MAYBE 1139.53/298.85 MAYBE 1139.53/298.85 1139.53/298.85 We are left with following problem, upon which TcT provides the 1139.53/298.85 certificate MAYBE. 1139.53/298.85 1139.53/298.85 Strict Trs: 1139.53/298.85 { a__U11(X1, X2, X3) -> U11(X1, X2, X3) 1139.53/298.85 , a__U11(tt(), N, XS) -> a__U12(tt(), N, XS) 1139.53/298.85 , a__U12(X1, X2, X3) -> U12(X1, X2, X3) 1139.53/298.85 , a__U12(tt(), N, XS) -> a__snd(a__splitAt(mark(N), mark(XS))) 1139.53/298.85 , a__snd(X) -> snd(X) 1139.53/298.85 , a__snd(pair(X, Y)) -> a__U51(tt(), Y) 1139.53/298.85 , a__splitAt(X1, X2) -> splitAt(X1, X2) 1139.53/298.85 , a__splitAt(s(N), cons(X, XS)) -> a__U61(tt(), N, X, XS) 1139.53/298.85 , a__splitAt(0(), XS) -> pair(nil(), mark(XS)) 1139.53/298.85 , mark(tt()) -> tt() 1139.53/298.85 , mark(pair(X1, X2)) -> pair(mark(X1), mark(X2)) 1139.53/298.85 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1139.53/298.85 , mark(natsFrom(X)) -> a__natsFrom(mark(X)) 1139.53/298.85 , mark(s(X)) -> s(mark(X)) 1139.53/298.85 , mark(0()) -> 0() 1139.53/298.85 , mark(nil()) -> nil() 1139.53/298.85 , mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) 1139.53/298.85 , mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) 1139.53/298.85 , mark(snd(X)) -> a__snd(mark(X)) 1139.53/298.85 , mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2)) 1139.53/298.85 , mark(U21(X1, X2)) -> a__U21(mark(X1), X2) 1139.53/298.85 , mark(U22(X1, X2)) -> a__U22(mark(X1), X2) 1139.53/298.85 , mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 1139.53/298.85 , mark(U32(X1, X2)) -> a__U32(mark(X1), X2) 1139.53/298.85 , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 1139.53/298.85 , mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) 1139.53/298.85 , mark(head(X)) -> a__head(mark(X)) 1139.53/298.85 , mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2)) 1139.53/298.85 , mark(U51(X1, X2)) -> a__U51(mark(X1), X2) 1139.53/298.85 , mark(U52(X1, X2)) -> a__U52(mark(X1), X2) 1139.53/298.85 , mark(U61(X1, X2, X3, X4)) -> a__U61(mark(X1), X2, X3, X4) 1139.53/298.85 , mark(U62(X1, X2, X3, X4)) -> a__U62(mark(X1), X2, X3, X4) 1139.53/298.85 , mark(U63(X1, X2, X3, X4)) -> a__U63(mark(X1), X2, X3, X4) 1139.53/298.85 , mark(U64(X1, X2)) -> a__U64(mark(X1), X2) 1139.53/298.85 , mark(U71(X1, X2)) -> a__U71(mark(X1), X2) 1139.53/298.85 , mark(U72(X1, X2)) -> a__U72(mark(X1), X2) 1139.53/298.85 , mark(U81(X1, X2, X3)) -> a__U81(mark(X1), X2, X3) 1139.53/298.85 , mark(U82(X1, X2, X3)) -> a__U82(mark(X1), X2, X3) 1139.53/298.85 , mark(fst(X)) -> a__fst(mark(X)) 1139.53/298.85 , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 1139.53/298.85 , mark(tail(X)) -> a__tail(mark(X)) 1139.53/298.85 , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) 1139.53/298.85 , a__U21(X1, X2) -> U21(X1, X2) 1139.53/298.85 , a__U21(tt(), X) -> a__U22(tt(), X) 1139.53/298.85 , a__U22(X1, X2) -> U22(X1, X2) 1139.53/298.85 , a__U22(tt(), X) -> mark(X) 1139.53/298.85 , a__U31(X1, X2) -> U31(X1, X2) 1139.53/298.85 , a__U31(tt(), N) -> a__U32(tt(), N) 1139.53/298.85 , a__U32(X1, X2) -> U32(X1, X2) 1139.53/298.85 , a__U32(tt(), N) -> mark(N) 1139.53/298.85 , a__U41(X1, X2, X3) -> U41(X1, X2, X3) 1139.53/298.85 , a__U41(tt(), N, XS) -> a__U42(tt(), N, XS) 1139.53/298.85 , a__U42(X1, X2, X3) -> U42(X1, X2, X3) 1139.53/298.85 , a__U42(tt(), N, XS) -> a__head(a__afterNth(mark(N), mark(XS))) 1139.53/298.85 , a__head(X) -> head(X) 1139.53/298.85 , a__head(cons(N, XS)) -> a__U31(tt(), N) 1139.53/298.85 , a__afterNth(N, XS) -> a__U11(tt(), N, XS) 1139.53/298.85 , a__afterNth(X1, X2) -> afterNth(X1, X2) 1139.53/298.85 , a__U51(X1, X2) -> U51(X1, X2) 1139.53/298.85 , a__U51(tt(), Y) -> a__U52(tt(), Y) 1139.53/298.85 , a__U52(X1, X2) -> U52(X1, X2) 1139.53/298.85 , a__U52(tt(), Y) -> mark(Y) 1139.53/298.85 , a__U61(X1, X2, X3, X4) -> U61(X1, X2, X3, X4) 1139.53/298.85 , a__U61(tt(), N, X, XS) -> a__U62(tt(), N, X, XS) 1139.53/298.85 , a__U62(X1, X2, X3, X4) -> U62(X1, X2, X3, X4) 1139.53/298.85 , a__U62(tt(), N, X, XS) -> a__U63(tt(), N, X, XS) 1139.53/298.85 , a__U63(X1, X2, X3, X4) -> U63(X1, X2, X3, X4) 1139.53/298.85 , a__U63(tt(), N, X, XS) -> 1139.53/298.85 a__U64(a__splitAt(mark(N), mark(XS)), X) 1139.53/298.85 , a__U64(X1, X2) -> U64(X1, X2) 1139.53/298.85 , a__U64(pair(YS, ZS), X) -> pair(cons(mark(X), YS), mark(ZS)) 1139.53/298.85 , a__U71(X1, X2) -> U71(X1, X2) 1139.53/298.85 , a__U71(tt(), XS) -> a__U72(tt(), XS) 1139.53/298.85 , a__U72(X1, X2) -> U72(X1, X2) 1139.53/298.85 , a__U72(tt(), XS) -> mark(XS) 1139.53/298.85 , a__U81(X1, X2, X3) -> U81(X1, X2, X3) 1139.53/298.85 , a__U81(tt(), N, XS) -> a__U82(tt(), N, XS) 1139.53/298.85 , a__U82(X1, X2, X3) -> U82(X1, X2, X3) 1139.53/298.85 , a__U82(tt(), N, XS) -> a__fst(a__splitAt(mark(N), mark(XS))) 1139.53/298.85 , a__fst(X) -> fst(X) 1139.53/298.85 , a__fst(pair(X, Y)) -> a__U21(tt(), X) 1139.53/298.85 , a__natsFrom(N) -> cons(mark(N), natsFrom(s(N))) 1139.53/298.85 , a__natsFrom(X) -> natsFrom(X) 1139.53/298.85 , a__sel(N, XS) -> a__U41(tt(), N, XS) 1139.53/298.85 , a__sel(X1, X2) -> sel(X1, X2) 1139.53/298.85 , a__tail(X) -> tail(X) 1139.53/298.85 , a__tail(cons(N, XS)) -> a__U71(tt(), XS) 1139.53/298.85 , a__take(N, XS) -> a__U81(tt(), N, XS) 1139.53/298.85 , a__take(X1, X2) -> take(X1, X2) } 1139.53/298.85 Obligation: 1139.53/298.85 runtime complexity 1139.53/298.85 Answer: 1139.53/298.85 MAYBE 1139.53/298.85 1139.53/298.85 None of the processors succeeded. 1139.53/298.85 1139.53/298.85 Details of failed attempt(s): 1139.53/298.85 ----------------------------- 1139.53/298.85 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1139.53/298.85 following reason: 1139.53/298.85 1139.53/298.85 Computation stopped due to timeout after 297.0 seconds. 1139.53/298.85 1139.53/298.85 2) 'Best' failed due to the following reason: 1139.53/298.85 1139.53/298.85 None of the processors succeeded. 1139.53/298.85 1139.53/298.85 Details of failed attempt(s): 1139.53/298.85 ----------------------------- 1139.53/298.85 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1139.53/298.85 seconds)' failed due to the following reason: 1139.53/298.85 1139.53/298.85 Computation stopped due to timeout after 148.0 seconds. 1139.53/298.85 1139.53/298.85 2) 'Best' failed due to the following reason: 1139.53/298.85 1139.53/298.85 None of the processors succeeded. 1139.53/298.85 1139.53/298.85 Details of failed attempt(s): 1139.53/298.85 ----------------------------- 1139.53/298.85 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1139.53/298.85 following reason: 1139.53/298.85 1139.53/298.85 The processor is inapplicable, reason: 1139.53/298.85 Processor only applicable for innermost runtime complexity analysis 1139.53/298.85 1139.53/298.85 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1139.53/298.85 to the following reason: 1139.53/298.85 1139.53/298.85 The processor is inapplicable, reason: 1139.53/298.85 Processor only applicable for innermost runtime complexity analysis 1139.53/298.85 1139.53/298.85 1139.53/298.85 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1139.53/298.85 failed due to the following reason: 1139.53/298.85 1139.53/298.85 None of the processors succeeded. 1139.53/298.85 1139.53/298.85 Details of failed attempt(s): 1139.53/298.85 ----------------------------- 1139.53/298.85 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1139.53/298.85 failed due to the following reason: 1139.53/298.85 1139.53/298.85 match-boundness of the problem could not be verified. 1139.53/298.85 1139.53/298.85 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1139.53/298.85 failed due to the following reason: 1139.53/298.85 1139.53/298.85 match-boundness of the problem could not be verified. 1139.53/298.85 1139.53/298.85 1139.53/298.85 1139.53/298.85 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1139.53/298.85 the following reason: 1139.53/298.85 1139.53/298.85 We add the following weak dependency pairs: 1139.53/298.85 1139.53/298.85 Strict DPs: 1139.53/298.85 { a__U11^#(X1, X2, X3) -> c_1(X1, X2, X3) 1139.53/298.85 , a__U11^#(tt(), N, XS) -> c_2(a__U12^#(tt(), N, XS)) 1139.53/298.85 , a__U12^#(X1, X2, X3) -> c_3(X1, X2, X3) 1139.53/298.85 , a__U12^#(tt(), N, XS) -> 1139.53/298.85 c_4(a__snd^#(a__splitAt(mark(N), mark(XS)))) 1139.53/298.85 , a__snd^#(X) -> c_5(X) 1139.53/298.85 , a__snd^#(pair(X, Y)) -> c_6(a__U51^#(tt(), Y)) 1139.53/298.85 , a__U51^#(X1, X2) -> c_59(X1, X2) 1139.53/298.85 , a__U51^#(tt(), Y) -> c_60(a__U52^#(tt(), Y)) 1139.53/298.85 , a__splitAt^#(X1, X2) -> c_7(X1, X2) 1139.53/298.85 , a__splitAt^#(s(N), cons(X, XS)) -> c_8(a__U61^#(tt(), N, X, XS)) 1139.53/298.85 , a__splitAt^#(0(), XS) -> c_9(mark^#(XS)) 1139.53/298.85 , a__U61^#(X1, X2, X3, X4) -> c_63(X1, X2, X3, X4) 1139.53/298.85 , a__U61^#(tt(), N, X, XS) -> c_64(a__U62^#(tt(), N, X, XS)) 1139.53/298.85 , mark^#(tt()) -> c_10() 1139.53/298.85 , mark^#(pair(X1, X2)) -> c_11(mark^#(X1), mark^#(X2)) 1139.53/298.85 , mark^#(cons(X1, X2)) -> c_12(mark^#(X1), X2) 1139.53/298.85 , mark^#(natsFrom(X)) -> c_13(a__natsFrom^#(mark(X))) 1139.53/298.85 , mark^#(s(X)) -> c_14(mark^#(X)) 1139.53/298.85 , mark^#(0()) -> c_15() 1139.53/298.85 , mark^#(nil()) -> c_16() 1139.53/298.85 , mark^#(U11(X1, X2, X3)) -> c_17(a__U11^#(mark(X1), X2, X3)) 1139.53/298.85 , mark^#(U12(X1, X2, X3)) -> c_18(a__U12^#(mark(X1), X2, X3)) 1139.53/298.85 , mark^#(snd(X)) -> c_19(a__snd^#(mark(X))) 1139.53/298.85 , mark^#(splitAt(X1, X2)) -> c_20(a__splitAt^#(mark(X1), mark(X2))) 1139.53/298.85 , mark^#(U21(X1, X2)) -> c_21(a__U21^#(mark(X1), X2)) 1139.53/298.85 , mark^#(U22(X1, X2)) -> c_22(a__U22^#(mark(X1), X2)) 1139.53/298.85 , mark^#(U31(X1, X2)) -> c_23(a__U31^#(mark(X1), X2)) 1139.53/298.85 , mark^#(U32(X1, X2)) -> c_24(a__U32^#(mark(X1), X2)) 1139.53/298.85 , mark^#(U41(X1, X2, X3)) -> c_25(a__U41^#(mark(X1), X2, X3)) 1139.53/298.85 , mark^#(U42(X1, X2, X3)) -> c_26(a__U42^#(mark(X1), X2, X3)) 1139.53/298.85 , mark^#(head(X)) -> c_27(a__head^#(mark(X))) 1139.53/298.85 , mark^#(afterNth(X1, X2)) -> 1139.53/298.85 c_28(a__afterNth^#(mark(X1), mark(X2))) 1139.53/298.85 , mark^#(U51(X1, X2)) -> c_29(a__U51^#(mark(X1), X2)) 1139.53/298.85 , mark^#(U52(X1, X2)) -> c_30(a__U52^#(mark(X1), X2)) 1139.53/298.85 , mark^#(U61(X1, X2, X3, X4)) -> 1139.53/298.85 c_31(a__U61^#(mark(X1), X2, X3, X4)) 1139.53/298.85 , mark^#(U62(X1, X2, X3, X4)) -> 1139.53/298.85 c_32(a__U62^#(mark(X1), X2, X3, X4)) 1139.53/298.86 , mark^#(U63(X1, X2, X3, X4)) -> 1139.53/298.86 c_33(a__U63^#(mark(X1), X2, X3, X4)) 1139.53/298.86 , mark^#(U64(X1, X2)) -> c_34(a__U64^#(mark(X1), X2)) 1139.53/298.86 , mark^#(U71(X1, X2)) -> c_35(a__U71^#(mark(X1), X2)) 1139.53/298.86 , mark^#(U72(X1, X2)) -> c_36(a__U72^#(mark(X1), X2)) 1139.53/298.86 , mark^#(U81(X1, X2, X3)) -> c_37(a__U81^#(mark(X1), X2, X3)) 1139.53/298.86 , mark^#(U82(X1, X2, X3)) -> c_38(a__U82^#(mark(X1), X2, X3)) 1139.53/298.86 , mark^#(fst(X)) -> c_39(a__fst^#(mark(X))) 1139.53/298.86 , mark^#(sel(X1, X2)) -> c_40(a__sel^#(mark(X1), mark(X2))) 1139.53/298.86 , mark^#(tail(X)) -> c_41(a__tail^#(mark(X))) 1139.53/298.86 , mark^#(take(X1, X2)) -> c_42(a__take^#(mark(X1), mark(X2))) 1139.53/298.86 , a__natsFrom^#(N) -> c_81(mark^#(N), N) 1139.53/298.86 , a__natsFrom^#(X) -> c_82(X) 1139.53/298.86 , a__U21^#(X1, X2) -> c_43(X1, X2) 1139.53/298.86 , a__U21^#(tt(), X) -> c_44(a__U22^#(tt(), X)) 1139.53/298.86 , a__U22^#(X1, X2) -> c_45(X1, X2) 1139.53/298.86 , a__U22^#(tt(), X) -> c_46(mark^#(X)) 1139.53/298.86 , a__U31^#(X1, X2) -> c_47(X1, X2) 1139.53/298.86 , a__U31^#(tt(), N) -> c_48(a__U32^#(tt(), N)) 1139.53/298.86 , a__U32^#(X1, X2) -> c_49(X1, X2) 1139.53/298.86 , a__U32^#(tt(), N) -> c_50(mark^#(N)) 1139.53/298.86 , a__U41^#(X1, X2, X3) -> c_51(X1, X2, X3) 1139.53/298.86 , a__U41^#(tt(), N, XS) -> c_52(a__U42^#(tt(), N, XS)) 1139.53/298.86 , a__U42^#(X1, X2, X3) -> c_53(X1, X2, X3) 1139.53/298.86 , a__U42^#(tt(), N, XS) -> 1139.53/298.86 c_54(a__head^#(a__afterNth(mark(N), mark(XS)))) 1139.53/298.86 , a__head^#(X) -> c_55(X) 1139.53/298.86 , a__head^#(cons(N, XS)) -> c_56(a__U31^#(tt(), N)) 1139.53/298.86 , a__afterNth^#(N, XS) -> c_57(a__U11^#(tt(), N, XS)) 1139.53/298.86 , a__afterNth^#(X1, X2) -> c_58(X1, X2) 1139.53/298.86 , a__U52^#(X1, X2) -> c_61(X1, X2) 1139.53/298.86 , a__U52^#(tt(), Y) -> c_62(mark^#(Y)) 1139.53/298.86 , a__U62^#(X1, X2, X3, X4) -> c_65(X1, X2, X3, X4) 1139.53/298.86 , a__U62^#(tt(), N, X, XS) -> c_66(a__U63^#(tt(), N, X, XS)) 1139.53/298.86 , a__U63^#(X1, X2, X3, X4) -> c_67(X1, X2, X3, X4) 1139.53/298.86 , a__U63^#(tt(), N, X, XS) -> 1139.53/298.86 c_68(a__U64^#(a__splitAt(mark(N), mark(XS)), X)) 1139.53/298.86 , a__U64^#(X1, X2) -> c_69(X1, X2) 1139.53/298.86 , a__U64^#(pair(YS, ZS), X) -> c_70(mark^#(X), YS, mark^#(ZS)) 1139.53/298.86 , a__U71^#(X1, X2) -> c_71(X1, X2) 1139.53/298.86 , a__U71^#(tt(), XS) -> c_72(a__U72^#(tt(), XS)) 1139.53/298.86 , a__U72^#(X1, X2) -> c_73(X1, X2) 1139.53/298.86 , a__U72^#(tt(), XS) -> c_74(mark^#(XS)) 1139.53/298.86 , a__U81^#(X1, X2, X3) -> c_75(X1, X2, X3) 1139.53/298.86 , a__U81^#(tt(), N, XS) -> c_76(a__U82^#(tt(), N, XS)) 1139.53/298.86 , a__U82^#(X1, X2, X3) -> c_77(X1, X2, X3) 1139.53/298.86 , a__U82^#(tt(), N, XS) -> 1139.53/298.86 c_78(a__fst^#(a__splitAt(mark(N), mark(XS)))) 1139.53/298.86 , a__fst^#(X) -> c_79(X) 1139.53/298.86 , a__fst^#(pair(X, Y)) -> c_80(a__U21^#(tt(), X)) 1139.53/298.86 , a__sel^#(N, XS) -> c_83(a__U41^#(tt(), N, XS)) 1139.53/298.86 , a__sel^#(X1, X2) -> c_84(X1, X2) 1139.53/298.86 , a__tail^#(X) -> c_85(X) 1139.53/298.86 , a__tail^#(cons(N, XS)) -> c_86(a__U71^#(tt(), XS)) 1139.53/298.86 , a__take^#(N, XS) -> c_87(a__U81^#(tt(), N, XS)) 1139.53/298.86 , a__take^#(X1, X2) -> c_88(X1, X2) } 1139.53/298.86 1139.53/298.86 and mark the set of starting terms. 1139.53/298.86 1139.53/298.86 We are left with following problem, upon which TcT provides the 1139.53/298.86 certificate MAYBE. 1139.53/298.86 1139.53/298.86 Strict DPs: 1139.53/298.86 { a__U11^#(X1, X2, X3) -> c_1(X1, X2, X3) 1139.53/298.86 , a__U11^#(tt(), N, XS) -> c_2(a__U12^#(tt(), N, XS)) 1139.53/298.86 , a__U12^#(X1, X2, X3) -> c_3(X1, X2, X3) 1139.53/298.86 , a__U12^#(tt(), N, XS) -> 1139.53/298.86 c_4(a__snd^#(a__splitAt(mark(N), mark(XS)))) 1139.53/298.86 , a__snd^#(X) -> c_5(X) 1139.53/298.86 , a__snd^#(pair(X, Y)) -> c_6(a__U51^#(tt(), Y)) 1139.53/298.86 , a__U51^#(X1, X2) -> c_59(X1, X2) 1139.53/298.86 , a__U51^#(tt(), Y) -> c_60(a__U52^#(tt(), Y)) 1139.53/298.86 , a__splitAt^#(X1, X2) -> c_7(X1, X2) 1139.53/298.86 , a__splitAt^#(s(N), cons(X, XS)) -> c_8(a__U61^#(tt(), N, X, XS)) 1139.53/298.86 , a__splitAt^#(0(), XS) -> c_9(mark^#(XS)) 1139.53/298.86 , a__U61^#(X1, X2, X3, X4) -> c_63(X1, X2, X3, X4) 1139.53/298.86 , a__U61^#(tt(), N, X, XS) -> c_64(a__U62^#(tt(), N, X, XS)) 1139.53/298.86 , mark^#(tt()) -> c_10() 1139.53/298.86 , mark^#(pair(X1, X2)) -> c_11(mark^#(X1), mark^#(X2)) 1139.53/298.86 , mark^#(cons(X1, X2)) -> c_12(mark^#(X1), X2) 1139.53/298.86 , mark^#(natsFrom(X)) -> c_13(a__natsFrom^#(mark(X))) 1139.53/298.86 , mark^#(s(X)) -> c_14(mark^#(X)) 1139.53/298.86 , mark^#(0()) -> c_15() 1139.53/298.86 , mark^#(nil()) -> c_16() 1139.53/298.86 , mark^#(U11(X1, X2, X3)) -> c_17(a__U11^#(mark(X1), X2, X3)) 1139.53/298.86 , mark^#(U12(X1, X2, X3)) -> c_18(a__U12^#(mark(X1), X2, X3)) 1139.53/298.86 , mark^#(snd(X)) -> c_19(a__snd^#(mark(X))) 1139.53/298.86 , mark^#(splitAt(X1, X2)) -> c_20(a__splitAt^#(mark(X1), mark(X2))) 1139.53/298.86 , mark^#(U21(X1, X2)) -> c_21(a__U21^#(mark(X1), X2)) 1139.53/298.86 , mark^#(U22(X1, X2)) -> c_22(a__U22^#(mark(X1), X2)) 1139.53/298.86 , mark^#(U31(X1, X2)) -> c_23(a__U31^#(mark(X1), X2)) 1139.53/298.86 , mark^#(U32(X1, X2)) -> c_24(a__U32^#(mark(X1), X2)) 1139.53/298.86 , mark^#(U41(X1, X2, X3)) -> c_25(a__U41^#(mark(X1), X2, X3)) 1139.53/298.86 , mark^#(U42(X1, X2, X3)) -> c_26(a__U42^#(mark(X1), X2, X3)) 1139.53/298.86 , mark^#(head(X)) -> c_27(a__head^#(mark(X))) 1139.53/298.86 , mark^#(afterNth(X1, X2)) -> 1139.53/298.86 c_28(a__afterNth^#(mark(X1), mark(X2))) 1139.53/298.86 , mark^#(U51(X1, X2)) -> c_29(a__U51^#(mark(X1), X2)) 1139.53/298.86 , mark^#(U52(X1, X2)) -> c_30(a__U52^#(mark(X1), X2)) 1139.53/298.86 , mark^#(U61(X1, X2, X3, X4)) -> 1139.53/298.86 c_31(a__U61^#(mark(X1), X2, X3, X4)) 1139.53/298.86 , mark^#(U62(X1, X2, X3, X4)) -> 1139.53/298.86 c_32(a__U62^#(mark(X1), X2, X3, X4)) 1139.53/298.86 , mark^#(U63(X1, X2, X3, X4)) -> 1139.53/298.86 c_33(a__U63^#(mark(X1), X2, X3, X4)) 1139.53/298.86 , mark^#(U64(X1, X2)) -> c_34(a__U64^#(mark(X1), X2)) 1139.53/298.86 , mark^#(U71(X1, X2)) -> c_35(a__U71^#(mark(X1), X2)) 1139.53/298.86 , mark^#(U72(X1, X2)) -> c_36(a__U72^#(mark(X1), X2)) 1139.53/298.86 , mark^#(U81(X1, X2, X3)) -> c_37(a__U81^#(mark(X1), X2, X3)) 1139.53/298.86 , mark^#(U82(X1, X2, X3)) -> c_38(a__U82^#(mark(X1), X2, X3)) 1139.53/298.86 , mark^#(fst(X)) -> c_39(a__fst^#(mark(X))) 1139.53/298.86 , mark^#(sel(X1, X2)) -> c_40(a__sel^#(mark(X1), mark(X2))) 1139.53/298.86 , mark^#(tail(X)) -> c_41(a__tail^#(mark(X))) 1139.53/298.86 , mark^#(take(X1, X2)) -> c_42(a__take^#(mark(X1), mark(X2))) 1139.53/298.86 , a__natsFrom^#(N) -> c_81(mark^#(N), N) 1139.53/298.86 , a__natsFrom^#(X) -> c_82(X) 1139.53/298.86 , a__U21^#(X1, X2) -> c_43(X1, X2) 1139.53/298.86 , a__U21^#(tt(), X) -> c_44(a__U22^#(tt(), X)) 1139.53/298.86 , a__U22^#(X1, X2) -> c_45(X1, X2) 1139.53/298.86 , a__U22^#(tt(), X) -> c_46(mark^#(X)) 1139.53/298.86 , a__U31^#(X1, X2) -> c_47(X1, X2) 1139.53/298.86 , a__U31^#(tt(), N) -> c_48(a__U32^#(tt(), N)) 1139.53/298.86 , a__U32^#(X1, X2) -> c_49(X1, X2) 1139.53/298.86 , a__U32^#(tt(), N) -> c_50(mark^#(N)) 1139.53/298.86 , a__U41^#(X1, X2, X3) -> c_51(X1, X2, X3) 1139.53/298.86 , a__U41^#(tt(), N, XS) -> c_52(a__U42^#(tt(), N, XS)) 1139.53/298.86 , a__U42^#(X1, X2, X3) -> c_53(X1, X2, X3) 1139.53/298.86 , a__U42^#(tt(), N, XS) -> 1139.53/298.86 c_54(a__head^#(a__afterNth(mark(N), mark(XS)))) 1139.53/298.86 , a__head^#(X) -> c_55(X) 1139.53/298.86 , a__head^#(cons(N, XS)) -> c_56(a__U31^#(tt(), N)) 1139.53/298.86 , a__afterNth^#(N, XS) -> c_57(a__U11^#(tt(), N, XS)) 1139.53/298.86 , a__afterNth^#(X1, X2) -> c_58(X1, X2) 1139.53/298.86 , a__U52^#(X1, X2) -> c_61(X1, X2) 1139.53/298.86 , a__U52^#(tt(), Y) -> c_62(mark^#(Y)) 1139.53/298.86 , a__U62^#(X1, X2, X3, X4) -> c_65(X1, X2, X3, X4) 1139.53/298.86 , a__U62^#(tt(), N, X, XS) -> c_66(a__U63^#(tt(), N, X, XS)) 1139.53/298.86 , a__U63^#(X1, X2, X3, X4) -> c_67(X1, X2, X3, X4) 1139.53/298.86 , a__U63^#(tt(), N, X, XS) -> 1139.53/298.86 c_68(a__U64^#(a__splitAt(mark(N), mark(XS)), X)) 1139.53/298.86 , a__U64^#(X1, X2) -> c_69(X1, X2) 1139.53/298.86 , a__U64^#(pair(YS, ZS), X) -> c_70(mark^#(X), YS, mark^#(ZS)) 1139.53/298.86 , a__U71^#(X1, X2) -> c_71(X1, X2) 1139.53/298.86 , a__U71^#(tt(), XS) -> c_72(a__U72^#(tt(), XS)) 1139.53/298.86 , a__U72^#(X1, X2) -> c_73(X1, X2) 1139.53/298.86 , a__U72^#(tt(), XS) -> c_74(mark^#(XS)) 1139.53/298.86 , a__U81^#(X1, X2, X3) -> c_75(X1, X2, X3) 1139.53/298.86 , a__U81^#(tt(), N, XS) -> c_76(a__U82^#(tt(), N, XS)) 1139.53/298.86 , a__U82^#(X1, X2, X3) -> c_77(X1, X2, X3) 1139.53/298.86 , a__U82^#(tt(), N, XS) -> 1139.53/298.86 c_78(a__fst^#(a__splitAt(mark(N), mark(XS)))) 1139.53/298.86 , a__fst^#(X) -> c_79(X) 1139.53/298.86 , a__fst^#(pair(X, Y)) -> c_80(a__U21^#(tt(), X)) 1139.53/298.86 , a__sel^#(N, XS) -> c_83(a__U41^#(tt(), N, XS)) 1139.53/298.86 , a__sel^#(X1, X2) -> c_84(X1, X2) 1139.53/298.86 , a__tail^#(X) -> c_85(X) 1139.53/298.86 , a__tail^#(cons(N, XS)) -> c_86(a__U71^#(tt(), XS)) 1139.53/298.86 , a__take^#(N, XS) -> c_87(a__U81^#(tt(), N, XS)) 1139.53/298.86 , a__take^#(X1, X2) -> c_88(X1, X2) } 1139.53/298.86 Strict Trs: 1139.53/298.86 { a__U11(X1, X2, X3) -> U11(X1, X2, X3) 1139.53/298.86 , a__U11(tt(), N, XS) -> a__U12(tt(), N, XS) 1139.53/298.86 , a__U12(X1, X2, X3) -> U12(X1, X2, X3) 1139.53/298.86 , a__U12(tt(), N, XS) -> a__snd(a__splitAt(mark(N), mark(XS))) 1139.53/298.86 , a__snd(X) -> snd(X) 1139.53/298.86 , a__snd(pair(X, Y)) -> a__U51(tt(), Y) 1139.53/298.86 , a__splitAt(X1, X2) -> splitAt(X1, X2) 1139.53/298.86 , a__splitAt(s(N), cons(X, XS)) -> a__U61(tt(), N, X, XS) 1139.53/298.86 , a__splitAt(0(), XS) -> pair(nil(), mark(XS)) 1139.53/298.86 , mark(tt()) -> tt() 1139.53/298.86 , mark(pair(X1, X2)) -> pair(mark(X1), mark(X2)) 1139.53/298.86 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1139.53/298.86 , mark(natsFrom(X)) -> a__natsFrom(mark(X)) 1139.53/298.86 , mark(s(X)) -> s(mark(X)) 1139.53/298.86 , mark(0()) -> 0() 1139.53/298.86 , mark(nil()) -> nil() 1139.53/298.86 , mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) 1139.53/298.86 , mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) 1139.53/298.86 , mark(snd(X)) -> a__snd(mark(X)) 1139.53/298.86 , mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2)) 1139.53/298.86 , mark(U21(X1, X2)) -> a__U21(mark(X1), X2) 1139.53/298.86 , mark(U22(X1, X2)) -> a__U22(mark(X1), X2) 1139.53/298.86 , mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 1139.53/298.86 , mark(U32(X1, X2)) -> a__U32(mark(X1), X2) 1139.53/298.86 , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 1139.53/298.86 , mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) 1139.53/298.86 , mark(head(X)) -> a__head(mark(X)) 1139.53/298.86 , mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2)) 1139.53/298.86 , mark(U51(X1, X2)) -> a__U51(mark(X1), X2) 1139.53/298.86 , mark(U52(X1, X2)) -> a__U52(mark(X1), X2) 1139.53/298.86 , mark(U61(X1, X2, X3, X4)) -> a__U61(mark(X1), X2, X3, X4) 1139.53/298.86 , mark(U62(X1, X2, X3, X4)) -> a__U62(mark(X1), X2, X3, X4) 1139.53/298.86 , mark(U63(X1, X2, X3, X4)) -> a__U63(mark(X1), X2, X3, X4) 1139.53/298.86 , mark(U64(X1, X2)) -> a__U64(mark(X1), X2) 1139.53/298.86 , mark(U71(X1, X2)) -> a__U71(mark(X1), X2) 1139.53/298.86 , mark(U72(X1, X2)) -> a__U72(mark(X1), X2) 1139.53/298.86 , mark(U81(X1, X2, X3)) -> a__U81(mark(X1), X2, X3) 1139.53/298.86 , mark(U82(X1, X2, X3)) -> a__U82(mark(X1), X2, X3) 1139.53/298.86 , mark(fst(X)) -> a__fst(mark(X)) 1139.53/298.86 , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 1139.53/298.86 , mark(tail(X)) -> a__tail(mark(X)) 1139.53/298.86 , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) 1139.53/298.86 , a__U21(X1, X2) -> U21(X1, X2) 1139.53/298.86 , a__U21(tt(), X) -> a__U22(tt(), X) 1139.53/298.86 , a__U22(X1, X2) -> U22(X1, X2) 1139.53/298.86 , a__U22(tt(), X) -> mark(X) 1139.53/298.86 , a__U31(X1, X2) -> U31(X1, X2) 1139.53/298.86 , a__U31(tt(), N) -> a__U32(tt(), N) 1139.53/298.86 , a__U32(X1, X2) -> U32(X1, X2) 1139.53/298.86 , a__U32(tt(), N) -> mark(N) 1139.53/298.86 , a__U41(X1, X2, X3) -> U41(X1, X2, X3) 1139.53/298.86 , a__U41(tt(), N, XS) -> a__U42(tt(), N, XS) 1139.53/298.86 , a__U42(X1, X2, X3) -> U42(X1, X2, X3) 1139.53/298.86 , a__U42(tt(), N, XS) -> a__head(a__afterNth(mark(N), mark(XS))) 1139.53/298.86 , a__head(X) -> head(X) 1139.53/298.86 , a__head(cons(N, XS)) -> a__U31(tt(), N) 1139.53/298.86 , a__afterNth(N, XS) -> a__U11(tt(), N, XS) 1139.53/298.86 , a__afterNth(X1, X2) -> afterNth(X1, X2) 1139.53/298.86 , a__U51(X1, X2) -> U51(X1, X2) 1139.53/298.86 , a__U51(tt(), Y) -> a__U52(tt(), Y) 1139.53/298.86 , a__U52(X1, X2) -> U52(X1, X2) 1139.53/298.86 , a__U52(tt(), Y) -> mark(Y) 1139.53/298.86 , a__U61(X1, X2, X3, X4) -> U61(X1, X2, X3, X4) 1139.53/298.86 , a__U61(tt(), N, X, XS) -> a__U62(tt(), N, X, XS) 1139.53/298.86 , a__U62(X1, X2, X3, X4) -> U62(X1, X2, X3, X4) 1139.53/298.86 , a__U62(tt(), N, X, XS) -> a__U63(tt(), N, X, XS) 1139.53/298.86 , a__U63(X1, X2, X3, X4) -> U63(X1, X2, X3, X4) 1139.53/298.86 , a__U63(tt(), N, X, XS) -> 1139.53/298.86 a__U64(a__splitAt(mark(N), mark(XS)), X) 1139.53/298.86 , a__U64(X1, X2) -> U64(X1, X2) 1139.53/298.86 , a__U64(pair(YS, ZS), X) -> pair(cons(mark(X), YS), mark(ZS)) 1139.53/298.86 , a__U71(X1, X2) -> U71(X1, X2) 1139.53/298.86 , a__U71(tt(), XS) -> a__U72(tt(), XS) 1139.53/298.86 , a__U72(X1, X2) -> U72(X1, X2) 1139.53/298.86 , a__U72(tt(), XS) -> mark(XS) 1139.53/298.86 , a__U81(X1, X2, X3) -> U81(X1, X2, X3) 1139.53/298.86 , a__U81(tt(), N, XS) -> a__U82(tt(), N, XS) 1139.53/298.86 , a__U82(X1, X2, X3) -> U82(X1, X2, X3) 1139.53/298.86 , a__U82(tt(), N, XS) -> a__fst(a__splitAt(mark(N), mark(XS))) 1139.53/298.86 , a__fst(X) -> fst(X) 1139.53/298.86 , a__fst(pair(X, Y)) -> a__U21(tt(), X) 1139.53/298.86 , a__natsFrom(N) -> cons(mark(N), natsFrom(s(N))) 1139.53/298.86 , a__natsFrom(X) -> natsFrom(X) 1139.53/298.86 , a__sel(N, XS) -> a__U41(tt(), N, XS) 1139.53/298.86 , a__sel(X1, X2) -> sel(X1, X2) 1139.53/298.86 , a__tail(X) -> tail(X) 1139.53/298.86 , a__tail(cons(N, XS)) -> a__U71(tt(), XS) 1139.53/298.86 , a__take(N, XS) -> a__U81(tt(), N, XS) 1139.53/298.86 , a__take(X1, X2) -> take(X1, X2) } 1139.53/298.86 Obligation: 1139.53/298.86 runtime complexity 1139.53/298.86 Answer: 1139.53/298.86 MAYBE 1139.53/298.86 1139.53/298.86 We estimate the number of application of {14,19,20} by applications 1139.53/298.86 of Pre({14,19,20}) = 1139.53/298.86 {1,3,5,7,9,11,12,15,16,18,47,48,49,51,52,53,55,56,57,59,61,64,65,66,67,69,71,72,73,75,76,77,79,81,84,85,88}. 1139.53/298.86 Here rules are labeled as follows: 1139.53/298.86 1139.53/298.86 DPs: 1139.53/298.86 { 1: a__U11^#(X1, X2, X3) -> c_1(X1, X2, X3) 1139.53/298.86 , 2: a__U11^#(tt(), N, XS) -> c_2(a__U12^#(tt(), N, XS)) 1139.53/298.86 , 3: a__U12^#(X1, X2, X3) -> c_3(X1, X2, X3) 1139.53/298.86 , 4: a__U12^#(tt(), N, XS) -> 1139.53/298.86 c_4(a__snd^#(a__splitAt(mark(N), mark(XS)))) 1139.53/298.86 , 5: a__snd^#(X) -> c_5(X) 1139.53/298.86 , 6: a__snd^#(pair(X, Y)) -> c_6(a__U51^#(tt(), Y)) 1139.53/298.86 , 7: a__U51^#(X1, X2) -> c_59(X1, X2) 1139.53/298.86 , 8: a__U51^#(tt(), Y) -> c_60(a__U52^#(tt(), Y)) 1139.53/298.86 , 9: a__splitAt^#(X1, X2) -> c_7(X1, X2) 1139.53/298.86 , 10: a__splitAt^#(s(N), cons(X, XS)) -> 1139.53/298.86 c_8(a__U61^#(tt(), N, X, XS)) 1139.53/298.86 , 11: a__splitAt^#(0(), XS) -> c_9(mark^#(XS)) 1139.53/298.86 , 12: a__U61^#(X1, X2, X3, X4) -> c_63(X1, X2, X3, X4) 1139.53/298.86 , 13: a__U61^#(tt(), N, X, XS) -> c_64(a__U62^#(tt(), N, X, XS)) 1139.53/298.86 , 14: mark^#(tt()) -> c_10() 1139.53/298.86 , 15: mark^#(pair(X1, X2)) -> c_11(mark^#(X1), mark^#(X2)) 1139.53/298.86 , 16: mark^#(cons(X1, X2)) -> c_12(mark^#(X1), X2) 1139.53/298.86 , 17: mark^#(natsFrom(X)) -> c_13(a__natsFrom^#(mark(X))) 1139.53/298.86 , 18: mark^#(s(X)) -> c_14(mark^#(X)) 1139.53/298.86 , 19: mark^#(0()) -> c_15() 1139.53/298.86 , 20: mark^#(nil()) -> c_16() 1139.53/298.86 , 21: mark^#(U11(X1, X2, X3)) -> c_17(a__U11^#(mark(X1), X2, X3)) 1139.53/298.86 , 22: mark^#(U12(X1, X2, X3)) -> c_18(a__U12^#(mark(X1), X2, X3)) 1139.53/298.86 , 23: mark^#(snd(X)) -> c_19(a__snd^#(mark(X))) 1139.53/298.86 , 24: mark^#(splitAt(X1, X2)) -> 1139.53/298.86 c_20(a__splitAt^#(mark(X1), mark(X2))) 1139.53/298.86 , 25: mark^#(U21(X1, X2)) -> c_21(a__U21^#(mark(X1), X2)) 1139.53/298.86 , 26: mark^#(U22(X1, X2)) -> c_22(a__U22^#(mark(X1), X2)) 1139.53/298.86 , 27: mark^#(U31(X1, X2)) -> c_23(a__U31^#(mark(X1), X2)) 1139.53/298.86 , 28: mark^#(U32(X1, X2)) -> c_24(a__U32^#(mark(X1), X2)) 1139.53/298.86 , 29: mark^#(U41(X1, X2, X3)) -> c_25(a__U41^#(mark(X1), X2, X3)) 1139.53/298.86 , 30: mark^#(U42(X1, X2, X3)) -> c_26(a__U42^#(mark(X1), X2, X3)) 1139.53/298.86 , 31: mark^#(head(X)) -> c_27(a__head^#(mark(X))) 1139.53/298.86 , 32: mark^#(afterNth(X1, X2)) -> 1139.53/298.86 c_28(a__afterNth^#(mark(X1), mark(X2))) 1139.53/298.86 , 33: mark^#(U51(X1, X2)) -> c_29(a__U51^#(mark(X1), X2)) 1139.53/298.86 , 34: mark^#(U52(X1, X2)) -> c_30(a__U52^#(mark(X1), X2)) 1139.53/298.86 , 35: mark^#(U61(X1, X2, X3, X4)) -> 1139.53/298.86 c_31(a__U61^#(mark(X1), X2, X3, X4)) 1139.53/298.86 , 36: mark^#(U62(X1, X2, X3, X4)) -> 1139.53/298.86 c_32(a__U62^#(mark(X1), X2, X3, X4)) 1139.53/298.86 , 37: mark^#(U63(X1, X2, X3, X4)) -> 1139.53/298.86 c_33(a__U63^#(mark(X1), X2, X3, X4)) 1139.53/298.86 , 38: mark^#(U64(X1, X2)) -> c_34(a__U64^#(mark(X1), X2)) 1139.53/298.86 , 39: mark^#(U71(X1, X2)) -> c_35(a__U71^#(mark(X1), X2)) 1139.53/298.86 , 40: mark^#(U72(X1, X2)) -> c_36(a__U72^#(mark(X1), X2)) 1139.53/298.86 , 41: mark^#(U81(X1, X2, X3)) -> c_37(a__U81^#(mark(X1), X2, X3)) 1139.53/298.86 , 42: mark^#(U82(X1, X2, X3)) -> c_38(a__U82^#(mark(X1), X2, X3)) 1139.53/298.86 , 43: mark^#(fst(X)) -> c_39(a__fst^#(mark(X))) 1139.53/298.86 , 44: mark^#(sel(X1, X2)) -> c_40(a__sel^#(mark(X1), mark(X2))) 1139.53/298.86 , 45: mark^#(tail(X)) -> c_41(a__tail^#(mark(X))) 1139.53/298.86 , 46: mark^#(take(X1, X2)) -> c_42(a__take^#(mark(X1), mark(X2))) 1139.53/298.86 , 47: a__natsFrom^#(N) -> c_81(mark^#(N), N) 1139.53/298.86 , 48: a__natsFrom^#(X) -> c_82(X) 1139.53/298.86 , 49: a__U21^#(X1, X2) -> c_43(X1, X2) 1139.53/298.86 , 50: a__U21^#(tt(), X) -> c_44(a__U22^#(tt(), X)) 1139.53/298.86 , 51: a__U22^#(X1, X2) -> c_45(X1, X2) 1139.53/298.86 , 52: a__U22^#(tt(), X) -> c_46(mark^#(X)) 1139.53/298.86 , 53: a__U31^#(X1, X2) -> c_47(X1, X2) 1139.53/298.86 , 54: a__U31^#(tt(), N) -> c_48(a__U32^#(tt(), N)) 1139.53/298.86 , 55: a__U32^#(X1, X2) -> c_49(X1, X2) 1139.53/298.86 , 56: a__U32^#(tt(), N) -> c_50(mark^#(N)) 1139.53/298.86 , 57: a__U41^#(X1, X2, X3) -> c_51(X1, X2, X3) 1139.53/298.86 , 58: a__U41^#(tt(), N, XS) -> c_52(a__U42^#(tt(), N, XS)) 1139.53/298.86 , 59: a__U42^#(X1, X2, X3) -> c_53(X1, X2, X3) 1139.53/298.86 , 60: a__U42^#(tt(), N, XS) -> 1139.53/298.86 c_54(a__head^#(a__afterNth(mark(N), mark(XS)))) 1139.53/298.86 , 61: a__head^#(X) -> c_55(X) 1139.53/298.86 , 62: a__head^#(cons(N, XS)) -> c_56(a__U31^#(tt(), N)) 1139.53/298.86 , 63: a__afterNth^#(N, XS) -> c_57(a__U11^#(tt(), N, XS)) 1139.53/298.86 , 64: a__afterNth^#(X1, X2) -> c_58(X1, X2) 1139.53/298.86 , 65: a__U52^#(X1, X2) -> c_61(X1, X2) 1139.53/298.86 , 66: a__U52^#(tt(), Y) -> c_62(mark^#(Y)) 1139.53/298.88 , 67: a__U62^#(X1, X2, X3, X4) -> c_65(X1, X2, X3, X4) 1139.53/298.88 , 68: a__U62^#(tt(), N, X, XS) -> c_66(a__U63^#(tt(), N, X, XS)) 1139.53/298.88 , 69: a__U63^#(X1, X2, X3, X4) -> c_67(X1, X2, X3, X4) 1139.53/298.88 , 70: a__U63^#(tt(), N, X, XS) -> 1139.53/298.88 c_68(a__U64^#(a__splitAt(mark(N), mark(XS)), X)) 1139.53/298.88 , 71: a__U64^#(X1, X2) -> c_69(X1, X2) 1139.53/298.88 , 72: a__U64^#(pair(YS, ZS), X) -> c_70(mark^#(X), YS, mark^#(ZS)) 1139.53/298.88 , 73: a__U71^#(X1, X2) -> c_71(X1, X2) 1139.53/298.88 , 74: a__U71^#(tt(), XS) -> c_72(a__U72^#(tt(), XS)) 1139.53/298.88 , 75: a__U72^#(X1, X2) -> c_73(X1, X2) 1139.53/298.88 , 76: a__U72^#(tt(), XS) -> c_74(mark^#(XS)) 1139.53/298.88 , 77: a__U81^#(X1, X2, X3) -> c_75(X1, X2, X3) 1139.53/298.88 , 78: a__U81^#(tt(), N, XS) -> c_76(a__U82^#(tt(), N, XS)) 1139.53/298.88 , 79: a__U82^#(X1, X2, X3) -> c_77(X1, X2, X3) 1139.53/298.88 , 80: a__U82^#(tt(), N, XS) -> 1139.53/298.88 c_78(a__fst^#(a__splitAt(mark(N), mark(XS)))) 1139.53/298.88 , 81: a__fst^#(X) -> c_79(X) 1139.53/298.88 , 82: a__fst^#(pair(X, Y)) -> c_80(a__U21^#(tt(), X)) 1139.53/298.88 , 83: a__sel^#(N, XS) -> c_83(a__U41^#(tt(), N, XS)) 1139.53/298.88 , 84: a__sel^#(X1, X2) -> c_84(X1, X2) 1139.53/298.88 , 85: a__tail^#(X) -> c_85(X) 1139.53/298.88 , 86: a__tail^#(cons(N, XS)) -> c_86(a__U71^#(tt(), XS)) 1139.53/298.88 , 87: a__take^#(N, XS) -> c_87(a__U81^#(tt(), N, XS)) 1139.53/298.88 , 88: a__take^#(X1, X2) -> c_88(X1, X2) } 1139.53/298.88 1139.53/298.88 We are left with following problem, upon which TcT provides the 1139.53/298.88 certificate MAYBE. 1139.53/298.88 1139.53/298.88 Strict DPs: 1139.53/298.88 { a__U11^#(X1, X2, X3) -> c_1(X1, X2, X3) 1139.53/298.88 , a__U11^#(tt(), N, XS) -> c_2(a__U12^#(tt(), N, XS)) 1139.53/298.88 , a__U12^#(X1, X2, X3) -> c_3(X1, X2, X3) 1139.53/298.88 , a__U12^#(tt(), N, XS) -> 1139.53/298.88 c_4(a__snd^#(a__splitAt(mark(N), mark(XS)))) 1139.53/298.88 , a__snd^#(X) -> c_5(X) 1139.53/298.88 , a__snd^#(pair(X, Y)) -> c_6(a__U51^#(tt(), Y)) 1139.53/298.88 , a__U51^#(X1, X2) -> c_59(X1, X2) 1139.53/298.88 , a__U51^#(tt(), Y) -> c_60(a__U52^#(tt(), Y)) 1139.53/298.88 , a__splitAt^#(X1, X2) -> c_7(X1, X2) 1139.53/298.88 , a__splitAt^#(s(N), cons(X, XS)) -> c_8(a__U61^#(tt(), N, X, XS)) 1139.53/298.88 , a__splitAt^#(0(), XS) -> c_9(mark^#(XS)) 1139.53/298.88 , a__U61^#(X1, X2, X3, X4) -> c_63(X1, X2, X3, X4) 1139.53/298.88 , a__U61^#(tt(), N, X, XS) -> c_64(a__U62^#(tt(), N, X, XS)) 1139.53/298.88 , mark^#(pair(X1, X2)) -> c_11(mark^#(X1), mark^#(X2)) 1139.53/298.88 , mark^#(cons(X1, X2)) -> c_12(mark^#(X1), X2) 1139.53/298.88 , mark^#(natsFrom(X)) -> c_13(a__natsFrom^#(mark(X))) 1139.53/298.88 , mark^#(s(X)) -> c_14(mark^#(X)) 1139.53/298.88 , mark^#(U11(X1, X2, X3)) -> c_17(a__U11^#(mark(X1), X2, X3)) 1139.53/298.88 , mark^#(U12(X1, X2, X3)) -> c_18(a__U12^#(mark(X1), X2, X3)) 1139.53/298.88 , mark^#(snd(X)) -> c_19(a__snd^#(mark(X))) 1139.53/298.88 , mark^#(splitAt(X1, X2)) -> c_20(a__splitAt^#(mark(X1), mark(X2))) 1139.53/298.88 , mark^#(U21(X1, X2)) -> c_21(a__U21^#(mark(X1), X2)) 1139.53/298.88 , mark^#(U22(X1, X2)) -> c_22(a__U22^#(mark(X1), X2)) 1139.53/298.88 , mark^#(U31(X1, X2)) -> c_23(a__U31^#(mark(X1), X2)) 1139.53/298.88 , mark^#(U32(X1, X2)) -> c_24(a__U32^#(mark(X1), X2)) 1139.53/298.88 , mark^#(U41(X1, X2, X3)) -> c_25(a__U41^#(mark(X1), X2, X3)) 1139.53/298.88 , mark^#(U42(X1, X2, X3)) -> c_26(a__U42^#(mark(X1), X2, X3)) 1139.53/298.88 , mark^#(head(X)) -> c_27(a__head^#(mark(X))) 1139.53/298.88 , mark^#(afterNth(X1, X2)) -> 1139.53/298.88 c_28(a__afterNth^#(mark(X1), mark(X2))) 1139.53/298.88 , mark^#(U51(X1, X2)) -> c_29(a__U51^#(mark(X1), X2)) 1139.53/298.88 , mark^#(U52(X1, X2)) -> c_30(a__U52^#(mark(X1), X2)) 1139.53/298.88 , mark^#(U61(X1, X2, X3, X4)) -> 1139.53/298.88 c_31(a__U61^#(mark(X1), X2, X3, X4)) 1139.53/298.88 , mark^#(U62(X1, X2, X3, X4)) -> 1139.53/298.88 c_32(a__U62^#(mark(X1), X2, X3, X4)) 1139.53/298.88 , mark^#(U63(X1, X2, X3, X4)) -> 1139.53/298.88 c_33(a__U63^#(mark(X1), X2, X3, X4)) 1139.53/298.88 , mark^#(U64(X1, X2)) -> c_34(a__U64^#(mark(X1), X2)) 1139.53/298.88 , mark^#(U71(X1, X2)) -> c_35(a__U71^#(mark(X1), X2)) 1139.53/298.88 , mark^#(U72(X1, X2)) -> c_36(a__U72^#(mark(X1), X2)) 1139.53/298.88 , mark^#(U81(X1, X2, X3)) -> c_37(a__U81^#(mark(X1), X2, X3)) 1139.53/298.88 , mark^#(U82(X1, X2, X3)) -> c_38(a__U82^#(mark(X1), X2, X3)) 1139.53/298.88 , mark^#(fst(X)) -> c_39(a__fst^#(mark(X))) 1139.53/298.88 , mark^#(sel(X1, X2)) -> c_40(a__sel^#(mark(X1), mark(X2))) 1139.53/298.88 , mark^#(tail(X)) -> c_41(a__tail^#(mark(X))) 1139.53/298.88 , mark^#(take(X1, X2)) -> c_42(a__take^#(mark(X1), mark(X2))) 1139.53/298.88 , a__natsFrom^#(N) -> c_81(mark^#(N), N) 1139.53/298.88 , a__natsFrom^#(X) -> c_82(X) 1139.53/298.88 , a__U21^#(X1, X2) -> c_43(X1, X2) 1139.53/298.88 , a__U21^#(tt(), X) -> c_44(a__U22^#(tt(), X)) 1139.53/298.88 , a__U22^#(X1, X2) -> c_45(X1, X2) 1139.53/298.88 , a__U22^#(tt(), X) -> c_46(mark^#(X)) 1139.53/298.88 , a__U31^#(X1, X2) -> c_47(X1, X2) 1139.53/298.88 , a__U31^#(tt(), N) -> c_48(a__U32^#(tt(), N)) 1139.53/298.88 , a__U32^#(X1, X2) -> c_49(X1, X2) 1139.53/298.88 , a__U32^#(tt(), N) -> c_50(mark^#(N)) 1139.53/298.88 , a__U41^#(X1, X2, X3) -> c_51(X1, X2, X3) 1139.53/298.88 , a__U41^#(tt(), N, XS) -> c_52(a__U42^#(tt(), N, XS)) 1139.53/298.88 , a__U42^#(X1, X2, X3) -> c_53(X1, X2, X3) 1139.53/298.88 , a__U42^#(tt(), N, XS) -> 1139.53/298.88 c_54(a__head^#(a__afterNth(mark(N), mark(XS)))) 1139.53/298.88 , a__head^#(X) -> c_55(X) 1139.53/298.88 , a__head^#(cons(N, XS)) -> c_56(a__U31^#(tt(), N)) 1139.53/298.88 , a__afterNth^#(N, XS) -> c_57(a__U11^#(tt(), N, XS)) 1139.53/298.88 , a__afterNth^#(X1, X2) -> c_58(X1, X2) 1139.53/298.88 , a__U52^#(X1, X2) -> c_61(X1, X2) 1139.53/298.88 , a__U52^#(tt(), Y) -> c_62(mark^#(Y)) 1139.53/298.88 , a__U62^#(X1, X2, X3, X4) -> c_65(X1, X2, X3, X4) 1139.53/298.88 , a__U62^#(tt(), N, X, XS) -> c_66(a__U63^#(tt(), N, X, XS)) 1139.53/298.88 , a__U63^#(X1, X2, X3, X4) -> c_67(X1, X2, X3, X4) 1139.53/298.88 , a__U63^#(tt(), N, X, XS) -> 1139.53/298.88 c_68(a__U64^#(a__splitAt(mark(N), mark(XS)), X)) 1139.53/298.88 , a__U64^#(X1, X2) -> c_69(X1, X2) 1139.53/298.88 , a__U64^#(pair(YS, ZS), X) -> c_70(mark^#(X), YS, mark^#(ZS)) 1139.53/298.88 , a__U71^#(X1, X2) -> c_71(X1, X2) 1139.53/298.88 , a__U71^#(tt(), XS) -> c_72(a__U72^#(tt(), XS)) 1139.53/298.88 , a__U72^#(X1, X2) -> c_73(X1, X2) 1139.53/298.88 , a__U72^#(tt(), XS) -> c_74(mark^#(XS)) 1139.53/298.88 , a__U81^#(X1, X2, X3) -> c_75(X1, X2, X3) 1139.53/298.88 , a__U81^#(tt(), N, XS) -> c_76(a__U82^#(tt(), N, XS)) 1139.53/298.88 , a__U82^#(X1, X2, X3) -> c_77(X1, X2, X3) 1139.53/298.88 , a__U82^#(tt(), N, XS) -> 1139.53/298.88 c_78(a__fst^#(a__splitAt(mark(N), mark(XS)))) 1139.53/298.88 , a__fst^#(X) -> c_79(X) 1139.53/298.88 , a__fst^#(pair(X, Y)) -> c_80(a__U21^#(tt(), X)) 1139.53/298.88 , a__sel^#(N, XS) -> c_83(a__U41^#(tt(), N, XS)) 1139.53/298.88 , a__sel^#(X1, X2) -> c_84(X1, X2) 1139.53/298.88 , a__tail^#(X) -> c_85(X) 1139.53/298.88 , a__tail^#(cons(N, XS)) -> c_86(a__U71^#(tt(), XS)) 1139.53/298.88 , a__take^#(N, XS) -> c_87(a__U81^#(tt(), N, XS)) 1139.53/298.88 , a__take^#(X1, X2) -> c_88(X1, X2) } 1139.53/298.88 Strict Trs: 1139.53/298.88 { a__U11(X1, X2, X3) -> U11(X1, X2, X3) 1139.53/298.88 , a__U11(tt(), N, XS) -> a__U12(tt(), N, XS) 1139.53/298.88 , a__U12(X1, X2, X3) -> U12(X1, X2, X3) 1139.53/298.88 , a__U12(tt(), N, XS) -> a__snd(a__splitAt(mark(N), mark(XS))) 1139.53/298.88 , a__snd(X) -> snd(X) 1139.53/298.88 , a__snd(pair(X, Y)) -> a__U51(tt(), Y) 1139.53/298.88 , a__splitAt(X1, X2) -> splitAt(X1, X2) 1139.53/298.88 , a__splitAt(s(N), cons(X, XS)) -> a__U61(tt(), N, X, XS) 1139.53/298.88 , a__splitAt(0(), XS) -> pair(nil(), mark(XS)) 1139.53/298.88 , mark(tt()) -> tt() 1139.53/298.88 , mark(pair(X1, X2)) -> pair(mark(X1), mark(X2)) 1139.53/298.88 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1139.53/298.88 , mark(natsFrom(X)) -> a__natsFrom(mark(X)) 1139.53/298.88 , mark(s(X)) -> s(mark(X)) 1139.53/298.88 , mark(0()) -> 0() 1139.53/298.88 , mark(nil()) -> nil() 1139.53/298.88 , mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) 1139.53/298.88 , mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) 1139.53/298.88 , mark(snd(X)) -> a__snd(mark(X)) 1139.53/298.88 , mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2)) 1139.53/298.88 , mark(U21(X1, X2)) -> a__U21(mark(X1), X2) 1139.53/298.88 , mark(U22(X1, X2)) -> a__U22(mark(X1), X2) 1139.53/298.88 , mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 1139.53/298.88 , mark(U32(X1, X2)) -> a__U32(mark(X1), X2) 1139.53/298.88 , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 1139.53/298.88 , mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) 1139.53/298.88 , mark(head(X)) -> a__head(mark(X)) 1139.53/298.88 , mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2)) 1139.53/298.88 , mark(U51(X1, X2)) -> a__U51(mark(X1), X2) 1139.53/298.88 , mark(U52(X1, X2)) -> a__U52(mark(X1), X2) 1139.53/298.88 , mark(U61(X1, X2, X3, X4)) -> a__U61(mark(X1), X2, X3, X4) 1139.53/298.88 , mark(U62(X1, X2, X3, X4)) -> a__U62(mark(X1), X2, X3, X4) 1139.53/298.88 , mark(U63(X1, X2, X3, X4)) -> a__U63(mark(X1), X2, X3, X4) 1139.53/298.88 , mark(U64(X1, X2)) -> a__U64(mark(X1), X2) 1139.53/298.88 , mark(U71(X1, X2)) -> a__U71(mark(X1), X2) 1139.53/298.88 , mark(U72(X1, X2)) -> a__U72(mark(X1), X2) 1139.53/298.88 , mark(U81(X1, X2, X3)) -> a__U81(mark(X1), X2, X3) 1139.53/298.88 , mark(U82(X1, X2, X3)) -> a__U82(mark(X1), X2, X3) 1139.53/298.88 , mark(fst(X)) -> a__fst(mark(X)) 1139.53/298.89 , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 1139.53/298.89 , mark(tail(X)) -> a__tail(mark(X)) 1139.53/298.89 , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) 1139.53/298.89 , a__U21(X1, X2) -> U21(X1, X2) 1139.53/298.89 , a__U21(tt(), X) -> a__U22(tt(), X) 1139.53/298.89 , a__U22(X1, X2) -> U22(X1, X2) 1139.53/298.89 , a__U22(tt(), X) -> mark(X) 1139.53/298.89 , a__U31(X1, X2) -> U31(X1, X2) 1139.53/298.89 , a__U31(tt(), N) -> a__U32(tt(), N) 1139.53/298.89 , a__U32(X1, X2) -> U32(X1, X2) 1139.53/298.89 , a__U32(tt(), N) -> mark(N) 1139.53/298.89 , a__U41(X1, X2, X3) -> U41(X1, X2, X3) 1139.53/298.89 , a__U41(tt(), N, XS) -> a__U42(tt(), N, XS) 1139.53/298.89 , a__U42(X1, X2, X3) -> U42(X1, X2, X3) 1139.53/298.89 , a__U42(tt(), N, XS) -> a__head(a__afterNth(mark(N), mark(XS))) 1139.53/298.89 , a__head(X) -> head(X) 1139.53/298.89 , a__head(cons(N, XS)) -> a__U31(tt(), N) 1139.53/298.89 , a__afterNth(N, XS) -> a__U11(tt(), N, XS) 1139.53/298.89 , a__afterNth(X1, X2) -> afterNth(X1, X2) 1139.53/298.89 , a__U51(X1, X2) -> U51(X1, X2) 1139.53/298.89 , a__U51(tt(), Y) -> a__U52(tt(), Y) 1139.53/298.89 , a__U52(X1, X2) -> U52(X1, X2) 1139.53/298.89 , a__U52(tt(), Y) -> mark(Y) 1139.53/298.89 , a__U61(X1, X2, X3, X4) -> U61(X1, X2, X3, X4) 1139.53/298.89 , a__U61(tt(), N, X, XS) -> a__U62(tt(), N, X, XS) 1139.53/298.89 , a__U62(X1, X2, X3, X4) -> U62(X1, X2, X3, X4) 1139.53/298.89 , a__U62(tt(), N, X, XS) -> a__U63(tt(), N, X, XS) 1139.53/298.89 , a__U63(X1, X2, X3, X4) -> U63(X1, X2, X3, X4) 1139.53/298.89 , a__U63(tt(), N, X, XS) -> 1139.53/298.89 a__U64(a__splitAt(mark(N), mark(XS)), X) 1139.53/298.89 , a__U64(X1, X2) -> U64(X1, X2) 1139.53/298.89 , a__U64(pair(YS, ZS), X) -> pair(cons(mark(X), YS), mark(ZS)) 1139.53/298.89 , a__U71(X1, X2) -> U71(X1, X2) 1139.53/298.89 , a__U71(tt(), XS) -> a__U72(tt(), XS) 1139.53/298.89 , a__U72(X1, X2) -> U72(X1, X2) 1139.53/298.89 , a__U72(tt(), XS) -> mark(XS) 1139.53/298.89 , a__U81(X1, X2, X3) -> U81(X1, X2, X3) 1139.53/298.89 , a__U81(tt(), N, XS) -> a__U82(tt(), N, XS) 1139.53/298.89 , a__U82(X1, X2, X3) -> U82(X1, X2, X3) 1139.53/298.89 , a__U82(tt(), N, XS) -> a__fst(a__splitAt(mark(N), mark(XS))) 1139.53/298.89 , a__fst(X) -> fst(X) 1139.53/298.89 , a__fst(pair(X, Y)) -> a__U21(tt(), X) 1139.53/298.89 , a__natsFrom(N) -> cons(mark(N), natsFrom(s(N))) 1139.53/298.89 , a__natsFrom(X) -> natsFrom(X) 1139.53/298.89 , a__sel(N, XS) -> a__U41(tt(), N, XS) 1139.53/298.89 , a__sel(X1, X2) -> sel(X1, X2) 1139.53/298.89 , a__tail(X) -> tail(X) 1139.53/298.89 , a__tail(cons(N, XS)) -> a__U71(tt(), XS) 1139.53/298.89 , a__take(N, XS) -> a__U81(tt(), N, XS) 1139.53/298.89 , a__take(X1, X2) -> take(X1, X2) } 1139.53/298.89 Weak DPs: 1139.53/298.89 { mark^#(tt()) -> c_10() 1139.53/298.89 , mark^#(0()) -> c_15() 1139.53/298.89 , mark^#(nil()) -> c_16() } 1139.53/298.89 Obligation: 1139.53/298.89 runtime complexity 1139.53/298.89 Answer: 1139.53/298.89 MAYBE 1139.53/298.89 1139.53/298.89 Empty strict component of the problem is NOT empty. 1139.53/298.89 1139.53/298.89 1139.53/298.89 Arrrr.. 1140.37/299.39 EOF