/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(NON_POLY, ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). (0) CpxTRS (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (2) TRS for Loop Detection (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (4) BEST (5) proven lower bound (6) LowerBoundPropagationProof [FINISHED, 0 ms] (7) BOUNDS(n^1, INF) (8) TRS for Loop Detection (9) DecreasingLoopProof [FINISHED, 370 ms] (10) BOUNDS(EXP, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). The TRS R consists of the following rules: U101(tt, V2) -> U102(isLNat(activate(V2))) U102(tt) -> tt U11(tt, N, XS) -> U12(isLNat(activate(XS)), activate(N), activate(XS)) U111(tt) -> tt U12(tt, N, XS) -> snd(splitAt(activate(N), activate(XS))) U121(tt) -> tt U131(tt, V2) -> U132(isLNat(activate(V2))) U132(tt) -> tt U141(tt, V2) -> U142(isLNat(activate(V2))) U142(tt) -> tt U151(tt, V2) -> U152(isLNat(activate(V2))) U152(tt) -> tt U161(tt, N) -> cons(activate(N), n__natsFrom(n__s(activate(N)))) U171(tt, N, XS) -> U172(isLNat(activate(XS)), activate(N), activate(XS)) U172(tt, N, XS) -> head(afterNth(activate(N), activate(XS))) U181(tt, Y) -> U182(isLNat(activate(Y)), activate(Y)) U182(tt, Y) -> activate(Y) U191(tt, XS) -> pair(nil, activate(XS)) U201(tt, N, X, XS) -> U202(isNatural(activate(X)), activate(N), activate(X), activate(XS)) U202(tt, N, X, XS) -> U203(isLNat(activate(XS)), activate(N), activate(X), activate(XS)) U203(tt, N, X, XS) -> U204(splitAt(activate(N), activate(XS)), activate(X)) U204(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) U21(tt, X, Y) -> U22(isLNat(activate(Y)), activate(X)) U211(tt, XS) -> U212(isLNat(activate(XS)), activate(XS)) U212(tt, XS) -> activate(XS) U22(tt, X) -> activate(X) U221(tt, N, XS) -> U222(isLNat(activate(XS)), activate(N), activate(XS)) U222(tt, N, XS) -> fst(splitAt(activate(N), activate(XS))) U31(tt, N, XS) -> U32(isLNat(activate(XS)), activate(N)) U32(tt, N) -> activate(N) U41(tt, V2) -> U42(isLNat(activate(V2))) U42(tt) -> tt U51(tt, V2) -> U52(isLNat(activate(V2))) U52(tt) -> tt U61(tt) -> tt U71(tt) -> tt U81(tt) -> tt U91(tt) -> tt afterNth(N, XS) -> U11(isNatural(N), N, XS) fst(pair(X, Y)) -> U21(isLNat(X), X, Y) head(cons(N, XS)) -> U31(isNatural(N), N, activate(XS)) isLNat(n__nil) -> tt isLNat(n__afterNth(V1, V2)) -> U41(isNatural(activate(V1)), activate(V2)) isLNat(n__cons(V1, V2)) -> U51(isNatural(activate(V1)), activate(V2)) isLNat(n__fst(V1)) -> U61(isPLNat(activate(V1))) isLNat(n__natsFrom(V1)) -> U71(isNatural(activate(V1))) isLNat(n__snd(V1)) -> U81(isPLNat(activate(V1))) isLNat(n__tail(V1)) -> U91(isLNat(activate(V1))) isLNat(n__take(V1, V2)) -> U101(isNatural(activate(V1)), activate(V2)) isNatural(n__0) -> tt isNatural(n__head(V1)) -> U111(isLNat(activate(V1))) isNatural(n__s(V1)) -> U121(isNatural(activate(V1))) isNatural(n__sel(V1, V2)) -> U131(isNatural(activate(V1)), activate(V2)) isPLNat(n__pair(V1, V2)) -> U141(isLNat(activate(V1)), activate(V2)) isPLNat(n__splitAt(V1, V2)) -> U151(isNatural(activate(V1)), activate(V2)) natsFrom(N) -> U161(isNatural(N), N) sel(N, XS) -> U171(isNatural(N), N, XS) snd(pair(X, Y)) -> U181(isLNat(X), Y) splitAt(0, XS) -> U191(isLNat(XS), XS) splitAt(s(N), cons(X, XS)) -> U201(isNatural(N), N, X, activate(XS)) tail(cons(N, XS)) -> U211(isNatural(N), activate(XS)) take(N, XS) -> U221(isNatural(N), N, XS) natsFrom(X) -> n__natsFrom(X) s(X) -> n__s(X) nil -> n__nil afterNth(X1, X2) -> n__afterNth(X1, X2) cons(X1, X2) -> n__cons(X1, X2) fst(X) -> n__fst(X) snd(X) -> n__snd(X) tail(X) -> n__tail(X) take(X1, X2) -> n__take(X1, X2) 0 -> n__0 head(X) -> n__head(X) sel(X1, X2) -> n__sel(X1, X2) pair(X1, X2) -> n__pair(X1, X2) splitAt(X1, X2) -> n__splitAt(X1, X2) activate(n__natsFrom(X)) -> natsFrom(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__nil) -> nil activate(n__afterNth(X1, X2)) -> afterNth(activate(X1), activate(X2)) activate(n__cons(X1, X2)) -> cons(activate(X1), X2) activate(n__fst(X)) -> fst(activate(X)) activate(n__snd(X)) -> snd(activate(X)) activate(n__tail(X)) -> tail(activate(X)) activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)) activate(n__0) -> 0 activate(n__head(X)) -> head(activate(X)) activate(n__sel(X1, X2)) -> sel(activate(X1), activate(X2)) activate(n__pair(X1, X2)) -> pair(activate(X1), activate(X2)) activate(n__splitAt(X1, X2)) -> splitAt(activate(X1), activate(X2)) activate(X) -> X S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (2) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). The TRS R consists of the following rules: U101(tt, V2) -> U102(isLNat(activate(V2))) U102(tt) -> tt U11(tt, N, XS) -> U12(isLNat(activate(XS)), activate(N), activate(XS)) U111(tt) -> tt U12(tt, N, XS) -> snd(splitAt(activate(N), activate(XS))) U121(tt) -> tt U131(tt, V2) -> U132(isLNat(activate(V2))) U132(tt) -> tt U141(tt, V2) -> U142(isLNat(activate(V2))) U142(tt) -> tt U151(tt, V2) -> U152(isLNat(activate(V2))) U152(tt) -> tt U161(tt, N) -> cons(activate(N), n__natsFrom(n__s(activate(N)))) U171(tt, N, XS) -> U172(isLNat(activate(XS)), activate(N), activate(XS)) U172(tt, N, XS) -> head(afterNth(activate(N), activate(XS))) U181(tt, Y) -> U182(isLNat(activate(Y)), activate(Y)) U182(tt, Y) -> activate(Y) U191(tt, XS) -> pair(nil, activate(XS)) U201(tt, N, X, XS) -> U202(isNatural(activate(X)), activate(N), activate(X), activate(XS)) U202(tt, N, X, XS) -> U203(isLNat(activate(XS)), activate(N), activate(X), activate(XS)) U203(tt, N, X, XS) -> U204(splitAt(activate(N), activate(XS)), activate(X)) U204(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) U21(tt, X, Y) -> U22(isLNat(activate(Y)), activate(X)) U211(tt, XS) -> U212(isLNat(activate(XS)), activate(XS)) U212(tt, XS) -> activate(XS) U22(tt, X) -> activate(X) U221(tt, N, XS) -> U222(isLNat(activate(XS)), activate(N), activate(XS)) U222(tt, N, XS) -> fst(splitAt(activate(N), activate(XS))) U31(tt, N, XS) -> U32(isLNat(activate(XS)), activate(N)) U32(tt, N) -> activate(N) U41(tt, V2) -> U42(isLNat(activate(V2))) U42(tt) -> tt U51(tt, V2) -> U52(isLNat(activate(V2))) U52(tt) -> tt U61(tt) -> tt U71(tt) -> tt U81(tt) -> tt U91(tt) -> tt afterNth(N, XS) -> U11(isNatural(N), N, XS) fst(pair(X, Y)) -> U21(isLNat(X), X, Y) head(cons(N, XS)) -> U31(isNatural(N), N, activate(XS)) isLNat(n__nil) -> tt isLNat(n__afterNth(V1, V2)) -> U41(isNatural(activate(V1)), activate(V2)) isLNat(n__cons(V1, V2)) -> U51(isNatural(activate(V1)), activate(V2)) isLNat(n__fst(V1)) -> U61(isPLNat(activate(V1))) isLNat(n__natsFrom(V1)) -> U71(isNatural(activate(V1))) isLNat(n__snd(V1)) -> U81(isPLNat(activate(V1))) isLNat(n__tail(V1)) -> U91(isLNat(activate(V1))) isLNat(n__take(V1, V2)) -> U101(isNatural(activate(V1)), activate(V2)) isNatural(n__0) -> tt isNatural(n__head(V1)) -> U111(isLNat(activate(V1))) isNatural(n__s(V1)) -> U121(isNatural(activate(V1))) isNatural(n__sel(V1, V2)) -> U131(isNatural(activate(V1)), activate(V2)) isPLNat(n__pair(V1, V2)) -> U141(isLNat(activate(V1)), activate(V2)) isPLNat(n__splitAt(V1, V2)) -> U151(isNatural(activate(V1)), activate(V2)) natsFrom(N) -> U161(isNatural(N), N) sel(N, XS) -> U171(isNatural(N), N, XS) snd(pair(X, Y)) -> U181(isLNat(X), Y) splitAt(0, XS) -> U191(isLNat(XS), XS) splitAt(s(N), cons(X, XS)) -> U201(isNatural(N), N, X, activate(XS)) tail(cons(N, XS)) -> U211(isNatural(N), activate(XS)) take(N, XS) -> U221(isNatural(N), N, XS) natsFrom(X) -> n__natsFrom(X) s(X) -> n__s(X) nil -> n__nil afterNth(X1, X2) -> n__afterNth(X1, X2) cons(X1, X2) -> n__cons(X1, X2) fst(X) -> n__fst(X) snd(X) -> n__snd(X) tail(X) -> n__tail(X) take(X1, X2) -> n__take(X1, X2) 0 -> n__0 head(X) -> n__head(X) sel(X1, X2) -> n__sel(X1, X2) pair(X1, X2) -> n__pair(X1, X2) splitAt(X1, X2) -> n__splitAt(X1, X2) activate(n__natsFrom(X)) -> natsFrom(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__nil) -> nil activate(n__afterNth(X1, X2)) -> afterNth(activate(X1), activate(X2)) activate(n__cons(X1, X2)) -> cons(activate(X1), X2) activate(n__fst(X)) -> fst(activate(X)) activate(n__snd(X)) -> snd(activate(X)) activate(n__tail(X)) -> tail(activate(X)) activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)) activate(n__0) -> 0 activate(n__head(X)) -> head(activate(X)) activate(n__sel(X1, X2)) -> sel(activate(X1), activate(X2)) activate(n__pair(X1, X2)) -> pair(activate(X1), activate(X2)) activate(n__splitAt(X1, X2)) -> splitAt(activate(X1), activate(X2)) activate(X) -> X S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) DecreasingLoopProof (LOWER BOUND(ID)) The following loop(s) give(s) rise to the lower bound Omega(n^1): The rewrite sequence activate(n__snd(X)) ->^+ snd(activate(X)) gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. The pumping substitution is [X / n__snd(X)]. The result substitution is [ ]. ---------------------------------------- (4) Complex Obligation (BEST) ---------------------------------------- (5) Obligation: Proved the lower bound n^1 for the following obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). The TRS R consists of the following rules: U101(tt, V2) -> U102(isLNat(activate(V2))) U102(tt) -> tt U11(tt, N, XS) -> U12(isLNat(activate(XS)), activate(N), activate(XS)) U111(tt) -> tt U12(tt, N, XS) -> snd(splitAt(activate(N), activate(XS))) U121(tt) -> tt U131(tt, V2) -> U132(isLNat(activate(V2))) U132(tt) -> tt U141(tt, V2) -> U142(isLNat(activate(V2))) U142(tt) -> tt U151(tt, V2) -> U152(isLNat(activate(V2))) U152(tt) -> tt U161(tt, N) -> cons(activate(N), n__natsFrom(n__s(activate(N)))) U171(tt, N, XS) -> U172(isLNat(activate(XS)), activate(N), activate(XS)) U172(tt, N, XS) -> head(afterNth(activate(N), activate(XS))) U181(tt, Y) -> U182(isLNat(activate(Y)), activate(Y)) U182(tt, Y) -> activate(Y) U191(tt, XS) -> pair(nil, activate(XS)) U201(tt, N, X, XS) -> U202(isNatural(activate(X)), activate(N), activate(X), activate(XS)) U202(tt, N, X, XS) -> U203(isLNat(activate(XS)), activate(N), activate(X), activate(XS)) U203(tt, N, X, XS) -> U204(splitAt(activate(N), activate(XS)), activate(X)) U204(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) U21(tt, X, Y) -> U22(isLNat(activate(Y)), activate(X)) U211(tt, XS) -> U212(isLNat(activate(XS)), activate(XS)) U212(tt, XS) -> activate(XS) U22(tt, X) -> activate(X) U221(tt, N, XS) -> U222(isLNat(activate(XS)), activate(N), activate(XS)) U222(tt, N, XS) -> fst(splitAt(activate(N), activate(XS))) U31(tt, N, XS) -> U32(isLNat(activate(XS)), activate(N)) U32(tt, N) -> activate(N) U41(tt, V2) -> U42(isLNat(activate(V2))) U42(tt) -> tt U51(tt, V2) -> U52(isLNat(activate(V2))) U52(tt) -> tt U61(tt) -> tt U71(tt) -> tt U81(tt) -> tt U91(tt) -> tt afterNth(N, XS) -> U11(isNatural(N), N, XS) fst(pair(X, Y)) -> U21(isLNat(X), X, Y) head(cons(N, XS)) -> U31(isNatural(N), N, activate(XS)) isLNat(n__nil) -> tt isLNat(n__afterNth(V1, V2)) -> U41(isNatural(activate(V1)), activate(V2)) isLNat(n__cons(V1, V2)) -> U51(isNatural(activate(V1)), activate(V2)) isLNat(n__fst(V1)) -> U61(isPLNat(activate(V1))) isLNat(n__natsFrom(V1)) -> U71(isNatural(activate(V1))) isLNat(n__snd(V1)) -> U81(isPLNat(activate(V1))) isLNat(n__tail(V1)) -> U91(isLNat(activate(V1))) isLNat(n__take(V1, V2)) -> U101(isNatural(activate(V1)), activate(V2)) isNatural(n__0) -> tt isNatural(n__head(V1)) -> U111(isLNat(activate(V1))) isNatural(n__s(V1)) -> U121(isNatural(activate(V1))) isNatural(n__sel(V1, V2)) -> U131(isNatural(activate(V1)), activate(V2)) isPLNat(n__pair(V1, V2)) -> U141(isLNat(activate(V1)), activate(V2)) isPLNat(n__splitAt(V1, V2)) -> U151(isNatural(activate(V1)), activate(V2)) natsFrom(N) -> U161(isNatural(N), N) sel(N, XS) -> U171(isNatural(N), N, XS) snd(pair(X, Y)) -> U181(isLNat(X), Y) splitAt(0, XS) -> U191(isLNat(XS), XS) splitAt(s(N), cons(X, XS)) -> U201(isNatural(N), N, X, activate(XS)) tail(cons(N, XS)) -> U211(isNatural(N), activate(XS)) take(N, XS) -> U221(isNatural(N), N, XS) natsFrom(X) -> n__natsFrom(X) s(X) -> n__s(X) nil -> n__nil afterNth(X1, X2) -> n__afterNth(X1, X2) cons(X1, X2) -> n__cons(X1, X2) fst(X) -> n__fst(X) snd(X) -> n__snd(X) tail(X) -> n__tail(X) take(X1, X2) -> n__take(X1, X2) 0 -> n__0 head(X) -> n__head(X) sel(X1, X2) -> n__sel(X1, X2) pair(X1, X2) -> n__pair(X1, X2) splitAt(X1, X2) -> n__splitAt(X1, X2) activate(n__natsFrom(X)) -> natsFrom(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__nil) -> nil activate(n__afterNth(X1, X2)) -> afterNth(activate(X1), activate(X2)) activate(n__cons(X1, X2)) -> cons(activate(X1), X2) activate(n__fst(X)) -> fst(activate(X)) activate(n__snd(X)) -> snd(activate(X)) activate(n__tail(X)) -> tail(activate(X)) activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)) activate(n__0) -> 0 activate(n__head(X)) -> head(activate(X)) activate(n__sel(X1, X2)) -> sel(activate(X1), activate(X2)) activate(n__pair(X1, X2)) -> pair(activate(X1), activate(X2)) activate(n__splitAt(X1, X2)) -> splitAt(activate(X1), activate(X2)) activate(X) -> X S is empty. Rewrite Strategy: FULL ---------------------------------------- (6) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (7) BOUNDS(n^1, INF) ---------------------------------------- (8) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). The TRS R consists of the following rules: U101(tt, V2) -> U102(isLNat(activate(V2))) U102(tt) -> tt U11(tt, N, XS) -> U12(isLNat(activate(XS)), activate(N), activate(XS)) U111(tt) -> tt U12(tt, N, XS) -> snd(splitAt(activate(N), activate(XS))) U121(tt) -> tt U131(tt, V2) -> U132(isLNat(activate(V2))) U132(tt) -> tt U141(tt, V2) -> U142(isLNat(activate(V2))) U142(tt) -> tt U151(tt, V2) -> U152(isLNat(activate(V2))) U152(tt) -> tt U161(tt, N) -> cons(activate(N), n__natsFrom(n__s(activate(N)))) U171(tt, N, XS) -> U172(isLNat(activate(XS)), activate(N), activate(XS)) U172(tt, N, XS) -> head(afterNth(activate(N), activate(XS))) U181(tt, Y) -> U182(isLNat(activate(Y)), activate(Y)) U182(tt, Y) -> activate(Y) U191(tt, XS) -> pair(nil, activate(XS)) U201(tt, N, X, XS) -> U202(isNatural(activate(X)), activate(N), activate(X), activate(XS)) U202(tt, N, X, XS) -> U203(isLNat(activate(XS)), activate(N), activate(X), activate(XS)) U203(tt, N, X, XS) -> U204(splitAt(activate(N), activate(XS)), activate(X)) U204(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) U21(tt, X, Y) -> U22(isLNat(activate(Y)), activate(X)) U211(tt, XS) -> U212(isLNat(activate(XS)), activate(XS)) U212(tt, XS) -> activate(XS) U22(tt, X) -> activate(X) U221(tt, N, XS) -> U222(isLNat(activate(XS)), activate(N), activate(XS)) U222(tt, N, XS) -> fst(splitAt(activate(N), activate(XS))) U31(tt, N, XS) -> U32(isLNat(activate(XS)), activate(N)) U32(tt, N) -> activate(N) U41(tt, V2) -> U42(isLNat(activate(V2))) U42(tt) -> tt U51(tt, V2) -> U52(isLNat(activate(V2))) U52(tt) -> tt U61(tt) -> tt U71(tt) -> tt U81(tt) -> tt U91(tt) -> tt afterNth(N, XS) -> U11(isNatural(N), N, XS) fst(pair(X, Y)) -> U21(isLNat(X), X, Y) head(cons(N, XS)) -> U31(isNatural(N), N, activate(XS)) isLNat(n__nil) -> tt isLNat(n__afterNth(V1, V2)) -> U41(isNatural(activate(V1)), activate(V2)) isLNat(n__cons(V1, V2)) -> U51(isNatural(activate(V1)), activate(V2)) isLNat(n__fst(V1)) -> U61(isPLNat(activate(V1))) isLNat(n__natsFrom(V1)) -> U71(isNatural(activate(V1))) isLNat(n__snd(V1)) -> U81(isPLNat(activate(V1))) isLNat(n__tail(V1)) -> U91(isLNat(activate(V1))) isLNat(n__take(V1, V2)) -> U101(isNatural(activate(V1)), activate(V2)) isNatural(n__0) -> tt isNatural(n__head(V1)) -> U111(isLNat(activate(V1))) isNatural(n__s(V1)) -> U121(isNatural(activate(V1))) isNatural(n__sel(V1, V2)) -> U131(isNatural(activate(V1)), activate(V2)) isPLNat(n__pair(V1, V2)) -> U141(isLNat(activate(V1)), activate(V2)) isPLNat(n__splitAt(V1, V2)) -> U151(isNatural(activate(V1)), activate(V2)) natsFrom(N) -> U161(isNatural(N), N) sel(N, XS) -> U171(isNatural(N), N, XS) snd(pair(X, Y)) -> U181(isLNat(X), Y) splitAt(0, XS) -> U191(isLNat(XS), XS) splitAt(s(N), cons(X, XS)) -> U201(isNatural(N), N, X, activate(XS)) tail(cons(N, XS)) -> U211(isNatural(N), activate(XS)) take(N, XS) -> U221(isNatural(N), N, XS) natsFrom(X) -> n__natsFrom(X) s(X) -> n__s(X) nil -> n__nil afterNth(X1, X2) -> n__afterNth(X1, X2) cons(X1, X2) -> n__cons(X1, X2) fst(X) -> n__fst(X) snd(X) -> n__snd(X) tail(X) -> n__tail(X) take(X1, X2) -> n__take(X1, X2) 0 -> n__0 head(X) -> n__head(X) sel(X1, X2) -> n__sel(X1, X2) pair(X1, X2) -> n__pair(X1, X2) splitAt(X1, X2) -> n__splitAt(X1, X2) activate(n__natsFrom(X)) -> natsFrom(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__nil) -> nil activate(n__afterNth(X1, X2)) -> afterNth(activate(X1), activate(X2)) activate(n__cons(X1, X2)) -> cons(activate(X1), X2) activate(n__fst(X)) -> fst(activate(X)) activate(n__snd(X)) -> snd(activate(X)) activate(n__tail(X)) -> tail(activate(X)) activate(n__take(X1, X2)) -> take(activate(X1), activate(X2)) activate(n__0) -> 0 activate(n__head(X)) -> head(activate(X)) activate(n__sel(X1, X2)) -> sel(activate(X1), activate(X2)) activate(n__pair(X1, X2)) -> pair(activate(X1), activate(X2)) activate(n__splitAt(X1, X2)) -> splitAt(activate(X1), activate(X2)) activate(X) -> X S is empty. Rewrite Strategy: FULL ---------------------------------------- (9) DecreasingLoopProof (FINISHED) The following loop(s) give(s) rise to the lower bound EXP: The rewrite sequence activate(n__natsFrom(X)) ->^+ U161(isNatural(activate(X)), activate(X)) gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0]. The pumping substitution is [X / n__natsFrom(X)]. The result substitution is [ ]. The rewrite sequence activate(n__natsFrom(X)) ->^+ U161(isNatural(activate(X)), activate(X)) gives rise to a decreasing loop by considering the right hand sides subterm at position [1]. The pumping substitution is [X / n__natsFrom(X)]. The result substitution is [ ]. ---------------------------------------- (10) BOUNDS(EXP, INF)