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

(0) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt)) → mark(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) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 22 trailing nodes:

MARK(u) → c54(ACTIVE(u))
ACTIVE(U22(tt)) → c5(MARK(tt))
ACTIVE(U31(tt)) → c6(MARK(tt))
MARK(o) → c53(ACTIVE(o))
MARK(tt) → c33(ACTIVE(tt))
ACTIVE(isList(nil)) → c16(MARK(tt))
MARK(e) → c51(ACTIVE(e))
ACTIVE(isQid(e)) → c26(MARK(tt))
ACTIVE(isPal(nil)) → c24(MARK(tt))
ACTIVE(isQid(o)) → c28(MARK(tt))
ACTIVE(U61(tt)) → c11(MARK(tt))
ACTIVE(U81(tt)) → c14(MARK(tt))
ACTIVE(U72(tt)) → c13(MARK(tt))
ACTIVE(isQid(a)) → c25(MARK(tt))
ACTIVE(isQid(i)) → c27(MARK(tt))
ACTIVE(U11(tt)) → c3(MARK(tt))
MARK(i) → c52(ACTIVE(i))
ACTIVE(isQid(u)) → c29(MARK(tt))
ACTIVE(U42(tt)) → c8(MARK(tt))
MARK(a) → c50(ACTIVE(a))
ACTIVE(U52(tt)) → c10(MARK(tt))
MARK(nil) → c31(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(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(U21(tt, z0)) → c4(MARK(U22(isList(z0))), U22'(isList(z0)), ISLIST(z0))
ACTIVE(U41(tt, z0)) → c7(MARK(U42(isNeList(z0))), U42'(isNeList(z0)), ISNELIST(z0))
ACTIVE(U51(tt, z0)) → c9(MARK(U52(isList(z0))), U52'(isList(z0)), ISLIST(z0))
ACTIVE(U71(tt, z0)) → c12(MARK(U72(isPal(z0))), U72'(isPal(z0)), ISPAL(z0))
ACTIVE(isList(z0)) → c15(MARK(U11(isNeList(z0))), U11'(isNeList(z0)), ISNELIST(z0))
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))
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))

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(U21(tt, z0)) → c4(MARK(U22(isList(z0))), U22'(isList(z0)), ISLIST(z0))
ACTIVE(U41(tt, z0)) → c7(MARK(U42(isNeList(z0))), U42'(isNeList(z0)), ISNELIST(z0))
ACTIVE(U51(tt, z0)) → c9(MARK(U52(isList(z0))), U52'(isList(z0)), ISLIST(z0))
ACTIVE(U71(tt, z0)) → c12(MARK(U72(isPal(z0))), U72'(isPal(z0)), ISPAL(z0))
ACTIVE(isList(z0)) → c15(MARK(U11(isNeList(z0))), U11'(isNeList(z0)), ISNELIST(z0))
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))
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))

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, c4, c7, c9, c12, c15, c17, c18, c19, c20, c21, c22, c23, c30, c32, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, 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

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

Use narrowing to replace ACTIVE(U21(tt, z0)) → c4(MARK(U22(isList(z0))), U22'(isList(z0)), ISLIST(z0)) by

ACTIVE(U21(tt, x0)) → c4(MARK(U22(isList(x0))), ISLIST(x0))

(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:

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(U41(tt, z0)) → c7(MARK(U42(isNeList(z0))), U42'(isNeList(z0)), ISNELIST(z0))
ACTIVE(U51(tt, z0)) → c9(MARK(U52(isList(z0))), U52'(isList(z0)), ISLIST(z0))
ACTIVE(U71(tt, z0)) → c12(MARK(U72(isPal(z0))), U72'(isPal(z0)), ISPAL(z0))
ACTIVE(isList(z0)) → c15(MARK(U11(isNeList(z0))), U11'(isNeList(z0)), ISNELIST(z0))
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))
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))
ACTIVE(U21(tt, x0)) → c4(MARK(U22(isList(x0))), ISLIST(x0))

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(U41(tt, z0)) → c7(MARK(U42(isNeList(z0))), U42'(isNeList(z0)), ISNELIST(z0))
ACTIVE(U51(tt, z0)) → c9(MARK(U52(isList(z0))), U52'(isList(z0)), ISLIST(z0))
ACTIVE(U71(tt, z0)) → c12(MARK(U72(isPal(z0))), U72'(isPal(z0)), ISPAL(z0))
ACTIVE(isList(z0)) → c15(MARK(U11(isNeList(z0))), U11'(isNeList(z0)), ISNELIST(z0))
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))
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))
ACTIVE(U21(tt, x0)) → c4(MARK(U22(isList(x0))), ISLIST(x0))

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, c7, c9, c12, c15, c17, c18, c19, c20, c21, c22, c23, c30, c32, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, 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, c4

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

Use narrowing to replace ACTIVE(U41(tt, z0)) → c7(MARK(U42(isNeList(z0))), U42'(isNeList(z0)), ISNELIST(z0)) by

ACTIVE(U41(tt, x0)) → c7(MARK(U42(isNeList(x0))), ISNELIST(x0))

(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(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(U51(tt, z0)) → c9(MARK(U52(isList(z0))), U52'(isList(z0)), ISLIST(z0))
ACTIVE(U71(tt, z0)) → c12(MARK(U72(isPal(z0))), U72'(isPal(z0)), ISPAL(z0))
ACTIVE(isList(z0)) → c15(MARK(U11(isNeList(z0))), U11'(isNeList(z0)), ISNELIST(z0))
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))
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))
ACTIVE(U21(tt, x0)) → c4(MARK(U22(isList(x0))), ISLIST(x0))
ACTIVE(U41(tt, x0)) → c7(MARK(U42(isNeList(x0))), ISNELIST(x0))

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(U51(tt, z0)) → c9(MARK(U52(isList(z0))), U52'(isList(z0)), ISLIST(z0))
ACTIVE(U71(tt, z0)) → c12(MARK(U72(isPal(z0))), U72'(isPal(z0)), ISPAL(z0))
ACTIVE(isList(z0)) → c15(MARK(U11(isNeList(z0))), U11'(isNeList(z0)), ISNELIST(z0))
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))
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))
ACTIVE(U21(tt, x0)) → c4(MARK(U22(isList(x0))), ISLIST(x0))
ACTIVE(U41(tt, x0)) → c7(MARK(U42(isNeList(x0))), ISNELIST(x0))

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, c9, c12, c15, c17, c18, c19, c20, c21, c22, c23, c30, c32, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, 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, c4, c7

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

Use narrowing to replace ACTIVE(U51(tt, z0)) → c9(MARK(U52(isList(z0))), U52'(isList(z0)), ISLIST(z0)) by

ACTIVE(U51(tt, x0)) → c9(MARK(U52(isList(x0))), ISLIST(x0))

(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(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(U71(tt, z0)) → c12(MARK(U72(isPal(z0))), U72'(isPal(z0)), ISPAL(z0))
ACTIVE(isList(z0)) → c15(MARK(U11(isNeList(z0))), U11'(isNeList(z0)), ISNELIST(z0))
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))
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))
ACTIVE(U21(tt, x0)) → c4(MARK(U22(isList(x0))), ISLIST(x0))
ACTIVE(U41(tt, x0)) → c7(MARK(U42(isNeList(x0))), ISNELIST(x0))
ACTIVE(U51(tt, x0)) → c9(MARK(U52(isList(x0))), ISLIST(x0))

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(U71(tt, z0)) → c12(MARK(U72(isPal(z0))), U72'(isPal(z0)), ISPAL(z0))
ACTIVE(isList(z0)) → c15(MARK(U11(isNeList(z0))), U11'(isNeList(z0)), ISNELIST(z0))
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))
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))
ACTIVE(U21(tt, x0)) → c4(MARK(U22(isList(x0))), ISLIST(x0))
ACTIVE(U41(tt, x0)) → c7(MARK(U42(isNeList(x0))), ISNELIST(x0))
ACTIVE(U51(tt, x0)) → c9(MARK(U52(isList(x0))), ISLIST(x0))

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, c12, c15, c17, c18, c19, c20, c21, c22, c23, c30, c32, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, 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, c4, c7, c9

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

Use narrowing to replace ACTIVE(U71(tt, z0)) → c12(MARK(U72(isPal(z0))), U72'(isPal(z0)), ISPAL(z0)) by

ACTIVE(U71(tt, x0)) → c12(MARK(U72(isPal(x0))), ISPAL(x0))

(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(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(isList(z0)) → c15(MARK(U11(isNeList(z0))), U11'(isNeList(z0)), ISNELIST(z0))
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))
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))
ACTIVE(U21(tt, x0)) → c4(MARK(U22(isList(x0))), ISLIST(x0))
ACTIVE(U41(tt, x0)) → c7(MARK(U42(isNeList(x0))), ISNELIST(x0))
ACTIVE(U51(tt, x0)) → c9(MARK(U52(isList(x0))), ISLIST(x0))
ACTIVE(U71(tt, x0)) → c12(MARK(U72(isPal(x0))), ISPAL(x0))

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(isList(z0)) → c15(MARK(U11(isNeList(z0))), U11'(isNeList(z0)), ISNELIST(z0))
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))
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))
ACTIVE(U21(tt, x0)) → c4(MARK(U22(isList(x0))), ISLIST(x0))
ACTIVE(U41(tt, x0)) → c7(MARK(U42(isNeList(x0))), ISNELIST(x0))
ACTIVE(U51(tt, x0)) → c9(MARK(U52(isList(x0))), ISLIST(x0))
ACTIVE(U71(tt, x0)) → c12(MARK(U72(isPal(x0))), ISPAL(x0))

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, c15, c17, c18, c19, c20, c21, c22, c23, c30, c32, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, 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, c4, c7, c9, c12

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

Use narrowing to replace ACTIVE(isList(z0)) → c15(MARK(U11(isNeList(z0))), U11'(isNeList(z0)), ISNELIST(z0)) by

ACTIVE(isList(x0)) → c15(MARK(U11(isNeList(x0))), ISNELIST(x0))

(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(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(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))
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))
ACTIVE(U21(tt, x0)) → c4(MARK(U22(isList(x0))), ISLIST(x0))
ACTIVE(U41(tt, x0)) → c7(MARK(U42(isNeList(x0))), ISNELIST(x0))
ACTIVE(U51(tt, x0)) → c9(MARK(U52(isList(x0))), ISLIST(x0))
ACTIVE(U71(tt, x0)) → c12(MARK(U72(isPal(x0))), ISPAL(x0))
ACTIVE(isList(x0)) → c15(MARK(U11(isNeList(x0))), ISNELIST(x0))

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(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))
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))
ACTIVE(U21(tt, x0)) → c4(MARK(U22(isList(x0))), ISLIST(x0))
ACTIVE(U41(tt, x0)) → c7(MARK(U42(isNeList(x0))), ISNELIST(x0))
ACTIVE(U51(tt, x0)) → c9(MARK(U52(isList(x0))), ISLIST(x0))
ACTIVE(U71(tt, x0)) → c12(MARK(U72(isPal(x0))), ISPAL(x0))
ACTIVE(isList(x0)) → c15(MARK(U11(isNeList(x0))), ISNELIST(x0))

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, c17, c18, c19, c20, c21, c22, c23, c30, c32, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, 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, c4, c7, c9, c12, c15

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

Use narrowing to replace ACTIVE(isNeList(z0)) → c18(MARK(U31(isQid(z0))), U31'(isQid(z0)), ISQID(z0)) by

ACTIVE(isNeList(x0)) → c18(MARK(U31(isQid(x0))), ISQID(x0))

(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(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(isList(__(z0, z1))) → c17(MARK(U21(isList(z0), z1)), U21'(isList(z0), z1), ISLIST(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))
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))
ACTIVE(U21(tt, x0)) → c4(MARK(U22(isList(x0))), ISLIST(x0))
ACTIVE(U41(tt, x0)) → c7(MARK(U42(isNeList(x0))), ISNELIST(x0))
ACTIVE(U51(tt, x0)) → c9(MARK(U52(isList(x0))), ISLIST(x0))
ACTIVE(U71(tt, x0)) → c12(MARK(U72(isPal(x0))), ISPAL(x0))
ACTIVE(isList(x0)) → c15(MARK(U11(isNeList(x0))), ISNELIST(x0))
ACTIVE(isNeList(x0)) → c18(MARK(U31(isQid(x0))), ISQID(x0))

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(isList(__(z0, z1))) → c17(MARK(U21(isList(z0), z1)), U21'(isList(z0), z1), ISLIST(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))
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))
ACTIVE(U21(tt, x0)) → c4(MARK(U22(isList(x0))), ISLIST(x0))
ACTIVE(U41(tt, x0)) → c7(MARK(U42(isNeList(x0))), ISNELIST(x0))
ACTIVE(U51(tt, x0)) → c9(MARK(U52(isList(x0))), ISLIST(x0))
ACTIVE(U71(tt, x0)) → c12(MARK(U72(isPal(x0))), ISPAL(x0))
ACTIVE(isList(x0)) → c15(MARK(U11(isNeList(x0))), ISNELIST(x0))
ACTIVE(isNeList(x0)) → c18(MARK(U31(isQid(x0))), ISQID(x0))

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, c17, c19, c20, c21, c22, c23, c30, c32, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, 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, c4, c7, c9, c12, c15, c18

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

Use narrowing to replace ACTIVE(isNePal(z0)) → c21(MARK(U61(isQid(z0))), U61'(isQid(z0)), ISQID(z0)) by

ACTIVE(isNePal(x0)) → c21(MARK(U61(isQid(x0))), ISQID(x0))

(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(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(isList(__(z0, z1))) → c17(MARK(U21(isList(z0), z1)), U21'(isList(z0), z1), ISLIST(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, __(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))
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))
ACTIVE(U21(tt, x0)) → c4(MARK(U22(isList(x0))), ISLIST(x0))
ACTIVE(U41(tt, x0)) → c7(MARK(U42(isNeList(x0))), ISNELIST(x0))
ACTIVE(U51(tt, x0)) → c9(MARK(U52(isList(x0))), ISLIST(x0))
ACTIVE(U71(tt, x0)) → c12(MARK(U72(isPal(x0))), ISPAL(x0))
ACTIVE(isList(x0)) → c15(MARK(U11(isNeList(x0))), ISNELIST(x0))
ACTIVE(isNeList(x0)) → c18(MARK(U31(isQid(x0))), ISQID(x0))
ACTIVE(isNePal(x0)) → c21(MARK(U61(isQid(x0))), ISQID(x0))

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(isList(__(z0, z1))) → c17(MARK(U21(isList(z0), z1)), U21'(isList(z0), z1), ISLIST(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, __(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))
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))
ACTIVE(U21(tt, x0)) → c4(MARK(U22(isList(x0))), ISLIST(x0))
ACTIVE(U41(tt, x0)) → c7(MARK(U42(isNeList(x0))), ISNELIST(x0))
ACTIVE(U51(tt, x0)) → c9(MARK(U52(isList(x0))), ISLIST(x0))
ACTIVE(U71(tt, x0)) → c12(MARK(U72(isPal(x0))), ISPAL(x0))
ACTIVE(isList(x0)) → c15(MARK(U11(isNeList(x0))), ISNELIST(x0))
ACTIVE(isNeList(x0)) → c18(MARK(U31(isQid(x0))), ISQID(x0))
ACTIVE(isNePal(x0)) → c21(MARK(U61(isQid(x0))), ISQID(x0))

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, c17, c19, c20, c22, c23, c30, c32, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, 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, c4, c7, c9, c12, c15, c18, c21

(19) 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, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]
transitions:
active0(0) → 1
mark0(0) → 2
__0(0, 0) → 3
U110(0) → 4
U210(0, 0) → 5
U220(0) → 6
isList0(0) → 7
U310(0) → 8
U410(0, 0) → 9
U420(0) → 10
isNeList0(0) → 11
U510(0, 0) → 12
U520(0) → 13
U610(0) → 14
U710(0, 0) → 15
U720(0) → 16
isPal0(0) → 17
U810(0) → 18
isQid0(0) → 19
isNePal0(0) → 20
nil1() → 21
active1(21) → 2
nil1() → 0
tt1() → 22
active1(22) → 2
tt1() → 0
a1() → 23
active1(23) → 2
a1() → 0
e1() → 24
active1(24) → 2
e1() → 0
i1() → 25
active1(25) → 2
i1() → 0
o1() → 26
active1(26) → 2
o1() → 0
u1() → 27
active1(27) → 2
u1() → 0
nil1() → 28
tt1() → 29
a1() → 30
e1() → 31
i1() → 32
o1() → 33
u1() → 34
active0(28) → 1
active0(29) → 1
active0(30) → 1
active0(31) → 1
active0(32) → 1
active0(33) → 1
active0(34) → 1
mark0(28) → 2
mark0(29) → 2
mark0(30) → 2
mark0(31) → 2
mark0(32) → 2
mark0(33) → 2
mark0(34) → 2
__0(28, 0) → 3
__0(0, 28) → 3
__0(29, 0) → 3
__0(0, 29) → 3
__0(30, 0) → 3
__0(0, 30) → 3
__0(31, 0) → 3
__0(0, 31) → 3
__0(32, 0) → 3
__0(0, 32) → 3
__0(33, 0) → 3
__0(0, 33) → 3
__0(34, 0) → 3
__0(0, 34) → 3
__0(28, 28) → 3
__0(28, 29) → 3
__0(28, 30) → 3
__0(28, 31) → 3
__0(28, 32) → 3
__0(28, 33) → 3
__0(28, 34) → 3
__0(29, 28) → 3
__0(30, 28) → 3
__0(31, 28) → 3
__0(32, 28) → 3
__0(33, 28) → 3
__0(34, 28) → 3
__0(29, 29) → 3
__0(29, 30) → 3
__0(29, 31) → 3
__0(29, 32) → 3
__0(29, 33) → 3
__0(29, 34) → 3
__0(30, 29) → 3
__0(31, 29) → 3
__0(32, 29) → 3
__0(33, 29) → 3
__0(34, 29) → 3
__0(30, 30) → 3
__0(30, 31) → 3
__0(30, 32) → 3
__0(30, 33) → 3
__0(30, 34) → 3
__0(31, 30) → 3
__0(32, 30) → 3
__0(33, 30) → 3
__0(34, 30) → 3
__0(31, 31) → 3
__0(31, 32) → 3
__0(31, 33) → 3
__0(31, 34) → 3
__0(32, 31) → 3
__0(33, 31) → 3
__0(34, 31) → 3
__0(32, 32) → 3
__0(32, 33) → 3
__0(32, 34) → 3
__0(33, 32) → 3
__0(34, 32) → 3
__0(33, 33) → 3
__0(33, 34) → 3
__0(34, 33) → 3
__0(34, 34) → 3
U110(28) → 4
U110(29) → 4
U110(30) → 4
U110(31) → 4
U110(32) → 4
U110(33) → 4
U110(34) → 4
U210(28, 0) → 5
U210(0, 28) → 5
U210(29, 0) → 5
U210(0, 29) → 5
U210(30, 0) → 5
U210(0, 30) → 5
U210(31, 0) → 5
U210(0, 31) → 5
U210(32, 0) → 5
U210(0, 32) → 5
U210(33, 0) → 5
U210(0, 33) → 5
U210(34, 0) → 5
U210(0, 34) → 5
U210(28, 28) → 5
U210(28, 29) → 5
U210(28, 30) → 5
U210(28, 31) → 5
U210(28, 32) → 5
U210(28, 33) → 5
U210(28, 34) → 5
U210(29, 28) → 5
U210(30, 28) → 5
U210(31, 28) → 5
U210(32, 28) → 5
U210(33, 28) → 5
U210(34, 28) → 5
U210(29, 29) → 5
U210(29, 30) → 5
U210(29, 31) → 5
U210(29, 32) → 5
U210(29, 33) → 5
U210(29, 34) → 5
U210(30, 29) → 5
U210(31, 29) → 5
U210(32, 29) → 5
U210(33, 29) → 5
U210(34, 29) → 5
U210(30, 30) → 5
U210(30, 31) → 5
U210(30, 32) → 5
U210(30, 33) → 5
U210(30, 34) → 5
U210(31, 30) → 5
U210(32, 30) → 5
U210(33, 30) → 5
U210(34, 30) → 5
U210(31, 31) → 5
U210(31, 32) → 5
U210(31, 33) → 5
U210(31, 34) → 5
U210(32, 31) → 5
U210(33, 31) → 5
U210(34, 31) → 5
U210(32, 32) → 5
U210(32, 33) → 5
U210(32, 34) → 5
U210(33, 32) → 5
U210(34, 32) → 5
U210(33, 33) → 5
U210(33, 34) → 5
U210(34, 33) → 5
U210(34, 34) → 5
U220(28) → 6
U220(29) → 6
U220(30) → 6
U220(31) → 6
U220(32) → 6
U220(33) → 6
U220(34) → 6
isList0(28) → 7
isList0(29) → 7
isList0(30) → 7
isList0(31) → 7
isList0(32) → 7
isList0(33) → 7
isList0(34) → 7
U310(28) → 8
U310(29) → 8
U310(30) → 8
U310(31) → 8
U310(32) → 8
U310(33) → 8
U310(34) → 8
U410(28, 0) → 9
U410(0, 28) → 9
U410(29, 0) → 9
U410(0, 29) → 9
U410(30, 0) → 9
U410(0, 30) → 9
U410(31, 0) → 9
U410(0, 31) → 9
U410(32, 0) → 9
U410(0, 32) → 9
U410(33, 0) → 9
U410(0, 33) → 9
U410(34, 0) → 9
U410(0, 34) → 9
U410(28, 28) → 9
U410(28, 29) → 9
U410(28, 30) → 9
U410(28, 31) → 9
U410(28, 32) → 9
U410(28, 33) → 9
U410(28, 34) → 9
U410(29, 28) → 9
U410(30, 28) → 9
U410(31, 28) → 9
U410(32, 28) → 9
U410(33, 28) → 9
U410(34, 28) → 9
U410(29, 29) → 9
U410(29, 30) → 9
U410(29, 31) → 9
U410(29, 32) → 9
U410(29, 33) → 9
U410(29, 34) → 9
U410(30, 29) → 9
U410(31, 29) → 9
U410(32, 29) → 9
U410(33, 29) → 9
U410(34, 29) → 9
U410(30, 30) → 9
U410(30, 31) → 9
U410(30, 32) → 9
U410(30, 33) → 9
U410(30, 34) → 9
U410(31, 30) → 9
U410(32, 30) → 9
U410(33, 30) → 9
U410(34, 30) → 9
U410(31, 31) → 9
U410(31, 32) → 9
U410(31, 33) → 9
U410(31, 34) → 9
U410(32, 31) → 9
U410(33, 31) → 9
U410(34, 31) → 9
U410(32, 32) → 9
U410(32, 33) → 9
U410(32, 34) → 9
U410(33, 32) → 9
U410(34, 32) → 9
U410(33, 33) → 9
U410(33, 34) → 9
U410(34, 33) → 9
U410(34, 34) → 9
U420(28) → 10
U420(29) → 10
U420(30) → 10
U420(31) → 10
U420(32) → 10
U420(33) → 10
U420(34) → 10
isNeList0(28) → 11
isNeList0(29) → 11
isNeList0(30) → 11
isNeList0(31) → 11
isNeList0(32) → 11
isNeList0(33) → 11
isNeList0(34) → 11
U510(28, 0) → 12
U510(0, 28) → 12
U510(29, 0) → 12
U510(0, 29) → 12
U510(30, 0) → 12
U510(0, 30) → 12
U510(31, 0) → 12
U510(0, 31) → 12
U510(32, 0) → 12
U510(0, 32) → 12
U510(33, 0) → 12
U510(0, 33) → 12
U510(34, 0) → 12
U510(0, 34) → 12
U510(28, 28) → 12
U510(28, 29) → 12
U510(28, 30) → 12
U510(28, 31) → 12
U510(28, 32) → 12
U510(28, 33) → 12
U510(28, 34) → 12
U510(29, 28) → 12
U510(30, 28) → 12
U510(31, 28) → 12
U510(32, 28) → 12
U510(33, 28) → 12
U510(34, 28) → 12
U510(29, 29) → 12
U510(29, 30) → 12
U510(29, 31) → 12
U510(29, 32) → 12
U510(29, 33) → 12
U510(29, 34) → 12
U510(30, 29) → 12
U510(31, 29) → 12
U510(32, 29) → 12
U510(33, 29) → 12
U510(34, 29) → 12
U510(30, 30) → 12
U510(30, 31) → 12
U510(30, 32) → 12
U510(30, 33) → 12
U510(30, 34) → 12
U510(31, 30) → 12
U510(32, 30) → 12
U510(33, 30) → 12
U510(34, 30) → 12
U510(31, 31) → 12
U510(31, 32) → 12
U510(31, 33) → 12
U510(31, 34) → 12
U510(32, 31) → 12
U510(33, 31) → 12
U510(34, 31) → 12
U510(32, 32) → 12
U510(32, 33) → 12
U510(32, 34) → 12
U510(33, 32) → 12
U510(34, 32) → 12
U510(33, 33) → 12
U510(33, 34) → 12
U510(34, 33) → 12
U510(34, 34) → 12
U520(28) → 13
U520(29) → 13
U520(30) → 13
U520(31) → 13
U520(32) → 13
U520(33) → 13
U520(34) → 13
U610(28) → 14
U610(29) → 14
U610(30) → 14
U610(31) → 14
U610(32) → 14
U610(33) → 14
U610(34) → 14
U710(28, 0) → 15
U710(0, 28) → 15
U710(29, 0) → 15
U710(0, 29) → 15
U710(30, 0) → 15
U710(0, 30) → 15
U710(31, 0) → 15
U710(0, 31) → 15
U710(32, 0) → 15
U710(0, 32) → 15
U710(33, 0) → 15
U710(0, 33) → 15
U710(34, 0) → 15
U710(0, 34) → 15
U710(28, 28) → 15
U710(28, 29) → 15
U710(28, 30) → 15
U710(28, 31) → 15
U710(28, 32) → 15
U710(28, 33) → 15
U710(28, 34) → 15
U710(29, 28) → 15
U710(30, 28) → 15
U710(31, 28) → 15
U710(32, 28) → 15
U710(33, 28) → 15
U710(34, 28) → 15
U710(29, 29) → 15
U710(29, 30) → 15
U710(29, 31) → 15
U710(29, 32) → 15
U710(29, 33) → 15
U710(29, 34) → 15
U710(30, 29) → 15
U710(31, 29) → 15
U710(32, 29) → 15
U710(33, 29) → 15
U710(34, 29) → 15
U710(30, 30) → 15
U710(30, 31) → 15
U710(30, 32) → 15
U710(30, 33) → 15
U710(30, 34) → 15
U710(31, 30) → 15
U710(32, 30) → 15
U710(33, 30) → 15
U710(34, 30) → 15
U710(31, 31) → 15
U710(31, 32) → 15
U710(31, 33) → 15
U710(31, 34) → 15
U710(32, 31) → 15
U710(33, 31) → 15
U710(34, 31) → 15
U710(32, 32) → 15
U710(32, 33) → 15
U710(32, 34) → 15
U710(33, 32) → 15
U710(34, 32) → 15
U710(33, 33) → 15
U710(33, 34) → 15
U710(34, 33) → 15
U710(34, 34) → 15
U720(28) → 16
U720(29) → 16
U720(30) → 16
U720(31) → 16
U720(32) → 16
U720(33) → 16
U720(34) → 16
isPal0(28) → 17
isPal0(29) → 17
isPal0(30) → 17
isPal0(31) → 17
isPal0(32) → 17
isPal0(33) → 17
isPal0(34) → 17
U810(28) → 18
U810(29) → 18
U810(30) → 18
U810(31) → 18
U810(32) → 18
U810(33) → 18
U810(34) → 18
isQid0(28) → 19
isQid0(29) → 19
isQid0(30) → 19
isQid0(31) → 19
isQid0(32) → 19
isQid0(33) → 19
isQid0(34) → 19
isNePal0(28) → 20
isNePal0(29) → 20
isNePal0(30) → 20
isNePal0(31) → 20
isNePal0(32) → 20
isNePal0(33) → 20
isNePal0(34) → 20
active1(28) → 2
active1(29) → 2
active1(30) → 2
active1(31) → 2
active1(32) → 2
active1(33) → 2
active1(34) → 2
active1(28) → 1
active1(29) → 1
active1(30) → 1
active1(31) → 1
active1(32) → 1
active1(33) → 1
active1(34) → 1

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