MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { U101(tt(), V1, V2) -> U102(isNaturalKind(activate(V1)), activate(V1), activate(V2)) , U102(tt(), V1, V2) -> U103(isLNatKind(activate(V2)), activate(V1), activate(V2)) , isNaturalKind(n__s(V1)) -> U221(isNaturalKind(activate(V1))) , isNaturalKind(n__0()) -> tt() , isNaturalKind(n__head(V1)) -> U211(isLNatKind(activate(V1))) , isNaturalKind(n__sel(V1, V2)) -> U231(isNaturalKind(activate(V1)), activate(V2)) , activate(X) -> X , 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)) , U103(tt(), V1, V2) -> U104(isLNatKind(activate(V2)), activate(V1), activate(V2)) , isLNatKind(n__natsFrom(V1)) -> U141(isNaturalKind(activate(V1))) , isLNatKind(n__nil()) -> tt() , isLNatKind(n__afterNth(V1, V2)) -> U111(isNaturalKind(activate(V1)), activate(V2)) , isLNatKind(n__cons(V1, V2)) -> U121(isNaturalKind(activate(V1)), activate(V2)) , isLNatKind(n__fst(V1)) -> U131(isPLNatKind(activate(V1))) , isLNatKind(n__snd(V1)) -> U151(isPLNatKind(activate(V1))) , isLNatKind(n__tail(V1)) -> U161(isLNatKind(activate(V1))) , isLNatKind(n__take(V1, V2)) -> U171(isNaturalKind(activate(V1)), activate(V2)) , U104(tt(), V1, V2) -> U105(isNatural(activate(V1)), activate(V2)) , U105(tt(), V2) -> U106(isLNat(activate(V2))) , isNatural(n__s(V1)) -> U191(isNaturalKind(activate(V1)), activate(V1)) , isNatural(n__0()) -> tt() , isNatural(n__head(V1)) -> U181(isLNatKind(activate(V1)), activate(V1)) , isNatural(n__sel(V1, V2)) -> U201(isNaturalKind(activate(V1)), activate(V1), activate(V2)) , U106(tt()) -> tt() , isLNat(n__natsFrom(V1)) -> U71(isNaturalKind(activate(V1)), activate(V1)) , isLNat(n__nil()) -> tt() , isLNat(n__afterNth(V1, V2)) -> U41(isNaturalKind(activate(V1)), activate(V1), activate(V2)) , isLNat(n__cons(V1, V2)) -> U51(isNaturalKind(activate(V1)), activate(V1), activate(V2)) , isLNat(n__fst(V1)) -> U61(isPLNatKind(activate(V1)), activate(V1)) , isLNat(n__snd(V1)) -> U81(isPLNatKind(activate(V1)), activate(V1)) , isLNat(n__tail(V1)) -> U91(isLNatKind(activate(V1)), activate(V1)) , isLNat(n__take(V1, V2)) -> U101(isNaturalKind(activate(V1)), activate(V1), activate(V2)) , U11(tt(), N, XS) -> U12(isNaturalKind(activate(N)), activate(N), activate(XS)) , U12(tt(), N, XS) -> U13(isLNat(activate(XS)), activate(N), activate(XS)) , U111(tt(), V2) -> U112(isLNatKind(activate(V2))) , U112(tt()) -> tt() , U13(tt(), N, XS) -> U14(isLNatKind(activate(XS)), activate(N), activate(XS)) , U121(tt(), V2) -> U122(isLNatKind(activate(V2))) , U122(tt()) -> tt() , U14(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS))) , U131(tt()) -> tt() , snd(X) -> n__snd(X) , snd(pair(X, Y)) -> U301(isLNat(X), X, Y) , splitAt(X1, X2) -> n__splitAt(X1, X2) , splitAt(0(), XS) -> U311(isLNat(XS), XS) , splitAt(s(N), cons(X, XS)) -> U321(isNatural(N), N, X, activate(XS)) , U141(tt()) -> tt() , U151(tt()) -> tt() , U161(tt()) -> tt() , U171(tt(), V2) -> U172(isLNatKind(activate(V2))) , U172(tt()) -> tt() , U181(tt(), V1) -> U182(isLNatKind(activate(V1)), activate(V1)) , U182(tt(), V1) -> U183(isLNat(activate(V1))) , U183(tt()) -> tt() , U191(tt(), V1) -> U192(isNaturalKind(activate(V1)), activate(V1)) , U192(tt(), V1) -> U193(isNatural(activate(V1))) , U193(tt()) -> tt() , U201(tt(), V1, V2) -> U202(isNaturalKind(activate(V1)), activate(V1), activate(V2)) , U202(tt(), V1, V2) -> U203(isLNatKind(activate(V2)), activate(V1), activate(V2)) , U203(tt(), V1, V2) -> U204(isLNatKind(activate(V2)), activate(V1), activate(V2)) , U204(tt(), V1, V2) -> U205(isNatural(activate(V1)), activate(V2)) , U205(tt(), V2) -> U206(isLNat(activate(V2))) , U206(tt()) -> tt() , U21(tt(), X, Y) -> U22(isLNatKind(activate(X)), activate(X), activate(Y)) , U22(tt(), X, Y) -> U23(isLNat(activate(Y)), activate(X), activate(Y)) , U211(tt()) -> tt() , U23(tt(), X, Y) -> U24(isLNatKind(activate(Y)), activate(X)) , U221(tt()) -> tt() , U24(tt(), X) -> activate(X) , U231(tt(), V2) -> U232(isLNatKind(activate(V2))) , U232(tt()) -> tt() , U241(tt(), V1, V2) -> U242(isLNatKind(activate(V1)), activate(V1), activate(V2)) , U242(tt(), V1, V2) -> U243(isLNatKind(activate(V2)), activate(V1), activate(V2)) , U243(tt(), V1, V2) -> U244(isLNatKind(activate(V2)), activate(V1), activate(V2)) , U244(tt(), V1, V2) -> U245(isLNat(activate(V1)), activate(V2)) , U245(tt(), V2) -> U246(isLNat(activate(V2))) , U246(tt()) -> tt() , U251(tt(), V1, V2) -> U252(isNaturalKind(activate(V1)), activate(V1), activate(V2)) , U252(tt(), V1, V2) -> U253(isLNatKind(activate(V2)), activate(V1), activate(V2)) , U253(tt(), V1, V2) -> U254(isLNatKind(activate(V2)), activate(V1), activate(V2)) , U254(tt(), V1, V2) -> U255(isNatural(activate(V1)), activate(V2)) , U255(tt(), V2) -> U256(isLNat(activate(V2))) , U256(tt()) -> tt() , U261(tt(), V2) -> U262(isLNatKind(activate(V2))) , U262(tt()) -> tt() , U271(tt(), V2) -> U272(isLNatKind(activate(V2))) , U272(tt()) -> tt() , U281(tt(), N) -> U282(isNaturalKind(activate(N)), activate(N)) , U282(tt(), N) -> cons(activate(N), n__natsFrom(n__s(activate(N)))) , cons(X1, X2) -> n__cons(X1, X2) , U291(tt(), N, XS) -> U292(isNaturalKind(activate(N)), activate(N), activate(XS)) , U292(tt(), N, XS) -> U293(isLNat(activate(XS)), activate(N), activate(XS)) , U293(tt(), N, XS) -> U294(isLNatKind(activate(XS)), activate(N), activate(XS)) , U294(tt(), N, XS) -> head(afterNth(activate(N), activate(XS))) , head(X) -> n__head(X) , head(cons(N, XS)) -> U31(isNatural(N), N, activate(XS)) , afterNth(N, XS) -> U11(isNatural(N), N, XS) , afterNth(X1, X2) -> n__afterNth(X1, X2) , U301(tt(), X, Y) -> U302(isLNatKind(activate(X)), activate(Y)) , U302(tt(), Y) -> U303(isLNat(activate(Y)), activate(Y)) , U303(tt(), Y) -> U304(isLNatKind(activate(Y)), activate(Y)) , U304(tt(), Y) -> activate(Y) , U31(tt(), N, XS) -> U32(isNaturalKind(activate(N)), activate(N), activate(XS)) , U32(tt(), N, XS) -> U33(isLNat(activate(XS)), activate(N), activate(XS)) , U311(tt(), XS) -> U312(isLNatKind(activate(XS)), activate(XS)) , U312(tt(), XS) -> pair(nil(), activate(XS)) , pair(X1, X2) -> n__pair(X1, X2) , nil() -> n__nil() , U33(tt(), N, XS) -> U34(isLNatKind(activate(XS)), activate(N)) , U321(tt(), N, X, XS) -> U322(isNaturalKind(activate(N)), activate(N), activate(X), activate(XS)) , U322(tt(), N, X, XS) -> U323(isNatural(activate(X)), activate(N), activate(X), activate(XS)) , U323(tt(), N, X, XS) -> U324(isNaturalKind(activate(X)), activate(N), activate(X), activate(XS)) , U324(tt(), N, X, XS) -> U325(isLNat(activate(XS)), activate(N), activate(X), activate(XS)) , U325(tt(), N, X, XS) -> U326(isLNatKind(activate(XS)), activate(N), activate(X), activate(XS)) , U326(tt(), N, X, XS) -> U327(splitAt(activate(N), activate(XS)), activate(X)) , U327(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) , U34(tt(), N) -> activate(N) , U331(tt(), N, XS) -> U332(isNaturalKind(activate(N)), activate(XS)) , U332(tt(), XS) -> U333(isLNat(activate(XS)), activate(XS)) , U333(tt(), XS) -> U334(isLNatKind(activate(XS)), activate(XS)) , U334(tt(), XS) -> activate(XS) , U341(tt(), N, XS) -> U342(isNaturalKind(activate(N)), activate(N), activate(XS)) , U342(tt(), N, XS) -> U343(isLNat(activate(XS)), activate(N), activate(XS)) , U343(tt(), N, XS) -> U344(isLNatKind(activate(XS)), activate(N), activate(XS)) , U344(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS))) , fst(X) -> n__fst(X) , fst(pair(X, Y)) -> U21(isLNat(X), X, Y) , U41(tt(), V1, V2) -> U42(isNaturalKind(activate(V1)), activate(V1), activate(V2)) , U42(tt(), V1, V2) -> U43(isLNatKind(activate(V2)), activate(V1), activate(V2)) , U43(tt(), V1, V2) -> U44(isLNatKind(activate(V2)), activate(V1), activate(V2)) , U44(tt(), V1, V2) -> U45(isNatural(activate(V1)), activate(V2)) , U45(tt(), V2) -> U46(isLNat(activate(V2))) , U46(tt()) -> tt() , U51(tt(), V1, V2) -> U52(isNaturalKind(activate(V1)), activate(V1), activate(V2)) , U52(tt(), V1, V2) -> U53(isLNatKind(activate(V2)), activate(V1), activate(V2)) , U53(tt(), V1, V2) -> U54(isLNatKind(activate(V2)), activate(V1), activate(V2)) , U54(tt(), V1, V2) -> U55(isNatural(activate(V1)), activate(V2)) , U55(tt(), V2) -> U56(isLNat(activate(V2))) , U56(tt()) -> tt() , U61(tt(), V1) -> U62(isPLNatKind(activate(V1)), activate(V1)) , U62(tt(), V1) -> U63(isPLNat(activate(V1))) , isPLNatKind(n__pair(V1, V2)) -> U261(isLNatKind(activate(V1)), activate(V2)) , isPLNatKind(n__splitAt(V1, V2)) -> U271(isNaturalKind(activate(V1)), activate(V2)) , U63(tt()) -> tt() , isPLNat(n__pair(V1, V2)) -> U241(isLNatKind(activate(V1)), activate(V1), activate(V2)) , isPLNat(n__splitAt(V1, V2)) -> U251(isNaturalKind(activate(V1)), activate(V1), activate(V2)) , U71(tt(), V1) -> U72(isNaturalKind(activate(V1)), activate(V1)) , U72(tt(), V1) -> U73(isNatural(activate(V1))) , U73(tt()) -> tt() , U81(tt(), V1) -> U82(isPLNatKind(activate(V1)), activate(V1)) , U82(tt(), V1) -> U83(isPLNat(activate(V1))) , U83(tt()) -> tt() , U91(tt(), V1) -> U92(isLNatKind(activate(V1)), activate(V1)) , U92(tt(), V1) -> U93(isLNat(activate(V1))) , U93(tt()) -> tt() , natsFrom(N) -> U281(isNatural(N), N) , natsFrom(X) -> n__natsFrom(X) , sel(N, XS) -> U291(isNatural(N), N, XS) , sel(X1, X2) -> n__sel(X1, X2) , 0() -> n__0() , s(X) -> n__s(X) , tail(X) -> n__tail(X) , tail(cons(N, XS)) -> U331(isNatural(N), N, activate(XS)) , take(N, XS) -> U341(isNatural(N), N, XS) , take(X1, X2) -> n__take(X1, X2) } Obligation: innermost runtime complexity Answer: MAYBE Arguments of following rules are not normal-forms: { snd(pair(X, Y)) -> U301(isLNat(X), X, Y) , splitAt(0(), XS) -> U311(isLNat(XS), XS) , splitAt(s(N), cons(X, XS)) -> U321(isNatural(N), N, X, activate(XS)) , head(cons(N, XS)) -> U31(isNatural(N), N, activate(XS)) , U327(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) , fst(pair(X, Y)) -> U21(isLNat(X), X, Y) , tail(cons(N, XS)) -> U331(isNatural(N), N, activate(XS)) } All above mentioned rules can be savely removed. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { U101(tt(), V1, V2) -> U102(isNaturalKind(activate(V1)), activate(V1), activate(V2)) , U102(tt(), V1, V2) -> U103(isLNatKind(activate(V2)), activate(V1), activate(V2)) , isNaturalKind(n__s(V1)) -> U221(isNaturalKind(activate(V1))) , isNaturalKind(n__0()) -> tt() , isNaturalKind(n__head(V1)) -> U211(isLNatKind(activate(V1))) , isNaturalKind(n__sel(V1, V2)) -> U231(isNaturalKind(activate(V1)), activate(V2)) , activate(X) -> X , 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)) , U103(tt(), V1, V2) -> U104(isLNatKind(activate(V2)), activate(V1), activate(V2)) , isLNatKind(n__natsFrom(V1)) -> U141(isNaturalKind(activate(V1))) , isLNatKind(n__nil()) -> tt() , isLNatKind(n__afterNth(V1, V2)) -> U111(isNaturalKind(activate(V1)), activate(V2)) , isLNatKind(n__cons(V1, V2)) -> U121(isNaturalKind(activate(V1)), activate(V2)) , isLNatKind(n__fst(V1)) -> U131(isPLNatKind(activate(V1))) , isLNatKind(n__snd(V1)) -> U151(isPLNatKind(activate(V1))) , isLNatKind(n__tail(V1)) -> U161(isLNatKind(activate(V1))) , isLNatKind(n__take(V1, V2)) -> U171(isNaturalKind(activate(V1)), activate(V2)) , U104(tt(), V1, V2) -> U105(isNatural(activate(V1)), activate(V2)) , U105(tt(), V2) -> U106(isLNat(activate(V2))) , isNatural(n__s(V1)) -> U191(isNaturalKind(activate(V1)), activate(V1)) , isNatural(n__0()) -> tt() , isNatural(n__head(V1)) -> U181(isLNatKind(activate(V1)), activate(V1)) , isNatural(n__sel(V1, V2)) -> U201(isNaturalKind(activate(V1)), activate(V1), activate(V2)) , U106(tt()) -> tt() , isLNat(n__natsFrom(V1)) -> U71(isNaturalKind(activate(V1)), activate(V1)) , isLNat(n__nil()) -> tt() , isLNat(n__afterNth(V1, V2)) -> U41(isNaturalKind(activate(V1)), activate(V1), activate(V2)) , isLNat(n__cons(V1, V2)) -> U51(isNaturalKind(activate(V1)), activate(V1), activate(V2)) , isLNat(n__fst(V1)) -> U61(isPLNatKind(activate(V1)), activate(V1)) , isLNat(n__snd(V1)) -> U81(isPLNatKind(activate(V1)), activate(V1)) , isLNat(n__tail(V1)) -> U91(isLNatKind(activate(V1)), activate(V1)) , isLNat(n__take(V1, V2)) -> U101(isNaturalKind(activate(V1)), activate(V1), activate(V2)) , U11(tt(), N, XS) -> U12(isNaturalKind(activate(N)), activate(N), activate(XS)) , U12(tt(), N, XS) -> U13(isLNat(activate(XS)), activate(N), activate(XS)) , U111(tt(), V2) -> U112(isLNatKind(activate(V2))) , U112(tt()) -> tt() , U13(tt(), N, XS) -> U14(isLNatKind(activate(XS)), activate(N), activate(XS)) , U121(tt(), V2) -> U122(isLNatKind(activate(V2))) , U122(tt()) -> tt() , U14(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS))) , U131(tt()) -> tt() , snd(X) -> n__snd(X) , splitAt(X1, X2) -> n__splitAt(X1, X2) , U141(tt()) -> tt() , U151(tt()) -> tt() , U161(tt()) -> tt() , U171(tt(), V2) -> U172(isLNatKind(activate(V2))) , U172(tt()) -> tt() , U181(tt(), V1) -> U182(isLNatKind(activate(V1)), activate(V1)) , U182(tt(), V1) -> U183(isLNat(activate(V1))) , U183(tt()) -> tt() , U191(tt(), V1) -> U192(isNaturalKind(activate(V1)), activate(V1)) , U192(tt(), V1) -> U193(isNatural(activate(V1))) , U193(tt()) -> tt() , U201(tt(), V1, V2) -> U202(isNaturalKind(activate(V1)), activate(V1), activate(V2)) , U202(tt(), V1, V2) -> U203(isLNatKind(activate(V2)), activate(V1), activate(V2)) , U203(tt(), V1, V2) -> U204(isLNatKind(activate(V2)), activate(V1), activate(V2)) , U204(tt(), V1, V2) -> U205(isNatural(activate(V1)), activate(V2)) , U205(tt(), V2) -> U206(isLNat(activate(V2))) , U206(tt()) -> tt() , U21(tt(), X, Y) -> U22(isLNatKind(activate(X)), activate(X), activate(Y)) , U22(tt(), X, Y) -> U23(isLNat(activate(Y)), activate(X), activate(Y)) , U211(tt()) -> tt() , U23(tt(), X, Y) -> U24(isLNatKind(activate(Y)), activate(X)) , U221(tt()) -> tt() , U24(tt(), X) -> activate(X) , U231(tt(), V2) -> U232(isLNatKind(activate(V2))) , U232(tt()) -> tt() , U241(tt(), V1, V2) -> U242(isLNatKind(activate(V1)), activate(V1), activate(V2)) , U242(tt(), V1, V2) -> U243(isLNatKind(activate(V2)), activate(V1), activate(V2)) , U243(tt(), V1, V2) -> U244(isLNatKind(activate(V2)), activate(V1), activate(V2)) , U244(tt(), V1, V2) -> U245(isLNat(activate(V1)), activate(V2)) , U245(tt(), V2) -> U246(isLNat(activate(V2))) , U246(tt()) -> tt() , U251(tt(), V1, V2) -> U252(isNaturalKind(activate(V1)), activate(V1), activate(V2)) , U252(tt(), V1, V2) -> U253(isLNatKind(activate(V2)), activate(V1), activate(V2)) , U253(tt(), V1, V2) -> U254(isLNatKind(activate(V2)), activate(V1), activate(V2)) , U254(tt(), V1, V2) -> U255(isNatural(activate(V1)), activate(V2)) , U255(tt(), V2) -> U256(isLNat(activate(V2))) , U256(tt()) -> tt() , U261(tt(), V2) -> U262(isLNatKind(activate(V2))) , U262(tt()) -> tt() , U271(tt(), V2) -> U272(isLNatKind(activate(V2))) , U272(tt()) -> tt() , U281(tt(), N) -> U282(isNaturalKind(activate(N)), activate(N)) , U282(tt(), N) -> cons(activate(N), n__natsFrom(n__s(activate(N)))) , cons(X1, X2) -> n__cons(X1, X2) , U291(tt(), N, XS) -> U292(isNaturalKind(activate(N)), activate(N), activate(XS)) , U292(tt(), N, XS) -> U293(isLNat(activate(XS)), activate(N), activate(XS)) , U293(tt(), N, XS) -> U294(isLNatKind(activate(XS)), activate(N), activate(XS)) , U294(tt(), N, XS) -> head(afterNth(activate(N), activate(XS))) , head(X) -> n__head(X) , afterNth(N, XS) -> U11(isNatural(N), N, XS) , afterNth(X1, X2) -> n__afterNth(X1, X2) , U301(tt(), X, Y) -> U302(isLNatKind(activate(X)), activate(Y)) , U302(tt(), Y) -> U303(isLNat(activate(Y)), activate(Y)) , U303(tt(), Y) -> U304(isLNatKind(activate(Y)), activate(Y)) , U304(tt(), Y) -> activate(Y) , U31(tt(), N, XS) -> U32(isNaturalKind(activate(N)), activate(N), activate(XS)) , U32(tt(), N, XS) -> U33(isLNat(activate(XS)), activate(N), activate(XS)) , U311(tt(), XS) -> U312(isLNatKind(activate(XS)), activate(XS)) , U312(tt(), XS) -> pair(nil(), activate(XS)) , pair(X1, X2) -> n__pair(X1, X2) , nil() -> n__nil() , U33(tt(), N, XS) -> U34(isLNatKind(activate(XS)), activate(N)) , U321(tt(), N, X, XS) -> U322(isNaturalKind(activate(N)), activate(N), activate(X), activate(XS)) , U322(tt(), N, X, XS) -> U323(isNatural(activate(X)), activate(N), activate(X), activate(XS)) , U323(tt(), N, X, XS) -> U324(isNaturalKind(activate(X)), activate(N), activate(X), activate(XS)) , U324(tt(), N, X, XS) -> U325(isLNat(activate(XS)), activate(N), activate(X), activate(XS)) , U325(tt(), N, X, XS) -> U326(isLNatKind(activate(XS)), activate(N), activate(X), activate(XS)) , U326(tt(), N, X, XS) -> U327(splitAt(activate(N), activate(XS)), activate(X)) , U34(tt(), N) -> activate(N) , U331(tt(), N, XS) -> U332(isNaturalKind(activate(N)), activate(XS)) , U332(tt(), XS) -> U333(isLNat(activate(XS)), activate(XS)) , U333(tt(), XS) -> U334(isLNatKind(activate(XS)), activate(XS)) , U334(tt(), XS) -> activate(XS) , U341(tt(), N, XS) -> U342(isNaturalKind(activate(N)), activate(N), activate(XS)) , U342(tt(), N, XS) -> U343(isLNat(activate(XS)), activate(N), activate(XS)) , U343(tt(), N, XS) -> U344(isLNatKind(activate(XS)), activate(N), activate(XS)) , U344(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS))) , fst(X) -> n__fst(X) , U41(tt(), V1, V2) -> U42(isNaturalKind(activate(V1)), activate(V1), activate(V2)) , U42(tt(), V1, V2) -> U43(isLNatKind(activate(V2)), activate(V1), activate(V2)) , U43(tt(), V1, V2) -> U44(isLNatKind(activate(V2)), activate(V1), activate(V2)) , U44(tt(), V1, V2) -> U45(isNatural(activate(V1)), activate(V2)) , U45(tt(), V2) -> U46(isLNat(activate(V2))) , U46(tt()) -> tt() , U51(tt(), V1, V2) -> U52(isNaturalKind(activate(V1)), activate(V1), activate(V2)) , U52(tt(), V1, V2) -> U53(isLNatKind(activate(V2)), activate(V1), activate(V2)) , U53(tt(), V1, V2) -> U54(isLNatKind(activate(V2)), activate(V1), activate(V2)) , U54(tt(), V1, V2) -> U55(isNatural(activate(V1)), activate(V2)) , U55(tt(), V2) -> U56(isLNat(activate(V2))) , U56(tt()) -> tt() , U61(tt(), V1) -> U62(isPLNatKind(activate(V1)), activate(V1)) , U62(tt(), V1) -> U63(isPLNat(activate(V1))) , isPLNatKind(n__pair(V1, V2)) -> U261(isLNatKind(activate(V1)), activate(V2)) , isPLNatKind(n__splitAt(V1, V2)) -> U271(isNaturalKind(activate(V1)), activate(V2)) , U63(tt()) -> tt() , isPLNat(n__pair(V1, V2)) -> U241(isLNatKind(activate(V1)), activate(V1), activate(V2)) , isPLNat(n__splitAt(V1, V2)) -> U251(isNaturalKind(activate(V1)), activate(V1), activate(V2)) , U71(tt(), V1) -> U72(isNaturalKind(activate(V1)), activate(V1)) , U72(tt(), V1) -> U73(isNatural(activate(V1))) , U73(tt()) -> tt() , U81(tt(), V1) -> U82(isPLNatKind(activate(V1)), activate(V1)) , U82(tt(), V1) -> U83(isPLNat(activate(V1))) , U83(tt()) -> tt() , U91(tt(), V1) -> U92(isLNatKind(activate(V1)), activate(V1)) , U92(tt(), V1) -> U93(isLNat(activate(V1))) , U93(tt()) -> tt() , natsFrom(N) -> U281(isNatural(N), N) , natsFrom(X) -> n__natsFrom(X) , sel(N, XS) -> U291(isNatural(N), N, XS) , sel(X1, X2) -> n__sel(X1, X2) , 0() -> n__0() , s(X) -> n__s(X) , tail(X) -> n__tail(X) , take(N, XS) -> U341(isNatural(N), N, XS) , take(X1, X2) -> n__take(X1, X2) } Obligation: innermost runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'Best' failed due to the following reason: 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. 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 minimal-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. Arrrr..