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)) → mark(tt)
active(U21(tt, V2)) → mark(U22(isList(V2)))
active(U22(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNeList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt)) → mark(tt)
active(U71(tt, P)) → mark(U72(isPal(P)))
active(U72(tt)) → mark(tt)
active(U81(tt)) → mark(tt)
active(isList(V)) → mark(U11(isNeList(V)))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isList(V1), V2))
active(isNeList(V)) → mark(U31(isQid(V)))
active(isNeList(__(V1, V2))) → mark(U41(isList(V1), V2))
active(isNeList(__(V1, V2))) → mark(U51(isNeList(V1), V2))
active(isNePal(V)) → mark(U61(isQid(V)))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), P))
active(isPal(V)) → mark(U81(isNePal(V)))
active(isPal(nil)) → mark(tt)
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(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X)) → active(U22(mark(X)))
mark(isList(X)) → active(isList(X))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(U61(X)) → active(U61(mark(X)))
mark(U71(X1, X2)) → active(U71(mark(X1), X2))
mark(U72(X)) → active(U72(mark(X)))
mark(isPal(X)) → active(isPal(X))
mark(U81(X)) → active(U81(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(isNePal(X)) → active(isNePal(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(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X)) → U22(X)
U22(active(X)) → U22(X)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
U61(mark(X)) → U61(X)
U61(active(X)) → U61(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)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(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(tt)
active(U21(tt, z0)) → mark(U22(isList(z0)))
active(U22(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, z0)) → mark(U42(isNeList(z0)))
active(U42(tt)) → mark(tt)
active(U51(tt, z0)) → mark(U52(isList(z0)))
active(U52(tt)) → mark(tt)
active(U61(tt)) → mark(tt)
active(U71(tt, z0)) → mark(U72(isPal(z0)))
active(U72(tt)) → mark(tt)
active(U81(tt)) → mark(tt)
active(isList(z0)) → mark(U11(isNeList(z0)))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(U21(isList(z0), z1))
active(isNeList(z0)) → mark(U31(isQid(z0)))
active(isNeList(__(z0, z1))) → mark(U41(isList(z0), z1))
active(isNeList(__(z0, z1))) → mark(U51(isNeList(z0), z1))
active(isNePal(z0)) → mark(U61(isQid(z0)))
active(isNePal(__(z0, __(z1, z0)))) → mark(U71(isQid(z0), z1))
active(isPal(z0)) → mark(U81(isNePal(z0)))
active(isPal(nil)) → mark(tt)
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)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U21(z0, z1)) → active(U21(mark(z0), z1))
mark(U22(z0)) → active(U22(mark(z0)))
mark(isList(z0)) → active(isList(z0))
mark(U31(z0)) → active(U31(mark(z0)))
mark(U41(z0, z1)) → active(U41(mark(z0), z1))
mark(U42(z0)) → active(U42(mark(z0)))
mark(isNeList(z0)) → active(isNeList(z0))
mark(U51(z0, z1)) → active(U51(mark(z0), z1))
mark(U52(z0)) → active(U52(mark(z0)))
mark(U61(z0)) → active(U61(mark(z0)))
mark(U71(z0, z1)) → active(U71(mark(z0), z1))
mark(U72(z0)) → active(U72(mark(z0)))
mark(isPal(z0)) → active(isPal(z0))
mark(U81(z0)) → active(U81(mark(z0)))
mark(isQid(z0)) → active(isQid(z0))
mark(isNePal(z0)) → active(isNePal(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)) → U11(z0)
U11(active(z0)) → U11(z0)
U21(mark(z0), z1) → U21(z0, z1)
U21(z0, mark(z1)) → U21(z0, z1)
U21(active(z0), z1) → U21(z0, z1)
U21(z0, active(z1)) → U21(z0, z1)
U22(mark(z0)) → U22(z0)
U22(active(z0)) → U22(z0)
isList(mark(z0)) → isList(z0)
isList(active(z0)) → isList(z0)
U31(mark(z0)) → U31(z0)
U31(active(z0)) → U31(z0)
U41(mark(z0), z1) → U41(z0, z1)
U41(z0, mark(z1)) → U41(z0, z1)
U41(active(z0), z1) → U41(z0, z1)
U41(z0, active(z1)) → U41(z0, z1)
U42(mark(z0)) → U42(z0)
U42(active(z0)) → U42(z0)
isNeList(mark(z0)) → isNeList(z0)
isNeList(active(z0)) → isNeList(z0)
U51(mark(z0), z1) → U51(z0, z1)
U51(z0, mark(z1)) → U51(z0, z1)
U51(active(z0), z1) → U51(z0, z1)
U51(z0, active(z1)) → U51(z0, z1)
U52(mark(z0)) → U52(z0)
U52(active(z0)) → U52(z0)
U61(mark(z0)) → U61(z0)
U61(active(z0)) → U61(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)
isPal(mark(z0)) → isPal(z0)
isPal(active(z0)) → isPal(z0)
U81(mark(z0)) → U81(z0)
U81(active(z0)) → U81(z0)
isQid(mark(z0)) → isQid(z0)
isQid(active(z0)) → isQid(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(tt))
ACTIVE(U21(tt, z0)) → c4(MARK(U22(isList(z0))), U22'(isList(z0)), ISLIST(z0))
ACTIVE(U22(tt)) → c5(MARK(tt))
ACTIVE(U31(tt)) → c6(MARK(tt))
ACTIVE(U41(tt, z0)) → c7(MARK(U42(isNeList(z0))), U42'(isNeList(z0)), ISNELIST(z0))
ACTIVE(U42(tt)) → c8(MARK(tt))
ACTIVE(U51(tt, z0)) → c9(MARK(U52(isList(z0))), U52'(isList(z0)), ISLIST(z0))
ACTIVE(U52(tt)) → c10(MARK(tt))
ACTIVE(U61(tt)) → c11(MARK(tt))
ACTIVE(U71(tt, z0)) → c12(MARK(U72(isPal(z0))), U72'(isPal(z0)), ISPAL(z0))
ACTIVE(U72(tt)) → c13(MARK(tt))
ACTIVE(U81(tt)) → c14(MARK(tt))
ACTIVE(isList(z0)) → c15(MARK(U11(isNeList(z0))), U11'(isNeList(z0)), ISNELIST(z0))
ACTIVE(isList(nil)) → c16(MARK(tt))
ACTIVE(isList(__(z0, z1))) → c17(MARK(U21(isList(z0), z1)), U21'(isList(z0), z1), ISLIST(z0))
ACTIVE(isNeList(z0)) → c18(MARK(U31(isQid(z0))), U31'(isQid(z0)), ISQID(z0))
ACTIVE(isNeList(__(z0, z1))) → c19(MARK(U41(isList(z0), z1)), U41'(isList(z0), z1), ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c20(MARK(U51(isNeList(z0), z1)), U51'(isNeList(z0), z1), ISNELIST(z0))
ACTIVE(isNePal(z0)) → c21(MARK(U61(isQid(z0))), U61'(isQid(z0)), ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c22(MARK(U71(isQid(z0), z1)), U71'(isQid(z0), z1), ISQID(z0))
ACTIVE(isPal(z0)) → c23(MARK(U81(isNePal(z0))), U81'(isNePal(z0)), ISNEPAL(z0))
ACTIVE(isPal(nil)) → c24(MARK(tt))
ACTIVE(isQid(a)) → c25(MARK(tt))
ACTIVE(isQid(e)) → c26(MARK(tt))
ACTIVE(isQid(i)) → c27(MARK(tt))
ACTIVE(isQid(o)) → c28(MARK(tt))
ACTIVE(isQid(u)) → c29(MARK(tt))
MARK(__(z0, z1)) → c30(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(nil) → c31(ACTIVE(nil))
MARK(U11(z0)) → c32(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(tt) → c33(ACTIVE(tt))
MARK(U21(z0, z1)) → c34(ACTIVE(U21(mark(z0), z1)), U21'(mark(z0), z1), MARK(z0))
MARK(U22(z0)) → c35(ACTIVE(U22(mark(z0))), U22'(mark(z0)), MARK(z0))
MARK(isList(z0)) → c36(ACTIVE(isList(z0)), ISLIST(z0))
MARK(U31(z0)) → c37(ACTIVE(U31(mark(z0))), U31'(mark(z0)), MARK(z0))
MARK(U41(z0, z1)) → c38(ACTIVE(U41(mark(z0), z1)), U41'(mark(z0), z1), MARK(z0))
MARK(U42(z0)) → c39(ACTIVE(U42(mark(z0))), U42'(mark(z0)), MARK(z0))
MARK(isNeList(z0)) → c40(ACTIVE(isNeList(z0)), ISNELIST(z0))
MARK(U51(z0, z1)) → c41(ACTIVE(U51(mark(z0), z1)), U51'(mark(z0), z1), MARK(z0))
MARK(U52(z0)) → c42(ACTIVE(U52(mark(z0))), U52'(mark(z0)), MARK(z0))
MARK(U61(z0)) → c43(ACTIVE(U61(mark(z0))), U61'(mark(z0)), MARK(z0))
MARK(U71(z0, z1)) → c44(ACTIVE(U71(mark(z0), z1)), U71'(mark(z0), z1), MARK(z0))
MARK(U72(z0)) → c45(ACTIVE(U72(mark(z0))), U72'(mark(z0)), MARK(z0))
MARK(isPal(z0)) → c46(ACTIVE(isPal(z0)), ISPAL(z0))
MARK(U81(z0)) → c47(ACTIVE(U81(mark(z0))), U81'(mark(z0)), MARK(z0))
MARK(isQid(z0)) → c48(ACTIVE(isQid(z0)), ISQID(z0))
MARK(isNePal(z0)) → c49(ACTIVE(isNePal(z0)), ISNEPAL(z0))
MARK(a) → c50(ACTIVE(a))
MARK(e) → c51(ACTIVE(e))
MARK(i) → c52(ACTIVE(i))
MARK(o) → c53(ACTIVE(o))
MARK(u) → c54(ACTIVE(u))
__'(mark(z0), z1) → c55(__'(z0, z1))
__'(z0, mark(z1)) → c56(__'(z0, z1))
__'(active(z0), z1) → c57(__'(z0, z1))
__'(z0, active(z1)) → c58(__'(z0, z1))
U11'(mark(z0)) → c59(U11'(z0))
U11'(active(z0)) → c60(U11'(z0))
U21'(mark(z0), z1) → c61(U21'(z0, z1))
U21'(z0, mark(z1)) → c62(U21'(z0, z1))
U21'(active(z0), z1) → c63(U21'(z0, z1))
U21'(z0, active(z1)) → c64(U21'(z0, z1))
U22'(mark(z0)) → c65(U22'(z0))
U22'(active(z0)) → c66(U22'(z0))
ISLIST(mark(z0)) → c67(ISLIST(z0))
ISLIST(active(z0)) → c68(ISLIST(z0))
U31'(mark(z0)) → c69(U31'(z0))
U31'(active(z0)) → c70(U31'(z0))
U41'(mark(z0), z1) → c71(U41'(z0, z1))
U41'(z0, mark(z1)) → c72(U41'(z0, z1))
U41'(active(z0), z1) → c73(U41'(z0, z1))
U41'(z0, active(z1)) → c74(U41'(z0, z1))
U42'(mark(z0)) → c75(U42'(z0))
U42'(active(z0)) → c76(U42'(z0))
ISNELIST(mark(z0)) → c77(ISNELIST(z0))
ISNELIST(active(z0)) → c78(ISNELIST(z0))
U51'(mark(z0), z1) → c79(U51'(z0, z1))
U51'(z0, mark(z1)) → c80(U51'(z0, z1))
U51'(active(z0), z1) → c81(U51'(z0, z1))
U51'(z0, active(z1)) → c82(U51'(z0, z1))
U52'(mark(z0)) → c83(U52'(z0))
U52'(active(z0)) → c84(U52'(z0))
U61'(mark(z0)) → c85(U61'(z0))
U61'(active(z0)) → c86(U61'(z0))
U71'(mark(z0), z1) → c87(U71'(z0, z1))
U71'(z0, mark(z1)) → c88(U71'(z0, z1))
U71'(active(z0), z1) → c89(U71'(z0, z1))
U71'(z0, active(z1)) → c90(U71'(z0, z1))
U72'(mark(z0)) → c91(U72'(z0))
U72'(active(z0)) → c92(U72'(z0))
ISPAL(mark(z0)) → c93(ISPAL(z0))
ISPAL(active(z0)) → c94(ISPAL(z0))
U81'(mark(z0)) → c95(U81'(z0))
U81'(active(z0)) → c96(U81'(z0))
ISQID(mark(z0)) → c97(ISQID(z0))
ISQID(active(z0)) → c98(ISQID(z0))
ISNEPAL(mark(z0)) → c99(ISNEPAL(z0))
ISNEPAL(active(z0)) → c100(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(tt))
ACTIVE(U21(tt, z0)) → c4(MARK(U22(isList(z0))), U22'(isList(z0)), ISLIST(z0))
ACTIVE(U22(tt)) → c5(MARK(tt))
ACTIVE(U31(tt)) → c6(MARK(tt))
ACTIVE(U41(tt, z0)) → c7(MARK(U42(isNeList(z0))), U42'(isNeList(z0)), ISNELIST(z0))
ACTIVE(U42(tt)) → c8(MARK(tt))
ACTIVE(U51(tt, z0)) → c9(MARK(U52(isList(z0))), U52'(isList(z0)), ISLIST(z0))
ACTIVE(U52(tt)) → c10(MARK(tt))
ACTIVE(U61(tt)) → c11(MARK(tt))
ACTIVE(U71(tt, z0)) → c12(MARK(U72(isPal(z0))), U72'(isPal(z0)), ISPAL(z0))
ACTIVE(U72(tt)) → c13(MARK(tt))
ACTIVE(U81(tt)) → c14(MARK(tt))
ACTIVE(isList(z0)) → c15(MARK(U11(isNeList(z0))), U11'(isNeList(z0)), ISNELIST(z0))
ACTIVE(isList(nil)) → c16(MARK(tt))
ACTIVE(isList(__(z0, z1))) → c17(MARK(U21(isList(z0), z1)), U21'(isList(z0), z1), ISLIST(z0))
ACTIVE(isNeList(z0)) → c18(MARK(U31(isQid(z0))), U31'(isQid(z0)), ISQID(z0))
ACTIVE(isNeList(__(z0, z1))) → c19(MARK(U41(isList(z0), z1)), U41'(isList(z0), z1), ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c20(MARK(U51(isNeList(z0), z1)), U51'(isNeList(z0), z1), ISNELIST(z0))
ACTIVE(isNePal(z0)) → c21(MARK(U61(isQid(z0))), U61'(isQid(z0)), ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c22(MARK(U71(isQid(z0), z1)), U71'(isQid(z0), z1), ISQID(z0))
ACTIVE(isPal(z0)) → c23(MARK(U81(isNePal(z0))), U81'(isNePal(z0)), ISNEPAL(z0))
ACTIVE(isPal(nil)) → c24(MARK(tt))
ACTIVE(isQid(a)) → c25(MARK(tt))
ACTIVE(isQid(e)) → c26(MARK(tt))
ACTIVE(isQid(i)) → c27(MARK(tt))
ACTIVE(isQid(o)) → c28(MARK(tt))
ACTIVE(isQid(u)) → c29(MARK(tt))
MARK(__(z0, z1)) → c30(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(nil) → c31(ACTIVE(nil))
MARK(U11(z0)) → c32(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(tt) → c33(ACTIVE(tt))
MARK(U21(z0, z1)) → c34(ACTIVE(U21(mark(z0), z1)), U21'(mark(z0), z1), MARK(z0))
MARK(U22(z0)) → c35(ACTIVE(U22(mark(z0))), U22'(mark(z0)), MARK(z0))
MARK(isList(z0)) → c36(ACTIVE(isList(z0)), ISLIST(z0))
MARK(U31(z0)) → c37(ACTIVE(U31(mark(z0))), U31'(mark(z0)), MARK(z0))
MARK(U41(z0, z1)) → c38(ACTIVE(U41(mark(z0), z1)), U41'(mark(z0), z1), MARK(z0))
MARK(U42(z0)) → c39(ACTIVE(U42(mark(z0))), U42'(mark(z0)), MARK(z0))
MARK(isNeList(z0)) → c40(ACTIVE(isNeList(z0)), ISNELIST(z0))
MARK(U51(z0, z1)) → c41(ACTIVE(U51(mark(z0), z1)), U51'(mark(z0), z1), MARK(z0))
MARK(U52(z0)) → c42(ACTIVE(U52(mark(z0))), U52'(mark(z0)), MARK(z0))
MARK(U61(z0)) → c43(ACTIVE(U61(mark(z0))), U61'(mark(z0)), MARK(z0))
MARK(U71(z0, z1)) → c44(ACTIVE(U71(mark(z0), z1)), U71'(mark(z0), z1), MARK(z0))
MARK(U72(z0)) → c45(ACTIVE(U72(mark(z0))), U72'(mark(z0)), MARK(z0))
MARK(isPal(z0)) → c46(ACTIVE(isPal(z0)), ISPAL(z0))
MARK(U81(z0)) → c47(ACTIVE(U81(mark(z0))), U81'(mark(z0)), MARK(z0))
MARK(isQid(z0)) → c48(ACTIVE(isQid(z0)), ISQID(z0))
MARK(isNePal(z0)) → c49(ACTIVE(isNePal(z0)), ISNEPAL(z0))
MARK(a) → c50(ACTIVE(a))
MARK(e) → c51(ACTIVE(e))
MARK(i) → c52(ACTIVE(i))
MARK(o) → c53(ACTIVE(o))
MARK(u) → c54(ACTIVE(u))
__'(mark(z0), z1) → c55(__'(z0, z1))
__'(z0, mark(z1)) → c56(__'(z0, z1))
__'(active(z0), z1) → c57(__'(z0, z1))
__'(z0, active(z1)) → c58(__'(z0, z1))
U11'(mark(z0)) → c59(U11'(z0))
U11'(active(z0)) → c60(U11'(z0))
U21'(mark(z0), z1) → c61(U21'(z0, z1))
U21'(z0, mark(z1)) → c62(U21'(z0, z1))
U21'(active(z0), z1) → c63(U21'(z0, z1))
U21'(z0, active(z1)) → c64(U21'(z0, z1))
U22'(mark(z0)) → c65(U22'(z0))
U22'(active(z0)) → c66(U22'(z0))
ISLIST(mark(z0)) → c67(ISLIST(z0))
ISLIST(active(z0)) → c68(ISLIST(z0))
U31'(mark(z0)) → c69(U31'(z0))
U31'(active(z0)) → c70(U31'(z0))
U41'(mark(z0), z1) → c71(U41'(z0, z1))
U41'(z0, mark(z1)) → c72(U41'(z0, z1))
U41'(active(z0), z1) → c73(U41'(z0, z1))
U41'(z0, active(z1)) → c74(U41'(z0, z1))
U42'(mark(z0)) → c75(U42'(z0))
U42'(active(z0)) → c76(U42'(z0))
ISNELIST(mark(z0)) → c77(ISNELIST(z0))
ISNELIST(active(z0)) → c78(ISNELIST(z0))
U51'(mark(z0), z1) → c79(U51'(z0, z1))
U51'(z0, mark(z1)) → c80(U51'(z0, z1))
U51'(active(z0), z1) → c81(U51'(z0, z1))
U51'(z0, active(z1)) → c82(U51'(z0, z1))
U52'(mark(z0)) → c83(U52'(z0))
U52'(active(z0)) → c84(U52'(z0))
U61'(mark(z0)) → c85(U61'(z0))
U61'(active(z0)) → c86(U61'(z0))
U71'(mark(z0), z1) → c87(U71'(z0, z1))
U71'(z0, mark(z1)) → c88(U71'(z0, z1))
U71'(active(z0), z1) → c89(U71'(z0, z1))
U71'(z0, active(z1)) → c90(U71'(z0, z1))
U72'(mark(z0)) → c91(U72'(z0))
U72'(active(z0)) → c92(U72'(z0))
ISPAL(mark(z0)) → c93(ISPAL(z0))
ISPAL(active(z0)) → c94(ISPAL(z0))
U81'(mark(z0)) → c95(U81'(z0))
U81'(active(z0)) → c96(U81'(z0))
ISQID(mark(z0)) → c97(ISQID(z0))
ISQID(active(z0)) → c98(ISQID(z0))
ISNEPAL(mark(z0)) → c99(ISNEPAL(z0))
ISNEPAL(active(z0)) → c100(ISNEPAL(z0))

K tuples:none
Defined Rule Symbols:

active, mark, __, U11, U21, U22, isList, U31, U41, U42, isNeList, U51, U52, U61, U71, U72, isPal, U81, isQid, isNePal

Defined Pair Symbols:

ACTIVE, MARK, __', U11', U21', U22', ISLIST, U31', U41', U42', ISNELIST, U51', U52', U61', U71', U72', ISPAL, U81', ISQID, 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, 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

(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)) → c3(MARK(tt))
ACTIVE(U21(tt, z0)) → c4(MARK(U22(isList(z0))), U22'(isList(z0)), ISLIST(z0))
ACTIVE(U22(tt)) → c5(MARK(tt))
ACTIVE(U31(tt)) → c6(MARK(tt))
ACTIVE(U41(tt, z0)) → c7(MARK(U42(isNeList(z0))), U42'(isNeList(z0)), ISNELIST(z0))
ACTIVE(U42(tt)) → c8(MARK(tt))
ACTIVE(U51(tt, z0)) → c9(MARK(U52(isList(z0))), U52'(isList(z0)), ISLIST(z0))
ACTIVE(U52(tt)) → c10(MARK(tt))
ACTIVE(U61(tt)) → c11(MARK(tt))
ACTIVE(U71(tt, z0)) → c12(MARK(U72(isPal(z0))), U72'(isPal(z0)), ISPAL(z0))
ACTIVE(U72(tt)) → c13(MARK(tt))
ACTIVE(U81(tt)) → c14(MARK(tt))
ACTIVE(isList(z0)) → c15(MARK(U11(isNeList(z0))), U11'(isNeList(z0)), ISNELIST(z0))
ACTIVE(isList(nil)) → c16(MARK(tt))
ACTIVE(isList(__(z0, z1))) → c17(MARK(U21(isList(z0), z1)), U21'(isList(z0), z1), ISLIST(z0))
ACTIVE(isNeList(z0)) → c18(MARK(U31(isQid(z0))), U31'(isQid(z0)), ISQID(z0))
ACTIVE(isNeList(__(z0, z1))) → c19(MARK(U41(isList(z0), z1)), U41'(isList(z0), z1), ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c20(MARK(U51(isNeList(z0), z1)), U51'(isNeList(z0), z1), ISNELIST(z0))
ACTIVE(isNePal(z0)) → c21(MARK(U61(isQid(z0))), U61'(isQid(z0)), ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c22(MARK(U71(isQid(z0), z1)), U71'(isQid(z0), z1), ISQID(z0))
ACTIVE(isPal(z0)) → c23(MARK(U81(isNePal(z0))), U81'(isNePal(z0)), ISNEPAL(z0))
ACTIVE(isPal(nil)) → c24(MARK(tt))
ACTIVE(isQid(a)) → c25(MARK(tt))
ACTIVE(isQid(e)) → c26(MARK(tt))
ACTIVE(isQid(i)) → c27(MARK(tt))
ACTIVE(isQid(o)) → c28(MARK(tt))
ACTIVE(isQid(u)) → c29(MARK(tt))
MARK(__(z0, z1)) → c30(ACTIVE(__(mark(z0), mark(z1))), __'(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U11(z0)) → c32(ACTIVE(U11(mark(z0))), U11'(mark(z0)), MARK(z0))
MARK(U21(z0, z1)) → c34(ACTIVE(U21(mark(z0), z1)), U21'(mark(z0), z1), MARK(z0))
MARK(U22(z0)) → c35(ACTIVE(U22(mark(z0))), U22'(mark(z0)), MARK(z0))
MARK(isList(z0)) → c36(ACTIVE(isList(z0)), ISLIST(z0))
MARK(U31(z0)) → c37(ACTIVE(U31(mark(z0))), U31'(mark(z0)), MARK(z0))
MARK(U41(z0, z1)) → c38(ACTIVE(U41(mark(z0), z1)), U41'(mark(z0), z1), MARK(z0))
MARK(U42(z0)) → c39(ACTIVE(U42(mark(z0))), U42'(mark(z0)), MARK(z0))
MARK(isNeList(z0)) → c40(ACTIVE(isNeList(z0)), ISNELIST(z0))
MARK(U51(z0, z1)) → c41(ACTIVE(U51(mark(z0), z1)), U51'(mark(z0), z1), MARK(z0))
MARK(U52(z0)) → c42(ACTIVE(U52(mark(z0))), U52'(mark(z0)), MARK(z0))
MARK(U61(z0)) → c43(ACTIVE(U61(mark(z0))), U61'(mark(z0)), MARK(z0))
MARK(U71(z0, z1)) → c44(ACTIVE(U71(mark(z0), z1)), U71'(mark(z0), z1), MARK(z0))
MARK(U72(z0)) → c45(ACTIVE(U72(mark(z0))), U72'(mark(z0)), MARK(z0))
MARK(isPal(z0)) → c46(ACTIVE(isPal(z0)), ISPAL(z0))
MARK(U81(z0)) → c47(ACTIVE(U81(mark(z0))), U81'(mark(z0)), MARK(z0))
MARK(isQid(z0)) → c48(ACTIVE(isQid(z0)), ISQID(z0))
MARK(isNePal(z0)) → c49(ACTIVE(isNePal(z0)), ISNEPAL(z0))
__'(mark(z0), z1) → c55(__'(z0, z1))
__'(z0, mark(z1)) → c56(__'(z0, z1))
__'(active(z0), z1) → c57(__'(z0, z1))
__'(z0, active(z1)) → c58(__'(z0, z1))
U11'(mark(z0)) → c59(U11'(z0))
U11'(active(z0)) → c60(U11'(z0))
U21'(mark(z0), z1) → c61(U21'(z0, z1))
U21'(z0, mark(z1)) → c62(U21'(z0, z1))
U21'(active(z0), z1) → c63(U21'(z0, z1))
U21'(z0, active(z1)) → c64(U21'(z0, z1))
U22'(mark(z0)) → c65(U22'(z0))
U22'(active(z0)) → c66(U22'(z0))
ISLIST(mark(z0)) → c67(ISLIST(z0))
ISLIST(active(z0)) → c68(ISLIST(z0))
U31'(mark(z0)) → c69(U31'(z0))
U31'(active(z0)) → c70(U31'(z0))
U41'(mark(z0), z1) → c71(U41'(z0, z1))
U41'(z0, mark(z1)) → c72(U41'(z0, z1))
U41'(active(z0), z1) → c73(U41'(z0, z1))
U41'(z0, active(z1)) → c74(U41'(z0, z1))
U42'(mark(z0)) → c75(U42'(z0))
U42'(active(z0)) → c76(U42'(z0))
ISNELIST(mark(z0)) → c77(ISNELIST(z0))
ISNELIST(active(z0)) → c78(ISNELIST(z0))
U51'(mark(z0), z1) → c79(U51'(z0, z1))
U51'(z0, mark(z1)) → c80(U51'(z0, z1))
U51'(active(z0), z1) → c81(U51'(z0, z1))
U51'(z0, active(z1)) → c82(U51'(z0, z1))
U52'(mark(z0)) → c83(U52'(z0))
U52'(active(z0)) → c84(U52'(z0))
U61'(mark(z0)) → c85(U61'(z0))
U61'(active(z0)) → c86(U61'(z0))
U71'(mark(z0), z1) → c87(U71'(z0, z1))
U71'(z0, mark(z1)) → c88(U71'(z0, z1))
U71'(active(z0), z1) → c89(U71'(z0, z1))
U71'(z0, active(z1)) → c90(U71'(z0, z1))
U72'(mark(z0)) → c91(U72'(z0))
U72'(active(z0)) → c92(U72'(z0))
ISPAL(mark(z0)) → c93(ISPAL(z0))
ISPAL(active(z0)) → c94(ISPAL(z0))
U81'(mark(z0)) → c95(U81'(z0))
U81'(active(z0)) → c96(U81'(z0))
ISQID(mark(z0)) → c97(ISQID(z0))
ISQID(active(z0)) → c98(ISQID(z0))
ISNEPAL(mark(z0)) → c99(ISNEPAL(z0))
ISNEPAL(active(z0)) → c100(ISNEPAL(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)) → mark(tt)
active(U21(tt, z0)) → mark(U22(isList(z0)))
active(U22(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, z0)) → mark(U42(isNeList(z0)))
active(U42(tt)) → mark(tt)
active(U51(tt, z0)) → mark(U52(isList(z0)))
active(U52(tt)) → mark(tt)
active(U61(tt)) → mark(tt)
active(U71(tt, z0)) → mark(U72(isPal(z0)))
active(U72(tt)) → mark(tt)
active(U81(tt)) → mark(tt)
active(isList(z0)) → mark(U11(isNeList(z0)))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(U21(isList(z0), z1))
active(isNeList(z0)) → mark(U31(isQid(z0)))
active(isNeList(__(z0, z1))) → mark(U41(isList(z0), z1))
active(isNeList(__(z0, z1))) → mark(U51(isNeList(z0), z1))
active(isNePal(z0)) → mark(U61(isQid(z0)))
active(isNePal(__(z0, __(z1, z0)))) → mark(U71(isQid(z0), z1))
active(isPal(z0)) → mark(U81(isNePal(z0)))
active(isPal(nil)) → mark(tt)
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)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U21(z0, z1)) → active(U21(mark(z0), z1))
mark(U22(z0)) → active(U22(mark(z0)))
mark(isList(z0)) → active(isList(z0))
mark(U31(z0)) → active(U31(mark(z0)))
mark(U41(z0, z1)) → active(U41(mark(z0), z1))
mark(U42(z0)) → active(U42(mark(z0)))
mark(isNeList(z0)) → active(isNeList(z0))
mark(U51(z0, z1)) → active(U51(mark(z0), z1))
mark(U52(z0)) → active(U52(mark(z0)))
mark(U61(z0)) → active(U61(mark(z0)))
mark(U71(z0, z1)) → active(U71(mark(z0), z1))
mark(U72(z0)) → active(U72(mark(z0)))
mark(isPal(z0)) → active(isPal(z0))
mark(U81(z0)) → active(U81(mark(z0)))
mark(isQid(z0)) → active(isQid(z0))
mark(isNePal(z0)) → active(isNePal(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)) → U11(z0)
U11(active(z0)) → U11(z0)
U21(mark(z0), z1) → U21(z0, z1)
U21(z0, mark(z1)) → U21(z0, z1)
U21(active(z0), z1) → U21(z0, z1)
U21(z0, active(z1)) → U21(z0, z1)
U22(mark(z0)) → U22(z0)
U22(active(z0)) → U22(z0)
isList(mark(z0)) → isList(z0)
isList(active(z0)) → isList(z0)
U31(mark(z0)) → U31(z0)
U31(active(z0)) → U31(z0)
U41(mark(z0), z1) → U41(z0, z1)
U41(z0, mark(z1)) → U41(z0, z1)
U41(active(z0), z1) → U41(z0, z1)
U41(z0, active(z1)) → U41(z0, z1)
U42(mark(z0)) → U42(z0)
U42(active(z0)) → U42(z0)
isNeList(mark(z0)) → isNeList(z0)
isNeList(active(z0)) → isNeList(z0)
U51(mark(z0), z1) → U51(z0, z1)
U51(z0, mark(z1)) → U51(z0, z1)
U51(active(z0), z1) → U51(z0, z1)
U51(z0, active(z1)) → U51(z0, z1)
U52(mark(z0)) → U52(z0)
U52(active(z0)) → U52(z0)
U61(mark(z0)) → U61(z0)
U61(active(z0)) → U61(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)
isPal(mark(z0)) → isPal(z0)
isPal(active(z0)) → isPal(z0)
U81(mark(z0)) → U81(z0)
U81(active(z0)) → U81(z0)
isQid(mark(z0)) → isQid(z0)
isQid(active(z0)) → isQid(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)

Tuples:

MARK(nil) → c31(ACTIVE(nil))
MARK(tt) → c33(ACTIVE(tt))
MARK(a) → c50(ACTIVE(a))
MARK(e) → c51(ACTIVE(e))
MARK(i) → c52(ACTIVE(i))
MARK(o) → c53(ACTIVE(o))
MARK(u) → c54(ACTIVE(u))

S tuples:

MARK(nil) → c31(ACTIVE(nil))
MARK(tt) → c33(ACTIVE(tt))
MARK(a) → c50(ACTIVE(a))
MARK(e) → c51(ACTIVE(e))
MARK(i) → c52(ACTIVE(i))
MARK(o) → c53(ACTIVE(o))
MARK(u) → c54(ACTIVE(u))

K tuples:none
Defined Rule Symbols:

active, mark, __, U11, U21, U22, isList, U31, U41, U42, isNeList, U51, U52, U61, U71, U72, isPal, U81, isQid, isNePal

Defined Pair Symbols:

MARK

Compound Symbols:

c31, c33, c50, c51, c52, c53, c54

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

Removed 7 trailing nodes:

MARK(u) → c54(ACTIVE(u))
MARK(o) → c53(ACTIVE(o))
MARK(tt) → c33(ACTIVE(tt))
MARK(i) → c52(ACTIVE(i))
MARK(e) → c51(ACTIVE(e))
MARK(a) → c50(ACTIVE(a))
MARK(nil) → c31(ACTIVE(nil))

(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(tt)
active(U21(tt, z0)) → mark(U22(isList(z0)))
active(U22(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, z0)) → mark(U42(isNeList(z0)))
active(U42(tt)) → mark(tt)
active(U51(tt, z0)) → mark(U52(isList(z0)))
active(U52(tt)) → mark(tt)
active(U61(tt)) → mark(tt)
active(U71(tt, z0)) → mark(U72(isPal(z0)))
active(U72(tt)) → mark(tt)
active(U81(tt)) → mark(tt)
active(isList(z0)) → mark(U11(isNeList(z0)))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(U21(isList(z0), z1))
active(isNeList(z0)) → mark(U31(isQid(z0)))
active(isNeList(__(z0, z1))) → mark(U41(isList(z0), z1))
active(isNeList(__(z0, z1))) → mark(U51(isNeList(z0), z1))
active(isNePal(z0)) → mark(U61(isQid(z0)))
active(isNePal(__(z0, __(z1, z0)))) → mark(U71(isQid(z0), z1))
active(isPal(z0)) → mark(U81(isNePal(z0)))
active(isPal(nil)) → mark(tt)
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)) → active(U11(mark(z0)))
mark(tt) → active(tt)
mark(U21(z0, z1)) → active(U21(mark(z0), z1))
mark(U22(z0)) → active(U22(mark(z0)))
mark(isList(z0)) → active(isList(z0))
mark(U31(z0)) → active(U31(mark(z0)))
mark(U41(z0, z1)) → active(U41(mark(z0), z1))
mark(U42(z0)) → active(U42(mark(z0)))
mark(isNeList(z0)) → active(isNeList(z0))
mark(U51(z0, z1)) → active(U51(mark(z0), z1))
mark(U52(z0)) → active(U52(mark(z0)))
mark(U61(z0)) → active(U61(mark(z0)))
mark(U71(z0, z1)) → active(U71(mark(z0), z1))
mark(U72(z0)) → active(U72(mark(z0)))
mark(isPal(z0)) → active(isPal(z0))
mark(U81(z0)) → active(U81(mark(z0)))
mark(isQid(z0)) → active(isQid(z0))
mark(isNePal(z0)) → active(isNePal(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)) → U11(z0)
U11(active(z0)) → U11(z0)
U21(mark(z0), z1) → U21(z0, z1)
U21(z0, mark(z1)) → U21(z0, z1)
U21(active(z0), z1) → U21(z0, z1)
U21(z0, active(z1)) → U21(z0, z1)
U22(mark(z0)) → U22(z0)
U22(active(z0)) → U22(z0)
isList(mark(z0)) → isList(z0)
isList(active(z0)) → isList(z0)
U31(mark(z0)) → U31(z0)
U31(active(z0)) → U31(z0)
U41(mark(z0), z1) → U41(z0, z1)
U41(z0, mark(z1)) → U41(z0, z1)
U41(active(z0), z1) → U41(z0, z1)
U41(z0, active(z1)) → U41(z0, z1)
U42(mark(z0)) → U42(z0)
U42(active(z0)) → U42(z0)
isNeList(mark(z0)) → isNeList(z0)
isNeList(active(z0)) → isNeList(z0)
U51(mark(z0), z1) → U51(z0, z1)
U51(z0, mark(z1)) → U51(z0, z1)
U51(active(z0), z1) → U51(z0, z1)
U51(z0, active(z1)) → U51(z0, z1)
U52(mark(z0)) → U52(z0)
U52(active(z0)) → U52(z0)
U61(mark(z0)) → U61(z0)
U61(active(z0)) → U61(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)
isPal(mark(z0)) → isPal(z0)
isPal(active(z0)) → isPal(z0)
U81(mark(z0)) → U81(z0)
U81(active(z0)) → U81(z0)
isQid(mark(z0)) → isQid(z0)
isQid(active(z0)) → isQid(z0)
isNePal(mark(z0)) → isNePal(z0)
isNePal(active(z0)) → isNePal(z0)

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

active, mark, __, U11, U21, U22, isList, U31, U41, U42, isNeList, U51, U52, U61, U71, U72, isPal, U81, isQid, isNePal

Defined Pair Symbols:none

Compound Symbols:none

(7) SIsEmptyProof (EQUIVALENT transformation)

The set S is empty

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