MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { U11(tt(), N, XS) -> U12(tt(), activate(N), activate(XS)) , U12(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS))) , activate(X) -> X , activate(n__natsFrom(X)) -> natsFrom(X) , snd(pair(X, Y)) -> U51(tt(), Y) , splitAt(s(N), cons(X, XS)) -> U61(tt(), N, X, activate(XS)) , splitAt(0(), XS) -> pair(nil(), XS) , U21(tt(), X) -> U22(tt(), activate(X)) , U22(tt(), X) -> activate(X) , U31(tt(), N) -> U32(tt(), activate(N)) , U32(tt(), N) -> activate(N) , U41(tt(), N, XS) -> U42(tt(), activate(N), activate(XS)) , U42(tt(), N, XS) -> head(afterNth(activate(N), activate(XS))) , head(cons(N, XS)) -> U31(tt(), N) , afterNth(N, XS) -> U11(tt(), N, XS) , U51(tt(), Y) -> U52(tt(), activate(Y)) , U52(tt(), Y) -> activate(Y) , U61(tt(), N, X, XS) -> U62(tt(), activate(N), activate(X), activate(XS)) , U62(tt(), N, X, XS) -> U63(tt(), activate(N), activate(X), activate(XS)) , U63(tt(), N, X, XS) -> U64(splitAt(activate(N), activate(XS)), activate(X)) , U64(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) , U71(tt(), XS) -> U72(tt(), activate(XS)) , U72(tt(), XS) -> activate(XS) , U81(tt(), N, XS) -> U82(tt(), activate(N), activate(XS)) , U82(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS))) , fst(pair(X, Y)) -> U21(tt(), X) , natsFrom(N) -> cons(N, n__natsFrom(s(N))) , natsFrom(X) -> n__natsFrom(X) , sel(N, XS) -> U41(tt(), N, XS) , tail(cons(N, XS)) -> U71(tt(), activate(XS)) , take(N, XS) -> U81(tt(), N, XS) } Obligation: runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 60 seconds)' failed due to the following reason: Computation stopped due to timeout after 60.0 seconds. 2) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)' failed due to the following reason: Computation stopped due to timeout after 30.0 seconds. 2) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'bsearch-popstar (timeout of 60 seconds)' failed due to the following reason: The processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due to the following reason: The processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 3) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed due to the following reason: We add the following weak dependency pairs: Strict DPs: { U11^#(tt(), N, XS) -> c_1(U12^#(tt(), activate(N), activate(XS))) , U12^#(tt(), N, XS) -> c_2(snd^#(splitAt(activate(N), activate(XS)))) , snd^#(pair(X, Y)) -> c_5(U51^#(tt(), Y)) , activate^#(X) -> c_3(X) , activate^#(n__natsFrom(X)) -> c_4(natsFrom^#(X)) , natsFrom^#(N) -> c_27(N, N) , natsFrom^#(X) -> c_28(X) , U51^#(tt(), Y) -> c_16(U52^#(tt(), activate(Y))) , splitAt^#(s(N), cons(X, XS)) -> c_6(U61^#(tt(), N, X, activate(XS))) , splitAt^#(0(), XS) -> c_7(XS) , U61^#(tt(), N, X, XS) -> c_18(U62^#(tt(), activate(N), activate(X), activate(XS))) , U21^#(tt(), X) -> c_8(U22^#(tt(), activate(X))) , U22^#(tt(), X) -> c_9(activate^#(X)) , U31^#(tt(), N) -> c_10(U32^#(tt(), activate(N))) , U32^#(tt(), N) -> c_11(activate^#(N)) , U41^#(tt(), N, XS) -> c_12(U42^#(tt(), activate(N), activate(XS))) , U42^#(tt(), N, XS) -> c_13(head^#(afterNth(activate(N), activate(XS)))) , head^#(cons(N, XS)) -> c_14(U31^#(tt(), N)) , afterNth^#(N, XS) -> c_15(U11^#(tt(), N, XS)) , U52^#(tt(), Y) -> c_17(activate^#(Y)) , U62^#(tt(), N, X, XS) -> c_19(U63^#(tt(), activate(N), activate(X), activate(XS))) , U63^#(tt(), N, X, XS) -> c_20(U64^#(splitAt(activate(N), activate(XS)), activate(X))) , U64^#(pair(YS, ZS), X) -> c_21(activate^#(X), YS, ZS) , U71^#(tt(), XS) -> c_22(U72^#(tt(), activate(XS))) , U72^#(tt(), XS) -> c_23(activate^#(XS)) , U81^#(tt(), N, XS) -> c_24(U82^#(tt(), activate(N), activate(XS))) , U82^#(tt(), N, XS) -> c_25(fst^#(splitAt(activate(N), activate(XS)))) , fst^#(pair(X, Y)) -> c_26(U21^#(tt(), X)) , sel^#(N, XS) -> c_29(U41^#(tt(), N, XS)) , tail^#(cons(N, XS)) -> c_30(U71^#(tt(), activate(XS))) , take^#(N, XS) -> c_31(U81^#(tt(), N, XS)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { U11^#(tt(), N, XS) -> c_1(U12^#(tt(), activate(N), activate(XS))) , U12^#(tt(), N, XS) -> c_2(snd^#(splitAt(activate(N), activate(XS)))) , snd^#(pair(X, Y)) -> c_5(U51^#(tt(), Y)) , activate^#(X) -> c_3(X) , activate^#(n__natsFrom(X)) -> c_4(natsFrom^#(X)) , natsFrom^#(N) -> c_27(N, N) , natsFrom^#(X) -> c_28(X) , U51^#(tt(), Y) -> c_16(U52^#(tt(), activate(Y))) , splitAt^#(s(N), cons(X, XS)) -> c_6(U61^#(tt(), N, X, activate(XS))) , splitAt^#(0(), XS) -> c_7(XS) , U61^#(tt(), N, X, XS) -> c_18(U62^#(tt(), activate(N), activate(X), activate(XS))) , U21^#(tt(), X) -> c_8(U22^#(tt(), activate(X))) , U22^#(tt(), X) -> c_9(activate^#(X)) , U31^#(tt(), N) -> c_10(U32^#(tt(), activate(N))) , U32^#(tt(), N) -> c_11(activate^#(N)) , U41^#(tt(), N, XS) -> c_12(U42^#(tt(), activate(N), activate(XS))) , U42^#(tt(), N, XS) -> c_13(head^#(afterNth(activate(N), activate(XS)))) , head^#(cons(N, XS)) -> c_14(U31^#(tt(), N)) , afterNth^#(N, XS) -> c_15(U11^#(tt(), N, XS)) , U52^#(tt(), Y) -> c_17(activate^#(Y)) , U62^#(tt(), N, X, XS) -> c_19(U63^#(tt(), activate(N), activate(X), activate(XS))) , U63^#(tt(), N, X, XS) -> c_20(U64^#(splitAt(activate(N), activate(XS)), activate(X))) , U64^#(pair(YS, ZS), X) -> c_21(activate^#(X), YS, ZS) , U71^#(tt(), XS) -> c_22(U72^#(tt(), activate(XS))) , U72^#(tt(), XS) -> c_23(activate^#(XS)) , U81^#(tt(), N, XS) -> c_24(U82^#(tt(), activate(N), activate(XS))) , U82^#(tt(), N, XS) -> c_25(fst^#(splitAt(activate(N), activate(XS)))) , fst^#(pair(X, Y)) -> c_26(U21^#(tt(), X)) , sel^#(N, XS) -> c_29(U41^#(tt(), N, XS)) , tail^#(cons(N, XS)) -> c_30(U71^#(tt(), activate(XS))) , take^#(N, XS) -> c_31(U81^#(tt(), N, XS)) } Strict Trs: { U11(tt(), N, XS) -> U12(tt(), activate(N), activate(XS)) , U12(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS))) , activate(X) -> X , activate(n__natsFrom(X)) -> natsFrom(X) , snd(pair(X, Y)) -> U51(tt(), Y) , splitAt(s(N), cons(X, XS)) -> U61(tt(), N, X, activate(XS)) , splitAt(0(), XS) -> pair(nil(), XS) , U21(tt(), X) -> U22(tt(), activate(X)) , U22(tt(), X) -> activate(X) , U31(tt(), N) -> U32(tt(), activate(N)) , U32(tt(), N) -> activate(N) , U41(tt(), N, XS) -> U42(tt(), activate(N), activate(XS)) , U42(tt(), N, XS) -> head(afterNth(activate(N), activate(XS))) , head(cons(N, XS)) -> U31(tt(), N) , afterNth(N, XS) -> U11(tt(), N, XS) , U51(tt(), Y) -> U52(tt(), activate(Y)) , U52(tt(), Y) -> activate(Y) , U61(tt(), N, X, XS) -> U62(tt(), activate(N), activate(X), activate(XS)) , U62(tt(), N, X, XS) -> U63(tt(), activate(N), activate(X), activate(XS)) , U63(tt(), N, X, XS) -> U64(splitAt(activate(N), activate(XS)), activate(X)) , U64(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) , U71(tt(), XS) -> U72(tt(), activate(XS)) , U72(tt(), XS) -> activate(XS) , U81(tt(), N, XS) -> U82(tt(), activate(N), activate(XS)) , U82(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS))) , fst(pair(X, Y)) -> U21(tt(), X) , natsFrom(N) -> cons(N, n__natsFrom(s(N))) , natsFrom(X) -> n__natsFrom(X) , sel(N, XS) -> U41(tt(), N, XS) , tail(cons(N, XS)) -> U71(tt(), activate(XS)) , take(N, XS) -> U81(tt(), N, XS) } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..