MAYBE 1017.39/297.03 MAYBE 1017.39/297.03 1017.39/297.03 We are left with following problem, upon which TcT provides the 1017.39/297.03 certificate MAYBE. 1017.39/297.03 1017.39/297.03 Strict Trs: 1017.39/297.03 { U11(tt(), N, XS) -> U12(tt(), activate(N), activate(XS)) 1017.39/297.03 , U12(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS))) 1017.39/297.03 , activate(X) -> X 1017.39/297.03 , activate(n__natsFrom(X)) -> natsFrom(X) 1017.39/297.03 , snd(pair(X, Y)) -> U51(tt(), Y) 1017.39/297.03 , splitAt(s(N), cons(X, XS)) -> U61(tt(), N, X, activate(XS)) 1017.39/297.03 , splitAt(0(), XS) -> pair(nil(), XS) 1017.39/297.03 , U21(tt(), X) -> U22(tt(), activate(X)) 1017.39/297.03 , U22(tt(), X) -> activate(X) 1017.39/297.03 , U31(tt(), N) -> U32(tt(), activate(N)) 1017.39/297.03 , U32(tt(), N) -> activate(N) 1017.39/297.03 , U41(tt(), N, XS) -> U42(tt(), activate(N), activate(XS)) 1017.39/297.03 , U42(tt(), N, XS) -> head(afterNth(activate(N), activate(XS))) 1017.39/297.03 , head(cons(N, XS)) -> U31(tt(), N) 1017.39/297.03 , afterNth(N, XS) -> U11(tt(), N, XS) 1017.39/297.03 , U51(tt(), Y) -> U52(tt(), activate(Y)) 1017.39/297.03 , U52(tt(), Y) -> activate(Y) 1017.39/297.03 , U61(tt(), N, X, XS) -> 1017.39/297.03 U62(tt(), activate(N), activate(X), activate(XS)) 1017.39/297.03 , U62(tt(), N, X, XS) -> 1017.39/297.03 U63(tt(), activate(N), activate(X), activate(XS)) 1017.39/297.03 , U63(tt(), N, X, XS) -> 1017.39/297.03 U64(splitAt(activate(N), activate(XS)), activate(X)) 1017.39/297.03 , U64(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) 1017.39/297.03 , U71(tt(), XS) -> U72(tt(), activate(XS)) 1017.39/297.03 , U72(tt(), XS) -> activate(XS) 1017.39/297.03 , U81(tt(), N, XS) -> U82(tt(), activate(N), activate(XS)) 1017.39/297.03 , U82(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS))) 1017.39/297.03 , fst(pair(X, Y)) -> U21(tt(), X) 1017.39/297.03 , natsFrom(N) -> cons(N, n__natsFrom(s(N))) 1017.39/297.03 , natsFrom(X) -> n__natsFrom(X) 1017.39/297.03 , sel(N, XS) -> U41(tt(), N, XS) 1017.39/297.03 , tail(cons(N, XS)) -> U71(tt(), activate(XS)) 1017.39/297.03 , take(N, XS) -> U81(tt(), N, XS) } 1017.39/297.03 Obligation: 1017.39/297.03 runtime complexity 1017.39/297.03 Answer: 1017.39/297.03 MAYBE 1017.39/297.03 1017.39/297.03 None of the processors succeeded. 1017.39/297.03 1017.39/297.03 Details of failed attempt(s): 1017.39/297.03 ----------------------------- 1017.39/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1017.39/297.03 following reason: 1017.39/297.03 1017.39/297.03 Computation stopped due to timeout after 297.0 seconds. 1017.39/297.03 1017.39/297.03 2) 'Best' failed due to the following reason: 1017.39/297.03 1017.39/297.03 None of the processors succeeded. 1017.39/297.03 1017.39/297.03 Details of failed attempt(s): 1017.39/297.03 ----------------------------- 1017.39/297.04 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1017.39/297.04 seconds)' failed due to the following reason: 1017.39/297.04 1017.39/297.04 Computation stopped due to timeout after 148.0 seconds. 1017.39/297.04 1017.39/297.04 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1017.39/297.04 failed due to the following reason: 1017.39/297.04 1017.39/297.04 None of the processors succeeded. 1017.39/297.04 1017.39/297.04 Details of failed attempt(s): 1017.39/297.04 ----------------------------- 1017.39/297.04 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1017.39/297.04 failed due to the following reason: 1017.39/297.04 1017.39/297.04 match-boundness of the problem could not be verified. 1017.39/297.04 1017.39/297.04 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1017.39/297.04 failed due to the following reason: 1017.39/297.04 1017.39/297.04 match-boundness of the problem could not be verified. 1017.39/297.04 1017.39/297.04 1017.39/297.04 3) 'Best' failed due to the following reason: 1017.39/297.04 1017.39/297.04 None of the processors succeeded. 1017.39/297.04 1017.39/297.04 Details of failed attempt(s): 1017.39/297.04 ----------------------------- 1017.39/297.04 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1017.39/297.04 following reason: 1017.39/297.04 1017.39/297.04 The processor is inapplicable, reason: 1017.39/297.04 Processor only applicable for innermost runtime complexity analysis 1017.39/297.04 1017.39/297.04 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1017.39/297.04 to the following reason: 1017.39/297.04 1017.39/297.04 The processor is inapplicable, reason: 1017.39/297.04 Processor only applicable for innermost runtime complexity analysis 1017.39/297.04 1017.39/297.04 1017.39/297.04 1017.39/297.04 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1017.39/297.04 the following reason: 1017.39/297.04 1017.39/297.04 We add the following weak dependency pairs: 1017.39/297.04 1017.39/297.04 Strict DPs: 1017.39/297.04 { U11^#(tt(), N, XS) -> c_1(U12^#(tt(), activate(N), activate(XS))) 1017.39/297.04 , U12^#(tt(), N, XS) -> 1017.39/297.04 c_2(snd^#(splitAt(activate(N), activate(XS)))) 1017.39/297.04 , snd^#(pair(X, Y)) -> c_5(U51^#(tt(), Y)) 1017.39/297.04 , activate^#(X) -> c_3(X) 1017.39/297.04 , activate^#(n__natsFrom(X)) -> c_4(natsFrom^#(X)) 1017.39/297.04 , natsFrom^#(N) -> c_27(N, N) 1017.39/297.04 , natsFrom^#(X) -> c_28(X) 1017.39/297.04 , U51^#(tt(), Y) -> c_16(U52^#(tt(), activate(Y))) 1017.39/297.04 , splitAt^#(s(N), cons(X, XS)) -> 1017.39/297.04 c_6(U61^#(tt(), N, X, activate(XS))) 1017.39/297.04 , splitAt^#(0(), XS) -> c_7(XS) 1017.39/297.04 , U61^#(tt(), N, X, XS) -> 1017.39/297.04 c_18(U62^#(tt(), activate(N), activate(X), activate(XS))) 1017.39/297.04 , U21^#(tt(), X) -> c_8(U22^#(tt(), activate(X))) 1017.39/297.04 , U22^#(tt(), X) -> c_9(activate^#(X)) 1017.39/297.04 , U31^#(tt(), N) -> c_10(U32^#(tt(), activate(N))) 1017.39/297.04 , U32^#(tt(), N) -> c_11(activate^#(N)) 1017.39/297.04 , U41^#(tt(), N, XS) -> 1017.39/297.04 c_12(U42^#(tt(), activate(N), activate(XS))) 1017.39/297.04 , U42^#(tt(), N, XS) -> 1017.39/297.04 c_13(head^#(afterNth(activate(N), activate(XS)))) 1017.39/297.04 , head^#(cons(N, XS)) -> c_14(U31^#(tt(), N)) 1017.39/297.04 , afterNth^#(N, XS) -> c_15(U11^#(tt(), N, XS)) 1017.39/297.04 , U52^#(tt(), Y) -> c_17(activate^#(Y)) 1017.39/297.04 , U62^#(tt(), N, X, XS) -> 1017.39/297.04 c_19(U63^#(tt(), activate(N), activate(X), activate(XS))) 1017.39/297.04 , U63^#(tt(), N, X, XS) -> 1017.39/297.04 c_20(U64^#(splitAt(activate(N), activate(XS)), activate(X))) 1017.39/297.04 , U64^#(pair(YS, ZS), X) -> c_21(activate^#(X), YS, ZS) 1017.39/297.04 , U71^#(tt(), XS) -> c_22(U72^#(tt(), activate(XS))) 1017.39/297.04 , U72^#(tt(), XS) -> c_23(activate^#(XS)) 1017.39/297.04 , U81^#(tt(), N, XS) -> 1017.39/297.04 c_24(U82^#(tt(), activate(N), activate(XS))) 1017.39/297.04 , U82^#(tt(), N, XS) -> 1017.39/297.04 c_25(fst^#(splitAt(activate(N), activate(XS)))) 1017.39/297.04 , fst^#(pair(X, Y)) -> c_26(U21^#(tt(), X)) 1017.39/297.04 , sel^#(N, XS) -> c_29(U41^#(tt(), N, XS)) 1017.39/297.04 , tail^#(cons(N, XS)) -> c_30(U71^#(tt(), activate(XS))) 1017.39/297.04 , take^#(N, XS) -> c_31(U81^#(tt(), N, XS)) } 1017.39/297.04 1017.39/297.04 and mark the set of starting terms. 1017.39/297.04 1017.39/297.04 We are left with following problem, upon which TcT provides the 1017.39/297.04 certificate MAYBE. 1017.39/297.04 1017.39/297.04 Strict DPs: 1017.39/297.04 { U11^#(tt(), N, XS) -> c_1(U12^#(tt(), activate(N), activate(XS))) 1017.39/297.04 , U12^#(tt(), N, XS) -> 1017.39/297.04 c_2(snd^#(splitAt(activate(N), activate(XS)))) 1017.39/297.04 , snd^#(pair(X, Y)) -> c_5(U51^#(tt(), Y)) 1017.39/297.04 , activate^#(X) -> c_3(X) 1017.39/297.04 , activate^#(n__natsFrom(X)) -> c_4(natsFrom^#(X)) 1017.39/297.04 , natsFrom^#(N) -> c_27(N, N) 1017.39/297.04 , natsFrom^#(X) -> c_28(X) 1017.39/297.04 , U51^#(tt(), Y) -> c_16(U52^#(tt(), activate(Y))) 1017.39/297.04 , splitAt^#(s(N), cons(X, XS)) -> 1017.39/297.04 c_6(U61^#(tt(), N, X, activate(XS))) 1017.39/297.04 , splitAt^#(0(), XS) -> c_7(XS) 1017.39/297.04 , U61^#(tt(), N, X, XS) -> 1017.39/297.04 c_18(U62^#(tt(), activate(N), activate(X), activate(XS))) 1017.39/297.04 , U21^#(tt(), X) -> c_8(U22^#(tt(), activate(X))) 1017.39/297.04 , U22^#(tt(), X) -> c_9(activate^#(X)) 1017.39/297.04 , U31^#(tt(), N) -> c_10(U32^#(tt(), activate(N))) 1017.39/297.04 , U32^#(tt(), N) -> c_11(activate^#(N)) 1017.39/297.04 , U41^#(tt(), N, XS) -> 1017.39/297.04 c_12(U42^#(tt(), activate(N), activate(XS))) 1017.39/297.04 , U42^#(tt(), N, XS) -> 1017.39/297.04 c_13(head^#(afterNth(activate(N), activate(XS)))) 1017.39/297.04 , head^#(cons(N, XS)) -> c_14(U31^#(tt(), N)) 1017.39/297.04 , afterNth^#(N, XS) -> c_15(U11^#(tt(), N, XS)) 1017.39/297.04 , U52^#(tt(), Y) -> c_17(activate^#(Y)) 1017.39/297.04 , U62^#(tt(), N, X, XS) -> 1017.39/297.04 c_19(U63^#(tt(), activate(N), activate(X), activate(XS))) 1017.39/297.04 , U63^#(tt(), N, X, XS) -> 1017.39/297.04 c_20(U64^#(splitAt(activate(N), activate(XS)), activate(X))) 1017.39/297.04 , U64^#(pair(YS, ZS), X) -> c_21(activate^#(X), YS, ZS) 1017.39/297.04 , U71^#(tt(), XS) -> c_22(U72^#(tt(), activate(XS))) 1017.39/297.04 , U72^#(tt(), XS) -> c_23(activate^#(XS)) 1017.39/297.04 , U81^#(tt(), N, XS) -> 1017.39/297.04 c_24(U82^#(tt(), activate(N), activate(XS))) 1017.39/297.04 , U82^#(tt(), N, XS) -> 1017.39/297.04 c_25(fst^#(splitAt(activate(N), activate(XS)))) 1017.39/297.04 , fst^#(pair(X, Y)) -> c_26(U21^#(tt(), X)) 1017.39/297.04 , sel^#(N, XS) -> c_29(U41^#(tt(), N, XS)) 1017.39/297.04 , tail^#(cons(N, XS)) -> c_30(U71^#(tt(), activate(XS))) 1017.39/297.04 , take^#(N, XS) -> c_31(U81^#(tt(), N, XS)) } 1017.39/297.04 Strict Trs: 1017.39/297.04 { U11(tt(), N, XS) -> U12(tt(), activate(N), activate(XS)) 1017.39/297.04 , U12(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS))) 1017.39/297.04 , activate(X) -> X 1017.39/297.04 , activate(n__natsFrom(X)) -> natsFrom(X) 1017.39/297.04 , snd(pair(X, Y)) -> U51(tt(), Y) 1017.39/297.04 , splitAt(s(N), cons(X, XS)) -> U61(tt(), N, X, activate(XS)) 1017.39/297.04 , splitAt(0(), XS) -> pair(nil(), XS) 1017.39/297.04 , U21(tt(), X) -> U22(tt(), activate(X)) 1017.39/297.04 , U22(tt(), X) -> activate(X) 1017.39/297.04 , U31(tt(), N) -> U32(tt(), activate(N)) 1017.39/297.04 , U32(tt(), N) -> activate(N) 1017.39/297.04 , U41(tt(), N, XS) -> U42(tt(), activate(N), activate(XS)) 1017.39/297.04 , U42(tt(), N, XS) -> head(afterNth(activate(N), activate(XS))) 1017.39/297.04 , head(cons(N, XS)) -> U31(tt(), N) 1017.39/297.04 , afterNth(N, XS) -> U11(tt(), N, XS) 1017.39/297.04 , U51(tt(), Y) -> U52(tt(), activate(Y)) 1017.39/297.04 , U52(tt(), Y) -> activate(Y) 1017.39/297.04 , U61(tt(), N, X, XS) -> 1017.39/297.04 U62(tt(), activate(N), activate(X), activate(XS)) 1017.39/297.04 , U62(tt(), N, X, XS) -> 1017.39/297.04 U63(tt(), activate(N), activate(X), activate(XS)) 1017.39/297.04 , U63(tt(), N, X, XS) -> 1017.39/297.04 U64(splitAt(activate(N), activate(XS)), activate(X)) 1017.39/297.04 , U64(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) 1017.39/297.04 , U71(tt(), XS) -> U72(tt(), activate(XS)) 1017.39/297.04 , U72(tt(), XS) -> activate(XS) 1017.39/297.04 , U81(tt(), N, XS) -> U82(tt(), activate(N), activate(XS)) 1017.39/297.04 , U82(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS))) 1017.39/297.04 , fst(pair(X, Y)) -> U21(tt(), X) 1017.39/297.04 , natsFrom(N) -> cons(N, n__natsFrom(s(N))) 1017.39/297.04 , natsFrom(X) -> n__natsFrom(X) 1017.39/297.04 , sel(N, XS) -> U41(tt(), N, XS) 1017.39/297.04 , tail(cons(N, XS)) -> U71(tt(), activate(XS)) 1017.39/297.04 , take(N, XS) -> U81(tt(), N, XS) } 1017.39/297.04 Obligation: 1017.39/297.04 runtime complexity 1017.39/297.04 Answer: 1017.39/297.04 MAYBE 1017.39/297.04 1017.39/297.04 Empty strict component of the problem is NOT empty. 1017.39/297.04 1017.39/297.04 1017.39/297.04 Arrrr.. 1017.39/297.06 EOF