1113.66/291.56 WORST_CASE(Omega(n^1), ?) 1114.18/291.61 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1114.18/291.61 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1114.18/291.61 1114.18/291.61 1114.18/291.61 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1114.18/291.61 1114.18/291.61 (0) CpxTRS 1114.18/291.61 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1114.18/291.61 (2) TRS for Loop Detection 1114.18/291.61 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1114.18/291.61 (4) BEST 1114.18/291.61 (5) proven lower bound 1114.18/291.61 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1114.18/291.61 (7) BOUNDS(n^1, INF) 1114.18/291.61 (8) TRS for Loop Detection 1114.18/291.61 1114.18/291.61 1114.18/291.61 ---------------------------------------- 1114.18/291.61 1114.18/291.61 (0) 1114.18/291.61 Obligation: 1114.18/291.61 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1114.18/291.61 1114.18/291.61 1114.18/291.61 The TRS R consists of the following rules: 1114.18/291.61 1114.18/291.61 a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z))) 1114.18/291.61 a____(X, nil) -> mark(X) 1114.18/291.61 a____(nil, X) -> mark(X) 1114.18/291.61 a__U11(tt) -> tt 1114.18/291.61 a__U21(tt, V2) -> a__U22(a__isList(V2)) 1114.18/291.61 a__U22(tt) -> tt 1114.18/291.61 a__U31(tt) -> tt 1114.18/291.61 a__U41(tt, V2) -> a__U42(a__isNeList(V2)) 1114.18/291.61 a__U42(tt) -> tt 1114.18/291.61 a__U51(tt, V2) -> a__U52(a__isList(V2)) 1114.18/291.61 a__U52(tt) -> tt 1114.18/291.61 a__U61(tt) -> tt 1114.18/291.61 a__U71(tt, P) -> a__U72(a__isPal(P)) 1114.18/291.61 a__U72(tt) -> tt 1114.18/291.61 a__U81(tt) -> tt 1114.18/291.61 a__isList(V) -> a__U11(a__isNeList(V)) 1114.18/291.61 a__isList(nil) -> tt 1114.18/291.61 a__isList(__(V1, V2)) -> a__U21(a__isList(V1), V2) 1114.18/291.61 a__isNeList(V) -> a__U31(a__isQid(V)) 1114.18/291.61 a__isNeList(__(V1, V2)) -> a__U41(a__isList(V1), V2) 1114.18/291.61 a__isNeList(__(V1, V2)) -> a__U51(a__isNeList(V1), V2) 1114.18/291.61 a__isNePal(V) -> a__U61(a__isQid(V)) 1114.18/291.61 a__isNePal(__(I, __(P, I))) -> a__U71(a__isQid(I), P) 1114.18/291.61 a__isPal(V) -> a__U81(a__isNePal(V)) 1114.18/291.61 a__isPal(nil) -> tt 1114.18/291.61 a__isQid(a) -> tt 1114.18/291.61 a__isQid(e) -> tt 1114.18/291.61 a__isQid(i) -> tt 1114.18/291.61 a__isQid(o) -> tt 1114.18/291.61 a__isQid(u) -> tt 1114.18/291.61 mark(__(X1, X2)) -> a____(mark(X1), mark(X2)) 1114.18/291.61 mark(U11(X)) -> a__U11(mark(X)) 1114.18/291.61 mark(U21(X1, X2)) -> a__U21(mark(X1), X2) 1114.18/291.61 mark(U22(X)) -> a__U22(mark(X)) 1114.18/291.61 mark(isList(X)) -> a__isList(X) 1114.18/291.61 mark(U31(X)) -> a__U31(mark(X)) 1114.18/291.61 mark(U41(X1, X2)) -> a__U41(mark(X1), X2) 1114.18/291.61 mark(U42(X)) -> a__U42(mark(X)) 1114.18/291.61 mark(isNeList(X)) -> a__isNeList(X) 1114.18/291.61 mark(U51(X1, X2)) -> a__U51(mark(X1), X2) 1114.18/291.61 mark(U52(X)) -> a__U52(mark(X)) 1114.18/291.61 mark(U61(X)) -> a__U61(mark(X)) 1114.18/291.61 mark(U71(X1, X2)) -> a__U71(mark(X1), X2) 1114.18/291.61 mark(U72(X)) -> a__U72(mark(X)) 1114.18/291.61 mark(isPal(X)) -> a__isPal(X) 1114.18/291.61 mark(U81(X)) -> a__U81(mark(X)) 1114.18/291.61 mark(isQid(X)) -> a__isQid(X) 1114.18/291.61 mark(isNePal(X)) -> a__isNePal(X) 1114.18/291.61 mark(nil) -> nil 1114.18/291.61 mark(tt) -> tt 1114.18/291.61 mark(a) -> a 1114.18/291.61 mark(e) -> e 1114.18/291.61 mark(i) -> i 1114.18/291.61 mark(o) -> o 1114.18/291.61 mark(u) -> u 1114.18/291.61 a____(X1, X2) -> __(X1, X2) 1114.18/291.61 a__U11(X) -> U11(X) 1114.18/291.61 a__U21(X1, X2) -> U21(X1, X2) 1114.18/291.61 a__U22(X) -> U22(X) 1114.18/291.61 a__isList(X) -> isList(X) 1114.18/291.61 a__U31(X) -> U31(X) 1114.18/291.61 a__U41(X1, X2) -> U41(X1, X2) 1114.18/291.61 a__U42(X) -> U42(X) 1114.18/291.61 a__isNeList(X) -> isNeList(X) 1114.18/291.61 a__U51(X1, X2) -> U51(X1, X2) 1114.18/291.61 a__U52(X) -> U52(X) 1114.18/291.61 a__U61(X) -> U61(X) 1114.18/291.61 a__U71(X1, X2) -> U71(X1, X2) 1114.18/291.61 a__U72(X) -> U72(X) 1114.18/291.61 a__isPal(X) -> isPal(X) 1114.18/291.61 a__U81(X) -> U81(X) 1114.18/291.61 a__isQid(X) -> isQid(X) 1114.18/291.61 a__isNePal(X) -> isNePal(X) 1114.18/291.61 1114.18/291.61 S is empty. 1114.18/291.61 Rewrite Strategy: FULL 1114.18/291.61 ---------------------------------------- 1114.18/291.61 1114.18/291.61 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1114.18/291.61 Transformed a relative TRS into a decreasing-loop problem. 1114.18/291.61 ---------------------------------------- 1114.18/291.61 1114.18/291.61 (2) 1114.18/291.61 Obligation: 1114.18/291.61 Analyzing the following TRS for decreasing loops: 1114.18/291.61 1114.18/291.61 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1114.18/291.61 1114.18/291.61 1114.18/291.61 The TRS R consists of the following rules: 1114.18/291.61 1114.18/291.61 a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z))) 1114.18/291.61 a____(X, nil) -> mark(X) 1114.18/291.61 a____(nil, X) -> mark(X) 1114.18/291.61 a__U11(tt) -> tt 1114.18/291.61 a__U21(tt, V2) -> a__U22(a__isList(V2)) 1114.18/291.61 a__U22(tt) -> tt 1114.18/291.61 a__U31(tt) -> tt 1114.18/291.61 a__U41(tt, V2) -> a__U42(a__isNeList(V2)) 1114.18/291.61 a__U42(tt) -> tt 1114.18/291.61 a__U51(tt, V2) -> a__U52(a__isList(V2)) 1114.18/291.61 a__U52(tt) -> tt 1114.18/291.61 a__U61(tt) -> tt 1114.18/291.61 a__U71(tt, P) -> a__U72(a__isPal(P)) 1114.18/291.61 a__U72(tt) -> tt 1114.18/291.61 a__U81(tt) -> tt 1114.18/291.61 a__isList(V) -> a__U11(a__isNeList(V)) 1114.18/291.61 a__isList(nil) -> tt 1114.18/291.61 a__isList(__(V1, V2)) -> a__U21(a__isList(V1), V2) 1114.18/291.61 a__isNeList(V) -> a__U31(a__isQid(V)) 1114.18/291.61 a__isNeList(__(V1, V2)) -> a__U41(a__isList(V1), V2) 1114.18/291.61 a__isNeList(__(V1, V2)) -> a__U51(a__isNeList(V1), V2) 1114.18/291.61 a__isNePal(V) -> a__U61(a__isQid(V)) 1114.18/291.61 a__isNePal(__(I, __(P, I))) -> a__U71(a__isQid(I), P) 1114.18/291.61 a__isPal(V) -> a__U81(a__isNePal(V)) 1114.18/291.61 a__isPal(nil) -> tt 1114.18/291.61 a__isQid(a) -> tt 1114.18/291.61 a__isQid(e) -> tt 1114.18/291.61 a__isQid(i) -> tt 1114.18/291.61 a__isQid(o) -> tt 1114.18/291.61 a__isQid(u) -> tt 1114.18/291.61 mark(__(X1, X2)) -> a____(mark(X1), mark(X2)) 1114.18/291.61 mark(U11(X)) -> a__U11(mark(X)) 1114.18/291.61 mark(U21(X1, X2)) -> a__U21(mark(X1), X2) 1114.18/291.61 mark(U22(X)) -> a__U22(mark(X)) 1114.18/291.61 mark(isList(X)) -> a__isList(X) 1114.18/291.61 mark(U31(X)) -> a__U31(mark(X)) 1114.18/291.61 mark(U41(X1, X2)) -> a__U41(mark(X1), X2) 1114.18/291.61 mark(U42(X)) -> a__U42(mark(X)) 1114.18/291.61 mark(isNeList(X)) -> a__isNeList(X) 1114.18/291.61 mark(U51(X1, X2)) -> a__U51(mark(X1), X2) 1114.18/291.61 mark(U52(X)) -> a__U52(mark(X)) 1114.18/291.61 mark(U61(X)) -> a__U61(mark(X)) 1114.18/291.61 mark(U71(X1, X2)) -> a__U71(mark(X1), X2) 1114.18/291.61 mark(U72(X)) -> a__U72(mark(X)) 1114.18/291.61 mark(isPal(X)) -> a__isPal(X) 1114.18/291.61 mark(U81(X)) -> a__U81(mark(X)) 1114.18/291.61 mark(isQid(X)) -> a__isQid(X) 1114.18/291.61 mark(isNePal(X)) -> a__isNePal(X) 1114.18/291.61 mark(nil) -> nil 1114.18/291.61 mark(tt) -> tt 1114.18/291.61 mark(a) -> a 1114.18/291.61 mark(e) -> e 1114.18/291.61 mark(i) -> i 1114.18/291.61 mark(o) -> o 1114.18/291.61 mark(u) -> u 1114.18/291.61 a____(X1, X2) -> __(X1, X2) 1114.18/291.61 a__U11(X) -> U11(X) 1114.18/291.61 a__U21(X1, X2) -> U21(X1, X2) 1114.18/291.61 a__U22(X) -> U22(X) 1114.18/291.61 a__isList(X) -> isList(X) 1114.18/291.61 a__U31(X) -> U31(X) 1114.18/291.61 a__U41(X1, X2) -> U41(X1, X2) 1114.18/291.61 a__U42(X) -> U42(X) 1114.18/291.61 a__isNeList(X) -> isNeList(X) 1114.18/291.61 a__U51(X1, X2) -> U51(X1, X2) 1114.18/291.61 a__U52(X) -> U52(X) 1114.18/291.61 a__U61(X) -> U61(X) 1114.18/291.61 a__U71(X1, X2) -> U71(X1, X2) 1114.18/291.61 a__U72(X) -> U72(X) 1114.18/291.61 a__isPal(X) -> isPal(X) 1114.18/291.61 a__U81(X) -> U81(X) 1114.18/291.61 a__isQid(X) -> isQid(X) 1114.18/291.61 a__isNePal(X) -> isNePal(X) 1114.18/291.61 1114.18/291.61 S is empty. 1114.18/291.61 Rewrite Strategy: FULL 1114.18/291.61 ---------------------------------------- 1114.18/291.61 1114.18/291.61 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1114.18/291.61 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1114.18/291.61 1114.18/291.61 The rewrite sequence 1114.18/291.61 1114.18/291.61 mark(U41(X1, X2)) ->^+ a__U41(mark(X1), X2) 1114.18/291.61 1114.18/291.61 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 1114.18/291.61 1114.18/291.61 The pumping substitution is [X1 / U41(X1, X2)]. 1114.18/291.61 1114.18/291.61 The result substitution is [ ]. 1114.18/291.61 1114.18/291.61 1114.18/291.61 1114.18/291.61 1114.18/291.61 ---------------------------------------- 1114.18/291.61 1114.18/291.61 (4) 1114.18/291.61 Complex Obligation (BEST) 1114.18/291.61 1114.18/291.61 ---------------------------------------- 1114.18/291.61 1114.18/291.61 (5) 1114.18/291.61 Obligation: 1114.18/291.61 Proved the lower bound n^1 for the following obligation: 1114.18/291.61 1114.18/291.61 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1114.18/291.61 1114.18/291.61 1114.18/291.61 The TRS R consists of the following rules: 1114.18/291.61 1114.18/291.61 a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z))) 1114.18/291.61 a____(X, nil) -> mark(X) 1114.18/291.61 a____(nil, X) -> mark(X) 1114.18/291.61 a__U11(tt) -> tt 1114.18/291.61 a__U21(tt, V2) -> a__U22(a__isList(V2)) 1114.18/291.61 a__U22(tt) -> tt 1114.18/291.61 a__U31(tt) -> tt 1114.18/291.61 a__U41(tt, V2) -> a__U42(a__isNeList(V2)) 1114.18/291.61 a__U42(tt) -> tt 1114.18/291.61 a__U51(tt, V2) -> a__U52(a__isList(V2)) 1114.18/291.61 a__U52(tt) -> tt 1114.18/291.61 a__U61(tt) -> tt 1114.18/291.61 a__U71(tt, P) -> a__U72(a__isPal(P)) 1114.18/291.61 a__U72(tt) -> tt 1114.18/291.61 a__U81(tt) -> tt 1114.18/291.61 a__isList(V) -> a__U11(a__isNeList(V)) 1114.18/291.61 a__isList(nil) -> tt 1114.18/291.61 a__isList(__(V1, V2)) -> a__U21(a__isList(V1), V2) 1114.18/291.61 a__isNeList(V) -> a__U31(a__isQid(V)) 1114.18/291.61 a__isNeList(__(V1, V2)) -> a__U41(a__isList(V1), V2) 1114.18/291.61 a__isNeList(__(V1, V2)) -> a__U51(a__isNeList(V1), V2) 1114.18/291.61 a__isNePal(V) -> a__U61(a__isQid(V)) 1114.18/291.61 a__isNePal(__(I, __(P, I))) -> a__U71(a__isQid(I), P) 1114.18/291.61 a__isPal(V) -> a__U81(a__isNePal(V)) 1114.18/291.61 a__isPal(nil) -> tt 1114.18/291.61 a__isQid(a) -> tt 1114.18/291.61 a__isQid(e) -> tt 1114.18/291.61 a__isQid(i) -> tt 1114.18/291.61 a__isQid(o) -> tt 1114.18/291.61 a__isQid(u) -> tt 1114.18/291.61 mark(__(X1, X2)) -> a____(mark(X1), mark(X2)) 1114.18/291.61 mark(U11(X)) -> a__U11(mark(X)) 1114.18/291.61 mark(U21(X1, X2)) -> a__U21(mark(X1), X2) 1114.18/291.61 mark(U22(X)) -> a__U22(mark(X)) 1114.18/291.61 mark(isList(X)) -> a__isList(X) 1114.18/291.61 mark(U31(X)) -> a__U31(mark(X)) 1114.18/291.61 mark(U41(X1, X2)) -> a__U41(mark(X1), X2) 1114.18/291.61 mark(U42(X)) -> a__U42(mark(X)) 1114.18/291.61 mark(isNeList(X)) -> a__isNeList(X) 1114.18/291.61 mark(U51(X1, X2)) -> a__U51(mark(X1), X2) 1114.18/291.61 mark(U52(X)) -> a__U52(mark(X)) 1114.18/291.61 mark(U61(X)) -> a__U61(mark(X)) 1114.18/291.61 mark(U71(X1, X2)) -> a__U71(mark(X1), X2) 1114.18/291.61 mark(U72(X)) -> a__U72(mark(X)) 1114.18/291.61 mark(isPal(X)) -> a__isPal(X) 1114.18/291.61 mark(U81(X)) -> a__U81(mark(X)) 1114.18/291.61 mark(isQid(X)) -> a__isQid(X) 1114.18/291.61 mark(isNePal(X)) -> a__isNePal(X) 1114.18/291.61 mark(nil) -> nil 1114.18/291.61 mark(tt) -> tt 1114.18/291.61 mark(a) -> a 1114.18/291.61 mark(e) -> e 1114.18/291.61 mark(i) -> i 1114.18/291.61 mark(o) -> o 1114.18/291.61 mark(u) -> u 1114.18/291.61 a____(X1, X2) -> __(X1, X2) 1114.18/291.61 a__U11(X) -> U11(X) 1114.18/291.61 a__U21(X1, X2) -> U21(X1, X2) 1114.18/291.61 a__U22(X) -> U22(X) 1114.18/291.61 a__isList(X) -> isList(X) 1114.18/291.61 a__U31(X) -> U31(X) 1114.18/291.61 a__U41(X1, X2) -> U41(X1, X2) 1114.18/291.61 a__U42(X) -> U42(X) 1114.18/291.61 a__isNeList(X) -> isNeList(X) 1114.18/291.61 a__U51(X1, X2) -> U51(X1, X2) 1114.18/291.61 a__U52(X) -> U52(X) 1114.18/291.61 a__U61(X) -> U61(X) 1114.18/291.61 a__U71(X1, X2) -> U71(X1, X2) 1114.18/291.61 a__U72(X) -> U72(X) 1114.18/291.61 a__isPal(X) -> isPal(X) 1114.18/291.61 a__U81(X) -> U81(X) 1114.18/291.61 a__isQid(X) -> isQid(X) 1114.18/291.61 a__isNePal(X) -> isNePal(X) 1114.18/291.61 1114.18/291.61 S is empty. 1114.18/291.61 Rewrite Strategy: FULL 1114.18/291.61 ---------------------------------------- 1114.18/291.61 1114.18/291.61 (6) LowerBoundPropagationProof (FINISHED) 1114.18/291.61 Propagated lower bound. 1114.18/291.61 ---------------------------------------- 1114.18/291.61 1114.18/291.61 (7) 1114.18/291.61 BOUNDS(n^1, INF) 1114.18/291.61 1114.18/291.61 ---------------------------------------- 1114.18/291.61 1114.18/291.61 (8) 1114.18/291.61 Obligation: 1114.18/291.61 Analyzing the following TRS for decreasing loops: 1114.18/291.61 1114.18/291.61 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1114.18/291.61 1114.18/291.61 1114.18/291.61 The TRS R consists of the following rules: 1114.18/291.61 1114.18/291.61 a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z))) 1114.18/291.61 a____(X, nil) -> mark(X) 1114.18/291.61 a____(nil, X) -> mark(X) 1114.18/291.61 a__U11(tt) -> tt 1114.18/291.61 a__U21(tt, V2) -> a__U22(a__isList(V2)) 1114.18/291.61 a__U22(tt) -> tt 1114.18/291.61 a__U31(tt) -> tt 1114.18/291.61 a__U41(tt, V2) -> a__U42(a__isNeList(V2)) 1114.18/291.61 a__U42(tt) -> tt 1114.18/291.61 a__U51(tt, V2) -> a__U52(a__isList(V2)) 1114.18/291.61 a__U52(tt) -> tt 1114.18/291.61 a__U61(tt) -> tt 1114.18/291.61 a__U71(tt, P) -> a__U72(a__isPal(P)) 1114.18/291.61 a__U72(tt) -> tt 1114.18/291.61 a__U81(tt) -> tt 1114.18/291.61 a__isList(V) -> a__U11(a__isNeList(V)) 1114.18/291.61 a__isList(nil) -> tt 1114.18/291.61 a__isList(__(V1, V2)) -> a__U21(a__isList(V1), V2) 1114.18/291.61 a__isNeList(V) -> a__U31(a__isQid(V)) 1114.18/291.61 a__isNeList(__(V1, V2)) -> a__U41(a__isList(V1), V2) 1114.18/291.61 a__isNeList(__(V1, V2)) -> a__U51(a__isNeList(V1), V2) 1114.18/291.61 a__isNePal(V) -> a__U61(a__isQid(V)) 1114.18/291.61 a__isNePal(__(I, __(P, I))) -> a__U71(a__isQid(I), P) 1114.18/291.61 a__isPal(V) -> a__U81(a__isNePal(V)) 1114.18/291.61 a__isPal(nil) -> tt 1114.18/291.61 a__isQid(a) -> tt 1114.18/291.61 a__isQid(e) -> tt 1114.18/291.61 a__isQid(i) -> tt 1114.18/291.61 a__isQid(o) -> tt 1114.18/291.61 a__isQid(u) -> tt 1114.18/291.61 mark(__(X1, X2)) -> a____(mark(X1), mark(X2)) 1114.18/291.61 mark(U11(X)) -> a__U11(mark(X)) 1114.18/291.61 mark(U21(X1, X2)) -> a__U21(mark(X1), X2) 1114.18/291.61 mark(U22(X)) -> a__U22(mark(X)) 1114.18/291.61 mark(isList(X)) -> a__isList(X) 1114.18/291.61 mark(U31(X)) -> a__U31(mark(X)) 1114.18/291.61 mark(U41(X1, X2)) -> a__U41(mark(X1), X2) 1114.18/291.61 mark(U42(X)) -> a__U42(mark(X)) 1114.18/291.61 mark(isNeList(X)) -> a__isNeList(X) 1114.18/291.61 mark(U51(X1, X2)) -> a__U51(mark(X1), X2) 1114.18/291.61 mark(U52(X)) -> a__U52(mark(X)) 1114.18/291.61 mark(U61(X)) -> a__U61(mark(X)) 1114.18/291.61 mark(U71(X1, X2)) -> a__U71(mark(X1), X2) 1114.18/291.61 mark(U72(X)) -> a__U72(mark(X)) 1114.18/291.61 mark(isPal(X)) -> a__isPal(X) 1114.18/291.61 mark(U81(X)) -> a__U81(mark(X)) 1114.18/291.61 mark(isQid(X)) -> a__isQid(X) 1114.18/291.61 mark(isNePal(X)) -> a__isNePal(X) 1114.18/291.61 mark(nil) -> nil 1114.18/291.61 mark(tt) -> tt 1114.18/291.61 mark(a) -> a 1114.18/291.61 mark(e) -> e 1114.18/291.61 mark(i) -> i 1114.18/291.61 mark(o) -> o 1114.18/291.61 mark(u) -> u 1114.18/291.61 a____(X1, X2) -> __(X1, X2) 1114.18/291.61 a__U11(X) -> U11(X) 1114.18/291.61 a__U21(X1, X2) -> U21(X1, X2) 1114.18/291.61 a__U22(X) -> U22(X) 1114.18/291.61 a__isList(X) -> isList(X) 1114.18/291.61 a__U31(X) -> U31(X) 1114.18/291.61 a__U41(X1, X2) -> U41(X1, X2) 1114.18/291.61 a__U42(X) -> U42(X) 1114.18/291.61 a__isNeList(X) -> isNeList(X) 1114.18/291.61 a__U51(X1, X2) -> U51(X1, X2) 1114.18/291.61 a__U52(X) -> U52(X) 1114.18/291.61 a__U61(X) -> U61(X) 1114.18/291.61 a__U71(X1, X2) -> U71(X1, X2) 1114.18/291.61 a__U72(X) -> U72(X) 1114.18/291.61 a__isPal(X) -> isPal(X) 1114.18/291.61 a__U81(X) -> U81(X) 1114.18/291.61 a__isQid(X) -> isQid(X) 1114.18/291.61 a__isNePal(X) -> isNePal(X) 1114.18/291.61 1114.18/291.61 S is empty. 1114.18/291.61 Rewrite Strategy: FULL 1114.23/291.67 EOF