MAYBE 1067.81/297.21 MAYBE 1067.81/297.21 1067.81/297.21 We are left with following problem, upon which TcT provides the 1067.81/297.21 certificate MAYBE. 1067.81/297.21 1067.81/297.21 Strict Trs: 1067.81/297.21 { U101(tt(), V1, V2) -> 1067.81/297.21 U102(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 1067.81/297.21 , U102(tt(), V1, V2) -> 1067.81/297.21 U103(isLNatKind(activate(V2)), activate(V1), activate(V2)) 1067.81/297.21 , isNaturalKind(n__0()) -> tt() 1067.81/297.21 , isNaturalKind(n__head(V1)) -> U211(isLNatKind(activate(V1))) 1067.81/297.21 , isNaturalKind(n__s(V1)) -> U221(isNaturalKind(activate(V1))) 1067.81/297.21 , isNaturalKind(n__sel(V1, V2)) -> 1067.81/297.21 U231(isNaturalKind(activate(V1)), activate(V2)) 1067.81/297.21 , activate(X) -> X 1067.81/297.21 , activate(n__natsFrom(X)) -> natsFrom(X) 1067.81/297.21 , activate(n__nil()) -> nil() 1067.81/297.21 , activate(n__afterNth(X1, X2)) -> afterNth(X1, X2) 1067.81/297.21 , activate(n__cons(X1, X2)) -> cons(X1, X2) 1067.81/297.21 , activate(n__fst(X)) -> fst(X) 1067.81/297.21 , activate(n__snd(X)) -> snd(X) 1067.81/297.21 , activate(n__tail(X)) -> tail(X) 1067.81/297.21 , activate(n__take(X1, X2)) -> take(X1, X2) 1067.81/297.21 , activate(n__0()) -> 0() 1067.81/297.21 , activate(n__head(X)) -> head(X) 1067.81/297.21 , activate(n__s(X)) -> s(X) 1067.81/297.21 , activate(n__sel(X1, X2)) -> sel(X1, X2) 1067.81/297.21 , activate(n__pair(X1, X2)) -> pair(X1, X2) 1067.81/297.21 , activate(n__splitAt(X1, X2)) -> splitAt(X1, X2) 1067.81/297.21 , U103(tt(), V1, V2) -> 1067.81/297.21 U104(isLNatKind(activate(V2)), activate(V1), activate(V2)) 1067.81/297.21 , isLNatKind(n__natsFrom(V1)) -> U141(isNaturalKind(activate(V1))) 1067.81/297.21 , isLNatKind(n__nil()) -> tt() 1067.81/297.21 , isLNatKind(n__afterNth(V1, V2)) -> 1067.81/297.21 U111(isNaturalKind(activate(V1)), activate(V2)) 1067.81/297.21 , isLNatKind(n__cons(V1, V2)) -> 1067.81/297.21 U121(isNaturalKind(activate(V1)), activate(V2)) 1067.81/297.21 , isLNatKind(n__fst(V1)) -> U131(isPLNatKind(activate(V1))) 1067.81/297.21 , isLNatKind(n__snd(V1)) -> U151(isPLNatKind(activate(V1))) 1067.81/297.21 , isLNatKind(n__tail(V1)) -> U161(isLNatKind(activate(V1))) 1067.81/297.21 , isLNatKind(n__take(V1, V2)) -> 1067.81/297.21 U171(isNaturalKind(activate(V1)), activate(V2)) 1067.81/297.21 , U104(tt(), V1, V2) -> U105(isNatural(activate(V1)), activate(V2)) 1067.81/297.21 , U105(tt(), V2) -> U106(isLNat(activate(V2))) 1067.81/297.21 , isNatural(n__0()) -> tt() 1067.81/297.21 , isNatural(n__head(V1)) -> 1067.81/297.21 U181(isLNatKind(activate(V1)), activate(V1)) 1067.81/297.21 , isNatural(n__s(V1)) -> 1067.81/297.21 U191(isNaturalKind(activate(V1)), activate(V1)) 1067.81/297.22 , isNatural(n__sel(V1, V2)) -> 1067.81/297.22 U201(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 1067.81/297.22 , U106(tt()) -> tt() 1067.81/297.22 , isLNat(n__natsFrom(V1)) -> 1067.81/297.22 U71(isNaturalKind(activate(V1)), activate(V1)) 1067.81/297.22 , isLNat(n__nil()) -> tt() 1067.81/297.22 , isLNat(n__afterNth(V1, V2)) -> 1067.81/297.22 U41(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 1067.81/297.22 , isLNat(n__cons(V1, V2)) -> 1067.81/297.22 U51(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 1067.81/297.22 , isLNat(n__fst(V1)) -> 1067.81/297.22 U61(isPLNatKind(activate(V1)), activate(V1)) 1067.81/297.22 , isLNat(n__snd(V1)) -> 1067.81/297.22 U81(isPLNatKind(activate(V1)), activate(V1)) 1067.81/297.22 , isLNat(n__tail(V1)) -> 1067.81/297.22 U91(isLNatKind(activate(V1)), activate(V1)) 1067.81/297.22 , isLNat(n__take(V1, V2)) -> 1067.81/297.22 U101(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 1067.81/297.22 , U11(tt(), N, XS) -> 1067.81/297.22 U12(isNaturalKind(activate(N)), activate(N), activate(XS)) 1067.81/297.22 , U12(tt(), N, XS) -> 1067.81/297.22 U13(isLNat(activate(XS)), activate(N), activate(XS)) 1067.81/297.22 , U111(tt(), V2) -> U112(isLNatKind(activate(V2))) 1067.81/297.22 , U112(tt()) -> tt() 1067.81/297.22 , U13(tt(), N, XS) -> 1067.81/297.22 U14(isLNatKind(activate(XS)), activate(N), activate(XS)) 1067.81/297.22 , U121(tt(), V2) -> U122(isLNatKind(activate(V2))) 1067.81/297.22 , U122(tt()) -> tt() 1067.81/297.22 , U14(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS))) 1067.81/297.22 , U131(tt()) -> tt() 1067.81/297.22 , snd(X) -> n__snd(X) 1067.81/297.22 , snd(pair(X, Y)) -> U301(isLNat(X), X, Y) 1067.81/297.22 , splitAt(X1, X2) -> n__splitAt(X1, X2) 1067.81/297.22 , splitAt(s(N), cons(X, XS)) -> 1067.81/297.22 U321(isNatural(N), N, X, activate(XS)) 1067.81/297.22 , splitAt(0(), XS) -> U311(isLNat(XS), XS) 1067.81/297.22 , U141(tt()) -> tt() 1067.81/297.22 , U151(tt()) -> tt() 1067.81/297.22 , U161(tt()) -> tt() 1067.81/297.22 , U171(tt(), V2) -> U172(isLNatKind(activate(V2))) 1067.81/297.22 , U172(tt()) -> tt() 1067.81/297.22 , U181(tt(), V1) -> U182(isLNatKind(activate(V1)), activate(V1)) 1067.81/297.22 , U182(tt(), V1) -> U183(isLNat(activate(V1))) 1067.81/297.22 , U183(tt()) -> tt() 1067.81/297.22 , U191(tt(), V1) -> U192(isNaturalKind(activate(V1)), activate(V1)) 1067.81/297.22 , U192(tt(), V1) -> U193(isNatural(activate(V1))) 1067.81/297.22 , U193(tt()) -> tt() 1067.81/297.22 , U201(tt(), V1, V2) -> 1067.81/297.22 U202(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 1067.81/297.22 , U202(tt(), V1, V2) -> 1067.81/297.22 U203(isLNatKind(activate(V2)), activate(V1), activate(V2)) 1067.81/297.22 , U203(tt(), V1, V2) -> 1067.81/297.22 U204(isLNatKind(activate(V2)), activate(V1), activate(V2)) 1067.81/297.22 , U204(tt(), V1, V2) -> U205(isNatural(activate(V1)), activate(V2)) 1067.81/297.22 , U205(tt(), V2) -> U206(isLNat(activate(V2))) 1067.81/297.22 , U206(tt()) -> tt() 1067.81/297.22 , U21(tt(), X, Y) -> 1067.81/297.22 U22(isLNatKind(activate(X)), activate(X), activate(Y)) 1067.81/297.22 , U22(tt(), X, Y) -> 1067.81/297.22 U23(isLNat(activate(Y)), activate(X), activate(Y)) 1067.81/297.22 , U211(tt()) -> tt() 1067.81/297.22 , U23(tt(), X, Y) -> U24(isLNatKind(activate(Y)), activate(X)) 1067.81/297.22 , U221(tt()) -> tt() 1067.81/297.22 , U24(tt(), X) -> activate(X) 1067.81/297.22 , U231(tt(), V2) -> U232(isLNatKind(activate(V2))) 1067.81/297.22 , U232(tt()) -> tt() 1067.81/297.22 , U241(tt(), V1, V2) -> 1067.81/297.22 U242(isLNatKind(activate(V1)), activate(V1), activate(V2)) 1067.81/297.22 , U242(tt(), V1, V2) -> 1067.81/297.22 U243(isLNatKind(activate(V2)), activate(V1), activate(V2)) 1067.81/297.22 , U243(tt(), V1, V2) -> 1067.81/297.22 U244(isLNatKind(activate(V2)), activate(V1), activate(V2)) 1067.81/297.22 , U244(tt(), V1, V2) -> U245(isLNat(activate(V1)), activate(V2)) 1067.81/297.22 , U245(tt(), V2) -> U246(isLNat(activate(V2))) 1067.81/297.22 , U246(tt()) -> tt() 1067.81/297.22 , U251(tt(), V1, V2) -> 1067.81/297.22 U252(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 1067.81/297.22 , U252(tt(), V1, V2) -> 1067.81/297.22 U253(isLNatKind(activate(V2)), activate(V1), activate(V2)) 1067.81/297.22 , U253(tt(), V1, V2) -> 1067.81/297.22 U254(isLNatKind(activate(V2)), activate(V1), activate(V2)) 1067.81/297.22 , U254(tt(), V1, V2) -> U255(isNatural(activate(V1)), activate(V2)) 1067.81/297.22 , U255(tt(), V2) -> U256(isLNat(activate(V2))) 1067.81/297.22 , U256(tt()) -> tt() 1067.81/297.22 , U261(tt(), V2) -> U262(isLNatKind(activate(V2))) 1067.81/297.22 , U262(tt()) -> tt() 1067.81/297.22 , U271(tt(), V2) -> U272(isLNatKind(activate(V2))) 1067.81/297.22 , U272(tt()) -> tt() 1067.81/297.22 , U281(tt(), N) -> U282(isNaturalKind(activate(N)), activate(N)) 1067.81/297.22 , U282(tt(), N) -> cons(activate(N), n__natsFrom(s(activate(N)))) 1067.81/297.22 , cons(X1, X2) -> n__cons(X1, X2) 1067.81/297.22 , s(X) -> n__s(X) 1067.81/297.22 , U291(tt(), N, XS) -> 1067.81/297.22 U292(isNaturalKind(activate(N)), activate(N), activate(XS)) 1067.81/297.22 , U292(tt(), N, XS) -> 1067.81/297.22 U293(isLNat(activate(XS)), activate(N), activate(XS)) 1067.81/297.22 , U293(tt(), N, XS) -> 1067.81/297.22 U294(isLNatKind(activate(XS)), activate(N), activate(XS)) 1067.81/297.22 , U294(tt(), N, XS) -> head(afterNth(activate(N), activate(XS))) 1067.81/297.22 , head(X) -> n__head(X) 1067.81/297.22 , head(cons(N, XS)) -> U31(isNatural(N), N, activate(XS)) 1067.81/297.22 , afterNth(N, XS) -> U11(isNatural(N), N, XS) 1067.81/297.22 , afterNth(X1, X2) -> n__afterNth(X1, X2) 1067.81/297.22 , U301(tt(), X, Y) -> U302(isLNatKind(activate(X)), activate(Y)) 1067.81/297.22 , U302(tt(), Y) -> U303(isLNat(activate(Y)), activate(Y)) 1067.81/297.22 , U303(tt(), Y) -> U304(isLNatKind(activate(Y)), activate(Y)) 1067.81/297.22 , U304(tt(), Y) -> activate(Y) 1067.81/297.22 , U31(tt(), N, XS) -> 1067.81/297.22 U32(isNaturalKind(activate(N)), activate(N), activate(XS)) 1067.81/297.22 , U32(tt(), N, XS) -> 1067.81/297.22 U33(isLNat(activate(XS)), activate(N), activate(XS)) 1067.81/297.22 , U311(tt(), XS) -> U312(isLNatKind(activate(XS)), activate(XS)) 1067.81/297.22 , U312(tt(), XS) -> pair(nil(), activate(XS)) 1067.81/297.22 , pair(X1, X2) -> n__pair(X1, X2) 1067.81/297.22 , nil() -> n__nil() 1067.81/297.22 , U33(tt(), N, XS) -> U34(isLNatKind(activate(XS)), activate(N)) 1067.81/297.22 , U321(tt(), N, X, XS) -> 1067.81/297.22 U322(isNaturalKind(activate(N)), 1067.81/297.22 activate(N), 1067.81/297.22 activate(X), 1067.81/297.22 activate(XS)) 1067.81/297.22 , U322(tt(), N, X, XS) -> 1067.81/297.22 U323(isNatural(activate(X)), 1067.81/297.22 activate(N), 1067.81/297.22 activate(X), 1067.81/297.22 activate(XS)) 1067.81/297.22 , U323(tt(), N, X, XS) -> 1067.81/297.22 U324(isNaturalKind(activate(X)), 1067.81/297.22 activate(N), 1067.81/297.22 activate(X), 1067.81/297.22 activate(XS)) 1067.81/297.22 , U324(tt(), N, X, XS) -> 1067.81/297.22 U325(isLNat(activate(XS)), activate(N), activate(X), activate(XS)) 1067.81/297.22 , U325(tt(), N, X, XS) -> 1067.81/297.22 U326(isLNatKind(activate(XS)), 1067.81/297.22 activate(N), 1067.81/297.22 activate(X), 1067.81/297.22 activate(XS)) 1067.81/297.22 , U326(tt(), N, X, XS) -> 1067.81/297.22 U327(splitAt(activate(N), activate(XS)), activate(X)) 1067.81/297.22 , U327(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) 1067.81/297.22 , U34(tt(), N) -> activate(N) 1067.81/297.22 , U331(tt(), N, XS) -> 1067.81/297.22 U332(isNaturalKind(activate(N)), activate(XS)) 1067.81/297.22 , U332(tt(), XS) -> U333(isLNat(activate(XS)), activate(XS)) 1067.81/297.22 , U333(tt(), XS) -> U334(isLNatKind(activate(XS)), activate(XS)) 1067.81/297.22 , U334(tt(), XS) -> activate(XS) 1067.81/297.22 , U341(tt(), N, XS) -> 1067.81/297.22 U342(isNaturalKind(activate(N)), activate(N), activate(XS)) 1067.81/297.22 , U342(tt(), N, XS) -> 1067.81/297.22 U343(isLNat(activate(XS)), activate(N), activate(XS)) 1067.81/297.22 , U343(tt(), N, XS) -> 1067.81/297.22 U344(isLNatKind(activate(XS)), activate(N), activate(XS)) 1067.81/297.22 , U344(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS))) 1067.81/297.22 , fst(X) -> n__fst(X) 1067.81/297.22 , fst(pair(X, Y)) -> U21(isLNat(X), X, Y) 1067.81/297.22 , U41(tt(), V1, V2) -> 1067.81/297.22 U42(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 1067.81/297.22 , U42(tt(), V1, V2) -> 1067.81/297.22 U43(isLNatKind(activate(V2)), activate(V1), activate(V2)) 1067.81/297.22 , U43(tt(), V1, V2) -> 1067.81/297.22 U44(isLNatKind(activate(V2)), activate(V1), activate(V2)) 1067.81/297.22 , U44(tt(), V1, V2) -> U45(isNatural(activate(V1)), activate(V2)) 1067.81/297.22 , U45(tt(), V2) -> U46(isLNat(activate(V2))) 1067.81/297.22 , U46(tt()) -> tt() 1067.81/297.22 , U51(tt(), V1, V2) -> 1067.81/297.22 U52(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 1067.81/297.22 , U52(tt(), V1, V2) -> 1067.81/297.22 U53(isLNatKind(activate(V2)), activate(V1), activate(V2)) 1067.81/297.22 , U53(tt(), V1, V2) -> 1067.81/297.22 U54(isLNatKind(activate(V2)), activate(V1), activate(V2)) 1067.81/297.22 , U54(tt(), V1, V2) -> U55(isNatural(activate(V1)), activate(V2)) 1067.81/297.22 , U55(tt(), V2) -> U56(isLNat(activate(V2))) 1067.81/297.22 , U56(tt()) -> tt() 1067.81/297.22 , U61(tt(), V1) -> U62(isPLNatKind(activate(V1)), activate(V1)) 1067.81/297.22 , U62(tt(), V1) -> U63(isPLNat(activate(V1))) 1067.81/297.22 , isPLNatKind(n__pair(V1, V2)) -> 1067.81/297.22 U261(isLNatKind(activate(V1)), activate(V2)) 1067.81/297.22 , isPLNatKind(n__splitAt(V1, V2)) -> 1067.81/297.22 U271(isNaturalKind(activate(V1)), activate(V2)) 1067.81/297.22 , U63(tt()) -> tt() 1067.81/297.22 , isPLNat(n__pair(V1, V2)) -> 1067.81/297.22 U241(isLNatKind(activate(V1)), activate(V1), activate(V2)) 1067.81/297.22 , isPLNat(n__splitAt(V1, V2)) -> 1067.81/297.22 U251(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 1067.81/297.22 , U71(tt(), V1) -> U72(isNaturalKind(activate(V1)), activate(V1)) 1067.81/297.22 , U72(tt(), V1) -> U73(isNatural(activate(V1))) 1067.81/297.22 , U73(tt()) -> tt() 1067.81/297.22 , U81(tt(), V1) -> U82(isPLNatKind(activate(V1)), activate(V1)) 1067.81/297.22 , U82(tt(), V1) -> U83(isPLNat(activate(V1))) 1067.81/297.22 , U83(tt()) -> tt() 1067.81/297.22 , U91(tt(), V1) -> U92(isLNatKind(activate(V1)), activate(V1)) 1067.81/297.22 , U92(tt(), V1) -> U93(isLNat(activate(V1))) 1067.81/297.22 , U93(tt()) -> tt() 1067.81/297.22 , natsFrom(N) -> U281(isNatural(N), N) 1067.81/297.22 , natsFrom(X) -> n__natsFrom(X) 1067.81/297.22 , sel(N, XS) -> U291(isNatural(N), N, XS) 1067.81/297.22 , sel(X1, X2) -> n__sel(X1, X2) 1067.81/297.22 , 0() -> n__0() 1067.81/297.22 , tail(X) -> n__tail(X) 1067.81/297.22 , tail(cons(N, XS)) -> U331(isNatural(N), N, activate(XS)) 1067.81/297.22 , take(N, XS) -> U341(isNatural(N), N, XS) 1067.81/297.22 , take(X1, X2) -> n__take(X1, X2) } 1067.81/297.22 Obligation: 1067.81/297.22 innermost runtime complexity 1067.81/297.22 Answer: 1067.81/297.22 MAYBE 1067.81/297.22 1067.81/297.22 Arguments of following rules are not normal-forms: 1067.81/297.22 1067.81/297.22 { snd(pair(X, Y)) -> U301(isLNat(X), X, Y) 1067.81/297.22 , splitAt(s(N), cons(X, XS)) -> 1067.81/297.22 U321(isNatural(N), N, X, activate(XS)) 1067.81/297.22 , splitAt(0(), XS) -> U311(isLNat(XS), XS) 1067.81/297.22 , head(cons(N, XS)) -> U31(isNatural(N), N, activate(XS)) 1067.81/297.22 , U327(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) 1067.81/297.22 , fst(pair(X, Y)) -> U21(isLNat(X), X, Y) 1067.81/297.22 , tail(cons(N, XS)) -> U331(isNatural(N), N, activate(XS)) } 1067.81/297.22 1067.81/297.22 All above mentioned rules can be savely removed. 1067.81/297.22 1067.81/297.22 We are left with following problem, upon which TcT provides the 1067.81/297.22 certificate MAYBE. 1067.81/297.22 1067.81/297.22 Strict Trs: 1067.81/297.22 { U101(tt(), V1, V2) -> 1067.81/297.22 U102(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 1067.81/297.22 , U102(tt(), V1, V2) -> 1067.81/297.22 U103(isLNatKind(activate(V2)), activate(V1), activate(V2)) 1067.81/297.22 , isNaturalKind(n__0()) -> tt() 1067.81/297.22 , isNaturalKind(n__head(V1)) -> U211(isLNatKind(activate(V1))) 1067.81/297.22 , isNaturalKind(n__s(V1)) -> U221(isNaturalKind(activate(V1))) 1067.81/297.22 , isNaturalKind(n__sel(V1, V2)) -> 1067.81/297.22 U231(isNaturalKind(activate(V1)), activate(V2)) 1067.81/297.22 , activate(X) -> X 1067.81/297.22 , activate(n__natsFrom(X)) -> natsFrom(X) 1067.81/297.22 , activate(n__nil()) -> nil() 1067.81/297.22 , activate(n__afterNth(X1, X2)) -> afterNth(X1, X2) 1067.81/297.22 , activate(n__cons(X1, X2)) -> cons(X1, X2) 1067.81/297.22 , activate(n__fst(X)) -> fst(X) 1067.81/297.22 , activate(n__snd(X)) -> snd(X) 1067.81/297.22 , activate(n__tail(X)) -> tail(X) 1067.81/297.22 , activate(n__take(X1, X2)) -> take(X1, X2) 1067.81/297.22 , activate(n__0()) -> 0() 1067.81/297.22 , activate(n__head(X)) -> head(X) 1067.81/297.22 , activate(n__s(X)) -> s(X) 1067.81/297.22 , activate(n__sel(X1, X2)) -> sel(X1, X2) 1067.81/297.22 , activate(n__pair(X1, X2)) -> pair(X1, X2) 1067.81/297.22 , activate(n__splitAt(X1, X2)) -> splitAt(X1, X2) 1067.81/297.22 , U103(tt(), V1, V2) -> 1067.81/297.22 U104(isLNatKind(activate(V2)), activate(V1), activate(V2)) 1067.81/297.22 , isLNatKind(n__natsFrom(V1)) -> U141(isNaturalKind(activate(V1))) 1067.81/297.22 , isLNatKind(n__nil()) -> tt() 1067.81/297.22 , isLNatKind(n__afterNth(V1, V2)) -> 1067.81/297.22 U111(isNaturalKind(activate(V1)), activate(V2)) 1067.81/297.22 , isLNatKind(n__cons(V1, V2)) -> 1067.81/297.22 U121(isNaturalKind(activate(V1)), activate(V2)) 1067.81/297.22 , isLNatKind(n__fst(V1)) -> U131(isPLNatKind(activate(V1))) 1067.81/297.22 , isLNatKind(n__snd(V1)) -> U151(isPLNatKind(activate(V1))) 1067.81/297.22 , isLNatKind(n__tail(V1)) -> U161(isLNatKind(activate(V1))) 1067.81/297.22 , isLNatKind(n__take(V1, V2)) -> 1067.81/297.22 U171(isNaturalKind(activate(V1)), activate(V2)) 1067.81/297.22 , U104(tt(), V1, V2) -> U105(isNatural(activate(V1)), activate(V2)) 1067.81/297.22 , U105(tt(), V2) -> U106(isLNat(activate(V2))) 1067.81/297.22 , isNatural(n__0()) -> tt() 1067.81/297.22 , isNatural(n__head(V1)) -> 1067.81/297.22 U181(isLNatKind(activate(V1)), activate(V1)) 1067.81/297.22 , isNatural(n__s(V1)) -> 1067.81/297.22 U191(isNaturalKind(activate(V1)), activate(V1)) 1067.81/297.22 , isNatural(n__sel(V1, V2)) -> 1067.81/297.22 U201(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 1067.81/297.22 , U106(tt()) -> tt() 1067.81/297.22 , isLNat(n__natsFrom(V1)) -> 1067.81/297.22 U71(isNaturalKind(activate(V1)), activate(V1)) 1067.81/297.22 , isLNat(n__nil()) -> tt() 1067.81/297.22 , isLNat(n__afterNth(V1, V2)) -> 1067.81/297.22 U41(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 1067.81/297.22 , isLNat(n__cons(V1, V2)) -> 1067.81/297.22 U51(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 1067.81/297.22 , isLNat(n__fst(V1)) -> 1067.81/297.22 U61(isPLNatKind(activate(V1)), activate(V1)) 1067.81/297.22 , isLNat(n__snd(V1)) -> 1067.81/297.22 U81(isPLNatKind(activate(V1)), activate(V1)) 1067.81/297.22 , isLNat(n__tail(V1)) -> 1067.81/297.22 U91(isLNatKind(activate(V1)), activate(V1)) 1067.81/297.22 , isLNat(n__take(V1, V2)) -> 1067.81/297.22 U101(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 1067.81/297.22 , U11(tt(), N, XS) -> 1067.81/297.22 U12(isNaturalKind(activate(N)), activate(N), activate(XS)) 1067.81/297.22 , U12(tt(), N, XS) -> 1067.81/297.22 U13(isLNat(activate(XS)), activate(N), activate(XS)) 1067.81/297.22 , U111(tt(), V2) -> U112(isLNatKind(activate(V2))) 1067.81/297.22 , U112(tt()) -> tt() 1067.81/297.22 , U13(tt(), N, XS) -> 1067.81/297.22 U14(isLNatKind(activate(XS)), activate(N), activate(XS)) 1067.81/297.22 , U121(tt(), V2) -> U122(isLNatKind(activate(V2))) 1067.81/297.22 , U122(tt()) -> tt() 1067.81/297.22 , U14(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS))) 1067.81/297.22 , U131(tt()) -> tt() 1067.81/297.22 , snd(X) -> n__snd(X) 1067.81/297.22 , splitAt(X1, X2) -> n__splitAt(X1, X2) 1067.81/297.22 , U141(tt()) -> tt() 1067.81/297.22 , U151(tt()) -> tt() 1067.81/297.22 , U161(tt()) -> tt() 1067.81/297.22 , U171(tt(), V2) -> U172(isLNatKind(activate(V2))) 1067.81/297.22 , U172(tt()) -> tt() 1067.81/297.22 , U181(tt(), V1) -> U182(isLNatKind(activate(V1)), activate(V1)) 1067.81/297.22 , U182(tt(), V1) -> U183(isLNat(activate(V1))) 1067.81/297.22 , U183(tt()) -> tt() 1067.81/297.22 , U191(tt(), V1) -> U192(isNaturalKind(activate(V1)), activate(V1)) 1067.81/297.22 , U192(tt(), V1) -> U193(isNatural(activate(V1))) 1067.81/297.22 , U193(tt()) -> tt() 1067.81/297.22 , U201(tt(), V1, V2) -> 1067.81/297.22 U202(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 1067.81/297.22 , U202(tt(), V1, V2) -> 1067.81/297.22 U203(isLNatKind(activate(V2)), activate(V1), activate(V2)) 1067.81/297.22 , U203(tt(), V1, V2) -> 1067.81/297.22 U204(isLNatKind(activate(V2)), activate(V1), activate(V2)) 1067.81/297.22 , U204(tt(), V1, V2) -> U205(isNatural(activate(V1)), activate(V2)) 1067.81/297.22 , U205(tt(), V2) -> U206(isLNat(activate(V2))) 1067.81/297.22 , U206(tt()) -> tt() 1067.81/297.22 , U21(tt(), X, Y) -> 1067.81/297.22 U22(isLNatKind(activate(X)), activate(X), activate(Y)) 1067.81/297.22 , U22(tt(), X, Y) -> 1067.81/297.22 U23(isLNat(activate(Y)), activate(X), activate(Y)) 1067.81/297.22 , U211(tt()) -> tt() 1067.81/297.22 , U23(tt(), X, Y) -> U24(isLNatKind(activate(Y)), activate(X)) 1067.81/297.22 , U221(tt()) -> tt() 1067.81/297.22 , U24(tt(), X) -> activate(X) 1067.81/297.22 , U231(tt(), V2) -> U232(isLNatKind(activate(V2))) 1067.81/297.22 , U232(tt()) -> tt() 1067.81/297.22 , U241(tt(), V1, V2) -> 1067.81/297.22 U242(isLNatKind(activate(V1)), activate(V1), activate(V2)) 1067.81/297.22 , U242(tt(), V1, V2) -> 1067.81/297.22 U243(isLNatKind(activate(V2)), activate(V1), activate(V2)) 1067.81/297.22 , U243(tt(), V1, V2) -> 1067.81/297.22 U244(isLNatKind(activate(V2)), activate(V1), activate(V2)) 1067.81/297.22 , U244(tt(), V1, V2) -> U245(isLNat(activate(V1)), activate(V2)) 1067.81/297.22 , U245(tt(), V2) -> U246(isLNat(activate(V2))) 1067.81/297.22 , U246(tt()) -> tt() 1067.81/297.22 , U251(tt(), V1, V2) -> 1067.81/297.22 U252(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 1067.81/297.22 , U252(tt(), V1, V2) -> 1067.81/297.22 U253(isLNatKind(activate(V2)), activate(V1), activate(V2)) 1067.81/297.22 , U253(tt(), V1, V2) -> 1067.81/297.22 U254(isLNatKind(activate(V2)), activate(V1), activate(V2)) 1067.81/297.22 , U254(tt(), V1, V2) -> U255(isNatural(activate(V1)), activate(V2)) 1067.81/297.22 , U255(tt(), V2) -> U256(isLNat(activate(V2))) 1067.81/297.22 , U256(tt()) -> tt() 1067.81/297.22 , U261(tt(), V2) -> U262(isLNatKind(activate(V2))) 1067.81/297.22 , U262(tt()) -> tt() 1067.81/297.22 , U271(tt(), V2) -> U272(isLNatKind(activate(V2))) 1067.81/297.22 , U272(tt()) -> tt() 1067.81/297.22 , U281(tt(), N) -> U282(isNaturalKind(activate(N)), activate(N)) 1067.81/297.22 , U282(tt(), N) -> cons(activate(N), n__natsFrom(s(activate(N)))) 1067.81/297.22 , cons(X1, X2) -> n__cons(X1, X2) 1067.81/297.22 , s(X) -> n__s(X) 1067.81/297.22 , U291(tt(), N, XS) -> 1067.81/297.22 U292(isNaturalKind(activate(N)), activate(N), activate(XS)) 1067.81/297.22 , U292(tt(), N, XS) -> 1067.81/297.22 U293(isLNat(activate(XS)), activate(N), activate(XS)) 1067.81/297.22 , U293(tt(), N, XS) -> 1067.81/297.22 U294(isLNatKind(activate(XS)), activate(N), activate(XS)) 1067.81/297.22 , U294(tt(), N, XS) -> head(afterNth(activate(N), activate(XS))) 1067.81/297.22 , head(X) -> n__head(X) 1067.81/297.22 , afterNth(N, XS) -> U11(isNatural(N), N, XS) 1067.81/297.22 , afterNth(X1, X2) -> n__afterNth(X1, X2) 1067.81/297.22 , U301(tt(), X, Y) -> U302(isLNatKind(activate(X)), activate(Y)) 1067.81/297.22 , U302(tt(), Y) -> U303(isLNat(activate(Y)), activate(Y)) 1067.81/297.22 , U303(tt(), Y) -> U304(isLNatKind(activate(Y)), activate(Y)) 1067.81/297.22 , U304(tt(), Y) -> activate(Y) 1067.81/297.22 , U31(tt(), N, XS) -> 1067.81/297.22 U32(isNaturalKind(activate(N)), activate(N), activate(XS)) 1067.81/297.22 , U32(tt(), N, XS) -> 1067.81/297.22 U33(isLNat(activate(XS)), activate(N), activate(XS)) 1067.81/297.22 , U311(tt(), XS) -> U312(isLNatKind(activate(XS)), activate(XS)) 1067.81/297.22 , U312(tt(), XS) -> pair(nil(), activate(XS)) 1067.81/297.22 , pair(X1, X2) -> n__pair(X1, X2) 1067.81/297.22 , nil() -> n__nil() 1067.81/297.22 , U33(tt(), N, XS) -> U34(isLNatKind(activate(XS)), activate(N)) 1067.81/297.22 , U321(tt(), N, X, XS) -> 1067.81/297.22 U322(isNaturalKind(activate(N)), 1067.81/297.22 activate(N), 1067.81/297.22 activate(X), 1067.81/297.22 activate(XS)) 1067.81/297.22 , U322(tt(), N, X, XS) -> 1067.81/297.22 U323(isNatural(activate(X)), 1067.81/297.22 activate(N), 1067.81/297.22 activate(X), 1067.81/297.22 activate(XS)) 1067.81/297.22 , U323(tt(), N, X, XS) -> 1067.81/297.22 U324(isNaturalKind(activate(X)), 1067.81/297.22 activate(N), 1067.81/297.22 activate(X), 1067.81/297.22 activate(XS)) 1067.81/297.22 , U324(tt(), N, X, XS) -> 1067.81/297.22 U325(isLNat(activate(XS)), activate(N), activate(X), activate(XS)) 1067.81/297.22 , U325(tt(), N, X, XS) -> 1067.81/297.22 U326(isLNatKind(activate(XS)), 1067.81/297.22 activate(N), 1067.81/297.22 activate(X), 1067.81/297.22 activate(XS)) 1067.81/297.22 , U326(tt(), N, X, XS) -> 1067.81/297.22 U327(splitAt(activate(N), activate(XS)), activate(X)) 1067.81/297.22 , U34(tt(), N) -> activate(N) 1067.81/297.22 , U331(tt(), N, XS) -> 1067.81/297.22 U332(isNaturalKind(activate(N)), activate(XS)) 1067.81/297.22 , U332(tt(), XS) -> U333(isLNat(activate(XS)), activate(XS)) 1067.81/297.22 , U333(tt(), XS) -> U334(isLNatKind(activate(XS)), activate(XS)) 1067.81/297.22 , U334(tt(), XS) -> activate(XS) 1067.81/297.22 , U341(tt(), N, XS) -> 1067.81/297.22 U342(isNaturalKind(activate(N)), activate(N), activate(XS)) 1067.81/297.22 , U342(tt(), N, XS) -> 1067.81/297.22 U343(isLNat(activate(XS)), activate(N), activate(XS)) 1067.81/297.22 , U343(tt(), N, XS) -> 1067.81/297.22 U344(isLNatKind(activate(XS)), activate(N), activate(XS)) 1067.81/297.22 , U344(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS))) 1067.81/297.22 , fst(X) -> n__fst(X) 1067.81/297.22 , U41(tt(), V1, V2) -> 1067.81/297.22 U42(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 1067.81/297.22 , U42(tt(), V1, V2) -> 1067.81/297.22 U43(isLNatKind(activate(V2)), activate(V1), activate(V2)) 1067.81/297.22 , U43(tt(), V1, V2) -> 1067.81/297.22 U44(isLNatKind(activate(V2)), activate(V1), activate(V2)) 1067.81/297.22 , U44(tt(), V1, V2) -> U45(isNatural(activate(V1)), activate(V2)) 1067.81/297.22 , U45(tt(), V2) -> U46(isLNat(activate(V2))) 1067.81/297.22 , U46(tt()) -> tt() 1067.81/297.22 , U51(tt(), V1, V2) -> 1067.81/297.22 U52(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 1067.81/297.22 , U52(tt(), V1, V2) -> 1067.81/297.22 U53(isLNatKind(activate(V2)), activate(V1), activate(V2)) 1067.81/297.22 , U53(tt(), V1, V2) -> 1067.81/297.22 U54(isLNatKind(activate(V2)), activate(V1), activate(V2)) 1067.81/297.22 , U54(tt(), V1, V2) -> U55(isNatural(activate(V1)), activate(V2)) 1067.81/297.22 , U55(tt(), V2) -> U56(isLNat(activate(V2))) 1067.81/297.22 , U56(tt()) -> tt() 1067.81/297.22 , U61(tt(), V1) -> U62(isPLNatKind(activate(V1)), activate(V1)) 1067.81/297.22 , U62(tt(), V1) -> U63(isPLNat(activate(V1))) 1067.81/297.22 , isPLNatKind(n__pair(V1, V2)) -> 1067.81/297.22 U261(isLNatKind(activate(V1)), activate(V2)) 1067.81/297.22 , isPLNatKind(n__splitAt(V1, V2)) -> 1067.81/297.22 U271(isNaturalKind(activate(V1)), activate(V2)) 1067.81/297.22 , U63(tt()) -> tt() 1067.81/297.22 , isPLNat(n__pair(V1, V2)) -> 1067.81/297.22 U241(isLNatKind(activate(V1)), activate(V1), activate(V2)) 1067.81/297.22 , isPLNat(n__splitAt(V1, V2)) -> 1067.81/297.22 U251(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 1067.81/297.22 , U71(tt(), V1) -> U72(isNaturalKind(activate(V1)), activate(V1)) 1067.81/297.22 , U72(tt(), V1) -> U73(isNatural(activate(V1))) 1067.81/297.22 , U73(tt()) -> tt() 1067.81/297.22 , U81(tt(), V1) -> U82(isPLNatKind(activate(V1)), activate(V1)) 1067.81/297.22 , U82(tt(), V1) -> U83(isPLNat(activate(V1))) 1067.81/297.22 , U83(tt()) -> tt() 1067.81/297.22 , U91(tt(), V1) -> U92(isLNatKind(activate(V1)), activate(V1)) 1067.81/297.22 , U92(tt(), V1) -> U93(isLNat(activate(V1))) 1067.81/297.22 , U93(tt()) -> tt() 1067.81/297.22 , natsFrom(N) -> U281(isNatural(N), N) 1067.81/297.22 , natsFrom(X) -> n__natsFrom(X) 1067.81/297.22 , sel(N, XS) -> U291(isNatural(N), N, XS) 1067.81/297.22 , sel(X1, X2) -> n__sel(X1, X2) 1067.81/297.22 , 0() -> n__0() 1067.81/297.22 , tail(X) -> n__tail(X) 1067.81/297.22 , take(N, XS) -> U341(isNatural(N), N, XS) 1067.81/297.22 , take(X1, X2) -> n__take(X1, X2) } 1067.81/297.22 Obligation: 1067.81/297.22 innermost runtime complexity 1067.81/297.22 Answer: 1067.81/297.22 MAYBE 1067.81/297.22 1067.81/297.22 None of the processors succeeded. 1067.81/297.22 1067.81/297.22 Details of failed attempt(s): 1067.81/297.22 ----------------------------- 1067.81/297.22 1) 'empty' failed due to the following reason: 1067.81/297.22 1067.81/297.22 Empty strict component of the problem is NOT empty. 1067.81/297.22 1067.81/297.22 2) 'Best' failed due to the following reason: 1067.81/297.22 1067.81/297.22 None of the processors succeeded. 1067.81/297.22 1067.81/297.22 Details of failed attempt(s): 1067.81/297.22 ----------------------------- 1067.81/297.22 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1067.81/297.22 following reason: 1067.81/297.22 1067.81/297.22 Computation stopped due to timeout after 297.0 seconds. 1067.81/297.22 1067.81/297.22 2) 'Best' failed due to the following reason: 1067.81/297.22 1067.81/297.22 None of the processors succeeded. 1067.81/297.22 1067.81/297.22 Details of failed attempt(s): 1067.81/297.22 ----------------------------- 1067.81/297.22 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1067.81/297.22 seconds)' failed due to the following reason: 1067.81/297.22 1067.81/297.22 Computation stopped due to timeout after 148.0 seconds. 1067.81/297.22 1067.81/297.22 2) 'Best' failed due to the following reason: 1067.81/297.22 1067.81/297.22 None of the processors succeeded. 1067.81/297.22 1067.81/297.22 Details of failed attempt(s): 1067.81/297.22 ----------------------------- 1067.81/297.22 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1067.81/297.22 to the following reason: 1067.81/297.22 1067.81/297.22 The input cannot be shown compatible 1067.81/297.22 1067.81/297.22 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1067.81/297.22 following reason: 1067.81/297.22 1067.81/297.22 The input cannot be shown compatible 1067.81/297.22 1067.81/297.22 1067.81/297.22 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1067.81/297.22 failed due to the following reason: 1067.81/297.22 1067.81/297.22 None of the processors succeeded. 1067.81/297.22 1067.81/297.22 Details of failed attempt(s): 1067.81/297.22 ----------------------------- 1067.81/297.22 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1067.81/297.22 failed due to the following reason: 1067.81/297.22 1067.81/297.22 match-boundness of the problem could not be verified. 1067.81/297.22 1067.81/297.22 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1067.81/297.22 failed due to the following reason: 1067.81/297.22 1067.81/297.22 match-boundness of the problem could not be verified. 1067.81/297.22 1067.81/297.22 1067.81/297.22 1067.81/297.22 1067.81/297.22 1067.81/297.22 Arrrr.. 1067.81/297.22 EOF