YES(O(1), O(n^2)) 25.17/6.80 YES(O(1), O(n^2)) 25.17/6.89 25.17/6.89 25.17/6.89 25.17/6.89 25.17/6.89 25.17/6.89 Runtime Complexity (innermost) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml.xml 25.17/6.89 25.17/6.89 25.17/6.89
25.17/6.89 25.17/6.89 25.17/6.89
25.17/6.89
25.17/6.89

(0) Obligation:

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

__(__(X, Y), Z) → __(X, __(Y, Z)) 25.17/6.89
__(X, nil) → X 25.17/6.89
__(nil, X) → X 25.17/6.89
U11(tt) → tt 25.17/6.89
U21(tt, V2) → U22(isList(activate(V2))) 25.17/6.89
U22(tt) → tt 25.17/6.89
U31(tt) → tt 25.17/6.89
U41(tt, V2) → U42(isNeList(activate(V2))) 25.17/6.89
U42(tt) → tt 25.17/6.89
U51(tt, V2) → U52(isList(activate(V2))) 25.17/6.89
U52(tt) → tt 25.17/6.89
U61(tt) → tt 25.17/6.89
U71(tt, P) → U72(isPal(activate(P))) 25.17/6.89
U72(tt) → tt 25.17/6.89
U81(tt) → tt 25.17/6.89
isList(V) → U11(isNeList(activate(V))) 25.17/6.89
isList(n__nil) → tt 25.17/6.89
isList(n____(V1, V2)) → U21(isList(activate(V1)), activate(V2)) 25.17/6.89
isNeList(V) → U31(isQid(activate(V))) 25.17/6.89
isNeList(n____(V1, V2)) → U41(isList(activate(V1)), activate(V2)) 25.17/6.89
isNeList(n____(V1, V2)) → U51(isNeList(activate(V1)), activate(V2)) 25.17/6.89
isNePal(V) → U61(isQid(activate(V))) 25.17/6.89
isNePal(n____(I, n____(P, I))) → U71(isQid(activate(I)), activate(P)) 25.17/6.89
isPal(V) → U81(isNePal(activate(V))) 25.17/6.89
isPal(n__nil) → tt 25.17/6.89
isQid(n__a) → tt 25.17/6.89
isQid(n__e) → tt 25.17/6.89
isQid(n__i) → tt 25.17/6.89
isQid(n__o) → tt 25.17/6.89
isQid(n__u) → tt 25.17/6.89
niln__nil 25.17/6.89
__(X1, X2) → n____(X1, X2) 25.17/6.89
an__a 25.17/6.89
en__e 25.17/6.89
in__i 25.17/6.89
on__o 25.17/6.89
un__u 25.17/6.89
activate(n__nil) → nil 25.17/6.89
activate(n____(X1, X2)) → __(activate(X1), activate(X2)) 25.17/6.89
activate(n__a) → a 25.17/6.89
activate(n__e) → e 25.17/6.89
activate(n__i) → i 25.17/6.89
activate(n__o) → o 25.17/6.89
activate(n__u) → u 25.17/6.89
activate(X) → X

Rewrite Strategy: INNERMOST
25.17/6.89
25.17/6.89

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

Converted CpxTRS to CDT
25.17/6.89
25.17/6.89

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

__(__(z0, z1), z2) → __(z0, __(z1, z2)) 25.17/6.89
__(z0, nil) → z0 25.17/6.89
__(nil, z0) → z0 25.17/6.89
__(z0, z1) → n____(z0, z1) 25.17/6.89
U11(tt) → tt 25.17/6.89
U21(tt, z0) → U22(isList(activate(z0))) 25.17/6.89
U22(tt) → tt 25.17/6.89
U31(tt) → tt 25.17/6.89
U41(tt, z0) → U42(isNeList(activate(z0))) 25.17/6.89
U42(tt) → tt 25.17/6.89
U51(tt, z0) → U52(isList(activate(z0))) 25.17/6.89
U52(tt) → tt 25.17/6.89
U61(tt) → tt 25.17/6.89
U71(tt, z0) → U72(isPal(activate(z0))) 25.17/6.89
U72(tt) → tt 25.17/6.89
U81(tt) → tt 25.17/6.89
isList(z0) → U11(isNeList(activate(z0))) 25.17/6.89
isList(n__nil) → tt 25.17/6.89
isList(n____(z0, z1)) → U21(isList(activate(z0)), activate(z1)) 25.17/6.89
isNeList(z0) → U31(isQid(activate(z0))) 25.17/6.89
isNeList(n____(z0, z1)) → U41(isList(activate(z0)), activate(z1)) 25.17/6.89
isNeList(n____(z0, z1)) → U51(isNeList(activate(z0)), activate(z1)) 25.17/6.89
isNePal(z0) → U61(isQid(activate(z0))) 25.17/6.89
isNePal(n____(z0, n____(z1, z0))) → U71(isQid(activate(z0)), activate(z1)) 25.17/6.89
isPal(z0) → U81(isNePal(activate(z0))) 25.17/6.89
isPal(n__nil) → tt 25.17/6.89
isQid(n__a) → tt 25.17/6.89
isQid(n__e) → tt 25.17/6.89
isQid(n__i) → tt 25.17/6.89
isQid(n__o) → tt 25.17/6.89
isQid(n__u) → tt 25.17/6.89
niln__nil 25.17/6.89
an__a 25.17/6.89
en__e 25.17/6.89
in__i 25.17/6.89
on__o 25.17/6.89
un__u 25.17/6.89
activate(n__nil) → nil 25.17/6.89
activate(n____(z0, z1)) → __(activate(z0), activate(z1)) 25.17/6.89
activate(n__a) → a 25.17/6.89
activate(n__e) → e 25.17/6.89
activate(n__i) → i 25.17/6.89
activate(n__o) → o 25.17/6.89
activate(n__u) → u 25.17/6.89
activate(z0) → z0
Tuples:

__'(__(z0, z1), z2) → c(__'(z0, __(z1, z2)), __'(z1, z2)) 25.17/6.89
U21'(tt, z0) → c5(U22'(isList(activate(z0))), ISLIST(activate(z0)), ACTIVATE(z0)) 25.17/6.89
U41'(tt, z0) → c8(U42'(isNeList(activate(z0))), ISNELIST(activate(z0)), ACTIVATE(z0)) 25.17/6.89
U51'(tt, z0) → c10(U52'(isList(activate(z0))), ISLIST(activate(z0)), ACTIVATE(z0)) 25.17/6.89
U71'(tt, z0) → c13(U72'(isPal(activate(z0))), ISPAL(activate(z0)), ACTIVATE(z0)) 25.17/6.89
ISLIST(z0) → c16(U11'(isNeList(activate(z0))), ISNELIST(activate(z0)), ACTIVATE(z0)) 25.17/6.89
ISLIST(n____(z0, z1)) → c18(U21'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.17/6.89
ISNELIST(z0) → c19(U31'(isQid(activate(z0))), ISQID(activate(z0)), ACTIVATE(z0)) 25.17/6.89
ISNELIST(n____(z0, z1)) → c20(U41'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.17/6.89
ISNELIST(n____(z0, z1)) → c21(U51'(isNeList(activate(z0)), activate(z1)), ISNELIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.17/6.89
ISNEPAL(z0) → c22(U61'(isQid(activate(z0))), ISQID(activate(z0)), ACTIVATE(z0)) 25.54/6.91
ISNEPAL(n____(z0, n____(z1, z0))) → c23(U71'(isQid(activate(z0)), activate(z1)), ISQID(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.91
ISPAL(z0) → c24(U81'(isNePal(activate(z0))), ISNEPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.91
ACTIVATE(n__nil) → c37(NIL) 25.54/6.91
ACTIVATE(n____(z0, z1)) → c38(__'(activate(z0), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.91
ACTIVATE(n__a) → c39(A) 25.54/6.91
ACTIVATE(n__e) → c40(E) 25.54/6.91
ACTIVATE(n__i) → c41(I) 25.54/6.91
ACTIVATE(n__o) → c42(O) 25.54/6.91
ACTIVATE(n__u) → c43(U)
S tuples:

__'(__(z0, z1), z2) → c(__'(z0, __(z1, z2)), __'(z1, z2)) 25.54/6.91
U21'(tt, z0) → c5(U22'(isList(activate(z0))), ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.91
U41'(tt, z0) → c8(U42'(isNeList(activate(z0))), ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.91
U51'(tt, z0) → c10(U52'(isList(activate(z0))), ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.91
U71'(tt, z0) → c13(U72'(isPal(activate(z0))), ISPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.91
ISLIST(z0) → c16(U11'(isNeList(activate(z0))), ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.91
ISLIST(n____(z0, z1)) → c18(U21'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.91
ISNELIST(z0) → c19(U31'(isQid(activate(z0))), ISQID(activate(z0)), ACTIVATE(z0)) 25.54/6.91
ISNELIST(n____(z0, z1)) → c20(U41'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.91
ISNELIST(n____(z0, z1)) → c21(U51'(isNeList(activate(z0)), activate(z1)), ISNELIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.91
ISNEPAL(z0) → c22(U61'(isQid(activate(z0))), ISQID(activate(z0)), ACTIVATE(z0)) 25.54/6.91
ISNEPAL(n____(z0, n____(z1, z0))) → c23(U71'(isQid(activate(z0)), activate(z1)), ISQID(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.91
ISPAL(z0) → c24(U81'(isNePal(activate(z0))), ISNEPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.91
ACTIVATE(n__nil) → c37(NIL) 25.54/6.91
ACTIVATE(n____(z0, z1)) → c38(__'(activate(z0), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.91
ACTIVATE(n__a) → c39(A) 25.54/6.91
ACTIVATE(n__e) → c40(E) 25.54/6.91
ACTIVATE(n__i) → c41(I) 25.54/6.91
ACTIVATE(n__o) → c42(O) 25.54/6.91
ACTIVATE(n__u) → c43(U)
K tuples:none
Defined Rule Symbols:

__, U11, U21, U22, U31, U41, U42, U51, U52, U61, U71, U72, U81, isList, isNeList, isNePal, isPal, isQid, nil, a, e, i, o, u, activate

Defined Pair Symbols:

__', U21', U41', U51', U71', ISLIST, ISNELIST, ISNEPAL, ISPAL, ACTIVATE

Compound Symbols:

c, c5, c8, c10, c13, c16, c18, c19, c20, c21, c22, c23, c24, c37, c38, c39, c40, c41, c42, c43

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25.54/6.91

(3) CdtUnreachableProof (EQUIVALENT transformation)

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

__'(__(z0, z1), z2) → c(__'(z0, __(z1, z2)), __'(z1, z2))
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25.54/6.91

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

__(__(z0, z1), z2) → __(z0, __(z1, z2)) 25.54/6.91
__(z0, nil) → z0 25.54/6.91
__(nil, z0) → z0 25.54/6.91
__(z0, z1) → n____(z0, z1) 25.54/6.91
U11(tt) → tt 25.54/6.91
U21(tt, z0) → U22(isList(activate(z0))) 25.54/6.91
U22(tt) → tt 25.54/6.91
U31(tt) → tt 25.54/6.91
U41(tt, z0) → U42(isNeList(activate(z0))) 25.54/6.91
U42(tt) → tt 25.54/6.91
U51(tt, z0) → U52(isList(activate(z0))) 25.54/6.91
U52(tt) → tt 25.54/6.91
U61(tt) → tt 25.54/6.91
U71(tt, z0) → U72(isPal(activate(z0))) 25.54/6.91
U72(tt) → tt 25.54/6.91
U81(tt) → tt 25.54/6.91
isList(z0) → U11(isNeList(activate(z0))) 25.54/6.91
isList(n__nil) → tt 25.54/6.91
isList(n____(z0, z1)) → U21(isList(activate(z0)), activate(z1)) 25.54/6.91
isNeList(z0) → U31(isQid(activate(z0))) 25.54/6.91
isNeList(n____(z0, z1)) → U41(isList(activate(z0)), activate(z1)) 25.54/6.91
isNeList(n____(z0, z1)) → U51(isNeList(activate(z0)), activate(z1)) 25.54/6.91
isNePal(z0) → U61(isQid(activate(z0))) 25.54/6.91
isNePal(n____(z0, n____(z1, z0))) → U71(isQid(activate(z0)), activate(z1)) 25.54/6.91
isPal(z0) → U81(isNePal(activate(z0))) 25.54/6.91
isPal(n__nil) → tt 25.54/6.91
isQid(n__a) → tt 25.54/6.91
isQid(n__e) → tt 25.54/6.91
isQid(n__i) → tt 25.54/6.91
isQid(n__o) → tt 25.54/6.91
isQid(n__u) → tt 25.54/6.91
niln__nil 25.54/6.91
an__a 25.54/6.91
en__e 25.54/6.91
in__i 25.54/6.91
on__o 25.54/6.91
un__u 25.54/6.91
activate(n__nil) → nil 25.54/6.91
activate(n____(z0, z1)) → __(activate(z0), activate(z1)) 25.54/6.91
activate(n__a) → a 25.54/6.91
activate(n__e) → e 25.54/6.91
activate(n__i) → i 25.54/6.91
activate(n__o) → o 25.54/6.91
activate(n__u) → u 25.54/6.91
activate(z0) → z0
Tuples:

U21'(tt, z0) → c5(U22'(isList(activate(z0))), ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.91
U41'(tt, z0) → c8(U42'(isNeList(activate(z0))), ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.91
U51'(tt, z0) → c10(U52'(isList(activate(z0))), ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.91
U71'(tt, z0) → c13(U72'(isPal(activate(z0))), ISPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.91
ISLIST(z0) → c16(U11'(isNeList(activate(z0))), ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.91
ISLIST(n____(z0, z1)) → c18(U21'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ISNELIST(z0) → c19(U31'(isQid(activate(z0))), ISQID(activate(z0)), ACTIVATE(z0)) 25.54/6.97
ISNELIST(n____(z0, z1)) → c20(U41'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ISNELIST(n____(z0, z1)) → c21(U51'(isNeList(activate(z0)), activate(z1)), ISNELIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ISNEPAL(z0) → c22(U61'(isQid(activate(z0))), ISQID(activate(z0)), ACTIVATE(z0)) 25.54/6.97
ISNEPAL(n____(z0, n____(z1, z0))) → c23(U71'(isQid(activate(z0)), activate(z1)), ISQID(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ISPAL(z0) → c24(U81'(isNePal(activate(z0))), ISNEPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.97
ACTIVATE(n__nil) → c37(NIL) 25.54/6.97
ACTIVATE(n____(z0, z1)) → c38(__'(activate(z0), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ACTIVATE(n__a) → c39(A) 25.54/6.97
ACTIVATE(n__e) → c40(E) 25.54/6.97
ACTIVATE(n__i) → c41(I) 25.54/6.97
ACTIVATE(n__o) → c42(O) 25.54/6.97
ACTIVATE(n__u) → c43(U)
S tuples:

U21'(tt, z0) → c5(U22'(isList(activate(z0))), ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.97
U41'(tt, z0) → c8(U42'(isNeList(activate(z0))), ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.97
U51'(tt, z0) → c10(U52'(isList(activate(z0))), ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.97
U71'(tt, z0) → c13(U72'(isPal(activate(z0))), ISPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.97
ISLIST(z0) → c16(U11'(isNeList(activate(z0))), ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.97
ISLIST(n____(z0, z1)) → c18(U21'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ISNELIST(z0) → c19(U31'(isQid(activate(z0))), ISQID(activate(z0)), ACTIVATE(z0)) 25.54/6.97
ISNELIST(n____(z0, z1)) → c20(U41'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ISNELIST(n____(z0, z1)) → c21(U51'(isNeList(activate(z0)), activate(z1)), ISNELIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ISNEPAL(z0) → c22(U61'(isQid(activate(z0))), ISQID(activate(z0)), ACTIVATE(z0)) 25.54/6.97
ISNEPAL(n____(z0, n____(z1, z0))) → c23(U71'(isQid(activate(z0)), activate(z1)), ISQID(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ISPAL(z0) → c24(U81'(isNePal(activate(z0))), ISNEPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.97
ACTIVATE(n__nil) → c37(NIL) 25.54/6.97
ACTIVATE(n____(z0, z1)) → c38(__'(activate(z0), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ACTIVATE(n__a) → c39(A) 25.54/6.97
ACTIVATE(n__e) → c40(E) 25.54/6.97
ACTIVATE(n__i) → c41(I) 25.54/6.97
ACTIVATE(n__o) → c42(O) 25.54/6.97
ACTIVATE(n__u) → c43(U)
K tuples:none
Defined Rule Symbols:

__, U11, U21, U22, U31, U41, U42, U51, U52, U61, U71, U72, U81, isList, isNeList, isNePal, isPal, isQid, nil, a, e, i, o, u, activate

Defined Pair Symbols:

U21', U41', U51', U71', ISLIST, ISNELIST, ISNEPAL, ISPAL, ACTIVATE

Compound Symbols:

c5, c8, c10, c13, c16, c18, c19, c20, c21, c22, c23, c24, c37, c38, c39, c40, c41, c42, c43

25.54/6.97
25.54/6.97

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

Removed 18 trailing tuple parts
25.54/6.97
25.54/6.97

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

__(__(z0, z1), z2) → __(z0, __(z1, z2)) 25.54/6.97
__(z0, nil) → z0 25.54/6.97
__(nil, z0) → z0 25.54/6.97
__(z0, z1) → n____(z0, z1) 25.54/6.97
U11(tt) → tt 25.54/6.97
U21(tt, z0) → U22(isList(activate(z0))) 25.54/6.97
U22(tt) → tt 25.54/6.97
U31(tt) → tt 25.54/6.97
U41(tt, z0) → U42(isNeList(activate(z0))) 25.54/6.97
U42(tt) → tt 25.54/6.97
U51(tt, z0) → U52(isList(activate(z0))) 25.54/6.97
U52(tt) → tt 25.54/6.97
U61(tt) → tt 25.54/6.97
U71(tt, z0) → U72(isPal(activate(z0))) 25.54/6.97
U72(tt) → tt 25.54/6.97
U81(tt) → tt 25.54/6.97
isList(z0) → U11(isNeList(activate(z0))) 25.54/6.97
isList(n__nil) → tt 25.54/6.97
isList(n____(z0, z1)) → U21(isList(activate(z0)), activate(z1)) 25.54/6.97
isNeList(z0) → U31(isQid(activate(z0))) 25.54/6.97
isNeList(n____(z0, z1)) → U41(isList(activate(z0)), activate(z1)) 25.54/6.97
isNeList(n____(z0, z1)) → U51(isNeList(activate(z0)), activate(z1)) 25.54/6.97
isNePal(z0) → U61(isQid(activate(z0))) 25.54/6.97
isNePal(n____(z0, n____(z1, z0))) → U71(isQid(activate(z0)), activate(z1)) 25.54/6.97
isPal(z0) → U81(isNePal(activate(z0))) 25.54/6.97
isPal(n__nil) → tt 25.54/6.97
isQid(n__a) → tt 25.54/6.97
isQid(n__e) → tt 25.54/6.97
isQid(n__i) → tt 25.54/6.97
isQid(n__o) → tt 25.54/6.97
isQid(n__u) → tt 25.54/6.97
niln__nil 25.54/6.97
an__a 25.54/6.97
en__e 25.54/6.97
in__i 25.54/6.97
on__o 25.54/6.97
un__u 25.54/6.97
activate(n__nil) → nil 25.54/6.97
activate(n____(z0, z1)) → __(activate(z0), activate(z1)) 25.54/6.97
activate(n__a) → a 25.54/6.97
activate(n__e) → e 25.54/6.97
activate(n__i) → i 25.54/6.97
activate(n__o) → o 25.54/6.97
activate(n__u) → u 25.54/6.97
activate(z0) → z0
Tuples:

ISLIST(n____(z0, z1)) → c18(U21'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ISNELIST(n____(z0, z1)) → c20(U41'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ISNELIST(n____(z0, z1)) → c21(U51'(isNeList(activate(z0)), activate(z1)), ISNELIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
U21'(tt, z0) → c5(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.97
U41'(tt, z0) → c8(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.97
U51'(tt, z0) → c10(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.97
U71'(tt, z0) → c13(ISPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.97
ISLIST(z0) → c16(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.97
ISNELIST(z0) → c19(ACTIVATE(z0)) 25.54/6.97
ISNEPAL(z0) → c22(ACTIVATE(z0)) 25.54/6.97
ISNEPAL(n____(z0, n____(z1, z0))) → c23(U71'(isQid(activate(z0)), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ISPAL(z0) → c24(ISNEPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.97
ACTIVATE(n__nil) → c37 25.54/6.97
ACTIVATE(n____(z0, z1)) → c38(ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ACTIVATE(n__a) → c39 25.54/6.97
ACTIVATE(n__e) → c40 25.54/6.97
ACTIVATE(n__i) → c41 25.54/6.97
ACTIVATE(n__o) → c42 25.54/6.97
ACTIVATE(n__u) → c43
S tuples:

ISLIST(n____(z0, z1)) → c18(U21'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ISNELIST(n____(z0, z1)) → c20(U41'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ISNELIST(n____(z0, z1)) → c21(U51'(isNeList(activate(z0)), activate(z1)), ISNELIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
U21'(tt, z0) → c5(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.97
U41'(tt, z0) → c8(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.97
U51'(tt, z0) → c10(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.97
U71'(tt, z0) → c13(ISPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.97
ISLIST(z0) → c16(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.97
ISNELIST(z0) → c19(ACTIVATE(z0)) 25.54/6.97
ISNEPAL(z0) → c22(ACTIVATE(z0)) 25.54/6.97
ISNEPAL(n____(z0, n____(z1, z0))) → c23(U71'(isQid(activate(z0)), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ISPAL(z0) → c24(ISNEPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.97
ACTIVATE(n__nil) → c37 25.54/6.97
ACTIVATE(n____(z0, z1)) → c38(ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ACTIVATE(n__a) → c39 25.54/6.97
ACTIVATE(n__e) → c40 25.54/6.97
ACTIVATE(n__i) → c41 25.54/6.97
ACTIVATE(n__o) → c42 25.54/6.97
ACTIVATE(n__u) → c43
K tuples:none
Defined Rule Symbols:

__, U11, U21, U22, U31, U41, U42, U51, U52, U61, U71, U72, U81, isList, isNeList, isNePal, isPal, isQid, nil, a, e, i, o, u, activate

Defined Pair Symbols:

ISLIST, ISNELIST, U21', U41', U51', U71', ISNEPAL, ISPAL, ACTIVATE

Compound Symbols:

c18, c20, c21, c5, c8, c10, c13, c16, c19, c22, c23, c24, c37, c38, c39, c40, c41, c42, c43

25.54/6.97
25.54/6.97

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

Removed 6 trailing nodes:

ACTIVATE(n__nil) → c37 25.54/6.97
ACTIVATE(n__a) → c39 25.54/6.97
ACTIVATE(n__o) → c42 25.54/6.97
ACTIVATE(n__i) → c41 25.54/6.97
ACTIVATE(n__u) → c43 25.54/6.97
ACTIVATE(n__e) → c40
25.54/6.97
25.54/6.97

(8) Obligation:

Complexity Dependency Tuples Problem
Rules:

__(__(z0, z1), z2) → __(z0, __(z1, z2)) 25.54/6.97
__(z0, nil) → z0 25.54/6.97
__(nil, z0) → z0 25.54/6.97
__(z0, z1) → n____(z0, z1) 25.54/6.97
U11(tt) → tt 25.54/6.97
U21(tt, z0) → U22(isList(activate(z0))) 25.54/6.97
U22(tt) → tt 25.54/6.97
U31(tt) → tt 25.54/6.97
U41(tt, z0) → U42(isNeList(activate(z0))) 25.54/6.97
U42(tt) → tt 25.54/6.97
U51(tt, z0) → U52(isList(activate(z0))) 25.54/6.97
U52(tt) → tt 25.54/6.97
U61(tt) → tt 25.54/6.97
U71(tt, z0) → U72(isPal(activate(z0))) 25.54/6.97
U72(tt) → tt 25.54/6.97
U81(tt) → tt 25.54/6.97
isList(z0) → U11(isNeList(activate(z0))) 25.54/6.97
isList(n__nil) → tt 25.54/6.97
isList(n____(z0, z1)) → U21(isList(activate(z0)), activate(z1)) 25.54/6.97
isNeList(z0) → U31(isQid(activate(z0))) 25.54/6.97
isNeList(n____(z0, z1)) → U41(isList(activate(z0)), activate(z1)) 25.54/6.97
isNeList(n____(z0, z1)) → U51(isNeList(activate(z0)), activate(z1)) 25.54/6.97
isNePal(z0) → U61(isQid(activate(z0))) 25.54/6.97
isNePal(n____(z0, n____(z1, z0))) → U71(isQid(activate(z0)), activate(z1)) 25.54/6.97
isPal(z0) → U81(isNePal(activate(z0))) 25.54/6.97
isPal(n__nil) → tt 25.54/6.97
isQid(n__a) → tt 25.54/6.97
isQid(n__e) → tt 25.54/6.97
isQid(n__i) → tt 25.54/6.97
isQid(n__o) → tt 25.54/6.97
isQid(n__u) → tt 25.54/6.97
niln__nil 25.54/6.97
an__a 25.54/6.97
en__e 25.54/6.97
in__i 25.54/6.97
on__o 25.54/6.97
un__u 25.54/6.97
activate(n__nil) → nil 25.54/6.97
activate(n____(z0, z1)) → __(activate(z0), activate(z1)) 25.54/6.97
activate(n__a) → a 25.54/6.97
activate(n__e) → e 25.54/6.97
activate(n__i) → i 25.54/6.97
activate(n__o) → o 25.54/6.97
activate(n__u) → u 25.54/6.97
activate(z0) → z0
Tuples:

ISLIST(n____(z0, z1)) → c18(U21'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ISNELIST(n____(z0, z1)) → c20(U41'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ISNELIST(n____(z0, z1)) → c21(U51'(isNeList(activate(z0)), activate(z1)), ISNELIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
U21'(tt, z0) → c5(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.97
U41'(tt, z0) → c8(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.97
U51'(tt, z0) → c10(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.97
U71'(tt, z0) → c13(ISPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.97
ISLIST(z0) → c16(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.97
ISNELIST(z0) → c19(ACTIVATE(z0)) 25.54/6.97
ISNEPAL(z0) → c22(ACTIVATE(z0)) 25.54/6.97
ISNEPAL(n____(z0, n____(z1, z0))) → c23(U71'(isQid(activate(z0)), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ISPAL(z0) → c24(ISNEPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.97
ACTIVATE(n__nil) → c37 25.54/6.97
ACTIVATE(n____(z0, z1)) → c38(ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ACTIVATE(n__a) → c39 25.54/6.97
ACTIVATE(n__e) → c40 25.54/6.97
ACTIVATE(n__i) → c41 25.54/6.97
ACTIVATE(n__o) → c42 25.54/6.97
ACTIVATE(n__u) → c43
S tuples:

ISLIST(n____(z0, z1)) → c18(U21'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ISNELIST(n____(z0, z1)) → c20(U41'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ISNELIST(n____(z0, z1)) → c21(U51'(isNeList(activate(z0)), activate(z1)), ISNELIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
U21'(tt, z0) → c5(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.97
U41'(tt, z0) → c8(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.97
U51'(tt, z0) → c10(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.97
U71'(tt, z0) → c13(ISPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.97
ISLIST(z0) → c16(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.97
ISNELIST(z0) → c19(ACTIVATE(z0)) 25.54/6.97
ISNEPAL(z0) → c22(ACTIVATE(z0)) 25.54/6.97
ISNEPAL(n____(z0, n____(z1, z0))) → c23(U71'(isQid(activate(z0)), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ISPAL(z0) → c24(ISNEPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.97
ACTIVATE(n__nil) → c37 25.54/6.97
ACTIVATE(n____(z0, z1)) → c38(ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ACTIVATE(n__a) → c39 25.54/6.97
ACTIVATE(n__e) → c40 25.54/6.97
ACTIVATE(n__i) → c41 25.54/6.97
ACTIVATE(n__o) → c42 25.54/6.97
ACTIVATE(n__u) → c43
K tuples:none
Defined Rule Symbols:

__, U11, U21, U22, U31, U41, U42, U51, U52, U61, U71, U72, U81, isList, isNeList, isNePal, isPal, isQid, nil, a, e, i, o, u, activate

Defined Pair Symbols:

ISLIST, ISNELIST, U21', U41', U51', U71', ISNEPAL, ISPAL, ACTIVATE

Compound Symbols:

c18, c20, c21, c5, c8, c10, c13, c16, c19, c22, c23, c24, c37, c38, c39, c40, c41, c42, c43

25.54/6.97
25.54/6.97

(9) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

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

ISPAL(z0) → c24(ISNEPAL(activate(z0)), ACTIVATE(z0))
We considered the (Usable) Rules:

activate(n__nil) → nil 25.54/6.97
activate(n____(z0, z1)) → __(activate(z0), activate(z1)) 25.54/6.97
activate(n__a) → a 25.54/6.97
activate(n__e) → e 25.54/6.97
activate(n__i) → i 25.54/6.97
activate(n__o) → o 25.54/6.97
activate(n__u) → u 25.54/6.97
activate(z0) → z0 25.54/6.97
un__u 25.54/6.97
on__o 25.54/6.97
in__i 25.54/6.97
en__e 25.54/6.97
an__a 25.54/6.97
__(z0, z1) → n____(z0, z1) 25.54/6.97
niln__nil 25.54/6.97
isQid(n__a) → tt 25.54/6.97
isQid(n__e) → tt 25.54/6.97
isQid(n__i) → tt 25.54/6.97
isQid(n__o) → tt 25.54/6.97
isQid(n__u) → tt 25.54/6.97
isNeList(z0) → U31(isQid(activate(z0))) 25.54/6.97
isNeList(n____(z0, z1)) → U41(isList(activate(z0)), activate(z1)) 25.54/6.97
isNeList(n____(z0, z1)) → U51(isNeList(activate(z0)), activate(z1)) 25.54/6.97
U51(tt, z0) → U52(isList(activate(z0))) 25.54/6.97
isList(z0) → U11(isNeList(activate(z0))) 25.54/6.97
isList(n__nil) → tt 25.54/6.97
isList(n____(z0, z1)) → U21(isList(activate(z0)), activate(z1)) 25.54/6.97
U52(tt) → tt 25.54/6.97
U21(tt, z0) → U22(isList(activate(z0))) 25.54/6.97
U22(tt) → tt 25.54/6.97
U11(tt) → tt 25.54/6.97
U41(tt, z0) → U42(isNeList(activate(z0))) 25.54/6.97
U42(tt) → tt 25.54/6.97
U31(tt) → tt
And the Tuples:

ISLIST(n____(z0, z1)) → c18(U21'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ISNELIST(n____(z0, z1)) → c20(U41'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
ISNELIST(n____(z0, z1)) → c21(U51'(isNeList(activate(z0)), activate(z1)), ISNELIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.97
U21'(tt, z0) → c5(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.97
U41'(tt, z0) → c8(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.97
U51'(tt, z0) → c10(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.97
U71'(tt, z0) → c13(ISPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.97
ISLIST(z0) → c16(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.97
ISNELIST(z0) → c19(ACTIVATE(z0)) 25.54/6.97
ISNEPAL(z0) → c22(ACTIVATE(z0)) 25.54/6.98
ISNEPAL(n____(z0, n____(z1, z0))) → c23(U71'(isQid(activate(z0)), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISPAL(z0) → c24(ISNEPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ACTIVATE(n__nil) → c37 25.54/6.98
ACTIVATE(n____(z0, z1)) → c38(ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ACTIVATE(n__a) → c39 25.54/6.98
ACTIVATE(n__e) → c40 25.54/6.98
ACTIVATE(n__i) → c41 25.54/6.98
ACTIVATE(n__o) → c42 25.54/6.98
ACTIVATE(n__u) → c43
The order we found is given by the following interpretation:
Polynomial interpretation : 25.54/6.98

POL(ACTIVATE(x1)) = 0    25.54/6.98
POL(ISLIST(x1)) = 0    25.54/6.98
POL(ISNELIST(x1)) = 0    25.54/6.98
POL(ISNEPAL(x1)) = x1    25.54/6.98
POL(ISPAL(x1)) = [1] + x1    25.54/6.98
POL(U11(x1)) = [3]    25.54/6.98
POL(U21(x1, x2)) = [3]    25.54/6.98
POL(U21'(x1, x2)) = 0    25.54/6.98
POL(U22(x1)) = [3] + [3]x1    25.54/6.98
POL(U31(x1)) = [3]    25.54/6.98
POL(U41(x1, x2)) = [3]    25.54/6.98
POL(U41'(x1, x2)) = 0    25.54/6.98
POL(U42(x1)) = [3] + [3]x1    25.54/6.98
POL(U51(x1, x2)) = [3] + [3]x1    25.54/6.98
POL(U51'(x1, x2)) = 0    25.54/6.98
POL(U52(x1)) = [3]    25.54/6.98
POL(U71'(x1, x2)) = x1 + x2    25.54/6.98
POL(__(x1, x2)) = x1 + x2    25.54/6.98
POL(a) = [2]    25.54/6.98
POL(activate(x1)) = x1    25.54/6.98
POL(c10(x1, x2)) = x1 + x2    25.54/6.98
POL(c13(x1, x2)) = x1 + x2    25.54/6.98
POL(c16(x1, x2)) = x1 + x2    25.54/6.98
POL(c18(x1, x2, x3, x4)) = x1 + x2 + x3 + x4    25.54/6.98
POL(c19(x1)) = x1    25.54/6.98
POL(c20(x1, x2, x3, x4)) = x1 + x2 + x3 + x4    25.54/6.98
POL(c21(x1, x2, x3, x4)) = x1 + x2 + x3 + x4    25.54/6.98
POL(c22(x1)) = x1    25.54/6.98
POL(c23(x1, x2, x3)) = x1 + x2 + x3    25.54/6.98
POL(c24(x1, x2)) = x1 + x2    25.54/6.98
POL(c37) = 0    25.54/6.98
POL(c38(x1, x2)) = x1 + x2    25.54/6.98
POL(c39) = 0    25.54/6.98
POL(c40) = 0    25.54/6.98
POL(c41) = 0    25.54/6.98
POL(c42) = 0    25.54/6.98
POL(c43) = 0    25.54/6.98
POL(c5(x1, x2)) = x1 + x2    25.54/6.98
POL(c8(x1, x2)) = x1 + x2    25.54/6.98
POL(e) = [1]    25.54/6.98
POL(i) = [4]    25.54/6.98
POL(isList(x1)) = 0    25.54/6.98
POL(isNeList(x1)) = 0    25.54/6.98
POL(isQid(x1)) = [2]x1    25.54/6.98
POL(n____(x1, x2)) = x1 + x2    25.54/6.98
POL(n__a) = [2]    25.54/6.98
POL(n__e) = [1]    25.54/6.98
POL(n__i) = [4]    25.54/6.98
POL(n__nil) = 0    25.54/6.98
POL(n__o) = [1]    25.54/6.98
POL(n__u) = [1]    25.54/6.98
POL(nil) = 0    25.54/6.98
POL(o) = [1]    25.54/6.98
POL(tt) = [1]    25.54/6.98
POL(u) = [1]   
25.54/6.98
25.54/6.98

(10) Obligation:

Complexity Dependency Tuples Problem
Rules:

__(__(z0, z1), z2) → __(z0, __(z1, z2)) 25.54/6.98
__(z0, nil) → z0 25.54/6.98
__(nil, z0) → z0 25.54/6.98
__(z0, z1) → n____(z0, z1) 25.54/6.98
U11(tt) → tt 25.54/6.98
U21(tt, z0) → U22(isList(activate(z0))) 25.54/6.98
U22(tt) → tt 25.54/6.98
U31(tt) → tt 25.54/6.98
U41(tt, z0) → U42(isNeList(activate(z0))) 25.54/6.98
U42(tt) → tt 25.54/6.98
U51(tt, z0) → U52(isList(activate(z0))) 25.54/6.98
U52(tt) → tt 25.54/6.98
U61(tt) → tt 25.54/6.98
U71(tt, z0) → U72(isPal(activate(z0))) 25.54/6.98
U72(tt) → tt 25.54/6.98
U81(tt) → tt 25.54/6.98
isList(z0) → U11(isNeList(activate(z0))) 25.54/6.98
isList(n__nil) → tt 25.54/6.98
isList(n____(z0, z1)) → U21(isList(activate(z0)), activate(z1)) 25.54/6.98
isNeList(z0) → U31(isQid(activate(z0))) 25.54/6.98
isNeList(n____(z0, z1)) → U41(isList(activate(z0)), activate(z1)) 25.54/6.98
isNeList(n____(z0, z1)) → U51(isNeList(activate(z0)), activate(z1)) 25.54/6.98
isNePal(z0) → U61(isQid(activate(z0))) 25.54/6.98
isNePal(n____(z0, n____(z1, z0))) → U71(isQid(activate(z0)), activate(z1)) 25.54/6.98
isPal(z0) → U81(isNePal(activate(z0))) 25.54/6.98
isPal(n__nil) → tt 25.54/6.98
isQid(n__a) → tt 25.54/6.98
isQid(n__e) → tt 25.54/6.98
isQid(n__i) → tt 25.54/6.98
isQid(n__o) → tt 25.54/6.98
isQid(n__u) → tt 25.54/6.98
niln__nil 25.54/6.98
an__a 25.54/6.98
en__e 25.54/6.98
in__i 25.54/6.98
on__o 25.54/6.98
un__u 25.54/6.98
activate(n__nil) → nil 25.54/6.98
activate(n____(z0, z1)) → __(activate(z0), activate(z1)) 25.54/6.98
activate(n__a) → a 25.54/6.98
activate(n__e) → e 25.54/6.98
activate(n__i) → i 25.54/6.98
activate(n__o) → o 25.54/6.98
activate(n__u) → u 25.54/6.98
activate(z0) → z0
Tuples:

ISLIST(n____(z0, z1)) → c18(U21'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c20(U41'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c21(U51'(isNeList(activate(z0)), activate(z1)), ISNELIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
U21'(tt, z0) → c5(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U41'(tt, z0) → c8(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U51'(tt, z0) → c10(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U71'(tt, z0) → c13(ISPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISLIST(z0) → c16(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISNELIST(z0) → c19(ACTIVATE(z0)) 25.54/6.98
ISNEPAL(z0) → c22(ACTIVATE(z0)) 25.54/6.98
ISNEPAL(n____(z0, n____(z1, z0))) → c23(U71'(isQid(activate(z0)), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISPAL(z0) → c24(ISNEPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ACTIVATE(n__nil) → c37 25.54/6.98
ACTIVATE(n____(z0, z1)) → c38(ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ACTIVATE(n__a) → c39 25.54/6.98
ACTIVATE(n__e) → c40 25.54/6.98
ACTIVATE(n__i) → c41 25.54/6.98
ACTIVATE(n__o) → c42 25.54/6.98
ACTIVATE(n__u) → c43
S tuples:

ISLIST(n____(z0, z1)) → c18(U21'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c20(U41'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c21(U51'(isNeList(activate(z0)), activate(z1)), ISNELIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
U21'(tt, z0) → c5(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U41'(tt, z0) → c8(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U51'(tt, z0) → c10(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U71'(tt, z0) → c13(ISPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISLIST(z0) → c16(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISNELIST(z0) → c19(ACTIVATE(z0)) 25.54/6.98
ISNEPAL(z0) → c22(ACTIVATE(z0)) 25.54/6.98
ISNEPAL(n____(z0, n____(z1, z0))) → c23(U71'(isQid(activate(z0)), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ACTIVATE(n__nil) → c37 25.54/6.98
ACTIVATE(n____(z0, z1)) → c38(ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ACTIVATE(n__a) → c39 25.54/6.98
ACTIVATE(n__e) → c40 25.54/6.98
ACTIVATE(n__i) → c41 25.54/6.98
ACTIVATE(n__o) → c42 25.54/6.98
ACTIVATE(n__u) → c43
K tuples:

ISPAL(z0) → c24(ISNEPAL(activate(z0)), ACTIVATE(z0))
Defined Rule Symbols:

__, U11, U21, U22, U31, U41, U42, U51, U52, U61, U71, U72, U81, isList, isNeList, isNePal, isPal, isQid, nil, a, e, i, o, u, activate

Defined Pair Symbols:

ISLIST, ISNELIST, U21', U41', U51', U71', ISNEPAL, ISPAL, ACTIVATE

Compound Symbols:

c18, c20, c21, c5, c8, c10, c13, c16, c19, c22, c23, c24, c37, c38, c39, c40, c41, c42, c43

25.54/6.98
25.54/6.98

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

The following tuples could be moved from S to K by knowledge propagation:

ISNEPAL(z0) → c22(ACTIVATE(z0)) 25.54/6.98
ISNEPAL(n____(z0, n____(z1, z0))) → c23(U71'(isQid(activate(z0)), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
U71'(tt, z0) → c13(ISPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISPAL(z0) → c24(ISNEPAL(activate(z0)), ACTIVATE(z0))
25.54/6.98
25.54/6.98

(12) Obligation:

Complexity Dependency Tuples Problem
Rules:

__(__(z0, z1), z2) → __(z0, __(z1, z2)) 25.54/6.98
__(z0, nil) → z0 25.54/6.98
__(nil, z0) → z0 25.54/6.98
__(z0, z1) → n____(z0, z1) 25.54/6.98
U11(tt) → tt 25.54/6.98
U21(tt, z0) → U22(isList(activate(z0))) 25.54/6.98
U22(tt) → tt 25.54/6.98
U31(tt) → tt 25.54/6.98
U41(tt, z0) → U42(isNeList(activate(z0))) 25.54/6.98
U42(tt) → tt 25.54/6.98
U51(tt, z0) → U52(isList(activate(z0))) 25.54/6.98
U52(tt) → tt 25.54/6.98
U61(tt) → tt 25.54/6.98
U71(tt, z0) → U72(isPal(activate(z0))) 25.54/6.98
U72(tt) → tt 25.54/6.98
U81(tt) → tt 25.54/6.98
isList(z0) → U11(isNeList(activate(z0))) 25.54/6.98
isList(n__nil) → tt 25.54/6.98
isList(n____(z0, z1)) → U21(isList(activate(z0)), activate(z1)) 25.54/6.98
isNeList(z0) → U31(isQid(activate(z0))) 25.54/6.98
isNeList(n____(z0, z1)) → U41(isList(activate(z0)), activate(z1)) 25.54/6.98
isNeList(n____(z0, z1)) → U51(isNeList(activate(z0)), activate(z1)) 25.54/6.98
isNePal(z0) → U61(isQid(activate(z0))) 25.54/6.98
isNePal(n____(z0, n____(z1, z0))) → U71(isQid(activate(z0)), activate(z1)) 25.54/6.98
isPal(z0) → U81(isNePal(activate(z0))) 25.54/6.98
isPal(n__nil) → tt 25.54/6.98
isQid(n__a) → tt 25.54/6.98
isQid(n__e) → tt 25.54/6.98
isQid(n__i) → tt 25.54/6.98
isQid(n__o) → tt 25.54/6.98
isQid(n__u) → tt 25.54/6.98
niln__nil 25.54/6.98
an__a 25.54/6.98
en__e 25.54/6.98
in__i 25.54/6.98
on__o 25.54/6.98
un__u 25.54/6.98
activate(n__nil) → nil 25.54/6.98
activate(n____(z0, z1)) → __(activate(z0), activate(z1)) 25.54/6.98
activate(n__a) → a 25.54/6.98
activate(n__e) → e 25.54/6.98
activate(n__i) → i 25.54/6.98
activate(n__o) → o 25.54/6.98
activate(n__u) → u 25.54/6.98
activate(z0) → z0
Tuples:

ISLIST(n____(z0, z1)) → c18(U21'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c20(U41'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c21(U51'(isNeList(activate(z0)), activate(z1)), ISNELIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
U21'(tt, z0) → c5(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U41'(tt, z0) → c8(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U51'(tt, z0) → c10(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U71'(tt, z0) → c13(ISPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISLIST(z0) → c16(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISNELIST(z0) → c19(ACTIVATE(z0)) 25.54/6.98
ISNEPAL(z0) → c22(ACTIVATE(z0)) 25.54/6.98
ISNEPAL(n____(z0, n____(z1, z0))) → c23(U71'(isQid(activate(z0)), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISPAL(z0) → c24(ISNEPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ACTIVATE(n__nil) → c37 25.54/6.98
ACTIVATE(n____(z0, z1)) → c38(ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ACTIVATE(n__a) → c39 25.54/6.98
ACTIVATE(n__e) → c40 25.54/6.98
ACTIVATE(n__i) → c41 25.54/6.98
ACTIVATE(n__o) → c42 25.54/6.98
ACTIVATE(n__u) → c43
S tuples:

ISLIST(n____(z0, z1)) → c18(U21'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c20(U41'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c21(U51'(isNeList(activate(z0)), activate(z1)), ISNELIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
U21'(tt, z0) → c5(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U41'(tt, z0) → c8(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U51'(tt, z0) → c10(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISLIST(z0) → c16(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISNELIST(z0) → c19(ACTIVATE(z0)) 25.54/6.98
ACTIVATE(n__nil) → c37 25.54/6.98
ACTIVATE(n____(z0, z1)) → c38(ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ACTIVATE(n__a) → c39 25.54/6.98
ACTIVATE(n__e) → c40 25.54/6.98
ACTIVATE(n__i) → c41 25.54/6.98
ACTIVATE(n__o) → c42 25.54/6.98
ACTIVATE(n__u) → c43
K tuples:

ISPAL(z0) → c24(ISNEPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISNEPAL(z0) → c22(ACTIVATE(z0)) 25.54/6.98
ISNEPAL(n____(z0, n____(z1, z0))) → c23(U71'(isQid(activate(z0)), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
U71'(tt, z0) → c13(ISPAL(activate(z0)), ACTIVATE(z0))
Defined Rule Symbols:

__, U11, U21, U22, U31, U41, U42, U51, U52, U61, U71, U72, U81, isList, isNeList, isNePal, isPal, isQid, nil, a, e, i, o, u, activate

Defined Pair Symbols:

ISLIST, ISNELIST, U21', U41', U51', U71', ISNEPAL, ISPAL, ACTIVATE

Compound Symbols:

c18, c20, c21, c5, c8, c10, c13, c16, c19, c22, c23, c24, c37, c38, c39, c40, c41, c42, c43

25.54/6.98
25.54/6.98

(13) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

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

ISLIST(n____(z0, z1)) → c18(U21'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c20(U41'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c21(U51'(isNeList(activate(z0)), activate(z1)), ISNELIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
U41'(tt, z0) → c8(ISNELIST(activate(z0)), ACTIVATE(z0))
We considered the (Usable) Rules:

activate(n__nil) → nil 25.54/6.98
activate(n____(z0, z1)) → __(activate(z0), activate(z1)) 25.54/6.98
activate(n__a) → a 25.54/6.98
activate(n__e) → e 25.54/6.98
activate(n__i) → i 25.54/6.98
activate(n__o) → o 25.54/6.98
activate(n__u) → u 25.54/6.98
activate(z0) → z0 25.54/6.98
un__u 25.54/6.98
on__o 25.54/6.98
in__i 25.54/6.98
en__e 25.54/6.98
an__a 25.54/6.98
__(z0, z1) → n____(z0, z1) 25.54/6.98
niln__nil 25.54/6.98
isQid(n__a) → tt 25.54/6.98
isQid(n__e) → tt 25.54/6.98
isQid(n__i) → tt 25.54/6.98
isQid(n__o) → tt 25.54/6.98
isQid(n__u) → tt 25.54/6.98
isNeList(z0) → U31(isQid(activate(z0))) 25.54/6.98
isNeList(n____(z0, z1)) → U41(isList(activate(z0)), activate(z1)) 25.54/6.98
isNeList(n____(z0, z1)) → U51(isNeList(activate(z0)), activate(z1)) 25.54/6.98
U51(tt, z0) → U52(isList(activate(z0))) 25.54/6.98
isList(z0) → U11(isNeList(activate(z0))) 25.54/6.98
isList(n__nil) → tt 25.54/6.98
isList(n____(z0, z1)) → U21(isList(activate(z0)), activate(z1)) 25.54/6.98
U52(tt) → tt 25.54/6.98
U21(tt, z0) → U22(isList(activate(z0))) 25.54/6.98
U22(tt) → tt 25.54/6.98
U11(tt) → tt 25.54/6.98
U41(tt, z0) → U42(isNeList(activate(z0))) 25.54/6.98
U42(tt) → tt 25.54/6.98
U31(tt) → tt
And the Tuples:

ISLIST(n____(z0, z1)) → c18(U21'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c20(U41'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c21(U51'(isNeList(activate(z0)), activate(z1)), ISNELIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
U21'(tt, z0) → c5(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U41'(tt, z0) → c8(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U51'(tt, z0) → c10(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U71'(tt, z0) → c13(ISPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISLIST(z0) → c16(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISNELIST(z0) → c19(ACTIVATE(z0)) 25.54/6.98
ISNEPAL(z0) → c22(ACTIVATE(z0)) 25.54/6.98
ISNEPAL(n____(z0, n____(z1, z0))) → c23(U71'(isQid(activate(z0)), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISPAL(z0) → c24(ISNEPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ACTIVATE(n__nil) → c37 25.54/6.98
ACTIVATE(n____(z0, z1)) → c38(ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ACTIVATE(n__a) → c39 25.54/6.98
ACTIVATE(n__e) → c40 25.54/6.98
ACTIVATE(n__i) → c41 25.54/6.98
ACTIVATE(n__o) → c42 25.54/6.98
ACTIVATE(n__u) → c43
The order we found is given by the following interpretation:
Polynomial interpretation : 25.54/6.98

POL(ACTIVATE(x1)) = 0    25.54/6.98
POL(ISLIST(x1)) = x1    25.54/6.98
POL(ISNELIST(x1)) = x1    25.54/6.98
POL(ISNEPAL(x1)) = [1] + x1    25.54/6.98
POL(ISPAL(x1)) = [1] + x1    25.54/6.98
POL(U11(x1)) = [3]    25.54/6.98
POL(U21(x1, x2)) = [3]    25.54/6.98
POL(U21'(x1, x2)) = x2    25.54/6.98
POL(U22(x1)) = [3] + [3]x1    25.54/6.98
POL(U31(x1)) = [3]    25.54/6.98
POL(U41(x1, x2)) = [3]    25.54/6.98
POL(U41'(x1, x2)) = [1] + x2    25.54/6.98
POL(U42(x1)) = [3] + [3]x1    25.54/6.98
POL(U51(x1, x2)) = [3] + [3]x1    25.54/6.98
POL(U51'(x1, x2)) = x2    25.54/6.98
POL(U52(x1)) = [3]    25.54/6.98
POL(U71'(x1, x2)) = [2]x1 + x2    25.54/6.98
POL(__(x1, x2)) = [4] + x1 + x2    25.54/6.98
POL(a) = 0    25.54/6.98
POL(activate(x1)) = x1    25.54/6.98
POL(c10(x1, x2)) = x1 + x2    25.54/6.98
POL(c13(x1, x2)) = x1 + x2    25.54/6.98
POL(c16(x1, x2)) = x1 + x2    25.54/6.98
POL(c18(x1, x2, x3, x4)) = x1 + x2 + x3 + x4    25.54/6.98
POL(c19(x1)) = x1    25.54/6.98
POL(c20(x1, x2, x3, x4)) = x1 + x2 + x3 + x4    25.54/6.98
POL(c21(x1, x2, x3, x4)) = x1 + x2 + x3 + x4    25.54/6.98
POL(c22(x1)) = x1    25.54/6.98
POL(c23(x1, x2, x3)) = x1 + x2 + x3    25.54/6.98
POL(c24(x1, x2)) = x1 + x2    25.54/6.98
POL(c37) = 0    25.54/6.98
POL(c38(x1, x2)) = x1 + x2    25.54/6.98
POL(c39) = 0    25.54/6.98
POL(c40) = 0    25.54/6.98
POL(c41) = 0    25.54/6.98
POL(c42) = 0    25.54/6.98
POL(c43) = 0    25.54/6.98
POL(c5(x1, x2)) = x1 + x2    25.54/6.98
POL(c8(x1, x2)) = x1 + x2    25.54/6.98
POL(e) = 0    25.54/6.98
POL(i) = 0    25.54/6.98
POL(isList(x1)) = 0    25.54/6.98
POL(isNeList(x1)) = 0    25.54/6.98
POL(isQid(x1)) = [4]    25.54/6.98
POL(n____(x1, x2)) = [4] + x1 + x2    25.54/6.98
POL(n__a) = 0    25.54/6.98
POL(n__e) = 0    25.54/6.98
POL(n__i) = 0    25.54/6.98
POL(n__nil) = 0    25.54/6.98
POL(n__o) = 0    25.54/6.98
POL(n__u) = 0    25.54/6.98
POL(nil) = 0    25.54/6.98
POL(o) = 0    25.54/6.98
POL(tt) = [1]    25.54/6.98
POL(u) = 0   
25.54/6.98
25.54/6.98

(14) Obligation:

Complexity Dependency Tuples Problem
Rules:

__(__(z0, z1), z2) → __(z0, __(z1, z2)) 25.54/6.98
__(z0, nil) → z0 25.54/6.98
__(nil, z0) → z0 25.54/6.98
__(z0, z1) → n____(z0, z1) 25.54/6.98
U11(tt) → tt 25.54/6.98
U21(tt, z0) → U22(isList(activate(z0))) 25.54/6.98
U22(tt) → tt 25.54/6.98
U31(tt) → tt 25.54/6.98
U41(tt, z0) → U42(isNeList(activate(z0))) 25.54/6.98
U42(tt) → tt 25.54/6.98
U51(tt, z0) → U52(isList(activate(z0))) 25.54/6.98
U52(tt) → tt 25.54/6.98
U61(tt) → tt 25.54/6.98
U71(tt, z0) → U72(isPal(activate(z0))) 25.54/6.98
U72(tt) → tt 25.54/6.98
U81(tt) → tt 25.54/6.98
isList(z0) → U11(isNeList(activate(z0))) 25.54/6.98
isList(n__nil) → tt 25.54/6.98
isList(n____(z0, z1)) → U21(isList(activate(z0)), activate(z1)) 25.54/6.98
isNeList(z0) → U31(isQid(activate(z0))) 25.54/6.98
isNeList(n____(z0, z1)) → U41(isList(activate(z0)), activate(z1)) 25.54/6.98
isNeList(n____(z0, z1)) → U51(isNeList(activate(z0)), activate(z1)) 25.54/6.98
isNePal(z0) → U61(isQid(activate(z0))) 25.54/6.98
isNePal(n____(z0, n____(z1, z0))) → U71(isQid(activate(z0)), activate(z1)) 25.54/6.98
isPal(z0) → U81(isNePal(activate(z0))) 25.54/6.98
isPal(n__nil) → tt 25.54/6.98
isQid(n__a) → tt 25.54/6.98
isQid(n__e) → tt 25.54/6.98
isQid(n__i) → tt 25.54/6.98
isQid(n__o) → tt 25.54/6.98
isQid(n__u) → tt 25.54/6.98
niln__nil 25.54/6.98
an__a 25.54/6.98
en__e 25.54/6.98
in__i 25.54/6.98
on__o 25.54/6.98
un__u 25.54/6.98
activate(n__nil) → nil 25.54/6.98
activate(n____(z0, z1)) → __(activate(z0), activate(z1)) 25.54/6.98
activate(n__a) → a 25.54/6.98
activate(n__e) → e 25.54/6.98
activate(n__i) → i 25.54/6.98
activate(n__o) → o 25.54/6.98
activate(n__u) → u 25.54/6.98
activate(z0) → z0
Tuples:

ISLIST(n____(z0, z1)) → c18(U21'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c20(U41'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c21(U51'(isNeList(activate(z0)), activate(z1)), ISNELIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
U21'(tt, z0) → c5(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U41'(tt, z0) → c8(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U51'(tt, z0) → c10(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U71'(tt, z0) → c13(ISPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISLIST(z0) → c16(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISNELIST(z0) → c19(ACTIVATE(z0)) 25.54/6.98
ISNEPAL(z0) → c22(ACTIVATE(z0)) 25.54/6.98
ISNEPAL(n____(z0, n____(z1, z0))) → c23(U71'(isQid(activate(z0)), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISPAL(z0) → c24(ISNEPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ACTIVATE(n__nil) → c37 25.54/6.98
ACTIVATE(n____(z0, z1)) → c38(ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ACTIVATE(n__a) → c39 25.54/6.98
ACTIVATE(n__e) → c40 25.54/6.98
ACTIVATE(n__i) → c41 25.54/6.98
ACTIVATE(n__o) → c42 25.54/6.98
ACTIVATE(n__u) → c43
S tuples:

U21'(tt, z0) → c5(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U51'(tt, z0) → c10(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISLIST(z0) → c16(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISNELIST(z0) → c19(ACTIVATE(z0)) 25.54/6.98
ACTIVATE(n__nil) → c37 25.54/6.98
ACTIVATE(n____(z0, z1)) → c38(ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ACTIVATE(n__a) → c39 25.54/6.98
ACTIVATE(n__e) → c40 25.54/6.98
ACTIVATE(n__i) → c41 25.54/6.98
ACTIVATE(n__o) → c42 25.54/6.98
ACTIVATE(n__u) → c43
K tuples:

ISPAL(z0) → c24(ISNEPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISNEPAL(z0) → c22(ACTIVATE(z0)) 25.54/6.98
ISNEPAL(n____(z0, n____(z1, z0))) → c23(U71'(isQid(activate(z0)), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
U71'(tt, z0) → c13(ISPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISLIST(n____(z0, z1)) → c18(U21'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c20(U41'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c21(U51'(isNeList(activate(z0)), activate(z1)), ISNELIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
U41'(tt, z0) → c8(ISNELIST(activate(z0)), ACTIVATE(z0))
Defined Rule Symbols:

__, U11, U21, U22, U31, U41, U42, U51, U52, U61, U71, U72, U81, isList, isNeList, isNePal, isPal, isQid, nil, a, e, i, o, u, activate

Defined Pair Symbols:

ISLIST, ISNELIST, U21', U41', U51', U71', ISNEPAL, ISPAL, ACTIVATE

Compound Symbols:

c18, c20, c21, c5, c8, c10, c13, c16, c19, c22, c23, c24, c37, c38, c39, c40, c41, c42, c43

25.54/6.98
25.54/6.98

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

The following tuples could be moved from S to K by knowledge propagation:

U21'(tt, z0) → c5(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U51'(tt, z0) → c10(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISLIST(z0) → c16(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISNELIST(z0) → c19(ACTIVATE(z0)) 25.54/6.98
ISLIST(n____(z0, z1)) → c18(U21'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISLIST(z0) → c16(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISLIST(n____(z0, z1)) → c18(U21'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISLIST(z0) → c16(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c20(U41'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c21(U51'(isNeList(activate(z0)), activate(z1)), ISNELIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(z0) → c19(ACTIVATE(z0))
25.54/6.98
25.54/6.98

(16) Obligation:

Complexity Dependency Tuples Problem
Rules:

__(__(z0, z1), z2) → __(z0, __(z1, z2)) 25.54/6.98
__(z0, nil) → z0 25.54/6.98
__(nil, z0) → z0 25.54/6.98
__(z0, z1) → n____(z0, z1) 25.54/6.98
U11(tt) → tt 25.54/6.98
U21(tt, z0) → U22(isList(activate(z0))) 25.54/6.98
U22(tt) → tt 25.54/6.98
U31(tt) → tt 25.54/6.98
U41(tt, z0) → U42(isNeList(activate(z0))) 25.54/6.98
U42(tt) → tt 25.54/6.98
U51(tt, z0) → U52(isList(activate(z0))) 25.54/6.98
U52(tt) → tt 25.54/6.98
U61(tt) → tt 25.54/6.98
U71(tt, z0) → U72(isPal(activate(z0))) 25.54/6.98
U72(tt) → tt 25.54/6.98
U81(tt) → tt 25.54/6.98
isList(z0) → U11(isNeList(activate(z0))) 25.54/6.98
isList(n__nil) → tt 25.54/6.98
isList(n____(z0, z1)) → U21(isList(activate(z0)), activate(z1)) 25.54/6.98
isNeList(z0) → U31(isQid(activate(z0))) 25.54/6.98
isNeList(n____(z0, z1)) → U41(isList(activate(z0)), activate(z1)) 25.54/6.98
isNeList(n____(z0, z1)) → U51(isNeList(activate(z0)), activate(z1)) 25.54/6.98
isNePal(z0) → U61(isQid(activate(z0))) 25.54/6.98
isNePal(n____(z0, n____(z1, z0))) → U71(isQid(activate(z0)), activate(z1)) 25.54/6.98
isPal(z0) → U81(isNePal(activate(z0))) 25.54/6.98
isPal(n__nil) → tt 25.54/6.98
isQid(n__a) → tt 25.54/6.98
isQid(n__e) → tt 25.54/6.98
isQid(n__i) → tt 25.54/6.98
isQid(n__o) → tt 25.54/6.98
isQid(n__u) → tt 25.54/6.98
niln__nil 25.54/6.98
an__a 25.54/6.98
en__e 25.54/6.98
in__i 25.54/6.98
on__o 25.54/6.98
un__u 25.54/6.98
activate(n__nil) → nil 25.54/6.98
activate(n____(z0, z1)) → __(activate(z0), activate(z1)) 25.54/6.98
activate(n__a) → a 25.54/6.98
activate(n__e) → e 25.54/6.98
activate(n__i) → i 25.54/6.98
activate(n__o) → o 25.54/6.98
activate(n__u) → u 25.54/6.98
activate(z0) → z0
Tuples:

ISLIST(n____(z0, z1)) → c18(U21'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c20(U41'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c21(U51'(isNeList(activate(z0)), activate(z1)), ISNELIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
U21'(tt, z0) → c5(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U41'(tt, z0) → c8(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U51'(tt, z0) → c10(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U71'(tt, z0) → c13(ISPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISLIST(z0) → c16(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISNELIST(z0) → c19(ACTIVATE(z0)) 25.54/6.98
ISNEPAL(z0) → c22(ACTIVATE(z0)) 25.54/6.98
ISNEPAL(n____(z0, n____(z1, z0))) → c23(U71'(isQid(activate(z0)), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISPAL(z0) → c24(ISNEPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ACTIVATE(n__nil) → c37 25.54/6.98
ACTIVATE(n____(z0, z1)) → c38(ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ACTIVATE(n__a) → c39 25.54/6.98
ACTIVATE(n__e) → c40 25.54/6.98
ACTIVATE(n__i) → c41 25.54/6.98
ACTIVATE(n__o) → c42 25.54/6.98
ACTIVATE(n__u) → c43
S tuples:

ACTIVATE(n__nil) → c37 25.54/6.98
ACTIVATE(n____(z0, z1)) → c38(ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ACTIVATE(n__a) → c39 25.54/6.98
ACTIVATE(n__e) → c40 25.54/6.98
ACTIVATE(n__i) → c41 25.54/6.98
ACTIVATE(n__o) → c42 25.54/6.98
ACTIVATE(n__u) → c43
K tuples:

ISPAL(z0) → c24(ISNEPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISNEPAL(z0) → c22(ACTIVATE(z0)) 25.54/6.98
ISNEPAL(n____(z0, n____(z1, z0))) → c23(U71'(isQid(activate(z0)), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
U71'(tt, z0) → c13(ISPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISLIST(n____(z0, z1)) → c18(U21'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c20(U41'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c21(U51'(isNeList(activate(z0)), activate(z1)), ISNELIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
U41'(tt, z0) → c8(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U21'(tt, z0) → c5(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U51'(tt, z0) → c10(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISLIST(z0) → c16(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISNELIST(z0) → c19(ACTIVATE(z0))
Defined Rule Symbols:

__, U11, U21, U22, U31, U41, U42, U51, U52, U61, U71, U72, U81, isList, isNeList, isNePal, isPal, isQid, nil, a, e, i, o, u, activate

Defined Pair Symbols:

ISLIST, ISNELIST, U21', U41', U51', U71', ISNEPAL, ISPAL, ACTIVATE

Compound Symbols:

c18, c20, c21, c5, c8, c10, c13, c16, c19, c22, c23, c24, c37, c38, c39, c40, c41, c42, c43

25.54/6.98
25.54/6.98

(17) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))) transformation)

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

ACTIVATE(n__nil) → c37 25.54/6.98
ACTIVATE(n____(z0, z1)) → c38(ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ACTIVATE(n__a) → c39 25.54/6.98
ACTIVATE(n__e) → c40 25.54/6.98
ACTIVATE(n__i) → c41 25.54/6.98
ACTIVATE(n__o) → c42 25.54/6.98
ACTIVATE(n__u) → c43
We considered the (Usable) Rules:

activate(n__nil) → nil 25.54/6.98
activate(n____(z0, z1)) → __(activate(z0), activate(z1)) 25.54/6.98
activate(n__a) → a 25.54/6.98
activate(n__e) → e 25.54/6.98
activate(n__i) → i 25.54/6.98
activate(n__o) → o 25.54/6.98
activate(n__u) → u 25.54/6.98
activate(z0) → z0 25.54/6.98
un__u 25.54/6.98
on__o 25.54/6.98
in__i 25.54/6.98
en__e 25.54/6.98
an__a 25.54/6.98
__(z0, z1) → n____(z0, z1) 25.54/6.98
niln__nil 25.54/6.98
isQid(n__a) → tt 25.54/6.98
isQid(n__e) → tt 25.54/6.98
isQid(n__i) → tt 25.54/6.98
isQid(n__o) → tt 25.54/6.98
isQid(n__u) → tt 25.54/6.98
isNeList(z0) → U31(isQid(activate(z0))) 25.54/6.98
isNeList(n____(z0, z1)) → U41(isList(activate(z0)), activate(z1)) 25.54/6.98
isNeList(n____(z0, z1)) → U51(isNeList(activate(z0)), activate(z1)) 25.54/6.98
U51(tt, z0) → U52(isList(activate(z0))) 25.54/6.98
isList(z0) → U11(isNeList(activate(z0))) 25.54/6.98
isList(n__nil) → tt 25.54/6.98
isList(n____(z0, z1)) → U21(isList(activate(z0)), activate(z1)) 25.54/6.98
U52(tt) → tt 25.54/6.98
U21(tt, z0) → U22(isList(activate(z0))) 25.54/6.98
U22(tt) → tt 25.54/6.98
U11(tt) → tt 25.54/6.98
U41(tt, z0) → U42(isNeList(activate(z0))) 25.54/6.98
U42(tt) → tt 25.54/6.98
U31(tt) → tt
And the Tuples:

ISLIST(n____(z0, z1)) → c18(U21'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c20(U41'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c21(U51'(isNeList(activate(z0)), activate(z1)), ISNELIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
U21'(tt, z0) → c5(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U41'(tt, z0) → c8(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U51'(tt, z0) → c10(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U71'(tt, z0) → c13(ISPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISLIST(z0) → c16(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISNELIST(z0) → c19(ACTIVATE(z0)) 25.54/6.98
ISNEPAL(z0) → c22(ACTIVATE(z0)) 25.54/6.98
ISNEPAL(n____(z0, n____(z1, z0))) → c23(U71'(isQid(activate(z0)), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISPAL(z0) → c24(ISNEPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ACTIVATE(n__nil) → c37 25.54/6.98
ACTIVATE(n____(z0, z1)) → c38(ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ACTIVATE(n__a) → c39 25.54/6.98
ACTIVATE(n__e) → c40 25.54/6.98
ACTIVATE(n__i) → c41 25.54/6.98
ACTIVATE(n__o) → c42 25.54/6.98
ACTIVATE(n__u) → c43
The order we found is given by the following interpretation:
Polynomial interpretation : 25.54/6.98

POL(ACTIVATE(x1)) = [1] + x1    25.54/6.98
POL(ISLIST(x1)) = [2] + [2]x1 + x12    25.54/6.98
POL(ISNELIST(x1)) = [1] + x1 + x12    25.54/6.98
POL(ISNEPAL(x1)) = [1] + x1 + [2]x12    25.54/6.98
POL(ISPAL(x1)) = [2] + [2]x1 + [2]x12    25.54/6.98
POL(U11(x1)) = [3]    25.54/6.98
POL(U21(x1, x2)) = [3] + [3]x1    25.54/6.98
POL(U21'(x1, x2)) = [3] + [3]x2 + x22    25.54/6.98
POL(U22(x1)) = [3] + [3]x1    25.54/6.98
POL(U31(x1)) = [3]    25.54/6.98
POL(U41(x1, x2)) = [3]    25.54/6.98
POL(U41'(x1, x2)) = [2] + [3]x2 + x22    25.54/6.98
POL(U42(x1)) = [3] + [3]x1    25.54/6.98
POL(U51(x1, x2)) = [3] + [3]x1    25.54/6.98
POL(U51'(x1, x2)) = [3] + [3]x2 + x22    25.54/6.98
POL(U52(x1)) = [3]    25.54/6.98
POL(U71'(x1, x2)) = [3] + [3]x2 + [2]x22    25.54/6.98
POL(__(x1, x2)) = [2] + x1 + x2    25.54/6.98
POL(a) = 0    25.54/6.98
POL(activate(x1)) = x1    25.54/6.98
POL(c10(x1, x2)) = x1 + x2    25.54/6.98
POL(c13(x1, x2)) = x1 + x2    25.54/6.98
POL(c16(x1, x2)) = x1 + x2    25.54/6.98
POL(c18(x1, x2, x3, x4)) = x1 + x2 + x3 + x4    25.54/6.98
POL(c19(x1)) = x1    25.54/6.98
POL(c20(x1, x2, x3, x4)) = x1 + x2 + x3 + x4    25.54/6.98
POL(c21(x1, x2, x3, x4)) = x1 + x2 + x3 + x4    25.54/6.98
POL(c22(x1)) = x1    25.54/6.98
POL(c23(x1, x2, x3)) = x1 + x2 + x3    25.54/6.98
POL(c24(x1, x2)) = x1 + x2    25.54/6.98
POL(c37) = 0    25.54/6.98
POL(c38(x1, x2)) = x1 + x2    25.54/6.98
POL(c39) = 0    25.54/6.98
POL(c40) = 0    25.54/6.98
POL(c41) = 0    25.54/6.98
POL(c42) = 0    25.54/6.98
POL(c43) = 0    25.54/6.98
POL(c5(x1, x2)) = x1 + x2    25.54/6.98
POL(c8(x1, x2)) = x1 + x2    25.54/6.98
POL(e) = 0    25.54/6.98
POL(i) = 0    25.54/6.98
POL(isList(x1)) = 0    25.54/6.98
POL(isNeList(x1)) = 0    25.54/6.98
POL(isQid(x1)) = 0    25.54/6.98
POL(n____(x1, x2)) = [2] + x1 + x2    25.54/6.98
POL(n__a) = 0    25.54/6.98
POL(n__e) = 0    25.54/6.98
POL(n__i) = 0    25.54/6.98
POL(n__nil) = 0    25.54/6.98
POL(n__o) = 0    25.54/6.98
POL(n__u) = 0    25.54/6.98
POL(nil) = 0    25.54/6.98
POL(o) = 0    25.54/6.98
POL(tt) = 0    25.54/6.98
POL(u) = 0   
25.54/6.98
25.54/6.98

(18) Obligation:

Complexity Dependency Tuples Problem
Rules:

__(__(z0, z1), z2) → __(z0, __(z1, z2)) 25.54/6.98
__(z0, nil) → z0 25.54/6.98
__(nil, z0) → z0 25.54/6.98
__(z0, z1) → n____(z0, z1) 25.54/6.98
U11(tt) → tt 25.54/6.98
U21(tt, z0) → U22(isList(activate(z0))) 25.54/6.98
U22(tt) → tt 25.54/6.98
U31(tt) → tt 25.54/6.98
U41(tt, z0) → U42(isNeList(activate(z0))) 25.54/6.98
U42(tt) → tt 25.54/6.98
U51(tt, z0) → U52(isList(activate(z0))) 25.54/6.98
U52(tt) → tt 25.54/6.98
U61(tt) → tt 25.54/6.98
U71(tt, z0) → U72(isPal(activate(z0))) 25.54/6.98
U72(tt) → tt 25.54/6.98
U81(tt) → tt 25.54/6.98
isList(z0) → U11(isNeList(activate(z0))) 25.54/6.98
isList(n__nil) → tt 25.54/6.98
isList(n____(z0, z1)) → U21(isList(activate(z0)), activate(z1)) 25.54/6.98
isNeList(z0) → U31(isQid(activate(z0))) 25.54/6.98
isNeList(n____(z0, z1)) → U41(isList(activate(z0)), activate(z1)) 25.54/6.98
isNeList(n____(z0, z1)) → U51(isNeList(activate(z0)), activate(z1)) 25.54/6.98
isNePal(z0) → U61(isQid(activate(z0))) 25.54/6.98
isNePal(n____(z0, n____(z1, z0))) → U71(isQid(activate(z0)), activate(z1)) 25.54/6.98
isPal(z0) → U81(isNePal(activate(z0))) 25.54/6.98
isPal(n__nil) → tt 25.54/6.98
isQid(n__a) → tt 25.54/6.98
isQid(n__e) → tt 25.54/6.98
isQid(n__i) → tt 25.54/6.98
isQid(n__o) → tt 25.54/6.98
isQid(n__u) → tt 25.54/6.98
niln__nil 25.54/6.98
an__a 25.54/6.98
en__e 25.54/6.98
in__i 25.54/6.98
on__o 25.54/6.98
un__u 25.54/6.98
activate(n__nil) → nil 25.54/6.98
activate(n____(z0, z1)) → __(activate(z0), activate(z1)) 25.54/6.98
activate(n__a) → a 25.54/6.98
activate(n__e) → e 25.54/6.98
activate(n__i) → i 25.54/6.98
activate(n__o) → o 25.54/6.98
activate(n__u) → u 25.54/6.98
activate(z0) → z0
Tuples:

ISLIST(n____(z0, z1)) → c18(U21'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c20(U41'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c21(U51'(isNeList(activate(z0)), activate(z1)), ISNELIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
U21'(tt, z0) → c5(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U41'(tt, z0) → c8(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U51'(tt, z0) → c10(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U71'(tt, z0) → c13(ISPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISLIST(z0) → c16(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISNELIST(z0) → c19(ACTIVATE(z0)) 25.54/6.98
ISNEPAL(z0) → c22(ACTIVATE(z0)) 25.54/6.98
ISNEPAL(n____(z0, n____(z1, z0))) → c23(U71'(isQid(activate(z0)), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISPAL(z0) → c24(ISNEPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ACTIVATE(n__nil) → c37 25.54/6.98
ACTIVATE(n____(z0, z1)) → c38(ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ACTIVATE(n__a) → c39 25.54/6.98
ACTIVATE(n__e) → c40 25.54/6.98
ACTIVATE(n__i) → c41 25.54/6.98
ACTIVATE(n__o) → c42 25.54/6.98
ACTIVATE(n__u) → c43
S tuples:none
K tuples:

ISPAL(z0) → c24(ISNEPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISNEPAL(z0) → c22(ACTIVATE(z0)) 25.54/6.98
ISNEPAL(n____(z0, n____(z1, z0))) → c23(U71'(isQid(activate(z0)), activate(z1)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
U71'(tt, z0) → c13(ISPAL(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISLIST(n____(z0, z1)) → c18(U21'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c20(U41'(isList(activate(z0)), activate(z1)), ISLIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ISNELIST(n____(z0, z1)) → c21(U51'(isNeList(activate(z0)), activate(z1)), ISNELIST(activate(z0)), ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
U41'(tt, z0) → c8(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U21'(tt, z0) → c5(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
U51'(tt, z0) → c10(ISLIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISLIST(z0) → c16(ISNELIST(activate(z0)), ACTIVATE(z0)) 25.54/6.98
ISNELIST(z0) → c19(ACTIVATE(z0)) 25.54/6.98
ACTIVATE(n__nil) → c37 25.54/6.98
ACTIVATE(n____(z0, z1)) → c38(ACTIVATE(z0), ACTIVATE(z1)) 25.54/6.98
ACTIVATE(n__a) → c39 25.54/6.98
ACTIVATE(n__e) → c40 25.54/6.98
ACTIVATE(n__i) → c41 25.54/6.98
ACTIVATE(n__o) → c42 25.54/6.98
ACTIVATE(n__u) → c43
Defined Rule Symbols:

__, U11, U21, U22, U31, U41, U42, U51, U52, U61, U71, U72, U81, isList, isNeList, isNePal, isPal, isQid, nil, a, e, i, o, u, activate

Defined Pair Symbols:

ISLIST, ISNELIST, U21', U41', U51', U71', ISNEPAL, ISPAL, ACTIVATE

Compound Symbols:

c18, c20, c21, c5, c8, c10, c13, c16, c19, c22, c23, c24, c37, c38, c39, c40, c41, c42, c43

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

The set S is empty
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(20) BOUNDS(O(1), O(1))

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25.91/7.05 EOF