MAYBE 1025.89/297.03 MAYBE 1025.89/297.03 1025.89/297.03 We are left with following problem, upon which TcT provides the 1025.89/297.03 certificate MAYBE. 1025.89/297.03 1025.89/297.03 Strict Trs: 1025.89/297.03 { U11(tt(), N, XS) -> U12(tt(), activate(N), activate(XS)) 1025.89/297.03 , U12(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS))) 1025.89/297.03 , activate(X) -> X 1025.89/297.03 , activate(n__natsFrom(X)) -> natsFrom(activate(X)) 1025.89/297.03 , activate(n__s(X)) -> s(activate(X)) 1025.89/297.03 , snd(pair(X, Y)) -> U51(tt(), Y) 1025.89/297.03 , splitAt(0(), XS) -> pair(nil(), XS) 1025.89/297.03 , splitAt(s(N), cons(X, XS)) -> U61(tt(), N, X, activate(XS)) 1025.89/297.03 , U21(tt(), X) -> U22(tt(), activate(X)) 1025.89/297.03 , U22(tt(), X) -> activate(X) 1025.89/297.03 , U31(tt(), N) -> U32(tt(), activate(N)) 1025.89/297.03 , U32(tt(), N) -> activate(N) 1025.89/297.03 , U41(tt(), N, XS) -> U42(tt(), activate(N), activate(XS)) 1025.89/297.03 , U42(tt(), N, XS) -> head(afterNth(activate(N), activate(XS))) 1025.89/297.03 , head(cons(N, XS)) -> U31(tt(), N) 1025.89/297.03 , afterNth(N, XS) -> U11(tt(), N, XS) 1025.89/297.03 , U51(tt(), Y) -> U52(tt(), activate(Y)) 1025.89/297.03 , U52(tt(), Y) -> activate(Y) 1025.89/297.03 , U61(tt(), N, X, XS) -> 1025.89/297.03 U62(tt(), activate(N), activate(X), activate(XS)) 1025.89/297.03 , U62(tt(), N, X, XS) -> 1025.89/297.03 U63(tt(), activate(N), activate(X), activate(XS)) 1025.89/297.03 , U63(tt(), N, X, XS) -> 1025.89/297.03 U64(splitAt(activate(N), activate(XS)), activate(X)) 1025.89/297.03 , U64(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) 1025.89/297.03 , U71(tt(), XS) -> U72(tt(), activate(XS)) 1025.89/297.03 , U72(tt(), XS) -> activate(XS) 1025.89/297.03 , U81(tt(), N, XS) -> U82(tt(), activate(N), activate(XS)) 1025.89/297.03 , U82(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS))) 1025.89/297.03 , fst(pair(X, Y)) -> U21(tt(), X) 1025.89/297.03 , natsFrom(N) -> cons(N, n__natsFrom(n__s(N))) 1025.89/297.03 , natsFrom(X) -> n__natsFrom(X) 1025.89/297.03 , sel(N, XS) -> U41(tt(), N, XS) 1025.89/297.03 , s(X) -> n__s(X) 1025.89/297.03 , tail(cons(N, XS)) -> U71(tt(), activate(XS)) 1025.89/297.03 , take(N, XS) -> U81(tt(), N, XS) } 1025.89/297.03 Obligation: 1025.89/297.03 runtime complexity 1025.89/297.03 Answer: 1025.89/297.03 MAYBE 1025.89/297.03 1025.89/297.03 None of the processors succeeded. 1025.89/297.03 1025.89/297.03 Details of failed attempt(s): 1025.89/297.03 ----------------------------- 1025.89/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1025.89/297.03 following reason: 1025.89/297.03 1025.89/297.03 Computation stopped due to timeout after 297.0 seconds. 1025.89/297.03 1025.89/297.03 2) 'Best' failed due to the following reason: 1025.89/297.03 1025.89/297.03 None of the processors succeeded. 1025.89/297.03 1025.89/297.03 Details of failed attempt(s): 1025.89/297.03 ----------------------------- 1025.89/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1025.89/297.03 seconds)' failed due to the following reason: 1025.89/297.03 1025.89/297.03 Computation stopped due to timeout after 148.0 seconds. 1025.89/297.03 1025.89/297.03 2) 'Best' failed due to the following reason: 1025.89/297.03 1025.89/297.03 None of the processors succeeded. 1025.89/297.03 1025.89/297.03 Details of failed attempt(s): 1025.89/297.03 ----------------------------- 1025.89/297.03 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1025.89/297.03 to the following reason: 1025.89/297.03 1025.89/297.03 The processor is inapplicable, reason: 1025.89/297.03 Processor only applicable for innermost runtime complexity analysis 1025.89/297.03 1025.89/297.03 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1025.89/297.03 following reason: 1025.89/297.03 1025.89/297.03 The processor is inapplicable, reason: 1025.89/297.03 Processor only applicable for innermost runtime complexity analysis 1025.89/297.03 1025.89/297.03 1025.89/297.03 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1025.89/297.03 failed due to the following reason: 1025.89/297.03 1025.89/297.03 None of the processors succeeded. 1025.89/297.03 1025.89/297.03 Details of failed attempt(s): 1025.89/297.03 ----------------------------- 1025.89/297.03 1) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1025.89/297.03 failed due to the following reason: 1025.89/297.03 1025.89/297.03 match-boundness of the problem could not be verified. 1025.89/297.03 1025.89/297.03 2) 'Bounds with minimal-enrichment and initial automaton 'match'' 1025.89/297.03 failed due to the following reason: 1025.89/297.03 1025.89/297.03 match-boundness of the problem could not be verified. 1025.89/297.03 1025.89/297.03 1025.89/297.03 1025.89/297.03 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1025.89/297.03 the following reason: 1025.89/297.03 1025.89/297.03 We add the following weak dependency pairs: 1025.89/297.03 1025.89/297.03 Strict DPs: 1025.89/297.03 { U11^#(tt(), N, XS) -> c_1(U12^#(tt(), activate(N), activate(XS))) 1025.89/297.03 , U12^#(tt(), N, XS) -> 1025.89/297.03 c_2(snd^#(splitAt(activate(N), activate(XS)))) 1025.89/297.03 , snd^#(pair(X, Y)) -> c_6(U51^#(tt(), Y)) 1025.89/297.03 , activate^#(X) -> c_3(X) 1025.89/297.03 , activate^#(n__natsFrom(X)) -> c_4(natsFrom^#(activate(X))) 1025.89/297.03 , activate^#(n__s(X)) -> c_5(s^#(activate(X))) 1025.89/297.03 , natsFrom^#(N) -> c_28(N, N) 1025.89/297.03 , natsFrom^#(X) -> c_29(X) 1025.89/297.03 , s^#(X) -> c_31(X) 1025.89/297.03 , U51^#(tt(), Y) -> c_17(U52^#(tt(), activate(Y))) 1025.89/297.03 , splitAt^#(0(), XS) -> c_7(XS) 1025.89/297.03 , splitAt^#(s(N), cons(X, XS)) -> 1025.89/297.03 c_8(U61^#(tt(), N, X, activate(XS))) 1025.89/297.03 , U61^#(tt(), N, X, XS) -> 1025.89/297.03 c_19(U62^#(tt(), activate(N), activate(X), activate(XS))) 1025.89/297.03 , U21^#(tt(), X) -> c_9(U22^#(tt(), activate(X))) 1025.89/297.03 , U22^#(tt(), X) -> c_10(activate^#(X)) 1025.89/297.03 , U31^#(tt(), N) -> c_11(U32^#(tt(), activate(N))) 1025.89/297.03 , U32^#(tt(), N) -> c_12(activate^#(N)) 1025.89/297.03 , U41^#(tt(), N, XS) -> 1025.89/297.03 c_13(U42^#(tt(), activate(N), activate(XS))) 1025.89/297.03 , U42^#(tt(), N, XS) -> 1025.89/297.03 c_14(head^#(afterNth(activate(N), activate(XS)))) 1025.89/297.03 , head^#(cons(N, XS)) -> c_15(U31^#(tt(), N)) 1025.89/297.03 , afterNth^#(N, XS) -> c_16(U11^#(tt(), N, XS)) 1025.89/297.03 , U52^#(tt(), Y) -> c_18(activate^#(Y)) 1025.89/297.03 , U62^#(tt(), N, X, XS) -> 1025.89/297.03 c_20(U63^#(tt(), activate(N), activate(X), activate(XS))) 1025.89/297.03 , U63^#(tt(), N, X, XS) -> 1025.89/297.03 c_21(U64^#(splitAt(activate(N), activate(XS)), activate(X))) 1025.89/297.03 , U64^#(pair(YS, ZS), X) -> c_22(activate^#(X), YS, ZS) 1025.89/297.03 , U71^#(tt(), XS) -> c_23(U72^#(tt(), activate(XS))) 1025.89/297.03 , U72^#(tt(), XS) -> c_24(activate^#(XS)) 1025.89/297.03 , U81^#(tt(), N, XS) -> 1025.89/297.03 c_25(U82^#(tt(), activate(N), activate(XS))) 1025.89/297.03 , U82^#(tt(), N, XS) -> 1025.89/297.03 c_26(fst^#(splitAt(activate(N), activate(XS)))) 1025.89/297.03 , fst^#(pair(X, Y)) -> c_27(U21^#(tt(), X)) 1025.89/297.03 , sel^#(N, XS) -> c_30(U41^#(tt(), N, XS)) 1025.89/297.03 , tail^#(cons(N, XS)) -> c_32(U71^#(tt(), activate(XS))) 1025.89/297.03 , take^#(N, XS) -> c_33(U81^#(tt(), N, XS)) } 1025.89/297.03 1025.89/297.03 and mark the set of starting terms. 1025.89/297.03 1025.89/297.03 We are left with following problem, upon which TcT provides the 1025.89/297.03 certificate MAYBE. 1025.89/297.03 1025.89/297.03 Strict DPs: 1025.89/297.03 { U11^#(tt(), N, XS) -> c_1(U12^#(tt(), activate(N), activate(XS))) 1025.89/297.03 , U12^#(tt(), N, XS) -> 1025.89/297.03 c_2(snd^#(splitAt(activate(N), activate(XS)))) 1025.89/297.03 , snd^#(pair(X, Y)) -> c_6(U51^#(tt(), Y)) 1025.89/297.03 , activate^#(X) -> c_3(X) 1025.89/297.03 , activate^#(n__natsFrom(X)) -> c_4(natsFrom^#(activate(X))) 1025.89/297.03 , activate^#(n__s(X)) -> c_5(s^#(activate(X))) 1025.89/297.03 , natsFrom^#(N) -> c_28(N, N) 1025.89/297.03 , natsFrom^#(X) -> c_29(X) 1025.89/297.03 , s^#(X) -> c_31(X) 1025.89/297.03 , U51^#(tt(), Y) -> c_17(U52^#(tt(), activate(Y))) 1025.89/297.03 , splitAt^#(0(), XS) -> c_7(XS) 1025.89/297.03 , splitAt^#(s(N), cons(X, XS)) -> 1025.89/297.03 c_8(U61^#(tt(), N, X, activate(XS))) 1025.89/297.03 , U61^#(tt(), N, X, XS) -> 1025.89/297.03 c_19(U62^#(tt(), activate(N), activate(X), activate(XS))) 1025.89/297.03 , U21^#(tt(), X) -> c_9(U22^#(tt(), activate(X))) 1025.89/297.03 , U22^#(tt(), X) -> c_10(activate^#(X)) 1025.89/297.03 , U31^#(tt(), N) -> c_11(U32^#(tt(), activate(N))) 1025.89/297.03 , U32^#(tt(), N) -> c_12(activate^#(N)) 1025.89/297.03 , U41^#(tt(), N, XS) -> 1025.89/297.03 c_13(U42^#(tt(), activate(N), activate(XS))) 1025.89/297.03 , U42^#(tt(), N, XS) -> 1025.89/297.03 c_14(head^#(afterNth(activate(N), activate(XS)))) 1025.89/297.03 , head^#(cons(N, XS)) -> c_15(U31^#(tt(), N)) 1025.89/297.03 , afterNth^#(N, XS) -> c_16(U11^#(tt(), N, XS)) 1025.89/297.03 , U52^#(tt(), Y) -> c_18(activate^#(Y)) 1025.89/297.03 , U62^#(tt(), N, X, XS) -> 1025.89/297.03 c_20(U63^#(tt(), activate(N), activate(X), activate(XS))) 1025.89/297.03 , U63^#(tt(), N, X, XS) -> 1025.89/297.03 c_21(U64^#(splitAt(activate(N), activate(XS)), activate(X))) 1025.89/297.03 , U64^#(pair(YS, ZS), X) -> c_22(activate^#(X), YS, ZS) 1025.89/297.03 , U71^#(tt(), XS) -> c_23(U72^#(tt(), activate(XS))) 1025.89/297.03 , U72^#(tt(), XS) -> c_24(activate^#(XS)) 1025.89/297.03 , U81^#(tt(), N, XS) -> 1025.89/297.03 c_25(U82^#(tt(), activate(N), activate(XS))) 1025.89/297.03 , U82^#(tt(), N, XS) -> 1025.89/297.03 c_26(fst^#(splitAt(activate(N), activate(XS)))) 1025.89/297.03 , fst^#(pair(X, Y)) -> c_27(U21^#(tt(), X)) 1025.89/297.03 , sel^#(N, XS) -> c_30(U41^#(tt(), N, XS)) 1025.89/297.03 , tail^#(cons(N, XS)) -> c_32(U71^#(tt(), activate(XS))) 1025.89/297.03 , take^#(N, XS) -> c_33(U81^#(tt(), N, XS)) } 1025.89/297.03 Strict Trs: 1025.89/297.03 { U11(tt(), N, XS) -> U12(tt(), activate(N), activate(XS)) 1025.89/297.03 , U12(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS))) 1025.89/297.03 , activate(X) -> X 1025.89/297.03 , activate(n__natsFrom(X)) -> natsFrom(activate(X)) 1025.89/297.03 , activate(n__s(X)) -> s(activate(X)) 1025.89/297.03 , snd(pair(X, Y)) -> U51(tt(), Y) 1025.89/297.03 , splitAt(0(), XS) -> pair(nil(), XS) 1025.89/297.03 , splitAt(s(N), cons(X, XS)) -> U61(tt(), N, X, activate(XS)) 1025.89/297.03 , U21(tt(), X) -> U22(tt(), activate(X)) 1025.89/297.03 , U22(tt(), X) -> activate(X) 1025.89/297.03 , U31(tt(), N) -> U32(tt(), activate(N)) 1025.89/297.03 , U32(tt(), N) -> activate(N) 1025.89/297.03 , U41(tt(), N, XS) -> U42(tt(), activate(N), activate(XS)) 1025.89/297.03 , U42(tt(), N, XS) -> head(afterNth(activate(N), activate(XS))) 1025.89/297.03 , head(cons(N, XS)) -> U31(tt(), N) 1025.89/297.03 , afterNth(N, XS) -> U11(tt(), N, XS) 1025.89/297.03 , U51(tt(), Y) -> U52(tt(), activate(Y)) 1025.89/297.03 , U52(tt(), Y) -> activate(Y) 1025.89/297.03 , U61(tt(), N, X, XS) -> 1025.89/297.03 U62(tt(), activate(N), activate(X), activate(XS)) 1025.89/297.03 , U62(tt(), N, X, XS) -> 1025.89/297.03 U63(tt(), activate(N), activate(X), activate(XS)) 1025.89/297.03 , U63(tt(), N, X, XS) -> 1025.89/297.03 U64(splitAt(activate(N), activate(XS)), activate(X)) 1025.89/297.03 , U64(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) 1025.89/297.03 , U71(tt(), XS) -> U72(tt(), activate(XS)) 1025.89/297.03 , U72(tt(), XS) -> activate(XS) 1025.89/297.03 , U81(tt(), N, XS) -> U82(tt(), activate(N), activate(XS)) 1025.89/297.03 , U82(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS))) 1025.89/297.03 , fst(pair(X, Y)) -> U21(tt(), X) 1025.89/297.03 , natsFrom(N) -> cons(N, n__natsFrom(n__s(N))) 1025.89/297.03 , natsFrom(X) -> n__natsFrom(X) 1025.89/297.03 , sel(N, XS) -> U41(tt(), N, XS) 1025.89/297.03 , s(X) -> n__s(X) 1025.89/297.03 , tail(cons(N, XS)) -> U71(tt(), activate(XS)) 1025.89/297.03 , take(N, XS) -> U81(tt(), N, XS) } 1025.89/297.03 Obligation: 1025.89/297.03 runtime complexity 1025.89/297.03 Answer: 1025.89/297.03 MAYBE 1025.89/297.03 1025.89/297.03 Empty strict component of the problem is NOT empty. 1025.89/297.03 1025.89/297.03 1025.89/297.03 Arrrr.. 1026.24/297.35 EOF