46(ACTIVE(tt))
MARK(U12(z0)) → c47(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNeList(z0)) → c48(ACTIVE(isNeList(z0)), ISNELIST(z0))
MARK(U21(z0, z1, z2)) → c49(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1)) → c50(ACTIVE(U22(mark(z0), z1)), U22'(mark(z0), z1), MARK(z0))
MARK(isList(z0)) → c51(ACTIVE(isList(z0)), ISLIST(z0))
MARK(U23(z0)) → c52(ACTIVE(U23(mark(z0))), U23'(mark(z0)), MARK(z0))
MARK(U31(z0, z1)) → c53(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0))
MARK(U32(z0)) → c54(ACTIVE(U32(mark(z0))), U32'(mark(z0)), MARK(z0))
MARK(isQid(z0)) → c55(ACTIVE(isQid(z0)), ISQID(z0))
MARK(U41(z0, z1, z2)) → c56(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0))
MARK(U42(z0, z1)) → c57(ACTIVE(U42(mark(z0), z1)), U42'(mark(z0), z1), MARK(z0))
MARK(U43(z0)) → c58(ACTIVE(U43(mark(z0))), U43'(mark(z0)), MARK(z0))
MARK(U51(z0, z1, z2)) → c59(ACTIVE(U51(mark(z0), z1, z2)), U51'(mark(z0), z1, z2), MARK(z0))
MARK(U52(z0, z1)) → c60(ACTIVE(U52(mark(z0), z1)), U52'(mark(z0), z1), MARK(z0))
MARK(U53(z0)) → c61(ACTIVE(U53(mark(z0))), U53'(mark(z0)), MARK(z0))
MARK(U61(z0, z1)) → c62(ACTIVE(U61(mark(z0), z1)), U61'(mark(z0), z1), MARK(z0))
MARK(U62(z0)) → c63(ACTIVE(U62(mark(z0))), U62'(mark(z0)), MARK(z0))
MARK(U71(z0, z1)) → c64(ACTIVE(U71(mark(z0), z1)), U71'(mark(z0), z1), MARK(z0))
MARK(U72(z0)) → c65(ACTIVE(U72(mark(z0))), U72'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c66(ACTIVE(isNePal(z0)), ISNEPAL(z0))
MARK(and(z0, z1)) → c67(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0))
MARK(isPalListKind(z0)) → c68(ACTIVE(isPalListKind(z0)), ISPALLISTKIND(z0))
MARK(isPal(z0)) → c69(ACTIVE(isPal(z0)), ISPAL(z0))
MARK(a) → c70(ACTIVE(a))
MARK(e) → c71(ACTIVE(e))
MARK(i) → c72(ACTIVE(i))
MARK(o) → c73(ACTIVE(o))
MARK(u) → c74(ACTIVE(u))
__'(mark(z0), z1) → c75(__'(z0, z1))
__'(z0, mark(z1)) → c76(__'(z0, z1))
__'(active(z0), z1) → c77(__'(z0, z1))
__'(z0, active(z1)) → c78(__'(z0, z1))
U11'(mark(z0), z1) → c79(U11'(z0, z1))
U11'(z0, mark(z1)) → c80(U11'(z0, z1))
U11'(active(z0), z1) → c81(U11'(z0, z1))
U11'(z0, active(z1)) → c82(U11'(z0, z1))
U12'(mark(z0)) → c83(U12'(z0))
U12'(active(z0)) → c84(U12'(z0))
ISNELIST(mark(z0)) → c85(ISNELIST(z0))
ISNELIST(active(z0)) → c86(ISNELIST(z0))
U21'(mark(z0), z1, z2) → c87(U21'(z0, z1, z2))
U21'(z0, mark(z1), z2) → c88(U21'(z0, z1, z2))
U21'(z0, z1, mark(z2)) → c89(U21'(z0, z1, z2))
U21'(active(z0), z1, z2) → c90(U21'(z0, z1, z2))
U21'(z0, active(z1), z2) → c91(U21'(z0, z1, z2))
U21'(z0, z1, active(z2)) → c92(U21'(z0, z1, z2))
U22'(mark(z0), z1) → c93(U22'(z0, z1))
U22'(z0, mark(z1)) → c94(U22'(z0, z1))
U22'(active(z0), z1) → c95(U22'(z0, z1))
U22'(z0, active(z1)) → c96(U22'(z0, z1))
ISLIST(mark(z0)) → c97(ISLIST(z0))
ISLIST(active(z0)) → c98(ISLIST(z0))
U23'(mark(z0)) → c99(U23'(z0))
U23'(active(z0)) → c100(U23'(z0))
U31'(mark(z0), z1) → c101(U31'(z0, z1))
U31'(z0, mark(z1)) → c102(U31'(z0, z1))
U31'(active(z0), z1) → c103(U31'(z0, z1))
U31'(z0, active(z1)) → c104(U31'(z0, z1))
U32'(mark(z0)) → c105(U32'(z0))
U32'(active(z0)) → c106(U32'(z0))
ISQID(mark(z0)) → c107(ISQID(z0))
ISQID(active(z0)) → c108(ISQID(z0))
U41'(mark(z0), z1, z2) → c109(U41'(z0, z1, z2))
U41'(z0, mark(z1), z2) → c110(U41'(z0, z1, z2))
U41'(z0, z1, mark(z2)) → c111(U41'(z0, z1, z2))
U41'(active(z0), z1, z2) → c112(U41'(z0, z1, z2))
U41'(z0, active(z1), z2) → c113(U41'(z0, z1, z2))
U41'(z0, z1, active(z2)) → c114(U41'(z0, z1, z2))
U42'(mark(z0), z1) → c115(U42'(z0, z1))
U42'(z0, mark(z1)) → c116(U42'(z0, z1))
U42'(active(z0), z1) → c117(U42'(z0, z1))
U42'(z0, active(z1)) → c118(U42'(z0, z1))
U43'(mark(z0)) → c119(U43'(z0))
U43'(active(z0)) → c120(U43'(z0))
U51'(mark(z0), z1, z2) → c121(U51'(z0, z1, z2))
U51'(z0, mark(z1), z2) → c122(U51'(z0, z1, z2))
U51'(z0, z1, mark(z2)) → c123(U51'(z0, z1, z2))
U51'(active(z0), z1, z2) → c124(U51'(z0, z1, z2))
U51'(z0, active(z1), z2) → c125(U51'(z0, z1, z2))
U51'(z0, z1, active(z2)) → c126(U51'(z0, z1, z2))
U52'(mark(z0), z1) → c127(U52'(z0, z1))
U52'(z0, mark(z1)) → c128(U52'(z0, z1))
U52'(active(z0), z1) → c129(U52'(z0, z1))
U52'(z0, active(z1)) → c130(U52'(z0, z1))
U53'(mark(z0)) → c131(U53'(z0))
U53'(active(z0)) → c132(U53'(z0))
U61'(mark(z0), z1) → c133(U61'(z0, z1))
U61'(z0, mark(z1)) → c134(U61'(z0, z1))
U61'(active(z0), z1) → c135(U61'(z0, z1))
U61'(z0, active(z1)) → c136(U61'(z0, z1))
U62'(mark(z0)) → c137(U62'(z0))
U62'(active(z0)) → c138(U62'(z0))
U71'(mark(z0), z1) → c139(U71'(z0, z1))
U71'(z0, mark(z1)) → c140(U71'(z0, z1))
U71'(active(z0), z1) → c141(U71'(z0, z1))
U71'(z0, active(z1)) → c142(U71'(z0, z1))
U72'(mark(z0)) → c143(U72'(z0))
U72'(active(z0)) → c144(U72'(z0))
ISNEPAL(mark(z0)) → c145(ISNEPAL(z0))
ISNEPAL(active(z0)) → c146(ISNEPAL(z0))
AND(mark(z0), z1) → c147(AND(z0, z1))
AND(z0, mark(z1)) → c148(AND(z0, z1))
AND(active(z0), z1) → c149(AND(z0, z1))
AND(z0, active(z1)) → c150(AND(z0, z1))
ISPALLISTKIND(mark(z0)) → c151(ISPALLISTKIND(z0))
ISPALLISTKIND(active(z0)) → c152(ISPALLISTKIND(z0))
ISPAL(mark(z0)) → c153(ISPAL(z0))
ISPAL(active(z0)) → c154(ISPAL(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, z0)) → c3(MARK(U12(isNeList(z0))), U12'(isNeList(z0)), ISNELIST(z0))
ACTIVE(U12(tt)) → c4(MARK(tt))
ACTIVE(U21(tt, z0, z1)) → c5(MARK(U22(isList(z0), z1)), U22'(isList(z0), z1), ISLIST(z0))
ACTIVE(U22(tt, z0)) → c6(MARK(U23(isList(z0))), U23'(isList(z0)), ISLIST(z0))
ACTIVE(U23(tt)) → c7(MARK(tt))
ACTIVE(U31(tt, z0)) → c8(MARK(U32(isQid(z0))), U32'(isQid(z0)), ISQID(z0))
ACTIVE(U32(tt)) → c9(MARK(tt))
ACTIVE(U41(tt, z0, z1)) → c10(MARK(U42(isList(z0), z1)), U42'(isList(z0), z1), ISLIST(z0))
ACTIVE(U42(tt, z0)) → c11(MARK(U43(isNeList(z0))), U43'(isNeList(z0)), ISNELIST(z0))
ACTIVE(U43(tt)) → c12(MARK(tt))
ACTIVE(U51(tt, z0, z1)) → c13(MARK(U52(isNeList(z0), z1)), U52'(isNeList(z0), z1), ISNELIST(z0))
ACTIVE(U52(tt, z0)) → c14(MARK(U53(isList(z0))), U53'(isList(z0)), ISLIST(z0))
ACTIVE(U53(tt)) → c15(MARK(tt))
ACTIVE(U61(tt, z0)) → c16(MARK(U62(isQid(z0))), U62'(isQid(z0)), ISQID(z0))
ACTIVE(U62(tt)) → c17(MARK(tt))
ACTIVE(U71(tt, z0)) → c18(MARK(U72(isNePal(z0))), U72'(isNePal(z0)), ISNEPAL(z0))
ACTIVE(U72(tt)) → c19(MARK(tt))
ACTIVE(and(tt, z0)) → c20(MARK(z0))
ACTIVE(isList(z0)) → c21(MARK(U11(isPalListKind(z0), z0)), U11'(isPalListKind(z0), z0), ISPALLISTKIND(z0))
ACTIVE(isList(nil)) → c22(MARK(tt))
ACTIVE(isList(__(z0, z1))) → c23(MARK(U21(and(isPalListKind(z0), isPalListKind(z1)), z0, z1)), U21'(and(isPalListKind(z0), isPalListKind(z1)), z0, z1), AND(isPalListKind(z0), isPalListKind(z1)), ISPALLISTKIND(z0), ISPALLISTKIND(z1))
ACTIVE(isNeList(z0)) → c24(MARK(U31(isPalListKind(z0), z0)), U31'(isPalListKind(z0), z0), ISPALLISTKIND(z0))
ACTIVE(isNeList(__(z0, z1))) → c25(MARK(U41(and(isPalListKind(z0), isPalListKind(z1)), z0, z1)), U41'(and(isPalListKind(z0), isPalListKind(z1)), z0, z1), AND(isPalListKind(z0), isPalListKind(z1)), ISPALLISTKIND(z0), ISPALLISTKIND(z1))
ACTIVE(isNeList(__(z0, z1))) → c26(MARK(U51(and(isPalListKind(z0), isPalListKind(z1)), z0, z1)), U51'(and(isPalListKind(z0), isPalListKind(z1)), z0, z1), AND(isPalListKind(z0), isPalListKind(z1)), ISPALLISTKIND(z0), ISPALLISTKIND(z1))
ACTIVE(isNePal(z0)) → c27(MARK(U61(isPalListKind(z0), z0)), U61'(isPalListKind(z0), z0), ISPALLISTKIND(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c28(MARK(and(and(isQid(z0), isPalListKind(z0)), and(isPal(z1), isPalListKind(z1)))), AND(and(isQid(z0), isPalListKind(z0)), and(isPal(z1), isPalListKind(z1))), AND(isQid(z0), isPalListKind(z0)), ISQID(z0), ISPALLISTKIND(z0), AND(isPal(z1), isPalListKind(z1)), ISPAL(z1), ISPALLISTKIND(z1))
ACTIVE(isPal(z0)) → c29(MARK(U71(isPalListKind(z0), z0)), U71'(isPalListKind(z0), z0), ISPALLISTKIND(z0))
ACTIVE(isPal(nil)) → c30(MARK(tt))
ACTIVE(isPalListKind(a)) → c31(MARK(tt))
ACTIVE(isPalListKind(e)) → c32(MARK(tt))
ACTIVE(isPalListKind(i)) → c33(MARK(tt))
ACTIVE(isPalListKind(nil)) → c34(MARK(tt))
ACTIVE(isPalListKind(o)) → c35(MARK(tt))
ACTIVE(isPalListKind(u)) → c36(MARK(tt))
ACTIVE(isPalListKind(__(z0, z1))) → c37(MARK(and(isPalListKind(z0), isPalListKind(z1))), AND(isPalListKind(z0), isPalListKind(z1)), ISPALLISTKIND(z0), ISPALLISTKIND(z1))
ACTIVE(isQid(a)) → c38(MARK(tt))
ACTIVE(isQid(e)) → c39(MARK(tt))
ACTIVE(isQid(i)) → c40(MARK(tt))
ACTIVE(isQid(o)) → c41(MARK(tt))
ACTIVE(isQid(u)) → c42(MARK(tt))
MARK(__(z0, z1)) → c43(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(nil) → c44(ACTIVE(nil))
MARK(U11(z0, z1)) → c45(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0))
MARK(tt) → c46(ACTIVE(tt))
MARK(U12(z0)) → c47(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNeList(z0)) → c48(ACTIVE(isNeList(z0)), ISNELIST(z0))
MARK(U21(z0, z1, z2)) → c49(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1)) → c50(ACTIVE(U22(mark(z0), z1)), U22'(mark(z0), z1), MARK(z0))
MARK(isList(z0)) → c51(ACTIVE(isList(z0)), ISLIST(z0))
MARK(U23(z0)) → c52(ACTIVE(U23(mark(z0))), U23'(mark(z0)), MARK(z0))
MARK(U31(z0, z1)) → c53(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0))
MARK(U32(z0)) → c54(ACTIVE(U32(mark(z0))), U32'(mark(z0)), MARK(z0))
MARK(isQid(z0)) → c55(ACTIVE(isQid(z0)), ISQID(z0))
MARK(U41(z0, z1, z2)) → c56(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0))
MARK(U42(z0, z1)) → c57(ACTIVE(U42(mark(z0), z1)), U42'(mark(z0), z1), MARK(z0))
MARK(U43(z0)) → c58(ACTIVE(U43(mark(z0))), U43'(mark(z0)), MARK(z0))
MARK(U51(z0, z1, z2)) → c59(ACTIVE(U51(mark(z0), z1, z2)), U51'(mark(z0), z1, z2), MARK(z0))
MARK(U52(z0, z1)) → c60(ACTIVE(U52(mark(z0), z1)), U52'(mark(z0), z1), MARK(z0))
MARK(U53(z0)) → c61(ACTIVE(U53(mark(z0))), U53'(mark(z0)), MARK(z0))
MARK(U61(z0, z1)) → c62(ACTIVE(U61(mark(z0), z1)), U61'(mark(z0), z1), MARK(z0))
MARK(U62(z0)) → c63(ACTIVE(U62(mark(z0))), U62'(mark(z0)), MARK(z0))
MARK(U71(z0, z1)) → c64(ACTIVE(U71(mark(z0), z1)), U71'(mark(z0), z1), MARK(z0))
MARK(U72(z0)) → c65(ACTIVE(U72(mark(z0))), U72'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c66(ACTIVE(isNePal(z0)), ISNEPAL(z0))
MARK(and(z0, z1)) → c67(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0))
MARK(isPalListKind(z0)) → c68(ACTIVE(isPalListKind(z0)), ISPALLISTKIND(z0))
MARK(isPal(z0)) → c69(ACTIVE(isPal(z0)), ISPAL(z0))
MARK(a) → c70(ACTIVE(a))
MARK(e) → c71(ACTIVE(e))
MARK(i) → c72(ACTIVE(i))
MARK(o) → c73(ACTIVE(o))
MARK(u) → c74(ACTIVE(u))
__'(mark(z0), z1) → c75(__'(z0, z1))
__'(z0, mark(z1)) → c76(__'(z0, z1))
__'(active(z0), z1) → c77(__'(z0, z1))
__'(z0, active(z1)) → c78(__'(z0, z1))
U11'(mark(z0), z1) → c79(U11'(z0, z1))
U11'(z0, mark(z1)) → c80(U11'(z0, z1))
U11'(active(z0), z1) → c81(U11'(z0, z1))
U11'(z0, active(z1)) → c82(U11'(z0, z1))
U12'(mark(z0)) → c83(U12'(z0))
U12'(active(z0)) → c84(U12'(z0))
ISNELIST(mark(z0)) → c85(ISNELIST(z0))
ISNELIST(active(z0)) → c86(ISNELIST(z0))
U21'(mark(z0), z1, z2) → c87(U21'(z0, z1, z2))
U21'(z0, mark(z1), z2) → c88(U21'(z0, z1, z2))
U21'(z0, z1, mark(z2)) → c89(U21'(z0, z1, z2))
U21'(active(z0), z1, z2) → c90(U21'(z0, z1, z2))
U21'(z0, active(z1), z2) → c91(U21'(z0, z1, z2))
U21'(z0, z1, active(z2)) → c92(U21'(z0, z1, z2))
U22'(mark(z0), z1) → c93(U22'(z0, z1))
U22'(z0, mark(z1)) → c94(U22'(z0, z1))
U22'(active(z0), z1) → c95(U22'(z0, z1))
U22'(z0, active(z1)) → c96(U22'(z0, z1))
ISLIST(mark(z0)) → c97(ISLIST(z0))
ISLIST(active(z0)) → c98(ISLIST(z0))
U23'(mark(z0)) → c99(U23'(z0))
U23'(active(z0)) → c100(U23'(z0))
U31'(mark(z0), z1) → c101(U31'(z0, z1))
U31'(z0, mark(z1)) → c102(U31'(z0, z1))
U31'(active(z0), z1) → c103(U31'(z0, z1))
U31'(z0, active(z1)) → c104(U31'(z0, z1))
U32'(mark(z0)) → c105(U32'(z0))
U32'(active(z0)) → c106(U32'(z0))
ISQID(mark(z0)) → c107(ISQID(z0))
ISQID(active(z0)) → c108(ISQID(z0))
U41'(mark(z0), z1, z2) → c109(U41'(z0, z1, z2))
U41'(z0, mark(z1), z2) → c110(U41'(z0, z1, z2))
U41'(z0, z1, mark(z2)) → c111(U41'(z0, z1, z2))
U41'(active(z0), z1, z2) → c112(U41'(z0, z1, z2))
U41'(z0, active(z1), z2) → c113(U41'(z0, z1, z2))
U41'(z0, z1, active(z2)) → c114(U41'(z0, z1, z2))
U42'(mark(z0), z1) → c115(U42'(z0, z1))
U42'(z0, mark(z1)) → c116(U42'(z0, z1))
U42'(active(z0), z1) → c117(U42'(z0, z1))
U42'(z0, active(z1)) → c118(U42'(z0, z1))
U43'(mark(z0)) → c119(U43'(z0))
U43'(active(z0)) → c120(U43'(z0))
U51'(mark(z0), z1, z2) → c121(U51'(z0, z1, z2))
U51'(z0, mark(z1), z2) → c122(U51'(z0, z1, z2))
U51'(z0, z1, mark(z2)) → c123(U51'(z0, z1, z2))
U51'(active(z0), z1, z2) → c124(U51'(z0, z1, z2))
U51'(z0, active(z1), z2) → c125(U51'(z0, z1, z2))
U51'(z0, z1, active(z2)) → c126(U51'(z0, z1, z2))
U52'(mark(z0), z1) → c127(U52'(z0, z1))
U52'(z0, mark(z1)) → c128(U52'(z0, z1))
U52'(active(z0), z1) → c129(U52'(z0, z1))
U52'(z0, active(z1)) → c130(U52'(z0, z1))
U53'(mark(z0)) → c131(U53'(z0))
U53'(active(z0)) → c132(U53'(z0))
U61'(mark(z0), z1) → c133(U61'(z0, z1))
U61'(z0, mark(z1)) → c134(U61'(z0, z1))
U61'(active(z0), z1) → c135(U61'(z0, z1))
U61'(z0, active(z1)) → c136(U61'(z0, z1))
U62'(mark(z0)) → c137(U62'(z0))
U62'(active(z0)) → c138(U62'(z0))
U71'(mark(z0), z1) → c139(U71'(z0, z1))
U71'(z0, mark(z1)) → c140(U71'(z0, z1))
U71'(active(z0), z1) → c141(U71'(z0, z1))
U71'(z0, active(z1)) → c142(U71'(z0, z1))
U72'(mark(z0)) → c143(U72'(z0))
U72'(active(z0)) → c144(U72'(z0))
ISNEPAL(mark(z0)) → c145(ISNEPAL(z0))
ISNEPAL(active(z0)) → c146(ISNEPAL(z0))
AND(mark(z0), z1) → c147(AND(z0, z1))
AND(z0, mark(z1)) → c148(AND(z0, z1))
AND(active(z0), z1) → c149(AND(z0, z1))
AND(z0, active(z1)) → c150(AND(z0, z1))
ISPALLISTKIND(mark(z0)) → c151(ISPALLISTKIND(z0))
ISPALLISTKIND(active(z0)) → c152(ISPALLISTKIND(z0))
ISPAL(mark(z0)) → c153(ISPAL(z0))
ISPAL(active(z0)) → c154(ISPAL(z0))

K tuples:none
Defined Rule Symbols:

active, mark, __, U11, U12, isNeList, U21, U22, isList, U23, U31, U32, isQid, U41, U42, U43, U51, U52, U53, U61, U62, U71, U72, isNePal, and, isPalListKind, isPal

Defined Pair Symbols:

ACTIVE, MARK, __', U11', U12', ISNELIST, U21', U22', ISLIST, U23', U31', U32', ISQID, U41', U42', U43', U51', U52', U53', U61', U62', U71', U72', ISNEPAL, AND, ISPALLISTKIND, ISPAL

Compound Symbols:

c, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c90, c91, c92, c93, c94, c95, c96, c97, c98, c99, c100, c101, c102, c103, c104, c105, c106, c107, c108, c109, c110, c111, c112, c113, c114, c115, c116, c117, c118, c119, c120, c121, c122, c123, c124, c125, c126, c127, c128, c129, c130, c131, c132, c133, c134, c135, c136, c137, c138, c139, c140, c141, c142, c143, c144, c145, c146, c147, c148, c149, c150, c151, c152, c153, c154

(3) CdtUnreachableProof (EQUIVALENT transformation)

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

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, z0)) → c3(MARK(U12(isNeList(z0))), U12'(isNeList(z0)), ISNELIST(z0))
ACTIVE(U12(tt)) → c4(MARK(tt))
ACTIVE(U21(tt, z0, z1)) → c5(MARK(U22(isList(z0), z1)), U22'(isList(z0), z1), ISLIST(z0))
ACTIVE(U22(tt, z0)) → c6(MARK(U23(isList(z0))), U23'(isList(z0)), ISLIST(z0))
ACTIVE(U23(tt)) → c7(MARK(tt))
ACTIVE(U31(tt, z0)) → c8(MARK(U32(isQid(z0))), U32'(isQid(z0)), ISQID(z0))
ACTIVE(U32(tt)) → c9(MARK(tt))
ACTIVE(U41(tt, z0, z1)) → c10(MARK(U42(isList(z0), z1)), U42'(isList(z0), z1), ISLIST(z0))
ACTIVE(U42(tt, z0)) → c11(MARK(U43(isNeList(z0))), U43'(isNeList(z0)), ISNELIST(z0))
ACTIVE(U43(tt)) → c12(MARK(tt))
ACTIVE(U51(tt, z0, z1)) → c13(MARK(U52(isNeList(z0), z1)), U52'(isNeList(z0), z1), ISNELIST(z0))
ACTIVE(U52(tt, z0)) → c14(MARK(U53(isList(z0))), U53'(isList(z0)), ISLIST(z0))
ACTIVE(U53(tt)) → c15(MARK(tt))
ACTIVE(U61(tt, z0)) → c16(MARK(U62(isQid(z0))), U62'(isQid(z0)), ISQID(z0))
ACTIVE(U62(tt)) → c17(MARK(tt))
ACTIVE(U71(tt, z0)) → c18(MARK(U72(isNePal(z0))), U72'(isNePal(z0)), ISNEPAL(z0))
ACTIVE(U72(tt)) → c19(MARK(tt))
ACTIVE(and(tt, z0)) → c20(MARK(z0))
ACTIVE(isList(z0)) → c21(MARK(U11(isPalListKind(z0), z0)), U11'(isPalListKind(z0), z0), ISPALLISTKIND(z0))
ACTIVE(isList(nil)) → c22(MARK(tt))
ACTIVE(isList(__(z0, z1))) → c23(MARK(U21(and(isPalListKind(z0), isPalListKind(z1)), z0, z1)), U21'(and(isPalListKind(z0), isPalListKind(z1)), z0, z1), AND(isPalListKind(z0), isPalListKind(z1)), ISPALLISTKIND(z0), ISPALLISTKIND(z1))
ACTIVE(isNeList(z0)) → c24(MARK(U31(isPalListKind(z0), z0)), U31'(isPalListKind(z0), z0), ISPALLISTKIND(z0))
ACTIVE(isNeList(__(z0, z1))) → c25(MARK(U41(and(isPalListKind(z0), isPalListKind(z1)), z0, z1)), U41'(and(isPalListKind(z0), isPalListKind(z1)), z0, z1), AND(isPalListKind(z0), isPalListKind(z1)), ISPALLISTKIND(z0), ISPALLISTKIND(z1))
ACTIVE(isNeList(__(z0, z1))) → c26(MARK(U51(and(isPalListKind(z0), isPalListKind(z1)), z0, z1)), U51'(and(isPalListKind(z0), isPalListKind(z1)), z0, z1), AND(isPalListKind(z0), isPalListKind(z1)), ISPALLISTKIND(z0), ISPALLISTKIND(z1))
ACTIVE(isNePal(z0)) → c27(MARK(U61(isPalListKind(z0), z0)), U61'(isPalListKind(z0), z0), ISPALLISTKIND(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c28(MARK(and(and(isQid(z0), isPalListKind(z0)), and(isPal(z1), isPalListKind(z1)))), AND(and(isQid(z0), isPalListKind(z0)), and(isPal(z1), isPalListKind(z1))), AND(isQid(z0), isPalListKind(z0)), ISQID(z0), ISPALLISTKIND(z0), AND(isPal(z1), isPalListKind(z1)), ISPAL(z1), ISPALLISTKIND(z1))
ACTIVE(isPal(z0)) → c29(MARK(U71(isPalListKind(z0), z0)), U71'(isPalListKind(z0), z0), ISPALLISTKIND(z0))
ACTIVE(isPal(nil)) → c30(MARK(tt))
ACTIVE(isPalListKind(a)) → c31(MARK(tt))
ACTIVE(isPalListKind(e)) → c32(MARK(tt))
ACTIVE(isPalListKind(i)) → c33(MARK(tt))
ACTIVE(isPalListKind(nil)) → c34(MARK(tt))
ACTIVE(isPalListKind(o)) → c35(MARK(tt))
ACTIVE(isPalListKind(u)) → c36(MARK(tt))
ACTIVE(isPalListKind(__(z0, z1))) → c37(MARK(and(isPalListKind(z0), isPalListKind(z1))), AND(isPalListKind(z0), isPalListKind(z1)), ISPALLISTKIND(z0), ISPALLISTKIND(z1))
ACTIVE(isQid(a)) → c38(MARK(tt))
ACTIVE(isQid(e)) → c39(MARK(tt))
ACTIVE(isQid(i)) → c40(MARK(tt))
ACTIVE(isQid(o)) → c41(MARK(tt))
ACTIVE(isQid(u)) → c42(MARK(tt))
MARK(__(z0, z1)) → c43(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U11(z0, z1)) → c45(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0))
MARK(U12(z0)) → c47(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0))
MARK(isNeList(z0)) → c48(ACTIVE(isNeList(z0)), ISNELIST(z0))
MARK(U21(z0, z1, z2)) → c49(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1)) → c50(ACTIVE(U22(mark(z0), z1)), U22'(mark(z0), z1), MARK(z0))
MARK(isList(z0)) → c51(ACTIVE(isList(z0)), ISLIST(z0))
MARK(U23(z0)) → c52(ACTIVE(U23(mark(z0))), U23'(mark(z0)), MARK(z0))
MARK(U31(z0, z1)) → c53(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0))
MARK(U32(z0)) → c54(ACTIVE(U32(mark(z0))), U32'(mark(z0)), MARK(z0))
MARK(isQid(z0)) → c55(ACTIVE(isQid(z0)), ISQID(z0))
MARK(U41(z0, z1, z2)) → c56(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0))
MARK(U42(z0, z1)) → c57(ACTIVE(U42(mark(z0), z1)), U42'(mark(z0), z1), MARK(z0))
MARK(U43(z0)) → c58(ACTIVE(U43(mark(z0))), U43'(mark(z0)), MARK(z0))
MARK(U51(z0, z1, z2)) → c59(ACTIVE(U51(mark(z0), z1, z2)), U51'(mark(z0), z1, z2), MARK(z0))
MARK(U52(z0, z1)) → c60(ACTIVE(U52(mark(z0), z1)), U52'(mark(z0), z1), MARK(z0))
MARK(U53(z0)) → c61(ACTIVE(U53(mark(z0))), U53'(mark(z0)), MARK(z0))
MARK(U61(z0, z1)) → c62(ACTIVE(U61(mark(z0), z1)), U61'(mark(z0), z1), MARK(z0))
MARK(U62(z0)) → c63(ACTIVE(U62(mark(z0))), U62'(mark(z0)), MARK(z0))
MARK(U71(z0, z1)) → c64(ACTIVE(U71(mark(z0), z1)), U71'(mark(z0), z1), MARK(z0))
MARK(U72(z0)) → c65(ACTIVE(U72(mark(z0))), U72'(mark(z0)), MARK(z0))
MARK(isNePal(z0)) → c66(ACTIVE(isNePal(z0)), ISNEPAL(z0))
MARK(and(z0, z1)) → c67(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0))
MARK(isPalListKind(z0)) → c68(ACTIVE(isPalListKind(z0)), ISPALLISTKIND(z0))
MARK(isPal(z0)) → c69(ACTIVE(isPal(z0)), ISPAL(z0))
__'(mark(z0), z1) → c75(__'(z0, z1))
__'(z0, mark(z1)) → c76(__'(z0, z1))
__'(active(z0), z1) → c77(__'(z0, z1))
__'(z0, active(z1)) → c78(__'(z0, z1))
U11'(mark(z0), z1) → c79(U11'(z0, z1))
U11'(z0, mark(z1)) → c80(U11'(z0, z1))
U11'(active(z0), z1) → c81(U11'(z0, z1))
U11'(z0, active(z1)) → c82(U11'(z0, z1))
U12'(mark(z0)) → c83(U12'(z0))
U12'(active(z0)) → c84(U12'(z0))
ISNELIST(mark(z0)) → c85(ISNELIST(z0))
ISNELIST(active(z0)) → c86(ISNELIST(z0))
U21'(mark(z0), z1, z2) → c87(U21'(z0, z1, z2))
U21'(z0, mark(z1), z2) → c88(U21'(z0, z1, z2))
U21'(z0, z1, mark(z2)) → c89(U21'(z0, z1, z2))
U21'(active(z0), z1, z2) → c90(U21'(z0, z1, z2))
U21'(z0, active(z1), z2) → c91(U21'(z0, z1, z2))
U21'(z0, z1, active(z2)) → c92(U21'(z0, z1, z2))
U22'(mark(z0), z1) → c93(U22'(z0, z1))
U22'(z0, mark(z1)) → c94(U22'(z0, z1))
U22'(active(z0), z1) → c95(U22'(z0, z1))
U22'(z0, active(z1)) → c96(U22'(z0, z1))
ISLIST(mark(z0)) → c97(ISLIST(z0))
ISLIST(active(z0)) → c98(ISLIST(z0))
U23'(mark(z0)) → c99(U23'(z0))
U23'(active(z0)) → c100(U23'(z0))
U31'(mark(z0), z1) → c101(U31'(z0, z1))
U31'(z0, mark(z1)) → c102(U31'(z0, z1))
U31'(active(z0), z1) → c103(U31'(z0, z1))
U31'(z0, active(z1)) → c104(U31'(z0, z1))
U32'(mark(z0)) → c105(U32'(z0))
U32'(active(z0)) → c106(U32'(z0))
ISQID(mark(z0)) → c107(ISQID(z0))
ISQID(active(z0)) → c108(ISQID(z0))
U41'(mark(z0), z1, z2) → c109(U41'(z0, z1, z2))
U41'(z0, mark(z1), z2) → c110(U41'(z0, z1, z2))
U41'(z0, z1, mark(z2)) → c111(U41'(z0, z1, z2))
U41'(active(z0), z1, z2) → c112(U41'(z0, z1, z2))
U41'(z0, active(z1), z2) → c113(U41'(z0, z1, z2))
U41'(z0, z1, active(z2)) → c114(U41'(z0, z1, z2))
U42'(mark(z0), z1) → c115(U42'(z0, z1))
U42'(z0, mark(z1)) → c116(U42'(z0, z1))
U42'(active(z0), z1) → c117(U42'(z0, z1))
U42'(z0, active(z1)) → c118(U42'(z0, z1))
U43'(mark(z0)) → c119(U43'(z0))
U43'(active(z0)) → c120(U43'(z0))
U51'(mark(z0), z1, z2) → c121(U51'(z0, z1, z2))
U51'(z0, mark(z1), z2) → c122(U51'(z0, z1, z2))
U51'(z0, z1, mark(z2)) → c123(U51'(z0, z1, z2))
U51'(active(z0), z1, z2) → c124(U51'(z0, z1, z2))
U51'(z0, active(z1), z2) → c125(U51'(z0, z1, z2))
U51'(z0, z1, active(z2)) → c126(U51'(z0, z1, z2))
U52'(mark(z0), z1) → c127(U52'(z0, z1))
U52'(z0, mark(z1)) → c128(U52'(z0, z1))
U52'(active(z0), z1) → c129(U52'(z0, z1))
U52'(z0, active(z1)) → c130(U52'(z0, z1))
U53'(mark(z0)) → c131(U53'(z0))
U53'(active(z0)) → c132(U53'(z0))
U61'(mark(z0), z1) → c133(U61'(z0, z1))
U61'(z0, mark(z1)) → c134(U61'(z0, z1))
U61'(active(z0), z1) → c135(U61'(z0, z1))
U61'(z0, active(z1)) → c136(U61'(z0, z1))
U62'(mark(z0)) → c137(U62'(z0))
U62'(active(z0)) → c138(U62'(z0))
U71'(mark(z0), z1) → c139(U71'(z0, z1))
U71'(z0, mark(z1)) → c140(U71'(z0, z1))
U71'(active(z0), z1) → c141(U71'(z0, z1))
U71'(z0, active(z1)) → c142(U71'(z0, z1))
U72'(mark(z0)) → c143(U72'(z0))
U72'(active(z0)) → c144(U72'(z0))
ISNEPAL(mark(z0)) → c145(ISNEPAL(z0))
ISNEPAL(active(z0)) → c146(ISNEPAL(z0))
AND(mark(z0), z1) → c147(AND(z0, z1))
AND(z0, mark(z1)) → c148(AND(z0, z1))
AND(active(z0), z1) → c149(AND(z0, z1))
AND(z0, active(z1)) → c150(AND(z0, z1))
ISPALLISTKIND(mark(z0)) → c151(ISPALLISTKIND(z0))
ISPALLISTKIND(active(z0)) → c152(ISPALLISTKIND(z0))
ISPAL(mark(z0)) → c153(ISPAL(z0))
ISPAL(active(z0)) → c154(ISPAL(z0))

(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, z0)) → mark(U12(isNeList(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt, z0, z1)) → mark(U22(isList(z0), z1))
active(U22(tt, z0)) → mark(U23(isList(z0)))
active(U23(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isQid(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0, z1)) → mark(U42(isList(z0), z1))
active(U42(tt, z0)) → mark(U43(isNeList(z0)))
active(U43(tt)) → mark(tt)
active(U51(tt, z0, z1)) → mark(U52(isNeList(z0), z1))
active(U52(tt, z0)) → mark(U53(isList(z0)))
active(U53(tt)) → mark(tt)
active(U61(tt, z0)) → mark(U62(isQid(z0)))
active(U62(tt)) → mark(tt)
active(U71(tt, z0)) → mark(U72(isNePal(z0)))
active(U72(tt)) → mark(tt)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(U11(isPalListKind(z0), z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(U21(and(isPalListKind(z0), isPalListKind(z1)), z0, z1))
active(isNeList(z0)) → mark(U31(isPalListKind(z0), z0))
active(isNeList(__(z0, z1))) → mark(U41(and(isPalListKind(z0), isPalListKind(z1)), z0, z1))
active(isNeList(__(z0, z1))) → mark(U51(and(isPalListKind(z0), isPalListKind(z1)), z0, z1))
active(isNePal(z0)) → mark(U61(isPalListKind(z0), z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(and(isQid(z0), isPalListKind(z0)), and(isPal(z1), isPalListKind(z1))))
active(isPal(z0)) → mark(U71(isPalListKind(z0), z0))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(z0, z1))) → mark(and(isPalListKind(z0), isPalListKind(z1)))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0, z1)) → active(U11(mark(z0), z1))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNeList(z0)) → active(isNeList(z0))
mark(U21(z0, z1, z2)) → active(U21(mark(z0), z1, z2))
mark(U22(z0, z1)) → active(U22(mark(z0), z1))
mark(isList(z0)) → active(isList(z0))
mark(U23(z0)) → active(U23(mark(z0)))
mark(U31(z0, z1)) → active(U31(mark(z0), z1))
mark(U32(z0)) → active(U32(mark(z0)))
mark(isQid(z0)) → active(isQid(z0))
mark(U41(z0, z1, z2)) → active(U41(mark(z0), z1, z2))
mark(U42(z0, z1)) → active(U42(mark(z0), z1))
mark(U43(z0)) → active(U43(mark(z0)))
mark(U51(z0, z1, z2)) → active(U51(mark(z0), z1, z2))
mark(U52(z0, z1)) → active(U52(mark(z0), z1))
mark(U53(z0)) → active(U53(mark(z0)))
mark(U61(z0, z1)) → active(U61(mark(z0), z1))
mark(U62(z0)) → active(U62(mark(z0)))
mark(U71(z0, z1)) → active(U71(mark(z0), z1))
mark(U72(z0)) → active(U72(mark(z0)))
mark(isNePal(z0)) → active(isNePal(z0))
mark(and(z0, z1)) → active(and(mark(z0), z1))
mark(isPalListKind(z0)) → active(isPalListKind(z0))
mark(isPal(z0)) → active(isPal(z0))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0), z1) → U11(z0, z1)
U11(z0, mark(z1)) → U11(z0, z1)
U11(active(z0), z1) → U11(z0, z1)
U11(z0, active(z1)) → U11(z0, z1)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNeList(mark(z0)) → isNeList(z0)
isNeList(active(z0)) → isNeList(z0)
U21(mark(z0), z1, z2) → U21(z0, z1, z2)
U21(z0, mark(z1), z2) → U21(z0, z1, z2)
U21(z0, z1, mark(z2)) → U21(z0, z1, z2)
U21(active(z0), z1, z2) → U21(z0, z1, z2)
U21(z0, active(z1), z2) → U21(z0, z1, z2)
U21(z0, z1, active(z2)) → U21(z0, z1, z2)
U22(mark(z0), z1) → U22(z0, z1)
U22(z0, mark(z1)) → U22(z0, z1)
U22(active(z0), z1) → U22(z0, z1)
U22(z0, active(z1)) → U22(z0, z1)
isList(mark(z0)) → isList(z0)
isList(active(z0)) → isList(z0)
U23(mark(z0)) → U23(z0)
U23(active(z0)) → U23(z0)
U31(mark(z0), z1) → U31(z0, z1)
U31(z0, mark(z1)) → U31(z0, z1)
U31(active(z0), z1) → U31(z0, z1)
U31(z0, active(z1)) → U31(z0, z1)
U32(mark(z0)) → U32(z0)
U32(active(z0)) → U32(z0)
isQid(mark(z0)) → isQid(z0)
isQid(active(z0)) → isQid(z0)
U41(mark(z0), z1, z2) → U41(z0, z1, z2)
U41(z0, mark(z1), z2) → U41(z0, z1, z2)
U41(z0, z1, mark(z2)) → U41(z0, z1, z2)
U41(active(z0), z1, z2) → U41(z0, z1, z2)
U41(z0, active(z1), z2) → U41(z0, z1, z2)
U41(z0, z1, active(z2)) → U41(z0, z1, z2)
U42(mark(z0), z1) → U42(z0, z1)
U42(z0, mark(z1)) → U42(z0, z1)
U42(active(z0), z1) → U42(z0, z1)
U42(z0, active(z1)) → U42(z0, z1)
U43(mark(z0)) → U43(z0)
U43(active(z0)) → U43(z0)
U51(mark(z0), z1, z2) → U51(z0, z1, z2)
U51(z0, mark(z1), z2) → U51(z0, z1, z2)
U51(z0, z1, mark(z2)) → U51(z0, z1, z2)
U51(active(z0), z1, z2) → U51(z0, z1, z2)
U51(z0, active(z1), z2) → U51(z0, z1, z2)
U51(z0, z1, active(z2)) → U51(z0, z1, z2)
U52(mark(z0), z1) → U52(z0, z1)
U52(z0, mark(z1)) → U52(z0, z1)
U52(active(z0), z1) → U52(z0, z1)
U52(z0, active(z1)) → U52(z0, z1)
U53(mark(z0)) → U53(z0)
U53(active(z0)) → U53(z0)
U61(mark(z0), z1) → U61(z0, z1)
U61(z0, mark(z1)) → U61(z0, z1)
U61(active(z0), z1) → U61(z0, z1)
U61(z0, active(z1)) → U61(z0, z1)
U62(mark(z0)) → U62(z0)
U62(active(z0)) → U62(z0)
U71(mark(z0), z1) → U71(z0, z1)
U71(z0, mark(z1)) → U71(z0, z1)
U71(active(z0), z1) → U71(z0, z1)
U71(z0, active(z1)) → U71(z0, z1)
U72(mark(z0)) → U72(z0)
U72(active(z0)) → U72(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)
and(mark(z0), z1) → and(z0, z1)
and(z0, mark(z1)) → and(z0, z1)
and(active(z0), z1) → and(z0, z1)
and(z0, active(z1)) → and(z0, z1)
isPalListKind(mark(z0)) → isPalListKind(z0)
isPalListKind(active(z0)) → isPalListKind(z0)
isPal(mark(z0)) → isPal(z0)
isPal(active(z0)) → isPal(z0)

Tuples:

MARK(nil) → c44(ACTIVE(nil))
MARK(tt) → c46(ACTIVE(tt))
MARK(a) → c70(ACTIVE(a))
MARK(e) → c71(ACTIVE(e))
MARK(i) → c72(ACTIVE(i))
MARK(o) → c73(ACTIVE(o))
MARK(u) → c74(ACTIVE(u))

S tuples:

MARK(nil) → c44(ACTIVE(nil))
MARK(tt) → c46(ACTIVE(tt))
MARK(a) → c70(ACTIVE(a))
MARK(e) → c71(ACTIVE(e))
MARK(i) → c72(ACTIVE(i))
MARK(o) → c73(ACTIVE(o))
MARK(u) → c74(ACTIVE(u))

K tuples:none
Defined Rule Symbols:

active, mark, __, U11, U12, isNeList, U21, U22, isList, U23, U31, U32, isQid, U41, U42, U43, U51, U52, U53, U61, U62, U71, U72, isNePal, and, isPalListKind, isPal

Defined Pair Symbols:

MARK

Compound Symbols:

c44, c46, c70, c71, c72, c73, c74

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

Removed 7 trailing nodes:

MARK(a) → c70(ACTIVE(a))
MARK(i) → c72(ACTIVE(i))
MARK(u) → c74(ACTIVE(u))
MARK(tt) → c46(ACTIVE(tt))
MARK(e) → c71(ACTIVE(e))
MARK(nil) → c44(ACTIVE(nil))
MARK(o) → c73(ACTIVE(o))

(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, z0)) → mark(U12(isNeList(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt, z0, z1)) → mark(U22(isList(z0), z1))
active(U22(tt, z0)) → mark(U23(isList(z0)))
active(U23(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isQid(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0, z1)) → mark(U42(isList(z0), z1))
active(U42(tt, z0)) → mark(U43(isNeList(z0)))
active(U43(tt)) → mark(tt)
active(U51(tt, z0, z1)) → mark(U52(isNeList(z0), z1))
active(U52(tt, z0)) → mark(U53(isList(z0)))
active(U53(tt)) → mark(tt)
active(U61(tt, z0)) → mark(U62(isQid(z0)))
active(U62(tt)) → mark(tt)
active(U71(tt, z0)) → mark(U72(isNePal(z0)))
active(U72(tt)) → mark(tt)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(U11(isPalListKind(z0), z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(U21(and(isPalListKind(z0), isPalListKind(z1)), z0, z1))
active(isNeList(z0)) → mark(U31(isPalListKind(z0), z0))
active(isNeList(__(z0, z1))) → mark(U41(and(isPalListKind(z0), isPalListKind(z1)), z0, z1))
active(isNeList(__(z0, z1))) → mark(U51(and(isPalListKind(z0), isPalListKind(z1)), z0, z1))
active(isNePal(z0)) → mark(U61(isPalListKind(z0), z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(and(isQid(z0), isPalListKind(z0)), and(isPal(z1), isPalListKind(z1))))
active(isPal(z0)) → mark(U71(isPalListKind(z0), z0))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(z0, z1))) → mark(and(isPalListKind(z0), isPalListKind(z1)))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(z0, z1)) → active(__(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U11(z0, z1)) → active(U11(mark(z0), z1))
mark(tt) → active(tt)
mark(U12(z0)) → active(U12(mark(z0)))
mark(isNeList(z0)) → active(isNeList(z0))
mark(U21(z0, z1, z2)) → active(U21(mark(z0), z1, z2))
mark(U22(z0, z1)) → active(U22(mark(z0), z1))
mark(isList(z0)) → active(isList(z0))
mark(U23(z0)) → active(U23(mark(z0)))
mark(U31(z0, z1)) → active(U31(mark(z0), z1))
mark(U32(z0)) → active(U32(mark(z0)))
mark(isQid(z0)) → active(isQid(z0))
mark(U41(z0, z1, z2)) → active(U41(mark(z0), z1, z2))
mark(U42(z0, z1)) → active(U42(mark(z0), z1))
mark(U43(z0)) → active(U43(mark(z0)))
mark(U51(z0, z1, z2)) → active(U51(mark(z0), z1, z2))
mark(U52(z0, z1)) → active(U52(mark(z0), z1))
mark(U53(z0)) → active(U53(mark(z0)))
mark(U61(z0, z1)) → active(U61(mark(z0), z1))
mark(U62(z0)) → active(U62(mark(z0)))
mark(U71(z0, z1)) → active(U71(mark(z0), z1))
mark(U72(z0)) → active(U72(mark(z0)))
mark(isNePal(z0)) → active(isNePal(z0))
mark(and(z0, z1)) → active(and(mark(z0), z1))
mark(isPalListKind(z0)) → active(isPalListKind(z0))
mark(isPal(z0)) → active(isPal(z0))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(z0), z1) → __(z0, z1)
__(z0, mark(z1)) → __(z0, z1)
__(active(z0), z1) → __(z0, z1)
__(z0, active(z1)) → __(z0, z1)
U11(mark(z0), z1) → U11(z0, z1)
U11(z0, mark(z1)) → U11(z0, z1)
U11(active(z0), z1) → U11(z0, z1)
U11(z0, active(z1)) → U11(z0, z1)
U12(mark(z0)) → U12(z0)
U12(active(z0)) → U12(z0)
isNeList(mark(z0)) → isNeList(z0)
isNeList(active(z0)) → isNeList(z0)
U21(mark(z0), z1, z2) → U21(z0, z1, z2)
U21(z0, mark(z1), z2) → U21(z0, z1, z2)
U21(z0, z1, mark(z2)) → U21(z0, z1, z2)
U21(active(z0), z1, z2) → U21(z0, z1, z2)
U21(z0, active(z1), z2) → U21(z0, z1, z2)
U21(z0, z1, active(z2)) → U21(z0, z1, z2)
U22(mark(z0), z1) → U22(z0, z1)
U22(z0, mark(z1)) → U22(z0, z1)
U22(active(z0), z1) → U22(z0, z1)
U22(z0, active(z1)) → U22(z0, z1)
isList(mark(z0)) → isList(z0)
isList(active(z0)) → isList(z0)
U23(mark(z0)) → U23(z0)
U23(active(z0)) → U23(z0)
U31(mark(z0), z1) → U31(z0, z1)
U31(z0, mark(z1)) → U31(z0, z1)
U31(active(z0), z1) → U31(z0, z1)
U31(z0, active(z1)) → U31(z0, z1)
U32(mark(z0)) → U32(z0)
U32(active(z0)) → U32(z0)
isQid(mark(z0)) → isQid(z0)
isQid(active(z0)) → isQid(z0)
U41(mark(z0), z1, z2) → U41(z0, z1, z2)
U41(z0, mark(z1), z2) → U41(z0, z1, z2)
U41(z0, z1, mark(z2)) → U41(z0, z1, z2)
U41(active(z0), z1, z2) → U41(z0, z1, z2)
U41(z0, active(z1), z2) → U41(z0, z1, z2)
U41(z0, z1, active(z2)) → U41(z0, z1, z2)
U42(mark(z0), z1) → U42(z0, z1)
U42(z0, mark(z1)) → U42(z0, z1)
U42(active(z0), z1) → U42(z0, z1)
U42(z0, active(z1)) → U42(z0, z1)
U43(mark(z0)) → U43(z0)
U43(active(z0)) → U43(z0)
U51(mark(z0), z1, z2) → U51(z0, z1, z2)
U51(z0, mark(z1), z2) → U51(z0, z1, z2)
U51(z0, z1, mark(z2)) → U51(z0, z1, z2)
U51(active(z0), z1, z2) → U51(z0, z1, z2)
U51(z0, active(z1), z2) → U51(z0, z1, z2)
U51(z0, z1, active(z2)) → U51(z0, z1, z2)
U52(mark(z0), z1) → U52(z0, z1)
U52(z0, mark(z1)) → U52(z0, z1)
U52(active(z0), z1) → U52(z0, z1)
U52(z0, active(z1)) → U52(z0, z1)
U53(mark(z0)) → U53(z0)
U53(active(z0)) → U53(z0)
U61(mark(z0), z1) → U61(z0, z1)
U61(z0, mark(z1)) → U61(z0, z1)
U61(active(z0), z1) → U61(z0, z1)
U61(z0, active(z1)) → U61(z0, z1)
U62(mark(z0)) → U62(z0)
U62(active(z0)) → U62(z0)
U71(mark(z0), z1) → U71(z0, z1)
U71(z0, mark(z1)) → U71(z0, z1)
U71(active(z0), z1) → U71(z0, z1)
U71(z0, active(z1)) → U71(z0, z1)
U72(mark(z0)) → U72(z0)
U72(active(z0)) → U72(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)
and(mark(z0), z1) → and(z0, z1)
and(z0, mark(z1)) → and(z0, z1)
and(active(z0), z1) → and(z0, z1)
and(z0, active(z1)) → and(z0, z1)
isPalListKind(mark(z0)) → isPalListKind(z0)
isPalListKind(active(z0)) → isPalListKind(z0)
isPal(mark(z0)) → isPal(z0)
isPal(active(z0)) → isPal(z0)

Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:

active, mark, __, U11, U12, isNeList, U21, U22, isList, U23, U31, U32, isQid, U41, U42, U43, U51, U52, U53, U61, U62, U71, U72, isNePal, and, isPalListKind, isPal

Defined Pair Symbols:none

Compound Symbols:none

(7) SIsEmptyProof (EQUIVALENT transformation)

The set S is empty

(8) BOUNDS(O(1), O(1))