316.43/291.58 WORST_CASE(Omega(n^1), ?) 316.54/291.59 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 316.54/291.59 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 316.54/291.59 316.54/291.59 316.54/291.59 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 316.54/291.59 316.54/291.59 (0) CpxTRS 316.54/291.59 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 316.54/291.59 (2) TRS for Loop Detection 316.54/291.59 (3) DecreasingLoopProof [LOWER BOUND(ID), 288 ms] 316.54/291.59 (4) BEST 316.54/291.59 (5) proven lower bound 316.54/291.59 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 316.54/291.59 (7) BOUNDS(n^1, INF) 316.54/291.59 (8) TRS for Loop Detection 316.54/291.59 316.54/291.59 316.54/291.59 ---------------------------------------- 316.54/291.59 316.54/291.59 (0) 316.54/291.59 Obligation: 316.54/291.59 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 316.54/291.59 316.54/291.59 316.54/291.59 The TRS R consists of the following rules: 316.54/291.59 316.54/291.59 __(__(X, Y), Z) -> __(X, __(Y, Z)) 316.54/291.59 __(X, nil) -> X 316.54/291.59 __(nil, X) -> X 316.54/291.59 U11(tt, V) -> U12(isPalListKind(activate(V)), activate(V)) 316.54/291.59 U12(tt, V) -> U13(isNeList(activate(V))) 316.54/291.59 U13(tt) -> tt 316.54/291.59 U21(tt, V1, V2) -> U22(isPalListKind(activate(V1)), activate(V1), activate(V2)) 316.54/291.59 U22(tt, V1, V2) -> U23(isPalListKind(activate(V2)), activate(V1), activate(V2)) 316.54/291.59 U23(tt, V1, V2) -> U24(isPalListKind(activate(V2)), activate(V1), activate(V2)) 316.54/291.59 U24(tt, V1, V2) -> U25(isList(activate(V1)), activate(V2)) 316.54/291.59 U25(tt, V2) -> U26(isList(activate(V2))) 316.54/291.59 U26(tt) -> tt 316.54/291.59 U31(tt, V) -> U32(isPalListKind(activate(V)), activate(V)) 316.54/291.59 U32(tt, V) -> U33(isQid(activate(V))) 316.54/291.59 U33(tt) -> tt 316.54/291.59 U41(tt, V1, V2) -> U42(isPalListKind(activate(V1)), activate(V1), activate(V2)) 316.54/291.59 U42(tt, V1, V2) -> U43(isPalListKind(activate(V2)), activate(V1), activate(V2)) 316.54/291.59 U43(tt, V1, V2) -> U44(isPalListKind(activate(V2)), activate(V1), activate(V2)) 316.54/291.59 U44(tt, V1, V2) -> U45(isList(activate(V1)), activate(V2)) 316.54/291.59 U45(tt, V2) -> U46(isNeList(activate(V2))) 316.54/291.59 U46(tt) -> tt 316.54/291.59 U51(tt, V1, V2) -> U52(isPalListKind(activate(V1)), activate(V1), activate(V2)) 316.54/291.59 U52(tt, V1, V2) -> U53(isPalListKind(activate(V2)), activate(V1), activate(V2)) 316.54/291.59 U53(tt, V1, V2) -> U54(isPalListKind(activate(V2)), activate(V1), activate(V2)) 316.54/291.59 U54(tt, V1, V2) -> U55(isNeList(activate(V1)), activate(V2)) 316.54/291.59 U55(tt, V2) -> U56(isList(activate(V2))) 316.54/291.59 U56(tt) -> tt 316.54/291.59 U61(tt, V) -> U62(isPalListKind(activate(V)), activate(V)) 316.54/291.59 U62(tt, V) -> U63(isQid(activate(V))) 316.54/291.59 U63(tt) -> tt 316.54/291.59 U71(tt, I, P) -> U72(isPalListKind(activate(I)), activate(P)) 316.54/291.59 U72(tt, P) -> U73(isPal(activate(P)), activate(P)) 316.54/291.59 U73(tt, P) -> U74(isPalListKind(activate(P))) 316.54/291.59 U74(tt) -> tt 316.54/291.59 U81(tt, V) -> U82(isPalListKind(activate(V)), activate(V)) 316.54/291.59 U82(tt, V) -> U83(isNePal(activate(V))) 316.54/291.59 U83(tt) -> tt 316.54/291.59 U91(tt, V2) -> U92(isPalListKind(activate(V2))) 316.54/291.59 U92(tt) -> tt 316.54/291.59 isList(V) -> U11(isPalListKind(activate(V)), activate(V)) 316.54/291.59 isList(n__nil) -> tt 316.54/291.59 isList(n____(V1, V2)) -> U21(isPalListKind(activate(V1)), activate(V1), activate(V2)) 316.54/291.59 isNeList(V) -> U31(isPalListKind(activate(V)), activate(V)) 316.54/291.59 isNeList(n____(V1, V2)) -> U41(isPalListKind(activate(V1)), activate(V1), activate(V2)) 316.54/291.59 isNeList(n____(V1, V2)) -> U51(isPalListKind(activate(V1)), activate(V1), activate(V2)) 316.54/291.59 isNePal(V) -> U61(isPalListKind(activate(V)), activate(V)) 316.54/291.59 isNePal(n____(I, __(P, I))) -> U71(isQid(activate(I)), activate(I), activate(P)) 316.54/291.59 isPal(V) -> U81(isPalListKind(activate(V)), activate(V)) 316.54/291.59 isPal(n__nil) -> tt 316.54/291.59 isPalListKind(n__a) -> tt 316.54/291.59 isPalListKind(n__e) -> tt 316.54/291.59 isPalListKind(n__i) -> tt 316.54/291.59 isPalListKind(n__nil) -> tt 316.54/291.59 isPalListKind(n__o) -> tt 316.54/291.59 isPalListKind(n__u) -> tt 316.54/291.59 isPalListKind(n____(V1, V2)) -> U91(isPalListKind(activate(V1)), activate(V2)) 316.54/291.59 isQid(n__a) -> tt 316.54/291.59 isQid(n__e) -> tt 316.54/291.59 isQid(n__i) -> tt 316.54/291.59 isQid(n__o) -> tt 316.54/291.59 isQid(n__u) -> tt 316.54/291.59 nil -> n__nil 316.54/291.59 __(X1, X2) -> n____(X1, X2) 316.54/291.59 a -> n__a 316.54/291.59 e -> n__e 316.54/291.59 i -> n__i 316.54/291.59 o -> n__o 316.54/291.59 u -> n__u 316.54/291.59 activate(n__nil) -> nil 316.54/291.59 activate(n____(X1, X2)) -> __(X1, X2) 316.54/291.59 activate(n__a) -> a 316.54/291.59 activate(n__e) -> e 316.54/291.59 activate(n__i) -> i 316.54/291.59 activate(n__o) -> o 316.54/291.59 activate(n__u) -> u 316.54/291.59 activate(X) -> X 316.54/291.59 316.54/291.59 S is empty. 316.54/291.59 Rewrite Strategy: FULL 316.54/291.59 ---------------------------------------- 316.54/291.59 316.54/291.59 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 316.54/291.59 Transformed a relative TRS into a decreasing-loop problem. 316.54/291.59 ---------------------------------------- 316.54/291.59 316.54/291.59 (2) 316.54/291.59 Obligation: 316.54/291.59 Analyzing the following TRS for decreasing loops: 316.54/291.59 316.54/291.59 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 316.54/291.59 316.54/291.59 316.54/291.59 The TRS R consists of the following rules: 316.54/291.59 316.54/291.59 __(__(X, Y), Z) -> __(X, __(Y, Z)) 316.54/291.59 __(X, nil) -> X 316.54/291.59 __(nil, X) -> X 316.54/291.59 U11(tt, V) -> U12(isPalListKind(activate(V)), activate(V)) 316.54/291.59 U12(tt, V) -> U13(isNeList(activate(V))) 316.54/291.59 U13(tt) -> tt 316.54/291.59 U21(tt, V1, V2) -> U22(isPalListKind(activate(V1)), activate(V1), activate(V2)) 316.54/291.59 U22(tt, V1, V2) -> U23(isPalListKind(activate(V2)), activate(V1), activate(V2)) 316.54/291.59 U23(tt, V1, V2) -> U24(isPalListKind(activate(V2)), activate(V1), activate(V2)) 316.54/291.59 U24(tt, V1, V2) -> U25(isList(activate(V1)), activate(V2)) 316.54/291.59 U25(tt, V2) -> U26(isList(activate(V2))) 316.54/291.59 U26(tt) -> tt 316.54/291.59 U31(tt, V) -> U32(isPalListKind(activate(V)), activate(V)) 316.54/291.59 U32(tt, V) -> U33(isQid(activate(V))) 316.54/291.59 U33(tt) -> tt 316.54/291.59 U41(tt, V1, V2) -> U42(isPalListKind(activate(V1)), activate(V1), activate(V2)) 316.54/291.59 U42(tt, V1, V2) -> U43(isPalListKind(activate(V2)), activate(V1), activate(V2)) 316.54/291.59 U43(tt, V1, V2) -> U44(isPalListKind(activate(V2)), activate(V1), activate(V2)) 316.54/291.59 U44(tt, V1, V2) -> U45(isList(activate(V1)), activate(V2)) 316.54/291.59 U45(tt, V2) -> U46(isNeList(activate(V2))) 316.54/291.59 U46(tt) -> tt 316.54/291.59 U51(tt, V1, V2) -> U52(isPalListKind(activate(V1)), activate(V1), activate(V2)) 316.54/291.59 U52(tt, V1, V2) -> U53(isPalListKind(activate(V2)), activate(V1), activate(V2)) 316.54/291.59 U53(tt, V1, V2) -> U54(isPalListKind(activate(V2)), activate(V1), activate(V2)) 316.54/291.59 U54(tt, V1, V2) -> U55(isNeList(activate(V1)), activate(V2)) 316.54/291.59 U55(tt, V2) -> U56(isList(activate(V2))) 316.54/291.59 U56(tt) -> tt 316.54/291.59 U61(tt, V) -> U62(isPalListKind(activate(V)), activate(V)) 316.54/291.59 U62(tt, V) -> U63(isQid(activate(V))) 316.54/291.59 U63(tt) -> tt 316.54/291.59 U71(tt, I, P) -> U72(isPalListKind(activate(I)), activate(P)) 316.54/291.59 U72(tt, P) -> U73(isPal(activate(P)), activate(P)) 316.54/291.59 U73(tt, P) -> U74(isPalListKind(activate(P))) 316.54/291.59 U74(tt) -> tt 316.54/291.59 U81(tt, V) -> U82(isPalListKind(activate(V)), activate(V)) 316.54/291.59 U82(tt, V) -> U83(isNePal(activate(V))) 316.54/291.59 U83(tt) -> tt 316.54/291.59 U91(tt, V2) -> U92(isPalListKind(activate(V2))) 316.54/291.59 U92(tt) -> tt 316.54/291.59 isList(V) -> U11(isPalListKind(activate(V)), activate(V)) 316.54/291.59 isList(n__nil) -> tt 316.54/291.59 isList(n____(V1, V2)) -> U21(isPalListKind(activate(V1)), activate(V1), activate(V2)) 316.54/291.59 isNeList(V) -> U31(isPalListKind(activate(V)), activate(V)) 316.54/291.59 isNeList(n____(V1, V2)) -> U41(isPalListKind(activate(V1)), activate(V1), activate(V2)) 316.54/291.59 isNeList(n____(V1, V2)) -> U51(isPalListKind(activate(V1)), activate(V1), activate(V2)) 316.54/291.59 isNePal(V) -> U61(isPalListKind(activate(V)), activate(V)) 316.54/291.59 isNePal(n____(I, __(P, I))) -> U71(isQid(activate(I)), activate(I), activate(P)) 316.54/291.59 isPal(V) -> U81(isPalListKind(activate(V)), activate(V)) 316.54/291.59 isPal(n__nil) -> tt 316.54/291.59 isPalListKind(n__a) -> tt 316.54/291.59 isPalListKind(n__e) -> tt 316.54/291.59 isPalListKind(n__i) -> tt 316.54/291.59 isPalListKind(n__nil) -> tt 316.54/291.59 isPalListKind(n__o) -> tt 316.54/291.59 isPalListKind(n__u) -> tt 316.54/291.59 isPalListKind(n____(V1, V2)) -> U91(isPalListKind(activate(V1)), activate(V2)) 316.54/291.59 isQid(n__a) -> tt 316.54/291.59 isQid(n__e) -> tt 316.54/291.59 isQid(n__i) -> tt 316.54/291.59 isQid(n__o) -> tt 316.54/291.59 isQid(n__u) -> tt 316.54/291.59 nil -> n__nil 316.54/291.59 __(X1, X2) -> n____(X1, X2) 316.54/291.59 a -> n__a 316.54/291.59 e -> n__e 316.54/291.59 i -> n__i 316.54/291.59 o -> n__o 316.54/291.59 u -> n__u 316.54/291.59 activate(n__nil) -> nil 316.54/291.59 activate(n____(X1, X2)) -> __(X1, X2) 316.54/291.59 activate(n__a) -> a 316.54/291.59 activate(n__e) -> e 316.54/291.59 activate(n__i) -> i 316.54/291.59 activate(n__o) -> o 316.54/291.59 activate(n__u) -> u 316.54/291.59 activate(X) -> X 316.54/291.59 316.54/291.59 S is empty. 316.54/291.59 Rewrite Strategy: FULL 316.54/291.59 ---------------------------------------- 316.54/291.59 316.54/291.59 (3) DecreasingLoopProof (LOWER BOUND(ID)) 316.54/291.59 The following loop(s) give(s) rise to the lower bound Omega(n^1): 316.54/291.59 316.54/291.59 The rewrite sequence 316.54/291.59 316.54/291.59 isPalListKind(n____(V1, V2)) ->^+ U91(isPalListKind(V1), activate(V2)) 316.54/291.59 316.54/291.59 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 316.54/291.59 316.54/291.59 The pumping substitution is [V1 / n____(V1, V2)]. 316.54/291.59 316.54/291.59 The result substitution is [ ]. 316.54/291.59 316.54/291.59 316.54/291.59 316.54/291.59 316.54/291.59 ---------------------------------------- 316.54/291.59 316.54/291.59 (4) 316.54/291.59 Complex Obligation (BEST) 316.54/291.59 316.54/291.59 ---------------------------------------- 316.54/291.59 316.54/291.59 (5) 316.54/291.59 Obligation: 316.54/291.59 Proved the lower bound n^1 for the following obligation: 316.54/291.59 316.54/291.59 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 316.54/291.59 316.54/291.59 316.54/291.59 The TRS R consists of the following rules: 316.54/291.59 316.54/291.59 __(__(X, Y), Z) -> __(X, __(Y, Z)) 316.54/291.59 __(X, nil) -> X 316.54/291.59 __(nil, X) -> X 316.54/291.59 U11(tt, V) -> U12(isPalListKind(activate(V)), activate(V)) 316.54/291.59 U12(tt, V) -> U13(isNeList(activate(V))) 316.54/291.59 U13(tt) -> tt 316.54/291.59 U21(tt, V1, V2) -> U22(isPalListKind(activate(V1)), activate(V1), activate(V2)) 316.54/291.59 U22(tt, V1, V2) -> U23(isPalListKind(activate(V2)), activate(V1), activate(V2)) 316.54/291.59 U23(tt, V1, V2) -> U24(isPalListKind(activate(V2)), activate(V1), activate(V2)) 316.54/291.59 U24(tt, V1, V2) -> U25(isList(activate(V1)), activate(V2)) 316.54/291.59 U25(tt, V2) -> U26(isList(activate(V2))) 316.54/291.59 U26(tt) -> tt 316.54/291.59 U31(tt, V) -> U32(isPalListKind(activate(V)), activate(V)) 316.54/291.59 U32(tt, V) -> U33(isQid(activate(V))) 316.54/291.59 U33(tt) -> tt 316.54/291.59 U41(tt, V1, V2) -> U42(isPalListKind(activate(V1)), activate(V1), activate(V2)) 316.54/291.59 U42(tt, V1, V2) -> U43(isPalListKind(activate(V2)), activate(V1), activate(V2)) 316.54/291.59 U43(tt, V1, V2) -> U44(isPalListKind(activate(V2)), activate(V1), activate(V2)) 316.54/291.59 U44(tt, V1, V2) -> U45(isList(activate(V1)), activate(V2)) 316.54/291.59 U45(tt, V2) -> U46(isNeList(activate(V2))) 316.54/291.59 U46(tt) -> tt 316.54/291.59 U51(tt, V1, V2) -> U52(isPalListKind(activate(V1)), activate(V1), activate(V2)) 316.54/291.59 U52(tt, V1, V2) -> U53(isPalListKind(activate(V2)), activate(V1), activate(V2)) 316.54/291.59 U53(tt, V1, V2) -> U54(isPalListKind(activate(V2)), activate(V1), activate(V2)) 316.54/291.59 U54(tt, V1, V2) -> U55(isNeList(activate(V1)), activate(V2)) 316.54/291.59 U55(tt, V2) -> U56(isList(activate(V2))) 316.54/291.59 U56(tt) -> tt 316.54/291.59 U61(tt, V) -> U62(isPalListKind(activate(V)), activate(V)) 316.54/291.59 U62(tt, V) -> U63(isQid(activate(V))) 316.54/291.59 U63(tt) -> tt 316.54/291.59 U71(tt, I, P) -> U72(isPalListKind(activate(I)), activate(P)) 316.54/291.59 U72(tt, P) -> U73(isPal(activate(P)), activate(P)) 316.54/291.59 U73(tt, P) -> U74(isPalListKind(activate(P))) 316.54/291.59 U74(tt) -> tt 316.54/291.59 U81(tt, V) -> U82(isPalListKind(activate(V)), activate(V)) 316.54/291.59 U82(tt, V) -> U83(isNePal(activate(V))) 316.54/291.59 U83(tt) -> tt 316.54/291.59 U91(tt, V2) -> U92(isPalListKind(activate(V2))) 316.54/291.59 U92(tt) -> tt 316.54/291.59 isList(V) -> U11(isPalListKind(activate(V)), activate(V)) 316.54/291.59 isList(n__nil) -> tt 316.54/291.59 isList(n____(V1, V2)) -> U21(isPalListKind(activate(V1)), activate(V1), activate(V2)) 316.54/291.59 isNeList(V) -> U31(isPalListKind(activate(V)), activate(V)) 316.54/291.59 isNeList(n____(V1, V2)) -> U41(isPalListKind(activate(V1)), activate(V1), activate(V2)) 316.54/291.59 isNeList(n____(V1, V2)) -> U51(isPalListKind(activate(V1)), activate(V1), activate(V2)) 316.54/291.59 isNePal(V) -> U61(isPalListKind(activate(V)), activate(V)) 316.54/291.59 isNePal(n____(I, __(P, I))) -> U71(isQid(activate(I)), activate(I), activate(P)) 316.54/291.59 isPal(V) -> U81(isPalListKind(activate(V)), activate(V)) 316.54/291.59 isPal(n__nil) -> tt 316.54/291.59 isPalListKind(n__a) -> tt 316.54/291.59 isPalListKind(n__e) -> tt 316.54/291.59 isPalListKind(n__i) -> tt 316.54/291.59 isPalListKind(n__nil) -> tt 316.54/291.59 isPalListKind(n__o) -> tt 316.54/291.59 isPalListKind(n__u) -> tt 316.54/291.59 isPalListKind(n____(V1, V2)) -> U91(isPalListKind(activate(V1)), activate(V2)) 316.54/291.59 isQid(n__a) -> tt 316.54/291.59 isQid(n__e) -> tt 316.54/291.59 isQid(n__i) -> tt 316.54/291.59 isQid(n__o) -> tt 316.54/291.59 isQid(n__u) -> tt 316.54/291.59 nil -> n__nil 316.54/291.59 __(X1, X2) -> n____(X1, X2) 316.54/291.59 a -> n__a 316.54/291.59 e -> n__e 316.54/291.59 i -> n__i 316.54/291.59 o -> n__o 316.54/291.59 u -> n__u 316.54/291.59 activate(n__nil) -> nil 316.54/291.59 activate(n____(X1, X2)) -> __(X1, X2) 316.54/291.59 activate(n__a) -> a 316.54/291.59 activate(n__e) -> e 316.54/291.59 activate(n__i) -> i 316.54/291.59 activate(n__o) -> o 316.54/291.59 activate(n__u) -> u 316.54/291.59 activate(X) -> X 316.54/291.59 316.54/291.59 S is empty. 316.54/291.59 Rewrite Strategy: FULL 316.54/291.59 ---------------------------------------- 316.54/291.59 316.54/291.59 (6) LowerBoundPropagationProof (FINISHED) 316.54/291.59 Propagated lower bound. 316.54/291.59 ---------------------------------------- 316.54/291.59 316.54/291.59 (7) 316.54/291.59 BOUNDS(n^1, INF) 316.54/291.59 316.54/291.59 ---------------------------------------- 316.54/291.59 316.54/291.59 (8) 316.54/291.59 Obligation: 316.54/291.59 Analyzing the following TRS for decreasing loops: 316.54/291.59 316.54/291.59 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 316.54/291.59 316.54/291.59 316.54/291.59 The TRS R consists of the following rules: 316.54/291.59 316.54/291.59 __(__(X, Y), Z) -> __(X, __(Y, Z)) 316.54/291.59 __(X, nil) -> X 316.54/291.59 __(nil, X) -> X 316.54/291.59 U11(tt, V) -> U12(isPalListKind(activate(V)), activate(V)) 316.54/291.59 U12(tt, V) -> U13(isNeList(activate(V))) 316.54/291.59 U13(tt) -> tt 316.54/291.59 U21(tt, V1, V2) -> U22(isPalListKind(activate(V1)), activate(V1), activate(V2)) 316.54/291.59 U22(tt, V1, V2) -> U23(isPalListKind(activate(V2)), activate(V1), activate(V2)) 316.54/291.59 U23(tt, V1, V2) -> U24(isPalListKind(activate(V2)), activate(V1), activate(V2)) 316.54/291.59 U24(tt, V1, V2) -> U25(isList(activate(V1)), activate(V2)) 316.54/291.59 U25(tt, V2) -> U26(isList(activate(V2))) 316.54/291.59 U26(tt) -> tt 316.54/291.59 U31(tt, V) -> U32(isPalListKind(activate(V)), activate(V)) 316.54/291.59 U32(tt, V) -> U33(isQid(activate(V))) 316.54/291.59 U33(tt) -> tt 316.54/291.59 U41(tt, V1, V2) -> U42(isPalListKind(activate(V1)), activate(V1), activate(V2)) 316.54/291.59 U42(tt, V1, V2) -> U43(isPalListKind(activate(V2)), activate(V1), activate(V2)) 316.54/291.59 U43(tt, V1, V2) -> U44(isPalListKind(activate(V2)), activate(V1), activate(V2)) 316.54/291.59 U44(tt, V1, V2) -> U45(isList(activate(V1)), activate(V2)) 316.54/291.59 U45(tt, V2) -> U46(isNeList(activate(V2))) 316.54/291.59 U46(tt) -> tt 316.54/291.59 U51(tt, V1, V2) -> U52(isPalListKind(activate(V1)), activate(V1), activate(V2)) 316.54/291.59 U52(tt, V1, V2) -> U53(isPalListKind(activate(V2)), activate(V1), activate(V2)) 316.54/291.59 U53(tt, V1, V2) -> U54(isPalListKind(activate(V2)), activate(V1), activate(V2)) 316.54/291.59 U54(tt, V1, V2) -> U55(isNeList(activate(V1)), activate(V2)) 316.54/291.59 U55(tt, V2) -> U56(isList(activate(V2))) 316.54/291.59 U56(tt) -> tt 316.54/291.59 U61(tt, V) -> U62(isPalListKind(activate(V)), activate(V)) 316.54/291.59 U62(tt, V) -> U63(isQid(activate(V))) 316.54/291.59 U63(tt) -> tt 316.54/291.59 U71(tt, I, P) -> U72(isPalListKind(activate(I)), activate(P)) 316.54/291.59 U72(tt, P) -> U73(isPal(activate(P)), activate(P)) 316.54/291.59 U73(tt, P) -> U74(isPalListKind(activate(P))) 316.54/291.59 U74(tt) -> tt 316.54/291.59 U81(tt, V) -> U82(isPalListKind(activate(V)), activate(V)) 316.54/291.59 U82(tt, V) -> U83(isNePal(activate(V))) 316.54/291.59 U83(tt) -> tt 316.54/291.59 U91(tt, V2) -> U92(isPalListKind(activate(V2))) 316.54/291.59 U92(tt) -> tt 316.54/291.59 isList(V) -> U11(isPalListKind(activate(V)), activate(V)) 316.54/291.59 isList(n__nil) -> tt 316.54/291.59 isList(n____(V1, V2)) -> U21(isPalListKind(activate(V1)), activate(V1), activate(V2)) 316.54/291.59 isNeList(V) -> U31(isPalListKind(activate(V)), activate(V)) 316.54/291.59 isNeList(n____(V1, V2)) -> U41(isPalListKind(activate(V1)), activate(V1), activate(V2)) 316.54/291.59 isNeList(n____(V1, V2)) -> U51(isPalListKind(activate(V1)), activate(V1), activate(V2)) 316.54/291.59 isNePal(V) -> U61(isPalListKind(activate(V)), activate(V)) 316.54/291.59 isNePal(n____(I, __(P, I))) -> U71(isQid(activate(I)), activate(I), activate(P)) 316.54/291.59 isPal(V) -> U81(isPalListKind(activate(V)), activate(V)) 316.54/291.59 isPal(n__nil) -> tt 316.54/291.59 isPalListKind(n__a) -> tt 316.54/291.59 isPalListKind(n__e) -> tt 316.54/291.59 isPalListKind(n__i) -> tt 316.54/291.59 isPalListKind(n__nil) -> tt 316.54/291.59 isPalListKind(n__o) -> tt 316.54/291.59 isPalListKind(n__u) -> tt 316.54/291.59 isPalListKind(n____(V1, V2)) -> U91(isPalListKind(activate(V1)), activate(V2)) 316.54/291.59 isQid(n__a) -> tt 316.54/291.59 isQid(n__e) -> tt 316.54/291.59 isQid(n__i) -> tt 316.54/291.59 isQid(n__o) -> tt 316.54/291.59 isQid(n__u) -> tt 316.54/291.59 nil -> n__nil 316.54/291.59 __(X1, X2) -> n____(X1, X2) 316.54/291.59 a -> n__a 316.54/291.59 e -> n__e 316.54/291.59 i -> n__i 316.54/291.59 o -> n__o 316.54/291.59 u -> n__u 316.54/291.59 activate(n__nil) -> nil 316.54/291.59 activate(n____(X1, X2)) -> __(X1, X2) 316.54/291.59 activate(n__a) -> a 316.54/291.59 activate(n__e) -> e 316.54/291.59 activate(n__i) -> i 316.54/291.59 activate(n__o) -> o 316.54/291.59 activate(n__u) -> u 316.54/291.59 activate(X) -> X 316.54/291.59 316.54/291.59 S is empty. 316.54/291.59 Rewrite Strategy: FULL 316.57/291.63 EOF