MAYBE 957.19/297.23 MAYBE 957.19/297.23 957.19/297.23 We are left with following problem, upon which TcT provides the 957.19/297.23 certificate MAYBE. 957.19/297.23 957.19/297.23 Strict Trs: 957.19/297.23 { U101(tt(), V1, V2) -> 957.19/297.23 U102(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.23 , U102(tt(), V1, V2) -> 957.19/297.23 U103(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.23 , isNaturalKind(n__0()) -> tt() 957.19/297.23 , isNaturalKind(n__head(V1)) -> U211(isLNatKind(activate(V1))) 957.19/297.23 , isNaturalKind(n__s(V1)) -> U221(isNaturalKind(activate(V1))) 957.19/297.23 , isNaturalKind(n__sel(V1, V2)) -> 957.19/297.23 U231(isNaturalKind(activate(V1)), activate(V2)) 957.19/297.23 , activate(X) -> X 957.19/297.23 , activate(n__natsFrom(X)) -> natsFrom(X) 957.19/297.23 , activate(n__nil()) -> nil() 957.19/297.23 , activate(n__afterNth(X1, X2)) -> afterNth(X1, X2) 957.19/297.23 , activate(n__cons(X1, X2)) -> cons(X1, X2) 957.19/297.23 , activate(n__fst(X)) -> fst(X) 957.19/297.23 , activate(n__snd(X)) -> snd(X) 957.19/297.23 , activate(n__tail(X)) -> tail(X) 957.19/297.23 , activate(n__take(X1, X2)) -> take(X1, X2) 957.19/297.23 , activate(n__0()) -> 0() 957.19/297.23 , activate(n__head(X)) -> head(X) 957.19/297.23 , activate(n__s(X)) -> s(X) 957.19/297.23 , activate(n__sel(X1, X2)) -> sel(X1, X2) 957.19/297.23 , activate(n__pair(X1, X2)) -> pair(X1, X2) 957.19/297.23 , activate(n__splitAt(X1, X2)) -> splitAt(X1, X2) 957.19/297.23 , U103(tt(), V1, V2) -> 957.19/297.23 U104(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.23 , isLNatKind(n__natsFrom(V1)) -> U141(isNaturalKind(activate(V1))) 957.19/297.23 , isLNatKind(n__nil()) -> tt() 957.19/297.23 , isLNatKind(n__afterNth(V1, V2)) -> 957.19/297.23 U111(isNaturalKind(activate(V1)), activate(V2)) 957.19/297.23 , isLNatKind(n__cons(V1, V2)) -> 957.19/297.23 U121(isNaturalKind(activate(V1)), activate(V2)) 957.19/297.23 , isLNatKind(n__fst(V1)) -> U131(isPLNatKind(activate(V1))) 957.19/297.23 , isLNatKind(n__snd(V1)) -> U151(isPLNatKind(activate(V1))) 957.19/297.23 , isLNatKind(n__tail(V1)) -> U161(isLNatKind(activate(V1))) 957.19/297.23 , isLNatKind(n__take(V1, V2)) -> 957.19/297.23 U171(isNaturalKind(activate(V1)), activate(V2)) 957.19/297.23 , U104(tt(), V1, V2) -> U105(isNatural(activate(V1)), activate(V2)) 957.19/297.23 , U105(tt(), V2) -> U106(isLNat(activate(V2))) 957.19/297.23 , isNatural(n__0()) -> tt() 957.19/297.23 , isNatural(n__head(V1)) -> 957.19/297.23 U181(isLNatKind(activate(V1)), activate(V1)) 957.19/297.23 , isNatural(n__s(V1)) -> 957.19/297.23 U191(isNaturalKind(activate(V1)), activate(V1)) 957.19/297.23 , isNatural(n__sel(V1, V2)) -> 957.19/297.23 U201(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.23 , U106(tt()) -> tt() 957.19/297.23 , isLNat(n__natsFrom(V1)) -> 957.19/297.23 U71(isNaturalKind(activate(V1)), activate(V1)) 957.19/297.23 , isLNat(n__nil()) -> tt() 957.19/297.23 , isLNat(n__afterNth(V1, V2)) -> 957.19/297.23 U41(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.23 , isLNat(n__cons(V1, V2)) -> 957.19/297.23 U51(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.23 , isLNat(n__fst(V1)) -> 957.19/297.23 U61(isPLNatKind(activate(V1)), activate(V1)) 957.19/297.23 , isLNat(n__snd(V1)) -> 957.19/297.23 U81(isPLNatKind(activate(V1)), activate(V1)) 957.19/297.23 , isLNat(n__tail(V1)) -> 957.19/297.23 U91(isLNatKind(activate(V1)), activate(V1)) 957.19/297.23 , isLNat(n__take(V1, V2)) -> 957.19/297.23 U101(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.23 , U11(tt(), N, XS) -> 957.19/297.23 U12(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.19/297.23 , U12(tt(), N, XS) -> 957.19/297.23 U13(isLNat(activate(XS)), activate(N), activate(XS)) 957.19/297.23 , U111(tt(), V2) -> U112(isLNatKind(activate(V2))) 957.19/297.23 , U112(tt()) -> tt() 957.19/297.23 , U13(tt(), N, XS) -> 957.19/297.23 U14(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.19/297.23 , U121(tt(), V2) -> U122(isLNatKind(activate(V2))) 957.19/297.23 , U122(tt()) -> tt() 957.19/297.23 , U14(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS))) 957.19/297.23 , U131(tt()) -> tt() 957.19/297.23 , snd(X) -> n__snd(X) 957.19/297.23 , snd(pair(X, Y)) -> U301(isLNat(X), X, Y) 957.19/297.23 , splitAt(X1, X2) -> n__splitAt(X1, X2) 957.19/297.23 , splitAt(s(N), cons(X, XS)) -> 957.19/297.23 U321(isNatural(N), N, X, activate(XS)) 957.19/297.23 , splitAt(0(), XS) -> U311(isLNat(XS), XS) 957.19/297.23 , U141(tt()) -> tt() 957.19/297.23 , U151(tt()) -> tt() 957.19/297.23 , U161(tt()) -> tt() 957.19/297.23 , U171(tt(), V2) -> U172(isLNatKind(activate(V2))) 957.19/297.23 , U172(tt()) -> tt() 957.19/297.23 , U181(tt(), V1) -> U182(isLNatKind(activate(V1)), activate(V1)) 957.19/297.23 , U182(tt(), V1) -> U183(isLNat(activate(V1))) 957.19/297.23 , U183(tt()) -> tt() 957.19/297.23 , U191(tt(), V1) -> U192(isNaturalKind(activate(V1)), activate(V1)) 957.19/297.23 , U192(tt(), V1) -> U193(isNatural(activate(V1))) 957.19/297.23 , U193(tt()) -> tt() 957.19/297.23 , U201(tt(), V1, V2) -> 957.19/297.23 U202(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.23 , U202(tt(), V1, V2) -> 957.19/297.23 U203(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.23 , U203(tt(), V1, V2) -> 957.19/297.23 U204(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.23 , U204(tt(), V1, V2) -> U205(isNatural(activate(V1)), activate(V2)) 957.19/297.23 , U205(tt(), V2) -> U206(isLNat(activate(V2))) 957.19/297.23 , U206(tt()) -> tt() 957.19/297.23 , U21(tt(), X, Y) -> 957.19/297.23 U22(isLNatKind(activate(X)), activate(X), activate(Y)) 957.19/297.23 , U22(tt(), X, Y) -> 957.19/297.23 U23(isLNat(activate(Y)), activate(X), activate(Y)) 957.19/297.23 , U211(tt()) -> tt() 957.19/297.23 , U23(tt(), X, Y) -> U24(isLNatKind(activate(Y)), activate(X)) 957.19/297.23 , U221(tt()) -> tt() 957.19/297.23 , U24(tt(), X) -> activate(X) 957.19/297.23 , U231(tt(), V2) -> U232(isLNatKind(activate(V2))) 957.19/297.23 , U232(tt()) -> tt() 957.19/297.23 , U241(tt(), V1, V2) -> 957.19/297.23 U242(isLNatKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.23 , U242(tt(), V1, V2) -> 957.19/297.23 U243(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.23 , U243(tt(), V1, V2) -> 957.19/297.23 U244(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.23 , U244(tt(), V1, V2) -> U245(isLNat(activate(V1)), activate(V2)) 957.19/297.23 , U245(tt(), V2) -> U246(isLNat(activate(V2))) 957.19/297.23 , U246(tt()) -> tt() 957.19/297.23 , U251(tt(), V1, V2) -> 957.19/297.23 U252(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.23 , U252(tt(), V1, V2) -> 957.19/297.23 U253(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.23 , U253(tt(), V1, V2) -> 957.19/297.23 U254(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.23 , U254(tt(), V1, V2) -> U255(isNatural(activate(V1)), activate(V2)) 957.19/297.23 , U255(tt(), V2) -> U256(isLNat(activate(V2))) 957.19/297.23 , U256(tt()) -> tt() 957.19/297.23 , U261(tt(), V2) -> U262(isLNatKind(activate(V2))) 957.19/297.23 , U262(tt()) -> tt() 957.19/297.23 , U271(tt(), V2) -> U272(isLNatKind(activate(V2))) 957.19/297.23 , U272(tt()) -> tt() 957.19/297.23 , U281(tt(), N) -> U282(isNaturalKind(activate(N)), activate(N)) 957.19/297.23 , U282(tt(), N) -> cons(activate(N), n__natsFrom(s(activate(N)))) 957.19/297.23 , cons(X1, X2) -> n__cons(X1, X2) 957.19/297.23 , s(X) -> n__s(X) 957.19/297.23 , U291(tt(), N, XS) -> 957.19/297.23 U292(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.19/297.23 , U292(tt(), N, XS) -> 957.19/297.23 U293(isLNat(activate(XS)), activate(N), activate(XS)) 957.19/297.23 , U293(tt(), N, XS) -> 957.19/297.23 U294(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.19/297.23 , U294(tt(), N, XS) -> head(afterNth(activate(N), activate(XS))) 957.19/297.23 , head(X) -> n__head(X) 957.19/297.23 , head(cons(N, XS)) -> U31(isNatural(N), N, activate(XS)) 957.19/297.23 , afterNth(N, XS) -> U11(isNatural(N), N, XS) 957.19/297.23 , afterNth(X1, X2) -> n__afterNth(X1, X2) 957.19/297.23 , U301(tt(), X, Y) -> U302(isLNatKind(activate(X)), activate(Y)) 957.19/297.23 , U302(tt(), Y) -> U303(isLNat(activate(Y)), activate(Y)) 957.19/297.23 , U303(tt(), Y) -> U304(isLNatKind(activate(Y)), activate(Y)) 957.19/297.23 , U304(tt(), Y) -> activate(Y) 957.19/297.23 , U31(tt(), N, XS) -> 957.19/297.23 U32(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.19/297.23 , U32(tt(), N, XS) -> 957.19/297.23 U33(isLNat(activate(XS)), activate(N), activate(XS)) 957.19/297.23 , U311(tt(), XS) -> U312(isLNatKind(activate(XS)), activate(XS)) 957.19/297.23 , U312(tt(), XS) -> pair(nil(), activate(XS)) 957.19/297.23 , pair(X1, X2) -> n__pair(X1, X2) 957.19/297.23 , nil() -> n__nil() 957.19/297.23 , U33(tt(), N, XS) -> U34(isLNatKind(activate(XS)), activate(N)) 957.19/297.23 , U321(tt(), N, X, XS) -> 957.19/297.23 U322(isNaturalKind(activate(N)), 957.19/297.23 activate(N), 957.19/297.23 activate(X), 957.19/297.23 activate(XS)) 957.19/297.23 , U322(tt(), N, X, XS) -> 957.19/297.23 U323(isNatural(activate(X)), 957.19/297.23 activate(N), 957.19/297.23 activate(X), 957.19/297.23 activate(XS)) 957.19/297.23 , U323(tt(), N, X, XS) -> 957.19/297.23 U324(isNaturalKind(activate(X)), 957.19/297.23 activate(N), 957.19/297.23 activate(X), 957.19/297.23 activate(XS)) 957.19/297.23 , U324(tt(), N, X, XS) -> 957.19/297.23 U325(isLNat(activate(XS)), activate(N), activate(X), activate(XS)) 957.19/297.23 , U325(tt(), N, X, XS) -> 957.19/297.23 U326(isLNatKind(activate(XS)), 957.19/297.23 activate(N), 957.19/297.23 activate(X), 957.19/297.23 activate(XS)) 957.19/297.23 , U326(tt(), N, X, XS) -> 957.19/297.23 U327(splitAt(activate(N), activate(XS)), activate(X)) 957.19/297.23 , U327(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) 957.19/297.23 , U34(tt(), N) -> activate(N) 957.19/297.23 , U331(tt(), N, XS) -> 957.19/297.23 U332(isNaturalKind(activate(N)), activate(XS)) 957.19/297.23 , U332(tt(), XS) -> U333(isLNat(activate(XS)), activate(XS)) 957.19/297.23 , U333(tt(), XS) -> U334(isLNatKind(activate(XS)), activate(XS)) 957.19/297.23 , U334(tt(), XS) -> activate(XS) 957.19/297.23 , U341(tt(), N, XS) -> 957.19/297.23 U342(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.19/297.23 , U342(tt(), N, XS) -> 957.19/297.23 U343(isLNat(activate(XS)), activate(N), activate(XS)) 957.19/297.23 , U343(tt(), N, XS) -> 957.19/297.23 U344(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.19/297.23 , U344(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS))) 957.19/297.23 , fst(X) -> n__fst(X) 957.19/297.23 , fst(pair(X, Y)) -> U21(isLNat(X), X, Y) 957.19/297.23 , U41(tt(), V1, V2) -> 957.19/297.23 U42(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.23 , U42(tt(), V1, V2) -> 957.19/297.23 U43(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.23 , U43(tt(), V1, V2) -> 957.19/297.23 U44(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.23 , U44(tt(), V1, V2) -> U45(isNatural(activate(V1)), activate(V2)) 957.19/297.23 , U45(tt(), V2) -> U46(isLNat(activate(V2))) 957.19/297.23 , U46(tt()) -> tt() 957.19/297.23 , U51(tt(), V1, V2) -> 957.19/297.23 U52(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.23 , U52(tt(), V1, V2) -> 957.19/297.23 U53(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.23 , U53(tt(), V1, V2) -> 957.19/297.23 U54(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.23 , U54(tt(), V1, V2) -> U55(isNatural(activate(V1)), activate(V2)) 957.19/297.23 , U55(tt(), V2) -> U56(isLNat(activate(V2))) 957.19/297.23 , U56(tt()) -> tt() 957.19/297.23 , U61(tt(), V1) -> U62(isPLNatKind(activate(V1)), activate(V1)) 957.19/297.23 , U62(tt(), V1) -> U63(isPLNat(activate(V1))) 957.19/297.23 , isPLNatKind(n__pair(V1, V2)) -> 957.19/297.23 U261(isLNatKind(activate(V1)), activate(V2)) 957.19/297.23 , isPLNatKind(n__splitAt(V1, V2)) -> 957.19/297.23 U271(isNaturalKind(activate(V1)), activate(V2)) 957.19/297.23 , U63(tt()) -> tt() 957.19/297.23 , isPLNat(n__pair(V1, V2)) -> 957.19/297.23 U241(isLNatKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.23 , isPLNat(n__splitAt(V1, V2)) -> 957.19/297.23 U251(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.23 , U71(tt(), V1) -> U72(isNaturalKind(activate(V1)), activate(V1)) 957.19/297.23 , U72(tt(), V1) -> U73(isNatural(activate(V1))) 957.19/297.23 , U73(tt()) -> tt() 957.19/297.23 , U81(tt(), V1) -> U82(isPLNatKind(activate(V1)), activate(V1)) 957.19/297.23 , U82(tt(), V1) -> U83(isPLNat(activate(V1))) 957.19/297.23 , U83(tt()) -> tt() 957.19/297.23 , U91(tt(), V1) -> U92(isLNatKind(activate(V1)), activate(V1)) 957.19/297.23 , U92(tt(), V1) -> U93(isLNat(activate(V1))) 957.19/297.23 , U93(tt()) -> tt() 957.19/297.23 , natsFrom(N) -> U281(isNatural(N), N) 957.19/297.23 , natsFrom(X) -> n__natsFrom(X) 957.19/297.23 , sel(N, XS) -> U291(isNatural(N), N, XS) 957.19/297.23 , sel(X1, X2) -> n__sel(X1, X2) 957.19/297.23 , 0() -> n__0() 957.19/297.23 , tail(X) -> n__tail(X) 957.19/297.23 , tail(cons(N, XS)) -> U331(isNatural(N), N, activate(XS)) 957.19/297.23 , take(N, XS) -> U341(isNatural(N), N, XS) 957.19/297.23 , take(X1, X2) -> n__take(X1, X2) } 957.19/297.23 Obligation: 957.19/297.23 runtime complexity 957.19/297.23 Answer: 957.19/297.23 MAYBE 957.19/297.23 957.19/297.23 None of the processors succeeded. 957.19/297.23 957.19/297.23 Details of failed attempt(s): 957.19/297.23 ----------------------------- 957.19/297.23 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 957.19/297.23 following reason: 957.19/297.23 957.19/297.23 Computation stopped due to timeout after 297.0 seconds. 957.19/297.23 957.19/297.23 2) 'Best' failed due to the following reason: 957.19/297.23 957.19/297.23 None of the processors succeeded. 957.19/297.23 957.19/297.23 Details of failed attempt(s): 957.19/297.23 ----------------------------- 957.19/297.23 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 957.19/297.23 seconds)' failed due to the following reason: 957.19/297.23 957.19/297.23 Computation stopped due to timeout after 148.0 seconds. 957.19/297.23 957.19/297.23 2) 'Best' failed due to the following reason: 957.19/297.23 957.19/297.23 None of the processors succeeded. 957.19/297.23 957.19/297.23 Details of failed attempt(s): 957.19/297.23 ----------------------------- 957.19/297.23 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 957.19/297.23 following reason: 957.19/297.23 957.19/297.23 The processor is inapplicable, reason: 957.19/297.23 Processor only applicable for innermost runtime complexity analysis 957.19/297.23 957.19/297.23 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 957.19/297.23 to the following reason: 957.19/297.23 957.19/297.23 The processor is inapplicable, reason: 957.19/297.23 Processor only applicable for innermost runtime complexity analysis 957.19/297.23 957.19/297.23 957.19/297.23 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 957.19/297.23 failed due to the following reason: 957.19/297.23 957.19/297.23 None of the processors succeeded. 957.19/297.23 957.19/297.23 Details of failed attempt(s): 957.19/297.23 ----------------------------- 957.19/297.23 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 957.19/297.23 failed due to the following reason: 957.19/297.23 957.19/297.23 match-boundness of the problem could not be verified. 957.19/297.23 957.19/297.23 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 957.19/297.23 failed due to the following reason: 957.19/297.23 957.19/297.23 match-boundness of the problem could not be verified. 957.19/297.23 957.19/297.23 957.19/297.23 957.19/297.23 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 957.19/297.23 the following reason: 957.19/297.23 957.19/297.23 We add the following weak dependency pairs: 957.19/297.23 957.19/297.23 Strict DPs: 957.19/297.23 { U101^#(tt(), V1, V2) -> 957.19/297.23 c_1(U102^#(isNaturalKind(activate(V1)), 957.19/297.23 activate(V1), 957.19/297.23 activate(V2))) 957.19/297.23 , U102^#(tt(), V1, V2) -> 957.19/297.23 c_2(U103^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.23 , U103^#(tt(), V1, V2) -> 957.19/297.23 c_22(U104^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.23 , isNaturalKind^#(n__0()) -> c_3() 957.19/297.23 , isNaturalKind^#(n__head(V1)) -> 957.19/297.23 c_4(U211^#(isLNatKind(activate(V1)))) 957.19/297.23 , isNaturalKind^#(n__s(V1)) -> 957.19/297.23 c_5(U221^#(isNaturalKind(activate(V1)))) 957.19/297.23 , isNaturalKind^#(n__sel(V1, V2)) -> 957.19/297.23 c_6(U231^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.23 , U211^#(tt()) -> c_79() 957.19/297.23 , U221^#(tt()) -> c_81() 957.19/297.23 , U231^#(tt(), V2) -> c_83(U232^#(isLNatKind(activate(V2)))) 957.19/297.23 , activate^#(X) -> c_7(X) 957.19/297.23 , activate^#(n__natsFrom(X)) -> c_8(natsFrom^#(X)) 957.19/297.23 , activate^#(n__nil()) -> c_9(nil^#()) 957.19/297.23 , activate^#(n__afterNth(X1, X2)) -> c_10(afterNth^#(X1, X2)) 957.19/297.23 , activate^#(n__cons(X1, X2)) -> c_11(cons^#(X1, X2)) 957.19/297.23 , activate^#(n__fst(X)) -> c_12(fst^#(X)) 957.19/297.23 , activate^#(n__snd(X)) -> c_13(snd^#(X)) 957.19/297.23 , activate^#(n__tail(X)) -> c_14(tail^#(X)) 957.19/297.23 , activate^#(n__take(X1, X2)) -> c_15(take^#(X1, X2)) 957.19/297.23 , activate^#(n__0()) -> c_16(0^#()) 957.19/297.23 , activate^#(n__head(X)) -> c_17(head^#(X)) 957.19/297.23 , activate^#(n__s(X)) -> c_18(s^#(X)) 957.19/297.23 , activate^#(n__sel(X1, X2)) -> c_19(sel^#(X1, X2)) 957.19/297.23 , activate^#(n__pair(X1, X2)) -> c_20(pair^#(X1, X2)) 957.19/297.23 , activate^#(n__splitAt(X1, X2)) -> c_21(splitAt^#(X1, X2)) 957.19/297.23 , natsFrom^#(N) -> c_170(U281^#(isNatural(N), N)) 957.19/297.23 , natsFrom^#(X) -> c_171(X) 957.19/297.23 , nil^#() -> c_122() 957.19/297.23 , afterNth^#(N, XS) -> c_111(U11^#(isNatural(N), N, XS)) 957.19/297.23 , afterNth^#(X1, X2) -> c_112(X1, X2) 957.19/297.23 , cons^#(X1, X2) -> c_103(X1, X2) 957.19/297.23 , fst^#(X) -> c_140(X) 957.19/297.23 , fst^#(pair(X, Y)) -> c_141(U21^#(isLNat(X), X, Y)) 957.19/297.23 , snd^#(X) -> c_55(X) 957.19/297.23 , snd^#(pair(X, Y)) -> c_56(U301^#(isLNat(X), X, Y)) 957.19/297.23 , tail^#(X) -> c_175(X) 957.19/297.23 , tail^#(cons(N, XS)) -> 957.19/297.23 c_176(U331^#(isNatural(N), N, activate(XS))) 957.19/297.23 , take^#(N, XS) -> c_177(U341^#(isNatural(N), N, XS)) 957.19/297.23 , take^#(X1, X2) -> c_178(X1, X2) 957.19/297.23 , 0^#() -> c_174() 957.19/297.23 , head^#(X) -> c_109(X) 957.19/297.23 , head^#(cons(N, XS)) -> 957.19/297.23 c_110(U31^#(isNatural(N), N, activate(XS))) 957.19/297.23 , s^#(X) -> c_104(X) 957.19/297.23 , sel^#(N, XS) -> c_172(U291^#(isNatural(N), N, XS)) 957.19/297.23 , sel^#(X1, X2) -> c_173(X1, X2) 957.19/297.23 , pair^#(X1, X2) -> c_121(X1, X2) 957.19/297.23 , splitAt^#(X1, X2) -> c_57(X1, X2) 957.19/297.23 , splitAt^#(s(N), cons(X, XS)) -> 957.19/297.23 c_58(U321^#(isNatural(N), N, X, activate(XS))) 957.19/297.23 , splitAt^#(0(), XS) -> c_59(U311^#(isLNat(XS), XS)) 957.19/297.23 , U104^#(tt(), V1, V2) -> 957.19/297.23 c_31(U105^#(isNatural(activate(V1)), activate(V2))) 957.19/297.23 , isLNatKind^#(n__natsFrom(V1)) -> 957.19/297.23 c_23(U141^#(isNaturalKind(activate(V1)))) 957.19/297.23 , isLNatKind^#(n__nil()) -> c_24() 957.19/297.23 , isLNatKind^#(n__afterNth(V1, V2)) -> 957.19/297.23 c_25(U111^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.23 , isLNatKind^#(n__cons(V1, V2)) -> 957.19/297.23 c_26(U121^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.23 , isLNatKind^#(n__fst(V1)) -> 957.19/297.23 c_27(U131^#(isPLNatKind(activate(V1)))) 957.19/297.23 , isLNatKind^#(n__snd(V1)) -> 957.19/297.23 c_28(U151^#(isPLNatKind(activate(V1)))) 957.19/297.23 , isLNatKind^#(n__tail(V1)) -> 957.19/297.23 c_29(U161^#(isLNatKind(activate(V1)))) 957.19/297.23 , isLNatKind^#(n__take(V1, V2)) -> 957.19/297.23 c_30(U171^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.23 , U141^#(tt()) -> c_60() 957.19/297.23 , U111^#(tt(), V2) -> c_48(U112^#(isLNatKind(activate(V2)))) 957.19/297.24 , U121^#(tt(), V2) -> c_51(U122^#(isLNatKind(activate(V2)))) 957.19/297.24 , U131^#(tt()) -> c_54() 957.19/297.24 , U151^#(tt()) -> c_61() 957.19/297.24 , U161^#(tt()) -> c_62() 957.19/297.24 , U171^#(tt(), V2) -> c_63(U172^#(isLNatKind(activate(V2)))) 957.19/297.24 , U105^#(tt(), V2) -> c_32(U106^#(isLNat(activate(V2)))) 957.19/297.24 , U106^#(tt()) -> c_37() 957.19/297.24 , isNatural^#(n__0()) -> c_33() 957.19/297.24 , isNatural^#(n__head(V1)) -> 957.19/297.24 c_34(U181^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.24 , isNatural^#(n__s(V1)) -> 957.19/297.24 c_35(U191^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.24 , isNatural^#(n__sel(V1, V2)) -> 957.19/297.24 c_36(U201^#(isNaturalKind(activate(V1)), 957.19/297.24 activate(V1), 957.19/297.24 activate(V2))) 957.19/297.24 , U181^#(tt(), V1) -> 957.19/297.24 c_65(U182^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.24 , U191^#(tt(), V1) -> 957.19/297.24 c_68(U192^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.24 , U201^#(tt(), V1, V2) -> 957.19/297.24 c_71(U202^#(isNaturalKind(activate(V1)), 957.19/297.24 activate(V1), 957.19/297.24 activate(V2))) 957.19/297.24 , isLNat^#(n__natsFrom(V1)) -> 957.19/297.24 c_38(U71^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.24 , isLNat^#(n__nil()) -> c_39() 957.19/297.24 , isLNat^#(n__afterNth(V1, V2)) -> 957.19/297.24 c_40(U41^#(isNaturalKind(activate(V1)), 957.19/297.24 activate(V1), 957.19/297.24 activate(V2))) 957.19/297.24 , isLNat^#(n__cons(V1, V2)) -> 957.19/297.24 c_41(U51^#(isNaturalKind(activate(V1)), 957.19/297.24 activate(V1), 957.19/297.24 activate(V2))) 957.19/297.24 , isLNat^#(n__fst(V1)) -> 957.19/297.24 c_42(U61^#(isPLNatKind(activate(V1)), activate(V1))) 957.19/297.24 , isLNat^#(n__snd(V1)) -> 957.19/297.24 c_43(U81^#(isPLNatKind(activate(V1)), activate(V1))) 957.19/297.24 , isLNat^#(n__tail(V1)) -> 957.19/297.24 c_44(U91^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.24 , isLNat^#(n__take(V1, V2)) -> 957.19/297.24 c_45(U101^#(isNaturalKind(activate(V1)), 957.19/297.24 activate(V1), 957.19/297.24 activate(V2))) 957.19/297.24 , U71^#(tt(), V1) -> 957.19/297.24 c_161(U72^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.24 , U41^#(tt(), V1, V2) -> 957.19/297.24 c_142(U42^#(isNaturalKind(activate(V1)), 957.19/297.24 activate(V1), 957.19/297.24 activate(V2))) 957.19/297.24 , U51^#(tt(), V1, V2) -> 957.19/297.24 c_148(U52^#(isNaturalKind(activate(V1)), 957.19/297.24 activate(V1), 957.19/297.24 activate(V2))) 957.19/297.24 , U61^#(tt(), V1) -> 957.19/297.24 c_154(U62^#(isPLNatKind(activate(V1)), activate(V1))) 957.19/297.24 , U81^#(tt(), V1) -> 957.19/297.24 c_164(U82^#(isPLNatKind(activate(V1)), activate(V1))) 957.19/297.24 , U91^#(tt(), V1) -> 957.19/297.24 c_167(U92^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.24 , U11^#(tt(), N, XS) -> 957.19/297.24 c_46(U12^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.19/297.24 , U12^#(tt(), N, XS) -> 957.19/297.24 c_47(U13^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.19/297.24 , U13^#(tt(), N, XS) -> 957.19/297.24 c_50(U14^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.19/297.24 , U112^#(tt()) -> c_49() 957.19/297.24 , U14^#(tt(), N, XS) -> 957.19/297.24 c_53(snd^#(splitAt(activate(N), activate(XS)))) 957.19/297.24 , U122^#(tt()) -> c_52() 957.19/297.24 , U301^#(tt(), X, Y) -> 957.19/297.24 c_113(U302^#(isLNatKind(activate(X)), activate(Y))) 957.19/297.24 , U321^#(tt(), N, X, XS) -> 957.19/297.24 c_124(U322^#(isNaturalKind(activate(N)), 957.19/297.24 activate(N), 957.19/297.24 activate(X), 957.19/297.24 activate(XS))) 957.19/297.24 , U311^#(tt(), XS) -> 957.19/297.24 c_119(U312^#(isLNatKind(activate(XS)), activate(XS))) 957.19/297.24 , U172^#(tt()) -> c_64() 957.19/297.24 , U182^#(tt(), V1) -> c_66(U183^#(isLNat(activate(V1)))) 957.19/297.24 , U183^#(tt()) -> c_67() 957.19/297.24 , U192^#(tt(), V1) -> c_69(U193^#(isNatural(activate(V1)))) 957.19/297.24 , U193^#(tt()) -> c_70() 957.19/297.24 , U202^#(tt(), V1, V2) -> 957.19/297.24 c_72(U203^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.24 , U203^#(tt(), V1, V2) -> 957.19/297.24 c_73(U204^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.24 , U204^#(tt(), V1, V2) -> 957.19/297.24 c_74(U205^#(isNatural(activate(V1)), activate(V2))) 957.19/297.24 , U205^#(tt(), V2) -> c_75(U206^#(isLNat(activate(V2)))) 957.19/297.24 , U206^#(tt()) -> c_76() 957.19/297.24 , U21^#(tt(), X, Y) -> 957.19/297.24 c_77(U22^#(isLNatKind(activate(X)), activate(X), activate(Y))) 957.19/297.24 , U22^#(tt(), X, Y) -> 957.19/297.24 c_78(U23^#(isLNat(activate(Y)), activate(X), activate(Y))) 957.19/297.24 , U23^#(tt(), X, Y) -> 957.19/297.24 c_80(U24^#(isLNatKind(activate(Y)), activate(X))) 957.19/297.24 , U24^#(tt(), X) -> c_82(activate^#(X)) 957.19/297.24 , U232^#(tt()) -> c_84() 957.19/297.24 , U241^#(tt(), V1, V2) -> 957.19/297.24 c_85(U242^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.19/297.24 , U242^#(tt(), V1, V2) -> 957.19/297.24 c_86(U243^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.24 , U243^#(tt(), V1, V2) -> 957.19/297.24 c_87(U244^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.24 , U244^#(tt(), V1, V2) -> 957.19/297.24 c_88(U245^#(isLNat(activate(V1)), activate(V2))) 957.19/297.24 , U245^#(tt(), V2) -> c_89(U246^#(isLNat(activate(V2)))) 957.19/297.24 , U246^#(tt()) -> c_90() 957.19/297.24 , U251^#(tt(), V1, V2) -> 957.19/297.24 c_91(U252^#(isNaturalKind(activate(V1)), 957.19/297.24 activate(V1), 957.19/297.24 activate(V2))) 957.19/297.24 , U252^#(tt(), V1, V2) -> 957.19/297.24 c_92(U253^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.24 , U253^#(tt(), V1, V2) -> 957.19/297.24 c_93(U254^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.24 , U254^#(tt(), V1, V2) -> 957.19/297.24 c_94(U255^#(isNatural(activate(V1)), activate(V2))) 957.19/297.24 , U255^#(tt(), V2) -> c_95(U256^#(isLNat(activate(V2)))) 957.19/297.24 , U256^#(tt()) -> c_96() 957.19/297.24 , U261^#(tt(), V2) -> c_97(U262^#(isLNatKind(activate(V2)))) 957.19/297.24 , U262^#(tt()) -> c_98() 957.19/297.24 , U271^#(tt(), V2) -> c_99(U272^#(isLNatKind(activate(V2)))) 957.19/297.24 , U272^#(tt()) -> c_100() 957.19/297.24 , U281^#(tt(), N) -> 957.19/297.24 c_101(U282^#(isNaturalKind(activate(N)), activate(N))) 957.19/297.24 , U282^#(tt(), N) -> 957.19/297.24 c_102(cons^#(activate(N), n__natsFrom(s(activate(N))))) 957.19/297.24 , U291^#(tt(), N, XS) -> 957.19/297.24 c_105(U292^#(isNaturalKind(activate(N)), 957.19/297.24 activate(N), 957.19/297.24 activate(XS))) 957.19/297.24 , U292^#(tt(), N, XS) -> 957.19/297.24 c_106(U293^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.19/297.24 , U293^#(tt(), N, XS) -> 957.19/297.24 c_107(U294^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.19/297.24 , U294^#(tt(), N, XS) -> 957.19/297.24 c_108(head^#(afterNth(activate(N), activate(XS)))) 957.19/297.24 , U31^#(tt(), N, XS) -> 957.19/297.24 c_117(U32^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.19/297.24 , U302^#(tt(), Y) -> 957.19/297.24 c_114(U303^#(isLNat(activate(Y)), activate(Y))) 957.19/297.24 , U303^#(tt(), Y) -> 957.19/297.24 c_115(U304^#(isLNatKind(activate(Y)), activate(Y))) 957.19/297.24 , U304^#(tt(), Y) -> c_116(activate^#(Y)) 957.19/297.24 , U32^#(tt(), N, XS) -> 957.19/297.24 c_118(U33^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.19/297.24 , U33^#(tt(), N, XS) -> 957.19/297.24 c_123(U34^#(isLNatKind(activate(XS)), activate(N))) 957.19/297.24 , U312^#(tt(), XS) -> c_120(pair^#(nil(), activate(XS))) 957.19/297.24 , U34^#(tt(), N) -> c_131(activate^#(N)) 957.19/297.24 , U322^#(tt(), N, X, XS) -> 957.19/297.24 c_125(U323^#(isNatural(activate(X)), 957.19/297.24 activate(N), 957.19/297.24 activate(X), 957.19/297.24 activate(XS))) 957.19/297.24 , U323^#(tt(), N, X, XS) -> 957.19/297.24 c_126(U324^#(isNaturalKind(activate(X)), 957.19/297.24 activate(N), 957.19/297.24 activate(X), 957.19/297.24 activate(XS))) 957.19/297.24 , U324^#(tt(), N, X, XS) -> 957.19/297.24 c_127(U325^#(isLNat(activate(XS)), 957.19/297.24 activate(N), 957.19/297.24 activate(X), 957.19/297.24 activate(XS))) 957.19/297.24 , U325^#(tt(), N, X, XS) -> 957.19/297.24 c_128(U326^#(isLNatKind(activate(XS)), 957.19/297.24 activate(N), 957.19/297.24 activate(X), 957.19/297.24 activate(XS))) 957.19/297.24 , U326^#(tt(), N, X, XS) -> 957.19/297.24 c_129(U327^#(splitAt(activate(N), activate(XS)), activate(X))) 957.19/297.24 , U327^#(pair(YS, ZS), X) -> 957.19/297.24 c_130(pair^#(cons(activate(X), YS), ZS)) 957.19/297.24 , U331^#(tt(), N, XS) -> 957.19/297.24 c_132(U332^#(isNaturalKind(activate(N)), activate(XS))) 957.19/297.24 , U332^#(tt(), XS) -> 957.19/297.24 c_133(U333^#(isLNat(activate(XS)), activate(XS))) 957.19/297.24 , U333^#(tt(), XS) -> 957.19/297.24 c_134(U334^#(isLNatKind(activate(XS)), activate(XS))) 957.19/297.24 , U334^#(tt(), XS) -> c_135(activate^#(XS)) 957.19/297.24 , U341^#(tt(), N, XS) -> 957.19/297.24 c_136(U342^#(isNaturalKind(activate(N)), 957.19/297.24 activate(N), 957.19/297.24 activate(XS))) 957.19/297.24 , U342^#(tt(), N, XS) -> 957.19/297.24 c_137(U343^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.19/297.24 , U343^#(tt(), N, XS) -> 957.19/297.24 c_138(U344^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.19/297.24 , U344^#(tt(), N, XS) -> 957.19/297.24 c_139(fst^#(splitAt(activate(N), activate(XS)))) 957.19/297.24 , U42^#(tt(), V1, V2) -> 957.19/297.24 c_143(U43^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.24 , U43^#(tt(), V1, V2) -> 957.19/297.24 c_144(U44^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.24 , U44^#(tt(), V1, V2) -> 957.19/297.24 c_145(U45^#(isNatural(activate(V1)), activate(V2))) 957.19/297.24 , U45^#(tt(), V2) -> c_146(U46^#(isLNat(activate(V2)))) 957.19/297.24 , U46^#(tt()) -> c_147() 957.19/297.24 , U52^#(tt(), V1, V2) -> 957.19/297.24 c_149(U53^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.24 , U53^#(tt(), V1, V2) -> 957.19/297.24 c_150(U54^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.24 , U54^#(tt(), V1, V2) -> 957.19/297.24 c_151(U55^#(isNatural(activate(V1)), activate(V2))) 957.19/297.24 , U55^#(tt(), V2) -> c_152(U56^#(isLNat(activate(V2)))) 957.19/297.24 , U56^#(tt()) -> c_153() 957.19/297.24 , U62^#(tt(), V1) -> c_155(U63^#(isPLNat(activate(V1)))) 957.19/297.24 , U63^#(tt()) -> c_158() 957.19/297.24 , isPLNatKind^#(n__pair(V1, V2)) -> 957.19/297.24 c_156(U261^#(isLNatKind(activate(V1)), activate(V2))) 957.19/297.24 , isPLNatKind^#(n__splitAt(V1, V2)) -> 957.19/297.24 c_157(U271^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.24 , isPLNat^#(n__pair(V1, V2)) -> 957.19/297.24 c_159(U241^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.19/297.24 , isPLNat^#(n__splitAt(V1, V2)) -> 957.19/297.24 c_160(U251^#(isNaturalKind(activate(V1)), 957.19/297.24 activate(V1), 957.19/297.24 activate(V2))) 957.19/297.24 , U72^#(tt(), V1) -> c_162(U73^#(isNatural(activate(V1)))) 957.19/297.24 , U73^#(tt()) -> c_163() 957.19/297.24 , U82^#(tt(), V1) -> c_165(U83^#(isPLNat(activate(V1)))) 957.19/297.24 , U83^#(tt()) -> c_166() 957.19/297.24 , U92^#(tt(), V1) -> c_168(U93^#(isLNat(activate(V1)))) 957.19/297.24 , U93^#(tt()) -> c_169() } 957.19/297.24 957.19/297.24 and mark the set of starting terms. 957.19/297.24 957.19/297.24 We are left with following problem, upon which TcT provides the 957.19/297.24 certificate MAYBE. 957.19/297.24 957.19/297.24 Strict DPs: 957.19/297.24 { U101^#(tt(), V1, V2) -> 957.19/297.24 c_1(U102^#(isNaturalKind(activate(V1)), 957.19/297.24 activate(V1), 957.19/297.24 activate(V2))) 957.19/297.24 , U102^#(tt(), V1, V2) -> 957.19/297.24 c_2(U103^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.24 , U103^#(tt(), V1, V2) -> 957.19/297.24 c_22(U104^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.24 , isNaturalKind^#(n__0()) -> c_3() 957.19/297.24 , isNaturalKind^#(n__head(V1)) -> 957.19/297.24 c_4(U211^#(isLNatKind(activate(V1)))) 957.19/297.24 , isNaturalKind^#(n__s(V1)) -> 957.19/297.24 c_5(U221^#(isNaturalKind(activate(V1)))) 957.19/297.24 , isNaturalKind^#(n__sel(V1, V2)) -> 957.19/297.24 c_6(U231^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.24 , U211^#(tt()) -> c_79() 957.19/297.24 , U221^#(tt()) -> c_81() 957.19/297.24 , U231^#(tt(), V2) -> c_83(U232^#(isLNatKind(activate(V2)))) 957.19/297.24 , activate^#(X) -> c_7(X) 957.19/297.24 , activate^#(n__natsFrom(X)) -> c_8(natsFrom^#(X)) 957.19/297.24 , activate^#(n__nil()) -> c_9(nil^#()) 957.19/297.24 , activate^#(n__afterNth(X1, X2)) -> c_10(afterNth^#(X1, X2)) 957.19/297.24 , activate^#(n__cons(X1, X2)) -> c_11(cons^#(X1, X2)) 957.19/297.24 , activate^#(n__fst(X)) -> c_12(fst^#(X)) 957.19/297.24 , activate^#(n__snd(X)) -> c_13(snd^#(X)) 957.19/297.24 , activate^#(n__tail(X)) -> c_14(tail^#(X)) 957.19/297.24 , activate^#(n__take(X1, X2)) -> c_15(take^#(X1, X2)) 957.19/297.24 , activate^#(n__0()) -> c_16(0^#()) 957.19/297.24 , activate^#(n__head(X)) -> c_17(head^#(X)) 957.19/297.24 , activate^#(n__s(X)) -> c_18(s^#(X)) 957.19/297.24 , activate^#(n__sel(X1, X2)) -> c_19(sel^#(X1, X2)) 957.19/297.24 , activate^#(n__pair(X1, X2)) -> c_20(pair^#(X1, X2)) 957.19/297.24 , activate^#(n__splitAt(X1, X2)) -> c_21(splitAt^#(X1, X2)) 957.19/297.24 , natsFrom^#(N) -> c_170(U281^#(isNatural(N), N)) 957.19/297.24 , natsFrom^#(X) -> c_171(X) 957.19/297.24 , nil^#() -> c_122() 957.19/297.24 , afterNth^#(N, XS) -> c_111(U11^#(isNatural(N), N, XS)) 957.19/297.24 , afterNth^#(X1, X2) -> c_112(X1, X2) 957.19/297.24 , cons^#(X1, X2) -> c_103(X1, X2) 957.19/297.24 , fst^#(X) -> c_140(X) 957.19/297.24 , fst^#(pair(X, Y)) -> c_141(U21^#(isLNat(X), X, Y)) 957.19/297.24 , snd^#(X) -> c_55(X) 957.19/297.24 , snd^#(pair(X, Y)) -> c_56(U301^#(isLNat(X), X, Y)) 957.19/297.24 , tail^#(X) -> c_175(X) 957.19/297.24 , tail^#(cons(N, XS)) -> 957.19/297.24 c_176(U331^#(isNatural(N), N, activate(XS))) 957.19/297.24 , take^#(N, XS) -> c_177(U341^#(isNatural(N), N, XS)) 957.19/297.24 , take^#(X1, X2) -> c_178(X1, X2) 957.19/297.24 , 0^#() -> c_174() 957.19/297.24 , head^#(X) -> c_109(X) 957.19/297.24 , head^#(cons(N, XS)) -> 957.19/297.24 c_110(U31^#(isNatural(N), N, activate(XS))) 957.19/297.24 , s^#(X) -> c_104(X) 957.19/297.24 , sel^#(N, XS) -> c_172(U291^#(isNatural(N), N, XS)) 957.19/297.24 , sel^#(X1, X2) -> c_173(X1, X2) 957.19/297.24 , pair^#(X1, X2) -> c_121(X1, X2) 957.19/297.24 , splitAt^#(X1, X2) -> c_57(X1, X2) 957.19/297.24 , splitAt^#(s(N), cons(X, XS)) -> 957.19/297.24 c_58(U321^#(isNatural(N), N, X, activate(XS))) 957.19/297.24 , splitAt^#(0(), XS) -> c_59(U311^#(isLNat(XS), XS)) 957.19/297.24 , U104^#(tt(), V1, V2) -> 957.19/297.24 c_31(U105^#(isNatural(activate(V1)), activate(V2))) 957.19/297.24 , isLNatKind^#(n__natsFrom(V1)) -> 957.19/297.24 c_23(U141^#(isNaturalKind(activate(V1)))) 957.19/297.24 , isLNatKind^#(n__nil()) -> c_24() 957.19/297.24 , isLNatKind^#(n__afterNth(V1, V2)) -> 957.19/297.24 c_25(U111^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.24 , isLNatKind^#(n__cons(V1, V2)) -> 957.19/297.24 c_26(U121^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.24 , isLNatKind^#(n__fst(V1)) -> 957.19/297.24 c_27(U131^#(isPLNatKind(activate(V1)))) 957.19/297.24 , isLNatKind^#(n__snd(V1)) -> 957.19/297.24 c_28(U151^#(isPLNatKind(activate(V1)))) 957.19/297.24 , isLNatKind^#(n__tail(V1)) -> 957.19/297.24 c_29(U161^#(isLNatKind(activate(V1)))) 957.19/297.24 , isLNatKind^#(n__take(V1, V2)) -> 957.19/297.24 c_30(U171^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.24 , U141^#(tt()) -> c_60() 957.19/297.24 , U111^#(tt(), V2) -> c_48(U112^#(isLNatKind(activate(V2)))) 957.19/297.24 , U121^#(tt(), V2) -> c_51(U122^#(isLNatKind(activate(V2)))) 957.19/297.24 , U131^#(tt()) -> c_54() 957.19/297.24 , U151^#(tt()) -> c_61() 957.19/297.24 , U161^#(tt()) -> c_62() 957.19/297.24 , U171^#(tt(), V2) -> c_63(U172^#(isLNatKind(activate(V2)))) 957.19/297.24 , U105^#(tt(), V2) -> c_32(U106^#(isLNat(activate(V2)))) 957.19/297.24 , U106^#(tt()) -> c_37() 957.19/297.24 , isNatural^#(n__0()) -> c_33() 957.19/297.24 , isNatural^#(n__head(V1)) -> 957.19/297.24 c_34(U181^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.24 , isNatural^#(n__s(V1)) -> 957.19/297.24 c_35(U191^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.24 , isNatural^#(n__sel(V1, V2)) -> 957.19/297.24 c_36(U201^#(isNaturalKind(activate(V1)), 957.19/297.24 activate(V1), 957.19/297.24 activate(V2))) 957.19/297.24 , U181^#(tt(), V1) -> 957.19/297.24 c_65(U182^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.24 , U191^#(tt(), V1) -> 957.19/297.24 c_68(U192^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.24 , U201^#(tt(), V1, V2) -> 957.19/297.24 c_71(U202^#(isNaturalKind(activate(V1)), 957.19/297.24 activate(V1), 957.19/297.24 activate(V2))) 957.19/297.24 , isLNat^#(n__natsFrom(V1)) -> 957.19/297.24 c_38(U71^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.24 , isLNat^#(n__nil()) -> c_39() 957.19/297.24 , isLNat^#(n__afterNth(V1, V2)) -> 957.19/297.24 c_40(U41^#(isNaturalKind(activate(V1)), 957.19/297.24 activate(V1), 957.19/297.24 activate(V2))) 957.19/297.24 , isLNat^#(n__cons(V1, V2)) -> 957.19/297.24 c_41(U51^#(isNaturalKind(activate(V1)), 957.19/297.24 activate(V1), 957.19/297.24 activate(V2))) 957.19/297.24 , isLNat^#(n__fst(V1)) -> 957.19/297.24 c_42(U61^#(isPLNatKind(activate(V1)), activate(V1))) 957.19/297.24 , isLNat^#(n__snd(V1)) -> 957.19/297.24 c_43(U81^#(isPLNatKind(activate(V1)), activate(V1))) 957.19/297.24 , isLNat^#(n__tail(V1)) -> 957.19/297.24 c_44(U91^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.24 , isLNat^#(n__take(V1, V2)) -> 957.19/297.24 c_45(U101^#(isNaturalKind(activate(V1)), 957.19/297.24 activate(V1), 957.19/297.24 activate(V2))) 957.19/297.24 , U71^#(tt(), V1) -> 957.19/297.24 c_161(U72^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.24 , U41^#(tt(), V1, V2) -> 957.19/297.24 c_142(U42^#(isNaturalKind(activate(V1)), 957.19/297.24 activate(V1), 957.19/297.24 activate(V2))) 957.19/297.24 , U51^#(tt(), V1, V2) -> 957.19/297.24 c_148(U52^#(isNaturalKind(activate(V1)), 957.19/297.24 activate(V1), 957.19/297.24 activate(V2))) 957.19/297.24 , U61^#(tt(), V1) -> 957.19/297.24 c_154(U62^#(isPLNatKind(activate(V1)), activate(V1))) 957.19/297.24 , U81^#(tt(), V1) -> 957.19/297.24 c_164(U82^#(isPLNatKind(activate(V1)), activate(V1))) 957.19/297.24 , U91^#(tt(), V1) -> 957.19/297.24 c_167(U92^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.24 , U11^#(tt(), N, XS) -> 957.19/297.24 c_46(U12^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.19/297.24 , U12^#(tt(), N, XS) -> 957.19/297.24 c_47(U13^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.19/297.24 , U13^#(tt(), N, XS) -> 957.19/297.24 c_50(U14^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.19/297.24 , U112^#(tt()) -> c_49() 957.19/297.24 , U14^#(tt(), N, XS) -> 957.19/297.24 c_53(snd^#(splitAt(activate(N), activate(XS)))) 957.19/297.24 , U122^#(tt()) -> c_52() 957.19/297.24 , U301^#(tt(), X, Y) -> 957.19/297.24 c_113(U302^#(isLNatKind(activate(X)), activate(Y))) 957.19/297.24 , U321^#(tt(), N, X, XS) -> 957.19/297.24 c_124(U322^#(isNaturalKind(activate(N)), 957.19/297.24 activate(N), 957.19/297.24 activate(X), 957.19/297.24 activate(XS))) 957.19/297.24 , U311^#(tt(), XS) -> 957.19/297.24 c_119(U312^#(isLNatKind(activate(XS)), activate(XS))) 957.19/297.24 , U172^#(tt()) -> c_64() 957.19/297.24 , U182^#(tt(), V1) -> c_66(U183^#(isLNat(activate(V1)))) 957.19/297.24 , U183^#(tt()) -> c_67() 957.19/297.24 , U192^#(tt(), V1) -> c_69(U193^#(isNatural(activate(V1)))) 957.19/297.24 , U193^#(tt()) -> c_70() 957.19/297.24 , U202^#(tt(), V1, V2) -> 957.19/297.24 c_72(U203^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.24 , U203^#(tt(), V1, V2) -> 957.19/297.24 c_73(U204^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.24 , U204^#(tt(), V1, V2) -> 957.19/297.24 c_74(U205^#(isNatural(activate(V1)), activate(V2))) 957.19/297.24 , U205^#(tt(), V2) -> c_75(U206^#(isLNat(activate(V2)))) 957.19/297.24 , U206^#(tt()) -> c_76() 957.19/297.24 , U21^#(tt(), X, Y) -> 957.19/297.24 c_77(U22^#(isLNatKind(activate(X)), activate(X), activate(Y))) 957.19/297.24 , U22^#(tt(), X, Y) -> 957.19/297.24 c_78(U23^#(isLNat(activate(Y)), activate(X), activate(Y))) 957.19/297.24 , U23^#(tt(), X, Y) -> 957.19/297.24 c_80(U24^#(isLNatKind(activate(Y)), activate(X))) 957.19/297.24 , U24^#(tt(), X) -> c_82(activate^#(X)) 957.19/297.24 , U232^#(tt()) -> c_84() 957.19/297.24 , U241^#(tt(), V1, V2) -> 957.19/297.24 c_85(U242^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.19/297.24 , U242^#(tt(), V1, V2) -> 957.19/297.24 c_86(U243^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.24 , U243^#(tt(), V1, V2) -> 957.19/297.24 c_87(U244^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.24 , U244^#(tt(), V1, V2) -> 957.19/297.24 c_88(U245^#(isLNat(activate(V1)), activate(V2))) 957.19/297.24 , U245^#(tt(), V2) -> c_89(U246^#(isLNat(activate(V2)))) 957.19/297.24 , U246^#(tt()) -> c_90() 957.19/297.24 , U251^#(tt(), V1, V2) -> 957.19/297.24 c_91(U252^#(isNaturalKind(activate(V1)), 957.19/297.24 activate(V1), 957.19/297.24 activate(V2))) 957.19/297.24 , U252^#(tt(), V1, V2) -> 957.19/297.24 c_92(U253^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.24 , U253^#(tt(), V1, V2) -> 957.19/297.24 c_93(U254^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.24 , U254^#(tt(), V1, V2) -> 957.19/297.24 c_94(U255^#(isNatural(activate(V1)), activate(V2))) 957.19/297.24 , U255^#(tt(), V2) -> c_95(U256^#(isLNat(activate(V2)))) 957.19/297.24 , U256^#(tt()) -> c_96() 957.19/297.24 , U261^#(tt(), V2) -> c_97(U262^#(isLNatKind(activate(V2)))) 957.19/297.24 , U262^#(tt()) -> c_98() 957.19/297.24 , U271^#(tt(), V2) -> c_99(U272^#(isLNatKind(activate(V2)))) 957.19/297.24 , U272^#(tt()) -> c_100() 957.19/297.24 , U281^#(tt(), N) -> 957.19/297.24 c_101(U282^#(isNaturalKind(activate(N)), activate(N))) 957.19/297.24 , U282^#(tt(), N) -> 957.19/297.24 c_102(cons^#(activate(N), n__natsFrom(s(activate(N))))) 957.19/297.24 , U291^#(tt(), N, XS) -> 957.19/297.24 c_105(U292^#(isNaturalKind(activate(N)), 957.19/297.24 activate(N), 957.19/297.24 activate(XS))) 957.19/297.24 , U292^#(tt(), N, XS) -> 957.19/297.24 c_106(U293^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.19/297.24 , U293^#(tt(), N, XS) -> 957.19/297.24 c_107(U294^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.19/297.24 , U294^#(tt(), N, XS) -> 957.19/297.24 c_108(head^#(afterNth(activate(N), activate(XS)))) 957.19/297.24 , U31^#(tt(), N, XS) -> 957.19/297.24 c_117(U32^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.19/297.24 , U302^#(tt(), Y) -> 957.19/297.24 c_114(U303^#(isLNat(activate(Y)), activate(Y))) 957.19/297.24 , U303^#(tt(), Y) -> 957.19/297.24 c_115(U304^#(isLNatKind(activate(Y)), activate(Y))) 957.19/297.24 , U304^#(tt(), Y) -> c_116(activate^#(Y)) 957.19/297.24 , U32^#(tt(), N, XS) -> 957.19/297.24 c_118(U33^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.19/297.24 , U33^#(tt(), N, XS) -> 957.19/297.24 c_123(U34^#(isLNatKind(activate(XS)), activate(N))) 957.19/297.24 , U312^#(tt(), XS) -> c_120(pair^#(nil(), activate(XS))) 957.19/297.24 , U34^#(tt(), N) -> c_131(activate^#(N)) 957.19/297.24 , U322^#(tt(), N, X, XS) -> 957.19/297.24 c_125(U323^#(isNatural(activate(X)), 957.19/297.24 activate(N), 957.19/297.24 activate(X), 957.19/297.24 activate(XS))) 957.19/297.24 , U323^#(tt(), N, X, XS) -> 957.19/297.24 c_126(U324^#(isNaturalKind(activate(X)), 957.19/297.24 activate(N), 957.19/297.24 activate(X), 957.19/297.24 activate(XS))) 957.19/297.24 , U324^#(tt(), N, X, XS) -> 957.19/297.24 c_127(U325^#(isLNat(activate(XS)), 957.19/297.24 activate(N), 957.19/297.24 activate(X), 957.19/297.24 activate(XS))) 957.19/297.24 , U325^#(tt(), N, X, XS) -> 957.19/297.24 c_128(U326^#(isLNatKind(activate(XS)), 957.19/297.24 activate(N), 957.19/297.24 activate(X), 957.19/297.24 activate(XS))) 957.19/297.24 , U326^#(tt(), N, X, XS) -> 957.19/297.24 c_129(U327^#(splitAt(activate(N), activate(XS)), activate(X))) 957.19/297.24 , U327^#(pair(YS, ZS), X) -> 957.19/297.24 c_130(pair^#(cons(activate(X), YS), ZS)) 957.19/297.24 , U331^#(tt(), N, XS) -> 957.19/297.24 c_132(U332^#(isNaturalKind(activate(N)), activate(XS))) 957.19/297.24 , U332^#(tt(), XS) -> 957.19/297.24 c_133(U333^#(isLNat(activate(XS)), activate(XS))) 957.19/297.24 , U333^#(tt(), XS) -> 957.19/297.24 c_134(U334^#(isLNatKind(activate(XS)), activate(XS))) 957.19/297.24 , U334^#(tt(), XS) -> c_135(activate^#(XS)) 957.19/297.24 , U341^#(tt(), N, XS) -> 957.19/297.24 c_136(U342^#(isNaturalKind(activate(N)), 957.19/297.24 activate(N), 957.19/297.24 activate(XS))) 957.19/297.24 , U342^#(tt(), N, XS) -> 957.19/297.24 c_137(U343^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.19/297.24 , U343^#(tt(), N, XS) -> 957.19/297.24 c_138(U344^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.19/297.24 , U344^#(tt(), N, XS) -> 957.19/297.24 c_139(fst^#(splitAt(activate(N), activate(XS)))) 957.19/297.24 , U42^#(tt(), V1, V2) -> 957.19/297.24 c_143(U43^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.24 , U43^#(tt(), V1, V2) -> 957.19/297.24 c_144(U44^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.24 , U44^#(tt(), V1, V2) -> 957.19/297.24 c_145(U45^#(isNatural(activate(V1)), activate(V2))) 957.19/297.24 , U45^#(tt(), V2) -> c_146(U46^#(isLNat(activate(V2)))) 957.19/297.24 , U46^#(tt()) -> c_147() 957.19/297.24 , U52^#(tt(), V1, V2) -> 957.19/297.24 c_149(U53^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.24 , U53^#(tt(), V1, V2) -> 957.19/297.24 c_150(U54^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.24 , U54^#(tt(), V1, V2) -> 957.19/297.24 c_151(U55^#(isNatural(activate(V1)), activate(V2))) 957.19/297.24 , U55^#(tt(), V2) -> c_152(U56^#(isLNat(activate(V2)))) 957.19/297.24 , U56^#(tt()) -> c_153() 957.19/297.24 , U62^#(tt(), V1) -> c_155(U63^#(isPLNat(activate(V1)))) 957.19/297.24 , U63^#(tt()) -> c_158() 957.19/297.24 , isPLNatKind^#(n__pair(V1, V2)) -> 957.19/297.24 c_156(U261^#(isLNatKind(activate(V1)), activate(V2))) 957.19/297.24 , isPLNatKind^#(n__splitAt(V1, V2)) -> 957.19/297.24 c_157(U271^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.24 , isPLNat^#(n__pair(V1, V2)) -> 957.19/297.24 c_159(U241^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.19/297.24 , isPLNat^#(n__splitAt(V1, V2)) -> 957.19/297.24 c_160(U251^#(isNaturalKind(activate(V1)), 957.19/297.24 activate(V1), 957.19/297.24 activate(V2))) 957.19/297.24 , U72^#(tt(), V1) -> c_162(U73^#(isNatural(activate(V1)))) 957.19/297.24 , U73^#(tt()) -> c_163() 957.19/297.24 , U82^#(tt(), V1) -> c_165(U83^#(isPLNat(activate(V1)))) 957.19/297.24 , U83^#(tt()) -> c_166() 957.19/297.24 , U92^#(tt(), V1) -> c_168(U93^#(isLNat(activate(V1)))) 957.19/297.24 , U93^#(tt()) -> c_169() } 957.19/297.24 Strict Trs: 957.19/297.24 { U101(tt(), V1, V2) -> 957.19/297.24 U102(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.24 , U102(tt(), V1, V2) -> 957.19/297.24 U103(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.24 , isNaturalKind(n__0()) -> tt() 957.19/297.24 , isNaturalKind(n__head(V1)) -> U211(isLNatKind(activate(V1))) 957.19/297.24 , isNaturalKind(n__s(V1)) -> U221(isNaturalKind(activate(V1))) 957.19/297.24 , isNaturalKind(n__sel(V1, V2)) -> 957.19/297.24 U231(isNaturalKind(activate(V1)), activate(V2)) 957.19/297.24 , activate(X) -> X 957.19/297.24 , activate(n__natsFrom(X)) -> natsFrom(X) 957.19/297.25 , activate(n__nil()) -> nil() 957.19/297.25 , activate(n__afterNth(X1, X2)) -> afterNth(X1, X2) 957.19/297.25 , activate(n__cons(X1, X2)) -> cons(X1, X2) 957.19/297.25 , activate(n__fst(X)) -> fst(X) 957.19/297.25 , activate(n__snd(X)) -> snd(X) 957.19/297.25 , activate(n__tail(X)) -> tail(X) 957.19/297.25 , activate(n__take(X1, X2)) -> take(X1, X2) 957.19/297.25 , activate(n__0()) -> 0() 957.19/297.25 , activate(n__head(X)) -> head(X) 957.19/297.25 , activate(n__s(X)) -> s(X) 957.19/297.25 , activate(n__sel(X1, X2)) -> sel(X1, X2) 957.19/297.25 , activate(n__pair(X1, X2)) -> pair(X1, X2) 957.19/297.25 , activate(n__splitAt(X1, X2)) -> splitAt(X1, X2) 957.19/297.25 , U103(tt(), V1, V2) -> 957.19/297.25 U104(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.25 , isLNatKind(n__natsFrom(V1)) -> U141(isNaturalKind(activate(V1))) 957.19/297.25 , isLNatKind(n__nil()) -> tt() 957.19/297.25 , isLNatKind(n__afterNth(V1, V2)) -> 957.19/297.25 U111(isNaturalKind(activate(V1)), activate(V2)) 957.19/297.25 , isLNatKind(n__cons(V1, V2)) -> 957.19/297.25 U121(isNaturalKind(activate(V1)), activate(V2)) 957.19/297.25 , isLNatKind(n__fst(V1)) -> U131(isPLNatKind(activate(V1))) 957.19/297.25 , isLNatKind(n__snd(V1)) -> U151(isPLNatKind(activate(V1))) 957.19/297.25 , isLNatKind(n__tail(V1)) -> U161(isLNatKind(activate(V1))) 957.19/297.25 , isLNatKind(n__take(V1, V2)) -> 957.19/297.25 U171(isNaturalKind(activate(V1)), activate(V2)) 957.19/297.25 , U104(tt(), V1, V2) -> U105(isNatural(activate(V1)), activate(V2)) 957.19/297.25 , U105(tt(), V2) -> U106(isLNat(activate(V2))) 957.19/297.25 , isNatural(n__0()) -> tt() 957.19/297.25 , isNatural(n__head(V1)) -> 957.19/297.25 U181(isLNatKind(activate(V1)), activate(V1)) 957.19/297.25 , isNatural(n__s(V1)) -> 957.19/297.25 U191(isNaturalKind(activate(V1)), activate(V1)) 957.19/297.25 , isNatural(n__sel(V1, V2)) -> 957.19/297.25 U201(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.25 , U106(tt()) -> tt() 957.19/297.25 , isLNat(n__natsFrom(V1)) -> 957.19/297.25 U71(isNaturalKind(activate(V1)), activate(V1)) 957.19/297.25 , isLNat(n__nil()) -> tt() 957.19/297.25 , isLNat(n__afterNth(V1, V2)) -> 957.19/297.25 U41(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.25 , isLNat(n__cons(V1, V2)) -> 957.19/297.25 U51(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.25 , isLNat(n__fst(V1)) -> 957.19/297.25 U61(isPLNatKind(activate(V1)), activate(V1)) 957.19/297.25 , isLNat(n__snd(V1)) -> 957.19/297.25 U81(isPLNatKind(activate(V1)), activate(V1)) 957.19/297.25 , isLNat(n__tail(V1)) -> 957.19/297.25 U91(isLNatKind(activate(V1)), activate(V1)) 957.19/297.25 , isLNat(n__take(V1, V2)) -> 957.19/297.25 U101(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.25 , U11(tt(), N, XS) -> 957.19/297.25 U12(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.19/297.25 , U12(tt(), N, XS) -> 957.19/297.25 U13(isLNat(activate(XS)), activate(N), activate(XS)) 957.19/297.25 , U111(tt(), V2) -> U112(isLNatKind(activate(V2))) 957.19/297.25 , U112(tt()) -> tt() 957.19/297.25 , U13(tt(), N, XS) -> 957.19/297.25 U14(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.19/297.25 , U121(tt(), V2) -> U122(isLNatKind(activate(V2))) 957.19/297.25 , U122(tt()) -> tt() 957.19/297.25 , U14(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS))) 957.19/297.25 , U131(tt()) -> tt() 957.19/297.25 , snd(X) -> n__snd(X) 957.19/297.25 , snd(pair(X, Y)) -> U301(isLNat(X), X, Y) 957.19/297.25 , splitAt(X1, X2) -> n__splitAt(X1, X2) 957.19/297.25 , splitAt(s(N), cons(X, XS)) -> 957.19/297.25 U321(isNatural(N), N, X, activate(XS)) 957.19/297.25 , splitAt(0(), XS) -> U311(isLNat(XS), XS) 957.19/297.25 , U141(tt()) -> tt() 957.19/297.25 , U151(tt()) -> tt() 957.19/297.25 , U161(tt()) -> tt() 957.19/297.25 , U171(tt(), V2) -> U172(isLNatKind(activate(V2))) 957.19/297.25 , U172(tt()) -> tt() 957.19/297.25 , U181(tt(), V1) -> U182(isLNatKind(activate(V1)), activate(V1)) 957.19/297.25 , U182(tt(), V1) -> U183(isLNat(activate(V1))) 957.19/297.25 , U183(tt()) -> tt() 957.19/297.25 , U191(tt(), V1) -> U192(isNaturalKind(activate(V1)), activate(V1)) 957.19/297.25 , U192(tt(), V1) -> U193(isNatural(activate(V1))) 957.19/297.25 , U193(tt()) -> tt() 957.19/297.25 , U201(tt(), V1, V2) -> 957.19/297.25 U202(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.25 , U202(tt(), V1, V2) -> 957.19/297.25 U203(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.25 , U203(tt(), V1, V2) -> 957.19/297.25 U204(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.25 , U204(tt(), V1, V2) -> U205(isNatural(activate(V1)), activate(V2)) 957.19/297.25 , U205(tt(), V2) -> U206(isLNat(activate(V2))) 957.19/297.25 , U206(tt()) -> tt() 957.19/297.25 , U21(tt(), X, Y) -> 957.19/297.25 U22(isLNatKind(activate(X)), activate(X), activate(Y)) 957.19/297.25 , U22(tt(), X, Y) -> 957.19/297.25 U23(isLNat(activate(Y)), activate(X), activate(Y)) 957.19/297.25 , U211(tt()) -> tt() 957.19/297.25 , U23(tt(), X, Y) -> U24(isLNatKind(activate(Y)), activate(X)) 957.19/297.25 , U221(tt()) -> tt() 957.19/297.25 , U24(tt(), X) -> activate(X) 957.19/297.25 , U231(tt(), V2) -> U232(isLNatKind(activate(V2))) 957.19/297.25 , U232(tt()) -> tt() 957.19/297.25 , U241(tt(), V1, V2) -> 957.19/297.25 U242(isLNatKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.25 , U242(tt(), V1, V2) -> 957.19/297.25 U243(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.25 , U243(tt(), V1, V2) -> 957.19/297.25 U244(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.25 , U244(tt(), V1, V2) -> U245(isLNat(activate(V1)), activate(V2)) 957.19/297.25 , U245(tt(), V2) -> U246(isLNat(activate(V2))) 957.19/297.25 , U246(tt()) -> tt() 957.19/297.25 , U251(tt(), V1, V2) -> 957.19/297.25 U252(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.25 , U252(tt(), V1, V2) -> 957.19/297.25 U253(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.25 , U253(tt(), V1, V2) -> 957.19/297.25 U254(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.25 , U254(tt(), V1, V2) -> U255(isNatural(activate(V1)), activate(V2)) 957.19/297.25 , U255(tt(), V2) -> U256(isLNat(activate(V2))) 957.19/297.25 , U256(tt()) -> tt() 957.19/297.25 , U261(tt(), V2) -> U262(isLNatKind(activate(V2))) 957.19/297.25 , U262(tt()) -> tt() 957.19/297.25 , U271(tt(), V2) -> U272(isLNatKind(activate(V2))) 957.19/297.25 , U272(tt()) -> tt() 957.19/297.25 , U281(tt(), N) -> U282(isNaturalKind(activate(N)), activate(N)) 957.19/297.25 , U282(tt(), N) -> cons(activate(N), n__natsFrom(s(activate(N)))) 957.19/297.25 , cons(X1, X2) -> n__cons(X1, X2) 957.19/297.25 , s(X) -> n__s(X) 957.19/297.25 , U291(tt(), N, XS) -> 957.19/297.25 U292(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.19/297.25 , U292(tt(), N, XS) -> 957.19/297.25 U293(isLNat(activate(XS)), activate(N), activate(XS)) 957.19/297.25 , U293(tt(), N, XS) -> 957.19/297.25 U294(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.19/297.25 , U294(tt(), N, XS) -> head(afterNth(activate(N), activate(XS))) 957.19/297.25 , head(X) -> n__head(X) 957.19/297.25 , head(cons(N, XS)) -> U31(isNatural(N), N, activate(XS)) 957.19/297.25 , afterNth(N, XS) -> U11(isNatural(N), N, XS) 957.19/297.25 , afterNth(X1, X2) -> n__afterNth(X1, X2) 957.19/297.25 , U301(tt(), X, Y) -> U302(isLNatKind(activate(X)), activate(Y)) 957.19/297.25 , U302(tt(), Y) -> U303(isLNat(activate(Y)), activate(Y)) 957.19/297.25 , U303(tt(), Y) -> U304(isLNatKind(activate(Y)), activate(Y)) 957.19/297.25 , U304(tt(), Y) -> activate(Y) 957.19/297.25 , U31(tt(), N, XS) -> 957.19/297.25 U32(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.19/297.25 , U32(tt(), N, XS) -> 957.19/297.25 U33(isLNat(activate(XS)), activate(N), activate(XS)) 957.19/297.25 , U311(tt(), XS) -> U312(isLNatKind(activate(XS)), activate(XS)) 957.19/297.25 , U312(tt(), XS) -> pair(nil(), activate(XS)) 957.19/297.25 , pair(X1, X2) -> n__pair(X1, X2) 957.19/297.25 , nil() -> n__nil() 957.19/297.25 , U33(tt(), N, XS) -> U34(isLNatKind(activate(XS)), activate(N)) 957.19/297.25 , U321(tt(), N, X, XS) -> 957.19/297.25 U322(isNaturalKind(activate(N)), 957.19/297.25 activate(N), 957.19/297.25 activate(X), 957.19/297.25 activate(XS)) 957.19/297.25 , U322(tt(), N, X, XS) -> 957.19/297.25 U323(isNatural(activate(X)), 957.19/297.25 activate(N), 957.19/297.25 activate(X), 957.19/297.25 activate(XS)) 957.19/297.25 , U323(tt(), N, X, XS) -> 957.19/297.25 U324(isNaturalKind(activate(X)), 957.19/297.25 activate(N), 957.19/297.25 activate(X), 957.19/297.25 activate(XS)) 957.19/297.25 , U324(tt(), N, X, XS) -> 957.19/297.25 U325(isLNat(activate(XS)), activate(N), activate(X), activate(XS)) 957.19/297.25 , U325(tt(), N, X, XS) -> 957.19/297.25 U326(isLNatKind(activate(XS)), 957.19/297.25 activate(N), 957.19/297.25 activate(X), 957.19/297.25 activate(XS)) 957.19/297.25 , U326(tt(), N, X, XS) -> 957.19/297.25 U327(splitAt(activate(N), activate(XS)), activate(X)) 957.19/297.25 , U327(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) 957.19/297.25 , U34(tt(), N) -> activate(N) 957.19/297.25 , U331(tt(), N, XS) -> 957.19/297.25 U332(isNaturalKind(activate(N)), activate(XS)) 957.19/297.25 , U332(tt(), XS) -> U333(isLNat(activate(XS)), activate(XS)) 957.19/297.25 , U333(tt(), XS) -> U334(isLNatKind(activate(XS)), activate(XS)) 957.19/297.25 , U334(tt(), XS) -> activate(XS) 957.19/297.25 , U341(tt(), N, XS) -> 957.19/297.25 U342(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.19/297.25 , U342(tt(), N, XS) -> 957.19/297.25 U343(isLNat(activate(XS)), activate(N), activate(XS)) 957.19/297.25 , U343(tt(), N, XS) -> 957.19/297.25 U344(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.19/297.25 , U344(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS))) 957.19/297.25 , fst(X) -> n__fst(X) 957.19/297.25 , fst(pair(X, Y)) -> U21(isLNat(X), X, Y) 957.19/297.25 , U41(tt(), V1, V2) -> 957.19/297.25 U42(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.25 , U42(tt(), V1, V2) -> 957.19/297.25 U43(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.25 , U43(tt(), V1, V2) -> 957.19/297.25 U44(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.25 , U44(tt(), V1, V2) -> U45(isNatural(activate(V1)), activate(V2)) 957.19/297.25 , U45(tt(), V2) -> U46(isLNat(activate(V2))) 957.19/297.25 , U46(tt()) -> tt() 957.19/297.25 , U51(tt(), V1, V2) -> 957.19/297.25 U52(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.25 , U52(tt(), V1, V2) -> 957.19/297.25 U53(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.25 , U53(tt(), V1, V2) -> 957.19/297.25 U54(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.25 , U54(tt(), V1, V2) -> U55(isNatural(activate(V1)), activate(V2)) 957.19/297.25 , U55(tt(), V2) -> U56(isLNat(activate(V2))) 957.19/297.25 , U56(tt()) -> tt() 957.19/297.25 , U61(tt(), V1) -> U62(isPLNatKind(activate(V1)), activate(V1)) 957.19/297.25 , U62(tt(), V1) -> U63(isPLNat(activate(V1))) 957.19/297.25 , isPLNatKind(n__pair(V1, V2)) -> 957.19/297.25 U261(isLNatKind(activate(V1)), activate(V2)) 957.19/297.25 , isPLNatKind(n__splitAt(V1, V2)) -> 957.19/297.25 U271(isNaturalKind(activate(V1)), activate(V2)) 957.19/297.25 , U63(tt()) -> tt() 957.19/297.25 , isPLNat(n__pair(V1, V2)) -> 957.19/297.25 U241(isLNatKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.25 , isPLNat(n__splitAt(V1, V2)) -> 957.19/297.25 U251(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.25 , U71(tt(), V1) -> U72(isNaturalKind(activate(V1)), activate(V1)) 957.19/297.25 , U72(tt(), V1) -> U73(isNatural(activate(V1))) 957.19/297.25 , U73(tt()) -> tt() 957.19/297.25 , U81(tt(), V1) -> U82(isPLNatKind(activate(V1)), activate(V1)) 957.19/297.25 , U82(tt(), V1) -> U83(isPLNat(activate(V1))) 957.19/297.25 , U83(tt()) -> tt() 957.19/297.25 , U91(tt(), V1) -> U92(isLNatKind(activate(V1)), activate(V1)) 957.19/297.25 , U92(tt(), V1) -> U93(isLNat(activate(V1))) 957.19/297.25 , U93(tt()) -> tt() 957.19/297.25 , natsFrom(N) -> U281(isNatural(N), N) 957.19/297.25 , natsFrom(X) -> n__natsFrom(X) 957.19/297.25 , sel(N, XS) -> U291(isNatural(N), N, XS) 957.19/297.25 , sel(X1, X2) -> n__sel(X1, X2) 957.19/297.25 , 0() -> n__0() 957.19/297.25 , tail(X) -> n__tail(X) 957.19/297.25 , tail(cons(N, XS)) -> U331(isNatural(N), N, activate(XS)) 957.19/297.25 , take(N, XS) -> U341(isNatural(N), N, XS) 957.19/297.25 , take(X1, X2) -> n__take(X1, X2) } 957.19/297.25 Obligation: 957.19/297.25 runtime complexity 957.19/297.25 Answer: 957.19/297.25 MAYBE 957.19/297.25 957.19/297.25 We estimate the number of application of 957.19/297.25 {4,8,9,28,40,52,59,62,63,64,67,68,76,92,94,98,100,102,107,112,118,124,126,128,161,166,168,174,176,178} 957.19/297.25 by applications of 957.19/297.25 Pre({4,8,9,28,40,52,59,62,63,64,67,68,76,92,94,98,100,102,107,112,118,124,126,128,161,166,168,174,176,178}) 957.19/297.25 = 957.19/297.25 {5,6,10,11,13,20,27,30,31,32,34,36,39,41,43,45,46,47,51,55,56,57,60,61,65,66,99,101,106,117,123,125,127,160,165,167,173,175,177}. 957.19/297.25 Here rules are labeled as follows: 957.19/297.25 957.19/297.25 DPs: 957.19/297.25 { 1: U101^#(tt(), V1, V2) -> 957.19/297.25 c_1(U102^#(isNaturalKind(activate(V1)), 957.19/297.25 activate(V1), 957.19/297.25 activate(V2))) 957.19/297.25 , 2: U102^#(tt(), V1, V2) -> 957.19/297.25 c_2(U103^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.25 , 3: U103^#(tt(), V1, V2) -> 957.19/297.25 c_22(U104^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.25 , 4: isNaturalKind^#(n__0()) -> c_3() 957.19/297.25 , 5: isNaturalKind^#(n__head(V1)) -> 957.19/297.25 c_4(U211^#(isLNatKind(activate(V1)))) 957.19/297.25 , 6: isNaturalKind^#(n__s(V1)) -> 957.19/297.25 c_5(U221^#(isNaturalKind(activate(V1)))) 957.19/297.25 , 7: isNaturalKind^#(n__sel(V1, V2)) -> 957.19/297.25 c_6(U231^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.25 , 8: U211^#(tt()) -> c_79() 957.19/297.25 , 9: U221^#(tt()) -> c_81() 957.19/297.25 , 10: U231^#(tt(), V2) -> c_83(U232^#(isLNatKind(activate(V2)))) 957.19/297.25 , 11: activate^#(X) -> c_7(X) 957.19/297.25 , 12: activate^#(n__natsFrom(X)) -> c_8(natsFrom^#(X)) 957.19/297.25 , 13: activate^#(n__nil()) -> c_9(nil^#()) 957.19/297.25 , 14: activate^#(n__afterNth(X1, X2)) -> c_10(afterNth^#(X1, X2)) 957.19/297.25 , 15: activate^#(n__cons(X1, X2)) -> c_11(cons^#(X1, X2)) 957.19/297.25 , 16: activate^#(n__fst(X)) -> c_12(fst^#(X)) 957.19/297.25 , 17: activate^#(n__snd(X)) -> c_13(snd^#(X)) 957.19/297.25 , 18: activate^#(n__tail(X)) -> c_14(tail^#(X)) 957.19/297.25 , 19: activate^#(n__take(X1, X2)) -> c_15(take^#(X1, X2)) 957.19/297.25 , 20: activate^#(n__0()) -> c_16(0^#()) 957.19/297.25 , 21: activate^#(n__head(X)) -> c_17(head^#(X)) 957.19/297.25 , 22: activate^#(n__s(X)) -> c_18(s^#(X)) 957.19/297.25 , 23: activate^#(n__sel(X1, X2)) -> c_19(sel^#(X1, X2)) 957.19/297.25 , 24: activate^#(n__pair(X1, X2)) -> c_20(pair^#(X1, X2)) 957.19/297.25 , 25: activate^#(n__splitAt(X1, X2)) -> c_21(splitAt^#(X1, X2)) 957.19/297.25 , 26: natsFrom^#(N) -> c_170(U281^#(isNatural(N), N)) 957.19/297.25 , 27: natsFrom^#(X) -> c_171(X) 957.19/297.25 , 28: nil^#() -> c_122() 957.19/297.25 , 29: afterNth^#(N, XS) -> c_111(U11^#(isNatural(N), N, XS)) 957.19/297.25 , 30: afterNth^#(X1, X2) -> c_112(X1, X2) 957.19/297.25 , 31: cons^#(X1, X2) -> c_103(X1, X2) 957.19/297.25 , 32: fst^#(X) -> c_140(X) 957.19/297.25 , 33: fst^#(pair(X, Y)) -> c_141(U21^#(isLNat(X), X, Y)) 957.19/297.25 , 34: snd^#(X) -> c_55(X) 957.19/297.25 , 35: snd^#(pair(X, Y)) -> c_56(U301^#(isLNat(X), X, Y)) 957.19/297.25 , 36: tail^#(X) -> c_175(X) 957.19/297.25 , 37: tail^#(cons(N, XS)) -> 957.19/297.25 c_176(U331^#(isNatural(N), N, activate(XS))) 957.19/297.25 , 38: take^#(N, XS) -> c_177(U341^#(isNatural(N), N, XS)) 957.19/297.25 , 39: take^#(X1, X2) -> c_178(X1, X2) 957.19/297.25 , 40: 0^#() -> c_174() 957.19/297.25 , 41: head^#(X) -> c_109(X) 957.19/297.25 , 42: head^#(cons(N, XS)) -> 957.19/297.25 c_110(U31^#(isNatural(N), N, activate(XS))) 957.19/297.25 , 43: s^#(X) -> c_104(X) 957.19/297.25 , 44: sel^#(N, XS) -> c_172(U291^#(isNatural(N), N, XS)) 957.19/297.25 , 45: sel^#(X1, X2) -> c_173(X1, X2) 957.19/297.25 , 46: pair^#(X1, X2) -> c_121(X1, X2) 957.19/297.25 , 47: splitAt^#(X1, X2) -> c_57(X1, X2) 957.19/297.25 , 48: splitAt^#(s(N), cons(X, XS)) -> 957.19/297.25 c_58(U321^#(isNatural(N), N, X, activate(XS))) 957.19/297.25 , 49: splitAt^#(0(), XS) -> c_59(U311^#(isLNat(XS), XS)) 957.19/297.25 , 50: U104^#(tt(), V1, V2) -> 957.19/297.25 c_31(U105^#(isNatural(activate(V1)), activate(V2))) 957.19/297.25 , 51: isLNatKind^#(n__natsFrom(V1)) -> 957.19/297.25 c_23(U141^#(isNaturalKind(activate(V1)))) 957.19/297.25 , 52: isLNatKind^#(n__nil()) -> c_24() 957.19/297.25 , 53: isLNatKind^#(n__afterNth(V1, V2)) -> 957.19/297.25 c_25(U111^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.25 , 54: isLNatKind^#(n__cons(V1, V2)) -> 957.19/297.25 c_26(U121^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.25 , 55: isLNatKind^#(n__fst(V1)) -> 957.19/297.25 c_27(U131^#(isPLNatKind(activate(V1)))) 957.19/297.25 , 56: isLNatKind^#(n__snd(V1)) -> 957.19/297.25 c_28(U151^#(isPLNatKind(activate(V1)))) 957.19/297.25 , 57: isLNatKind^#(n__tail(V1)) -> 957.19/297.25 c_29(U161^#(isLNatKind(activate(V1)))) 957.19/297.25 , 58: isLNatKind^#(n__take(V1, V2)) -> 957.19/297.25 c_30(U171^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.25 , 59: U141^#(tt()) -> c_60() 957.19/297.25 , 60: U111^#(tt(), V2) -> c_48(U112^#(isLNatKind(activate(V2)))) 957.19/297.25 , 61: U121^#(tt(), V2) -> c_51(U122^#(isLNatKind(activate(V2)))) 957.19/297.25 , 62: U131^#(tt()) -> c_54() 957.19/297.25 , 63: U151^#(tt()) -> c_61() 957.19/297.25 , 64: U161^#(tt()) -> c_62() 957.19/297.25 , 65: U171^#(tt(), V2) -> c_63(U172^#(isLNatKind(activate(V2)))) 957.19/297.25 , 66: U105^#(tt(), V2) -> c_32(U106^#(isLNat(activate(V2)))) 957.19/297.25 , 67: U106^#(tt()) -> c_37() 957.19/297.25 , 68: isNatural^#(n__0()) -> c_33() 957.19/297.25 , 69: isNatural^#(n__head(V1)) -> 957.19/297.25 c_34(U181^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.25 , 70: isNatural^#(n__s(V1)) -> 957.19/297.25 c_35(U191^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.25 , 71: isNatural^#(n__sel(V1, V2)) -> 957.19/297.25 c_36(U201^#(isNaturalKind(activate(V1)), 957.19/297.25 activate(V1), 957.19/297.25 activate(V2))) 957.19/297.25 , 72: U181^#(tt(), V1) -> 957.19/297.25 c_65(U182^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.25 , 73: U191^#(tt(), V1) -> 957.19/297.25 c_68(U192^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.26 , 74: U201^#(tt(), V1, V2) -> 957.19/297.26 c_71(U202^#(isNaturalKind(activate(V1)), 957.19/297.26 activate(V1), 957.19/297.26 activate(V2))) 957.19/297.26 , 75: isLNat^#(n__natsFrom(V1)) -> 957.19/297.26 c_38(U71^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.26 , 76: isLNat^#(n__nil()) -> c_39() 957.19/297.26 , 77: isLNat^#(n__afterNth(V1, V2)) -> 957.19/297.26 c_40(U41^#(isNaturalKind(activate(V1)), 957.19/297.26 activate(V1), 957.19/297.26 activate(V2))) 957.19/297.26 , 78: isLNat^#(n__cons(V1, V2)) -> 957.19/297.26 c_41(U51^#(isNaturalKind(activate(V1)), 957.19/297.26 activate(V1), 957.19/297.26 activate(V2))) 957.19/297.26 , 79: isLNat^#(n__fst(V1)) -> 957.19/297.26 c_42(U61^#(isPLNatKind(activate(V1)), activate(V1))) 957.19/297.26 , 80: isLNat^#(n__snd(V1)) -> 957.19/297.26 c_43(U81^#(isPLNatKind(activate(V1)), activate(V1))) 957.19/297.26 , 81: isLNat^#(n__tail(V1)) -> 957.19/297.26 c_44(U91^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.26 , 82: isLNat^#(n__take(V1, V2)) -> 957.19/297.26 c_45(U101^#(isNaturalKind(activate(V1)), 957.19/297.26 activate(V1), 957.19/297.26 activate(V2))) 957.19/297.26 , 83: U71^#(tt(), V1) -> 957.19/297.26 c_161(U72^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.26 , 84: U41^#(tt(), V1, V2) -> 957.19/297.26 c_142(U42^#(isNaturalKind(activate(V1)), 957.19/297.26 activate(V1), 957.19/297.26 activate(V2))) 957.19/297.26 , 85: U51^#(tt(), V1, V2) -> 957.19/297.26 c_148(U52^#(isNaturalKind(activate(V1)), 957.19/297.26 activate(V1), 957.19/297.26 activate(V2))) 957.19/297.26 , 86: U61^#(tt(), V1) -> 957.19/297.26 c_154(U62^#(isPLNatKind(activate(V1)), activate(V1))) 957.19/297.26 , 87: U81^#(tt(), V1) -> 957.19/297.26 c_164(U82^#(isPLNatKind(activate(V1)), activate(V1))) 957.19/297.26 , 88: U91^#(tt(), V1) -> 957.19/297.26 c_167(U92^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.26 , 89: U11^#(tt(), N, XS) -> 957.19/297.26 c_46(U12^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.19/297.26 , 90: U12^#(tt(), N, XS) -> 957.19/297.26 c_47(U13^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.19/297.26 , 91: U13^#(tt(), N, XS) -> 957.19/297.26 c_50(U14^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.19/297.26 , 92: U112^#(tt()) -> c_49() 957.19/297.26 , 93: U14^#(tt(), N, XS) -> 957.19/297.26 c_53(snd^#(splitAt(activate(N), activate(XS)))) 957.19/297.26 , 94: U122^#(tt()) -> c_52() 957.19/297.26 , 95: U301^#(tt(), X, Y) -> 957.19/297.26 c_113(U302^#(isLNatKind(activate(X)), activate(Y))) 957.19/297.26 , 96: U321^#(tt(), N, X, XS) -> 957.19/297.26 c_124(U322^#(isNaturalKind(activate(N)), 957.19/297.26 activate(N), 957.19/297.26 activate(X), 957.19/297.26 activate(XS))) 957.19/297.26 , 97: U311^#(tt(), XS) -> 957.19/297.26 c_119(U312^#(isLNatKind(activate(XS)), activate(XS))) 957.19/297.26 , 98: U172^#(tt()) -> c_64() 957.19/297.26 , 99: U182^#(tt(), V1) -> c_66(U183^#(isLNat(activate(V1)))) 957.19/297.26 , 100: U183^#(tt()) -> c_67() 957.19/297.26 , 101: U192^#(tt(), V1) -> c_69(U193^#(isNatural(activate(V1)))) 957.19/297.26 , 102: U193^#(tt()) -> c_70() 957.19/297.26 , 103: U202^#(tt(), V1, V2) -> 957.19/297.26 c_72(U203^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.26 , 104: U203^#(tt(), V1, V2) -> 957.19/297.26 c_73(U204^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.26 , 105: U204^#(tt(), V1, V2) -> 957.19/297.26 c_74(U205^#(isNatural(activate(V1)), activate(V2))) 957.19/297.26 , 106: U205^#(tt(), V2) -> c_75(U206^#(isLNat(activate(V2)))) 957.19/297.26 , 107: U206^#(tt()) -> c_76() 957.19/297.26 , 108: U21^#(tt(), X, Y) -> 957.19/297.26 c_77(U22^#(isLNatKind(activate(X)), activate(X), activate(Y))) 957.19/297.26 , 109: U22^#(tt(), X, Y) -> 957.19/297.26 c_78(U23^#(isLNat(activate(Y)), activate(X), activate(Y))) 957.19/297.26 , 110: U23^#(tt(), X, Y) -> 957.19/297.26 c_80(U24^#(isLNatKind(activate(Y)), activate(X))) 957.19/297.26 , 111: U24^#(tt(), X) -> c_82(activate^#(X)) 957.19/297.26 , 112: U232^#(tt()) -> c_84() 957.19/297.26 , 113: U241^#(tt(), V1, V2) -> 957.19/297.26 c_85(U242^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.19/297.26 , 114: U242^#(tt(), V1, V2) -> 957.19/297.26 c_86(U243^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.26 , 115: U243^#(tt(), V1, V2) -> 957.19/297.26 c_87(U244^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.26 , 116: U244^#(tt(), V1, V2) -> 957.19/297.26 c_88(U245^#(isLNat(activate(V1)), activate(V2))) 957.19/297.26 , 117: U245^#(tt(), V2) -> c_89(U246^#(isLNat(activate(V2)))) 957.19/297.26 , 118: U246^#(tt()) -> c_90() 957.19/297.26 , 119: U251^#(tt(), V1, V2) -> 957.19/297.26 c_91(U252^#(isNaturalKind(activate(V1)), 957.19/297.26 activate(V1), 957.19/297.26 activate(V2))) 957.19/297.26 , 120: U252^#(tt(), V1, V2) -> 957.19/297.26 c_92(U253^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.26 , 121: U253^#(tt(), V1, V2) -> 957.19/297.26 c_93(U254^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.26 , 122: U254^#(tt(), V1, V2) -> 957.19/297.26 c_94(U255^#(isNatural(activate(V1)), activate(V2))) 957.19/297.26 , 123: U255^#(tt(), V2) -> c_95(U256^#(isLNat(activate(V2)))) 957.19/297.26 , 124: U256^#(tt()) -> c_96() 957.19/297.26 , 125: U261^#(tt(), V2) -> c_97(U262^#(isLNatKind(activate(V2)))) 957.19/297.26 , 126: U262^#(tt()) -> c_98() 957.19/297.26 , 127: U271^#(tt(), V2) -> c_99(U272^#(isLNatKind(activate(V2)))) 957.19/297.26 , 128: U272^#(tt()) -> c_100() 957.19/297.26 , 129: U281^#(tt(), N) -> 957.19/297.26 c_101(U282^#(isNaturalKind(activate(N)), activate(N))) 957.19/297.26 , 130: U282^#(tt(), N) -> 957.19/297.26 c_102(cons^#(activate(N), n__natsFrom(s(activate(N))))) 957.19/297.26 , 131: U291^#(tt(), N, XS) -> 957.19/297.26 c_105(U292^#(isNaturalKind(activate(N)), 957.19/297.26 activate(N), 957.19/297.26 activate(XS))) 957.19/297.26 , 132: U292^#(tt(), N, XS) -> 957.19/297.26 c_106(U293^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.19/297.26 , 133: U293^#(tt(), N, XS) -> 957.19/297.26 c_107(U294^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.19/297.26 , 134: U294^#(tt(), N, XS) -> 957.19/297.26 c_108(head^#(afterNth(activate(N), activate(XS)))) 957.19/297.26 , 135: U31^#(tt(), N, XS) -> 957.19/297.26 c_117(U32^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.19/297.26 , 136: U302^#(tt(), Y) -> 957.19/297.26 c_114(U303^#(isLNat(activate(Y)), activate(Y))) 957.19/297.26 , 137: U303^#(tt(), Y) -> 957.19/297.26 c_115(U304^#(isLNatKind(activate(Y)), activate(Y))) 957.19/297.26 , 138: U304^#(tt(), Y) -> c_116(activate^#(Y)) 957.19/297.26 , 139: U32^#(tt(), N, XS) -> 957.19/297.26 c_118(U33^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.19/297.26 , 140: U33^#(tt(), N, XS) -> 957.19/297.26 c_123(U34^#(isLNatKind(activate(XS)), activate(N))) 957.19/297.26 , 141: U312^#(tt(), XS) -> c_120(pair^#(nil(), activate(XS))) 957.19/297.26 , 142: U34^#(tt(), N) -> c_131(activate^#(N)) 957.19/297.26 , 143: U322^#(tt(), N, X, XS) -> 957.19/297.26 c_125(U323^#(isNatural(activate(X)), 957.19/297.26 activate(N), 957.19/297.26 activate(X), 957.19/297.26 activate(XS))) 957.19/297.26 , 144: U323^#(tt(), N, X, XS) -> 957.19/297.26 c_126(U324^#(isNaturalKind(activate(X)), 957.19/297.26 activate(N), 957.19/297.26 activate(X), 957.19/297.26 activate(XS))) 957.19/297.26 , 145: U324^#(tt(), N, X, XS) -> 957.19/297.26 c_127(U325^#(isLNat(activate(XS)), 957.19/297.26 activate(N), 957.19/297.26 activate(X), 957.19/297.26 activate(XS))) 957.19/297.26 , 146: U325^#(tt(), N, X, XS) -> 957.19/297.26 c_128(U326^#(isLNatKind(activate(XS)), 957.19/297.26 activate(N), 957.19/297.26 activate(X), 957.19/297.26 activate(XS))) 957.19/297.26 , 147: U326^#(tt(), N, X, XS) -> 957.19/297.26 c_129(U327^#(splitAt(activate(N), activate(XS)), activate(X))) 957.19/297.26 , 148: U327^#(pair(YS, ZS), X) -> 957.19/297.26 c_130(pair^#(cons(activate(X), YS), ZS)) 957.19/297.26 , 149: U331^#(tt(), N, XS) -> 957.19/297.26 c_132(U332^#(isNaturalKind(activate(N)), activate(XS))) 957.19/297.26 , 150: U332^#(tt(), XS) -> 957.19/297.26 c_133(U333^#(isLNat(activate(XS)), activate(XS))) 957.19/297.26 , 151: U333^#(tt(), XS) -> 957.19/297.26 c_134(U334^#(isLNatKind(activate(XS)), activate(XS))) 957.19/297.26 , 152: U334^#(tt(), XS) -> c_135(activate^#(XS)) 957.19/297.26 , 153: U341^#(tt(), N, XS) -> 957.19/297.26 c_136(U342^#(isNaturalKind(activate(N)), 957.19/297.26 activate(N), 957.19/297.26 activate(XS))) 957.19/297.26 , 154: U342^#(tt(), N, XS) -> 957.19/297.26 c_137(U343^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.19/297.26 , 155: U343^#(tt(), N, XS) -> 957.19/297.26 c_138(U344^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.19/297.26 , 156: U344^#(tt(), N, XS) -> 957.19/297.26 c_139(fst^#(splitAt(activate(N), activate(XS)))) 957.19/297.26 , 157: U42^#(tt(), V1, V2) -> 957.19/297.26 c_143(U43^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.26 , 158: U43^#(tt(), V1, V2) -> 957.19/297.26 c_144(U44^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.26 , 159: U44^#(tt(), V1, V2) -> 957.19/297.26 c_145(U45^#(isNatural(activate(V1)), activate(V2))) 957.19/297.26 , 160: U45^#(tt(), V2) -> c_146(U46^#(isLNat(activate(V2)))) 957.19/297.26 , 161: U46^#(tt()) -> c_147() 957.19/297.26 , 162: U52^#(tt(), V1, V2) -> 957.19/297.26 c_149(U53^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.26 , 163: U53^#(tt(), V1, V2) -> 957.19/297.26 c_150(U54^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.26 , 164: U54^#(tt(), V1, V2) -> 957.19/297.26 c_151(U55^#(isNatural(activate(V1)), activate(V2))) 957.19/297.26 , 165: U55^#(tt(), V2) -> c_152(U56^#(isLNat(activate(V2)))) 957.19/297.26 , 166: U56^#(tt()) -> c_153() 957.19/297.26 , 167: U62^#(tt(), V1) -> c_155(U63^#(isPLNat(activate(V1)))) 957.19/297.26 , 168: U63^#(tt()) -> c_158() 957.19/297.26 , 169: isPLNatKind^#(n__pair(V1, V2)) -> 957.19/297.26 c_156(U261^#(isLNatKind(activate(V1)), activate(V2))) 957.19/297.26 , 170: isPLNatKind^#(n__splitAt(V1, V2)) -> 957.19/297.26 c_157(U271^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.26 , 171: isPLNat^#(n__pair(V1, V2)) -> 957.19/297.26 c_159(U241^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.19/297.26 , 172: isPLNat^#(n__splitAt(V1, V2)) -> 957.19/297.26 c_160(U251^#(isNaturalKind(activate(V1)), 957.19/297.26 activate(V1), 957.19/297.26 activate(V2))) 957.19/297.26 , 173: U72^#(tt(), V1) -> c_162(U73^#(isNatural(activate(V1)))) 957.19/297.26 , 174: U73^#(tt()) -> c_163() 957.19/297.26 , 175: U82^#(tt(), V1) -> c_165(U83^#(isPLNat(activate(V1)))) 957.19/297.26 , 176: U83^#(tt()) -> c_166() 957.19/297.26 , 177: U92^#(tt(), V1) -> c_168(U93^#(isLNat(activate(V1)))) 957.19/297.26 , 178: U93^#(tt()) -> c_169() } 957.19/297.26 957.19/297.26 We are left with following problem, upon which TcT provides the 957.19/297.26 certificate MAYBE. 957.19/297.26 957.19/297.26 Strict DPs: 957.19/297.26 { U101^#(tt(), V1, V2) -> 957.19/297.26 c_1(U102^#(isNaturalKind(activate(V1)), 957.19/297.26 activate(V1), 957.19/297.26 activate(V2))) 957.19/297.26 , U102^#(tt(), V1, V2) -> 957.19/297.26 c_2(U103^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.26 , U103^#(tt(), V1, V2) -> 957.19/297.26 c_22(U104^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.26 , isNaturalKind^#(n__head(V1)) -> 957.19/297.26 c_4(U211^#(isLNatKind(activate(V1)))) 957.19/297.26 , isNaturalKind^#(n__s(V1)) -> 957.19/297.26 c_5(U221^#(isNaturalKind(activate(V1)))) 957.19/297.26 , isNaturalKind^#(n__sel(V1, V2)) -> 957.19/297.26 c_6(U231^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.26 , U231^#(tt(), V2) -> c_83(U232^#(isLNatKind(activate(V2)))) 957.19/297.26 , activate^#(X) -> c_7(X) 957.19/297.26 , activate^#(n__natsFrom(X)) -> c_8(natsFrom^#(X)) 957.19/297.26 , activate^#(n__nil()) -> c_9(nil^#()) 957.19/297.26 , activate^#(n__afterNth(X1, X2)) -> c_10(afterNth^#(X1, X2)) 957.19/297.26 , activate^#(n__cons(X1, X2)) -> c_11(cons^#(X1, X2)) 957.19/297.26 , activate^#(n__fst(X)) -> c_12(fst^#(X)) 957.19/297.26 , activate^#(n__snd(X)) -> c_13(snd^#(X)) 957.19/297.26 , activate^#(n__tail(X)) -> c_14(tail^#(X)) 957.19/297.26 , activate^#(n__take(X1, X2)) -> c_15(take^#(X1, X2)) 957.19/297.26 , activate^#(n__0()) -> c_16(0^#()) 957.19/297.26 , activate^#(n__head(X)) -> c_17(head^#(X)) 957.19/297.26 , activate^#(n__s(X)) -> c_18(s^#(X)) 957.19/297.26 , activate^#(n__sel(X1, X2)) -> c_19(sel^#(X1, X2)) 957.19/297.26 , activate^#(n__pair(X1, X2)) -> c_20(pair^#(X1, X2)) 957.19/297.26 , activate^#(n__splitAt(X1, X2)) -> c_21(splitAt^#(X1, X2)) 957.19/297.26 , natsFrom^#(N) -> c_170(U281^#(isNatural(N), N)) 957.19/297.26 , natsFrom^#(X) -> c_171(X) 957.19/297.26 , afterNth^#(N, XS) -> c_111(U11^#(isNatural(N), N, XS)) 957.19/297.26 , afterNth^#(X1, X2) -> c_112(X1, X2) 957.19/297.26 , cons^#(X1, X2) -> c_103(X1, X2) 957.19/297.26 , fst^#(X) -> c_140(X) 957.19/297.26 , fst^#(pair(X, Y)) -> c_141(U21^#(isLNat(X), X, Y)) 957.19/297.26 , snd^#(X) -> c_55(X) 957.19/297.26 , snd^#(pair(X, Y)) -> c_56(U301^#(isLNat(X), X, Y)) 957.19/297.26 , tail^#(X) -> c_175(X) 957.19/297.26 , tail^#(cons(N, XS)) -> 957.19/297.26 c_176(U331^#(isNatural(N), N, activate(XS))) 957.19/297.26 , take^#(N, XS) -> c_177(U341^#(isNatural(N), N, XS)) 957.19/297.26 , take^#(X1, X2) -> c_178(X1, X2) 957.19/297.26 , head^#(X) -> c_109(X) 957.19/297.26 , head^#(cons(N, XS)) -> 957.19/297.26 c_110(U31^#(isNatural(N), N, activate(XS))) 957.19/297.26 , s^#(X) -> c_104(X) 957.19/297.26 , sel^#(N, XS) -> c_172(U291^#(isNatural(N), N, XS)) 957.19/297.26 , sel^#(X1, X2) -> c_173(X1, X2) 957.19/297.26 , pair^#(X1, X2) -> c_121(X1, X2) 957.19/297.26 , splitAt^#(X1, X2) -> c_57(X1, X2) 957.19/297.26 , splitAt^#(s(N), cons(X, XS)) -> 957.19/297.26 c_58(U321^#(isNatural(N), N, X, activate(XS))) 957.19/297.26 , splitAt^#(0(), XS) -> c_59(U311^#(isLNat(XS), XS)) 957.19/297.26 , U104^#(tt(), V1, V2) -> 957.19/297.26 c_31(U105^#(isNatural(activate(V1)), activate(V2))) 957.19/297.26 , isLNatKind^#(n__natsFrom(V1)) -> 957.19/297.26 c_23(U141^#(isNaturalKind(activate(V1)))) 957.19/297.26 , isLNatKind^#(n__afterNth(V1, V2)) -> 957.19/297.26 c_25(U111^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.26 , isLNatKind^#(n__cons(V1, V2)) -> 957.19/297.26 c_26(U121^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.26 , isLNatKind^#(n__fst(V1)) -> 957.19/297.26 c_27(U131^#(isPLNatKind(activate(V1)))) 957.19/297.26 , isLNatKind^#(n__snd(V1)) -> 957.19/297.26 c_28(U151^#(isPLNatKind(activate(V1)))) 957.19/297.26 , isLNatKind^#(n__tail(V1)) -> 957.19/297.26 c_29(U161^#(isLNatKind(activate(V1)))) 957.19/297.26 , isLNatKind^#(n__take(V1, V2)) -> 957.19/297.26 c_30(U171^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.26 , U111^#(tt(), V2) -> c_48(U112^#(isLNatKind(activate(V2)))) 957.19/297.26 , U121^#(tt(), V2) -> c_51(U122^#(isLNatKind(activate(V2)))) 957.19/297.26 , U171^#(tt(), V2) -> c_63(U172^#(isLNatKind(activate(V2)))) 957.19/297.26 , U105^#(tt(), V2) -> c_32(U106^#(isLNat(activate(V2)))) 957.19/297.26 , isNatural^#(n__head(V1)) -> 957.19/297.26 c_34(U181^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.26 , isNatural^#(n__s(V1)) -> 957.19/297.26 c_35(U191^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.26 , isNatural^#(n__sel(V1, V2)) -> 957.19/297.26 c_36(U201^#(isNaturalKind(activate(V1)), 957.19/297.26 activate(V1), 957.19/297.26 activate(V2))) 957.19/297.26 , U181^#(tt(), V1) -> 957.19/297.26 c_65(U182^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.26 , U191^#(tt(), V1) -> 957.19/297.26 c_68(U192^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.26 , U201^#(tt(), V1, V2) -> 957.19/297.26 c_71(U202^#(isNaturalKind(activate(V1)), 957.19/297.26 activate(V1), 957.19/297.26 activate(V2))) 957.19/297.26 , isLNat^#(n__natsFrom(V1)) -> 957.19/297.26 c_38(U71^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.26 , isLNat^#(n__afterNth(V1, V2)) -> 957.19/297.26 c_40(U41^#(isNaturalKind(activate(V1)), 957.19/297.26 activate(V1), 957.19/297.26 activate(V2))) 957.19/297.26 , isLNat^#(n__cons(V1, V2)) -> 957.19/297.26 c_41(U51^#(isNaturalKind(activate(V1)), 957.19/297.26 activate(V1), 957.19/297.26 activate(V2))) 957.19/297.26 , isLNat^#(n__fst(V1)) -> 957.19/297.26 c_42(U61^#(isPLNatKind(activate(V1)), activate(V1))) 957.19/297.26 , isLNat^#(n__snd(V1)) -> 957.19/297.26 c_43(U81^#(isPLNatKind(activate(V1)), activate(V1))) 957.19/297.26 , isLNat^#(n__tail(V1)) -> 957.19/297.26 c_44(U91^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.26 , isLNat^#(n__take(V1, V2)) -> 957.19/297.26 c_45(U101^#(isNaturalKind(activate(V1)), 957.19/297.26 activate(V1), 957.19/297.26 activate(V2))) 957.19/297.26 , U71^#(tt(), V1) -> 957.19/297.26 c_161(U72^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.26 , U41^#(tt(), V1, V2) -> 957.19/297.26 c_142(U42^#(isNaturalKind(activate(V1)), 957.19/297.26 activate(V1), 957.19/297.26 activate(V2))) 957.19/297.26 , U51^#(tt(), V1, V2) -> 957.19/297.26 c_148(U52^#(isNaturalKind(activate(V1)), 957.19/297.26 activate(V1), 957.19/297.26 activate(V2))) 957.19/297.26 , U61^#(tt(), V1) -> 957.19/297.26 c_154(U62^#(isPLNatKind(activate(V1)), activate(V1))) 957.19/297.26 , U81^#(tt(), V1) -> 957.19/297.27 c_164(U82^#(isPLNatKind(activate(V1)), activate(V1))) 957.19/297.27 , U91^#(tt(), V1) -> 957.19/297.27 c_167(U92^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.27 , U11^#(tt(), N, XS) -> 957.19/297.27 c_46(U12^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.19/297.27 , U12^#(tt(), N, XS) -> 957.19/297.27 c_47(U13^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.19/297.27 , U13^#(tt(), N, XS) -> 957.19/297.27 c_50(U14^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.19/297.27 , U14^#(tt(), N, XS) -> 957.19/297.27 c_53(snd^#(splitAt(activate(N), activate(XS)))) 957.19/297.27 , U301^#(tt(), X, Y) -> 957.19/297.27 c_113(U302^#(isLNatKind(activate(X)), activate(Y))) 957.19/297.27 , U321^#(tt(), N, X, XS) -> 957.19/297.27 c_124(U322^#(isNaturalKind(activate(N)), 957.19/297.27 activate(N), 957.19/297.27 activate(X), 957.19/297.27 activate(XS))) 957.19/297.27 , U311^#(tt(), XS) -> 957.19/297.27 c_119(U312^#(isLNatKind(activate(XS)), activate(XS))) 957.19/297.27 , U182^#(tt(), V1) -> c_66(U183^#(isLNat(activate(V1)))) 957.19/297.27 , U192^#(tt(), V1) -> c_69(U193^#(isNatural(activate(V1)))) 957.19/297.27 , U202^#(tt(), V1, V2) -> 957.19/297.27 c_72(U203^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.27 , U203^#(tt(), V1, V2) -> 957.19/297.27 c_73(U204^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.27 , U204^#(tt(), V1, V2) -> 957.19/297.27 c_74(U205^#(isNatural(activate(V1)), activate(V2))) 957.19/297.27 , U205^#(tt(), V2) -> c_75(U206^#(isLNat(activate(V2)))) 957.19/297.27 , U21^#(tt(), X, Y) -> 957.19/297.27 c_77(U22^#(isLNatKind(activate(X)), activate(X), activate(Y))) 957.19/297.27 , U22^#(tt(), X, Y) -> 957.19/297.27 c_78(U23^#(isLNat(activate(Y)), activate(X), activate(Y))) 957.19/297.27 , U23^#(tt(), X, Y) -> 957.19/297.27 c_80(U24^#(isLNatKind(activate(Y)), activate(X))) 957.19/297.27 , U24^#(tt(), X) -> c_82(activate^#(X)) 957.19/297.27 , U241^#(tt(), V1, V2) -> 957.19/297.27 c_85(U242^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.19/297.27 , U242^#(tt(), V1, V2) -> 957.19/297.27 c_86(U243^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.27 , U243^#(tt(), V1, V2) -> 957.19/297.27 c_87(U244^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.27 , U244^#(tt(), V1, V2) -> 957.19/297.27 c_88(U245^#(isLNat(activate(V1)), activate(V2))) 957.19/297.27 , U245^#(tt(), V2) -> c_89(U246^#(isLNat(activate(V2)))) 957.19/297.27 , U251^#(tt(), V1, V2) -> 957.19/297.27 c_91(U252^#(isNaturalKind(activate(V1)), 957.19/297.27 activate(V1), 957.19/297.27 activate(V2))) 957.19/297.27 , U252^#(tt(), V1, V2) -> 957.19/297.27 c_92(U253^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.27 , U253^#(tt(), V1, V2) -> 957.19/297.27 c_93(U254^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.27 , U254^#(tt(), V1, V2) -> 957.19/297.27 c_94(U255^#(isNatural(activate(V1)), activate(V2))) 957.19/297.27 , U255^#(tt(), V2) -> c_95(U256^#(isLNat(activate(V2)))) 957.19/297.27 , U261^#(tt(), V2) -> c_97(U262^#(isLNatKind(activate(V2)))) 957.19/297.27 , U271^#(tt(), V2) -> c_99(U272^#(isLNatKind(activate(V2)))) 957.19/297.27 , U281^#(tt(), N) -> 957.19/297.27 c_101(U282^#(isNaturalKind(activate(N)), activate(N))) 957.19/297.27 , U282^#(tt(), N) -> 957.19/297.27 c_102(cons^#(activate(N), n__natsFrom(s(activate(N))))) 957.19/297.27 , U291^#(tt(), N, XS) -> 957.19/297.27 c_105(U292^#(isNaturalKind(activate(N)), 957.19/297.27 activate(N), 957.19/297.27 activate(XS))) 957.19/297.27 , U292^#(tt(), N, XS) -> 957.19/297.27 c_106(U293^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.19/297.27 , U293^#(tt(), N, XS) -> 957.19/297.27 c_107(U294^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.19/297.27 , U294^#(tt(), N, XS) -> 957.19/297.27 c_108(head^#(afterNth(activate(N), activate(XS)))) 957.19/297.27 , U31^#(tt(), N, XS) -> 957.19/297.27 c_117(U32^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.19/297.27 , U302^#(tt(), Y) -> 957.19/297.27 c_114(U303^#(isLNat(activate(Y)), activate(Y))) 957.19/297.27 , U303^#(tt(), Y) -> 957.19/297.27 c_115(U304^#(isLNatKind(activate(Y)), activate(Y))) 957.19/297.27 , U304^#(tt(), Y) -> c_116(activate^#(Y)) 957.19/297.27 , U32^#(tt(), N, XS) -> 957.19/297.27 c_118(U33^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.19/297.27 , U33^#(tt(), N, XS) -> 957.19/297.27 c_123(U34^#(isLNatKind(activate(XS)), activate(N))) 957.19/297.27 , U312^#(tt(), XS) -> c_120(pair^#(nil(), activate(XS))) 957.19/297.27 , U34^#(tt(), N) -> c_131(activate^#(N)) 957.19/297.27 , U322^#(tt(), N, X, XS) -> 957.19/297.27 c_125(U323^#(isNatural(activate(X)), 957.19/297.27 activate(N), 957.19/297.27 activate(X), 957.19/297.27 activate(XS))) 957.19/297.27 , U323^#(tt(), N, X, XS) -> 957.19/297.27 c_126(U324^#(isNaturalKind(activate(X)), 957.19/297.27 activate(N), 957.19/297.27 activate(X), 957.19/297.27 activate(XS))) 957.19/297.27 , U324^#(tt(), N, X, XS) -> 957.19/297.27 c_127(U325^#(isLNat(activate(XS)), 957.19/297.27 activate(N), 957.19/297.27 activate(X), 957.19/297.27 activate(XS))) 957.19/297.27 , U325^#(tt(), N, X, XS) -> 957.19/297.27 c_128(U326^#(isLNatKind(activate(XS)), 957.19/297.27 activate(N), 957.19/297.27 activate(X), 957.19/297.27 activate(XS))) 957.19/297.27 , U326^#(tt(), N, X, XS) -> 957.19/297.27 c_129(U327^#(splitAt(activate(N), activate(XS)), activate(X))) 957.19/297.27 , U327^#(pair(YS, ZS), X) -> 957.19/297.27 c_130(pair^#(cons(activate(X), YS), ZS)) 957.19/297.27 , U331^#(tt(), N, XS) -> 957.19/297.27 c_132(U332^#(isNaturalKind(activate(N)), activate(XS))) 957.19/297.27 , U332^#(tt(), XS) -> 957.19/297.27 c_133(U333^#(isLNat(activate(XS)), activate(XS))) 957.19/297.27 , U333^#(tt(), XS) -> 957.19/297.27 c_134(U334^#(isLNatKind(activate(XS)), activate(XS))) 957.19/297.27 , U334^#(tt(), XS) -> c_135(activate^#(XS)) 957.19/297.27 , U341^#(tt(), N, XS) -> 957.19/297.27 c_136(U342^#(isNaturalKind(activate(N)), 957.19/297.27 activate(N), 957.19/297.27 activate(XS))) 957.19/297.27 , U342^#(tt(), N, XS) -> 957.19/297.27 c_137(U343^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.19/297.27 , U343^#(tt(), N, XS) -> 957.19/297.27 c_138(U344^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.19/297.27 , U344^#(tt(), N, XS) -> 957.19/297.27 c_139(fst^#(splitAt(activate(N), activate(XS)))) 957.19/297.27 , U42^#(tt(), V1, V2) -> 957.19/297.27 c_143(U43^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.27 , U43^#(tt(), V1, V2) -> 957.19/297.27 c_144(U44^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.27 , U44^#(tt(), V1, V2) -> 957.19/297.27 c_145(U45^#(isNatural(activate(V1)), activate(V2))) 957.19/297.27 , U45^#(tt(), V2) -> c_146(U46^#(isLNat(activate(V2)))) 957.19/297.27 , U52^#(tt(), V1, V2) -> 957.19/297.27 c_149(U53^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.27 , U53^#(tt(), V1, V2) -> 957.19/297.27 c_150(U54^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.27 , U54^#(tt(), V1, V2) -> 957.19/297.27 c_151(U55^#(isNatural(activate(V1)), activate(V2))) 957.19/297.27 , U55^#(tt(), V2) -> c_152(U56^#(isLNat(activate(V2)))) 957.19/297.27 , U62^#(tt(), V1) -> c_155(U63^#(isPLNat(activate(V1)))) 957.19/297.27 , isPLNatKind^#(n__pair(V1, V2)) -> 957.19/297.27 c_156(U261^#(isLNatKind(activate(V1)), activate(V2))) 957.19/297.27 , isPLNatKind^#(n__splitAt(V1, V2)) -> 957.19/297.27 c_157(U271^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.27 , isPLNat^#(n__pair(V1, V2)) -> 957.19/297.27 c_159(U241^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.19/297.27 , isPLNat^#(n__splitAt(V1, V2)) -> 957.19/297.27 c_160(U251^#(isNaturalKind(activate(V1)), 957.19/297.27 activate(V1), 957.19/297.27 activate(V2))) 957.19/297.27 , U72^#(tt(), V1) -> c_162(U73^#(isNatural(activate(V1)))) 957.19/297.27 , U82^#(tt(), V1) -> c_165(U83^#(isPLNat(activate(V1)))) 957.19/297.27 , U92^#(tt(), V1) -> c_168(U93^#(isLNat(activate(V1)))) } 957.19/297.27 Strict Trs: 957.19/297.27 { U101(tt(), V1, V2) -> 957.19/297.27 U102(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.27 , U102(tt(), V1, V2) -> 957.19/297.27 U103(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.27 , isNaturalKind(n__0()) -> tt() 957.19/297.27 , isNaturalKind(n__head(V1)) -> U211(isLNatKind(activate(V1))) 957.19/297.27 , isNaturalKind(n__s(V1)) -> U221(isNaturalKind(activate(V1))) 957.19/297.27 , isNaturalKind(n__sel(V1, V2)) -> 957.19/297.27 U231(isNaturalKind(activate(V1)), activate(V2)) 957.19/297.27 , activate(X) -> X 957.19/297.27 , activate(n__natsFrom(X)) -> natsFrom(X) 957.19/297.27 , activate(n__nil()) -> nil() 957.19/297.27 , activate(n__afterNth(X1, X2)) -> afterNth(X1, X2) 957.19/297.27 , activate(n__cons(X1, X2)) -> cons(X1, X2) 957.19/297.27 , activate(n__fst(X)) -> fst(X) 957.19/297.27 , activate(n__snd(X)) -> snd(X) 957.19/297.27 , activate(n__tail(X)) -> tail(X) 957.19/297.27 , activate(n__take(X1, X2)) -> take(X1, X2) 957.19/297.27 , activate(n__0()) -> 0() 957.19/297.27 , activate(n__head(X)) -> head(X) 957.19/297.27 , activate(n__s(X)) -> s(X) 957.19/297.27 , activate(n__sel(X1, X2)) -> sel(X1, X2) 957.19/297.27 , activate(n__pair(X1, X2)) -> pair(X1, X2) 957.19/297.27 , activate(n__splitAt(X1, X2)) -> splitAt(X1, X2) 957.19/297.27 , U103(tt(), V1, V2) -> 957.19/297.27 U104(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.27 , isLNatKind(n__natsFrom(V1)) -> U141(isNaturalKind(activate(V1))) 957.19/297.27 , isLNatKind(n__nil()) -> tt() 957.19/297.27 , isLNatKind(n__afterNth(V1, V2)) -> 957.19/297.27 U111(isNaturalKind(activate(V1)), activate(V2)) 957.19/297.27 , isLNatKind(n__cons(V1, V2)) -> 957.19/297.27 U121(isNaturalKind(activate(V1)), activate(V2)) 957.19/297.27 , isLNatKind(n__fst(V1)) -> U131(isPLNatKind(activate(V1))) 957.19/297.27 , isLNatKind(n__snd(V1)) -> U151(isPLNatKind(activate(V1))) 957.19/297.27 , isLNatKind(n__tail(V1)) -> U161(isLNatKind(activate(V1))) 957.19/297.27 , isLNatKind(n__take(V1, V2)) -> 957.19/297.27 U171(isNaturalKind(activate(V1)), activate(V2)) 957.19/297.27 , U104(tt(), V1, V2) -> U105(isNatural(activate(V1)), activate(V2)) 957.19/297.27 , U105(tt(), V2) -> U106(isLNat(activate(V2))) 957.19/297.27 , isNatural(n__0()) -> tt() 957.19/297.27 , isNatural(n__head(V1)) -> 957.19/297.27 U181(isLNatKind(activate(V1)), activate(V1)) 957.19/297.27 , isNatural(n__s(V1)) -> 957.19/297.27 U191(isNaturalKind(activate(V1)), activate(V1)) 957.19/297.27 , isNatural(n__sel(V1, V2)) -> 957.19/297.27 U201(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.27 , U106(tt()) -> tt() 957.19/297.27 , isLNat(n__natsFrom(V1)) -> 957.19/297.27 U71(isNaturalKind(activate(V1)), activate(V1)) 957.19/297.27 , isLNat(n__nil()) -> tt() 957.19/297.27 , isLNat(n__afterNth(V1, V2)) -> 957.19/297.27 U41(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.27 , isLNat(n__cons(V1, V2)) -> 957.19/297.27 U51(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.27 , isLNat(n__fst(V1)) -> 957.19/297.27 U61(isPLNatKind(activate(V1)), activate(V1)) 957.19/297.27 , isLNat(n__snd(V1)) -> 957.19/297.27 U81(isPLNatKind(activate(V1)), activate(V1)) 957.19/297.27 , isLNat(n__tail(V1)) -> 957.19/297.27 U91(isLNatKind(activate(V1)), activate(V1)) 957.19/297.27 , isLNat(n__take(V1, V2)) -> 957.19/297.27 U101(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.27 , U11(tt(), N, XS) -> 957.19/297.27 U12(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.19/297.27 , U12(tt(), N, XS) -> 957.19/297.27 U13(isLNat(activate(XS)), activate(N), activate(XS)) 957.19/297.27 , U111(tt(), V2) -> U112(isLNatKind(activate(V2))) 957.19/297.27 , U112(tt()) -> tt() 957.19/297.27 , U13(tt(), N, XS) -> 957.19/297.27 U14(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.19/297.27 , U121(tt(), V2) -> U122(isLNatKind(activate(V2))) 957.19/297.27 , U122(tt()) -> tt() 957.19/297.27 , U14(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS))) 957.19/297.27 , U131(tt()) -> tt() 957.19/297.27 , snd(X) -> n__snd(X) 957.19/297.27 , snd(pair(X, Y)) -> U301(isLNat(X), X, Y) 957.19/297.27 , splitAt(X1, X2) -> n__splitAt(X1, X2) 957.19/297.27 , splitAt(s(N), cons(X, XS)) -> 957.19/297.27 U321(isNatural(N), N, X, activate(XS)) 957.19/297.27 , splitAt(0(), XS) -> U311(isLNat(XS), XS) 957.19/297.27 , U141(tt()) -> tt() 957.19/297.27 , U151(tt()) -> tt() 957.19/297.27 , U161(tt()) -> tt() 957.19/297.27 , U171(tt(), V2) -> U172(isLNatKind(activate(V2))) 957.19/297.27 , U172(tt()) -> tt() 957.19/297.27 , U181(tt(), V1) -> U182(isLNatKind(activate(V1)), activate(V1)) 957.19/297.27 , U182(tt(), V1) -> U183(isLNat(activate(V1))) 957.19/297.27 , U183(tt()) -> tt() 957.19/297.27 , U191(tt(), V1) -> U192(isNaturalKind(activate(V1)), activate(V1)) 957.19/297.27 , U192(tt(), V1) -> U193(isNatural(activate(V1))) 957.19/297.27 , U193(tt()) -> tt() 957.19/297.27 , U201(tt(), V1, V2) -> 957.19/297.27 U202(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.27 , U202(tt(), V1, V2) -> 957.19/297.27 U203(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.27 , U203(tt(), V1, V2) -> 957.19/297.27 U204(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.27 , U204(tt(), V1, V2) -> U205(isNatural(activate(V1)), activate(V2)) 957.19/297.27 , U205(tt(), V2) -> U206(isLNat(activate(V2))) 957.19/297.27 , U206(tt()) -> tt() 957.19/297.27 , U21(tt(), X, Y) -> 957.19/297.27 U22(isLNatKind(activate(X)), activate(X), activate(Y)) 957.19/297.27 , U22(tt(), X, Y) -> 957.19/297.27 U23(isLNat(activate(Y)), activate(X), activate(Y)) 957.19/297.27 , U211(tt()) -> tt() 957.19/297.27 , U23(tt(), X, Y) -> U24(isLNatKind(activate(Y)), activate(X)) 957.19/297.27 , U221(tt()) -> tt() 957.19/297.27 , U24(tt(), X) -> activate(X) 957.19/297.27 , U231(tt(), V2) -> U232(isLNatKind(activate(V2))) 957.19/297.27 , U232(tt()) -> tt() 957.19/297.27 , U241(tt(), V1, V2) -> 957.19/297.27 U242(isLNatKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.27 , U242(tt(), V1, V2) -> 957.19/297.27 U243(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.27 , U243(tt(), V1, V2) -> 957.19/297.27 U244(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.27 , U244(tt(), V1, V2) -> U245(isLNat(activate(V1)), activate(V2)) 957.19/297.27 , U245(tt(), V2) -> U246(isLNat(activate(V2))) 957.19/297.27 , U246(tt()) -> tt() 957.19/297.27 , U251(tt(), V1, V2) -> 957.19/297.27 U252(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.27 , U252(tt(), V1, V2) -> 957.19/297.27 U253(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.27 , U253(tt(), V1, V2) -> 957.19/297.27 U254(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.27 , U254(tt(), V1, V2) -> U255(isNatural(activate(V1)), activate(V2)) 957.19/297.27 , U255(tt(), V2) -> U256(isLNat(activate(V2))) 957.19/297.27 , U256(tt()) -> tt() 957.19/297.27 , U261(tt(), V2) -> U262(isLNatKind(activate(V2))) 957.19/297.27 , U262(tt()) -> tt() 957.19/297.27 , U271(tt(), V2) -> U272(isLNatKind(activate(V2))) 957.19/297.27 , U272(tt()) -> tt() 957.19/297.27 , U281(tt(), N) -> U282(isNaturalKind(activate(N)), activate(N)) 957.19/297.27 , U282(tt(), N) -> cons(activate(N), n__natsFrom(s(activate(N)))) 957.19/297.27 , cons(X1, X2) -> n__cons(X1, X2) 957.19/297.27 , s(X) -> n__s(X) 957.19/297.27 , U291(tt(), N, XS) -> 957.19/297.27 U292(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.19/297.27 , U292(tt(), N, XS) -> 957.19/297.27 U293(isLNat(activate(XS)), activate(N), activate(XS)) 957.19/297.27 , U293(tt(), N, XS) -> 957.19/297.27 U294(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.19/297.27 , U294(tt(), N, XS) -> head(afterNth(activate(N), activate(XS))) 957.19/297.27 , head(X) -> n__head(X) 957.19/297.27 , head(cons(N, XS)) -> U31(isNatural(N), N, activate(XS)) 957.19/297.27 , afterNth(N, XS) -> U11(isNatural(N), N, XS) 957.19/297.27 , afterNth(X1, X2) -> n__afterNth(X1, X2) 957.19/297.27 , U301(tt(), X, Y) -> U302(isLNatKind(activate(X)), activate(Y)) 957.19/297.27 , U302(tt(), Y) -> U303(isLNat(activate(Y)), activate(Y)) 957.19/297.27 , U303(tt(), Y) -> U304(isLNatKind(activate(Y)), activate(Y)) 957.19/297.27 , U304(tt(), Y) -> activate(Y) 957.19/297.27 , U31(tt(), N, XS) -> 957.19/297.27 U32(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.19/297.27 , U32(tt(), N, XS) -> 957.19/297.27 U33(isLNat(activate(XS)), activate(N), activate(XS)) 957.19/297.27 , U311(tt(), XS) -> U312(isLNatKind(activate(XS)), activate(XS)) 957.19/297.27 , U312(tt(), XS) -> pair(nil(), activate(XS)) 957.19/297.27 , pair(X1, X2) -> n__pair(X1, X2) 957.19/297.27 , nil() -> n__nil() 957.19/297.27 , U33(tt(), N, XS) -> U34(isLNatKind(activate(XS)), activate(N)) 957.19/297.27 , U321(tt(), N, X, XS) -> 957.19/297.27 U322(isNaturalKind(activate(N)), 957.19/297.27 activate(N), 957.19/297.27 activate(X), 957.19/297.27 activate(XS)) 957.19/297.27 , U322(tt(), N, X, XS) -> 957.19/297.27 U323(isNatural(activate(X)), 957.19/297.27 activate(N), 957.19/297.27 activate(X), 957.19/297.27 activate(XS)) 957.19/297.27 , U323(tt(), N, X, XS) -> 957.19/297.27 U324(isNaturalKind(activate(X)), 957.19/297.27 activate(N), 957.19/297.27 activate(X), 957.19/297.27 activate(XS)) 957.19/297.27 , U324(tt(), N, X, XS) -> 957.19/297.27 U325(isLNat(activate(XS)), activate(N), activate(X), activate(XS)) 957.19/297.27 , U325(tt(), N, X, XS) -> 957.19/297.27 U326(isLNatKind(activate(XS)), 957.19/297.27 activate(N), 957.19/297.27 activate(X), 957.19/297.27 activate(XS)) 957.19/297.27 , U326(tt(), N, X, XS) -> 957.19/297.27 U327(splitAt(activate(N), activate(XS)), activate(X)) 957.19/297.27 , U327(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) 957.19/297.27 , U34(tt(), N) -> activate(N) 957.19/297.27 , U331(tt(), N, XS) -> 957.19/297.27 U332(isNaturalKind(activate(N)), activate(XS)) 957.19/297.27 , U332(tt(), XS) -> U333(isLNat(activate(XS)), activate(XS)) 957.19/297.27 , U333(tt(), XS) -> U334(isLNatKind(activate(XS)), activate(XS)) 957.19/297.27 , U334(tt(), XS) -> activate(XS) 957.19/297.27 , U341(tt(), N, XS) -> 957.19/297.27 U342(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.19/297.27 , U342(tt(), N, XS) -> 957.19/297.27 U343(isLNat(activate(XS)), activate(N), activate(XS)) 957.19/297.27 , U343(tt(), N, XS) -> 957.19/297.27 U344(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.19/297.27 , U344(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS))) 957.19/297.27 , fst(X) -> n__fst(X) 957.19/297.27 , fst(pair(X, Y)) -> U21(isLNat(X), X, Y) 957.19/297.27 , U41(tt(), V1, V2) -> 957.19/297.27 U42(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.27 , U42(tt(), V1, V2) -> 957.19/297.27 U43(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.27 , U43(tt(), V1, V2) -> 957.19/297.27 U44(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.27 , U44(tt(), V1, V2) -> U45(isNatural(activate(V1)), activate(V2)) 957.19/297.27 , U45(tt(), V2) -> U46(isLNat(activate(V2))) 957.19/297.27 , U46(tt()) -> tt() 957.19/297.27 , U51(tt(), V1, V2) -> 957.19/297.27 U52(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.27 , U52(tt(), V1, V2) -> 957.19/297.27 U53(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.27 , U53(tt(), V1, V2) -> 957.19/297.27 U54(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.27 , U54(tt(), V1, V2) -> U55(isNatural(activate(V1)), activate(V2)) 957.19/297.27 , U55(tt(), V2) -> U56(isLNat(activate(V2))) 957.19/297.27 , U56(tt()) -> tt() 957.19/297.27 , U61(tt(), V1) -> U62(isPLNatKind(activate(V1)), activate(V1)) 957.19/297.27 , U62(tt(), V1) -> U63(isPLNat(activate(V1))) 957.19/297.27 , isPLNatKind(n__pair(V1, V2)) -> 957.19/297.27 U261(isLNatKind(activate(V1)), activate(V2)) 957.19/297.27 , isPLNatKind(n__splitAt(V1, V2)) -> 957.19/297.27 U271(isNaturalKind(activate(V1)), activate(V2)) 957.19/297.27 , U63(tt()) -> tt() 957.19/297.27 , isPLNat(n__pair(V1, V2)) -> 957.19/297.27 U241(isLNatKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.27 , isPLNat(n__splitAt(V1, V2)) -> 957.19/297.27 U251(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.27 , U71(tt(), V1) -> U72(isNaturalKind(activate(V1)), activate(V1)) 957.19/297.27 , U72(tt(), V1) -> U73(isNatural(activate(V1))) 957.19/297.27 , U73(tt()) -> tt() 957.19/297.27 , U81(tt(), V1) -> U82(isPLNatKind(activate(V1)), activate(V1)) 957.19/297.27 , U82(tt(), V1) -> U83(isPLNat(activate(V1))) 957.19/297.27 , U83(tt()) -> tt() 957.19/297.27 , U91(tt(), V1) -> U92(isLNatKind(activate(V1)), activate(V1)) 957.19/297.27 , U92(tt(), V1) -> U93(isLNat(activate(V1))) 957.19/297.27 , U93(tt()) -> tt() 957.19/297.27 , natsFrom(N) -> U281(isNatural(N), N) 957.19/297.27 , natsFrom(X) -> n__natsFrom(X) 957.19/297.27 , sel(N, XS) -> U291(isNatural(N), N, XS) 957.19/297.27 , sel(X1, X2) -> n__sel(X1, X2) 957.19/297.27 , 0() -> n__0() 957.19/297.27 , tail(X) -> n__tail(X) 957.19/297.27 , tail(cons(N, XS)) -> U331(isNatural(N), N, activate(XS)) 957.19/297.27 , take(N, XS) -> U341(isNatural(N), N, XS) 957.19/297.27 , take(X1, X2) -> n__take(X1, X2) } 957.19/297.27 Weak DPs: 957.19/297.27 { isNaturalKind^#(n__0()) -> c_3() 957.19/297.27 , U211^#(tt()) -> c_79() 957.19/297.27 , U221^#(tt()) -> c_81() 957.19/297.27 , nil^#() -> c_122() 957.19/297.27 , 0^#() -> c_174() 957.19/297.27 , isLNatKind^#(n__nil()) -> c_24() 957.19/297.27 , U141^#(tt()) -> c_60() 957.19/297.27 , U131^#(tt()) -> c_54() 957.19/297.27 , U151^#(tt()) -> c_61() 957.19/297.27 , U161^#(tt()) -> c_62() 957.19/297.27 , U106^#(tt()) -> c_37() 957.19/297.27 , isNatural^#(n__0()) -> c_33() 957.19/297.27 , isLNat^#(n__nil()) -> c_39() 957.19/297.27 , U112^#(tt()) -> c_49() 957.19/297.27 , U122^#(tt()) -> c_52() 957.19/297.27 , U172^#(tt()) -> c_64() 957.19/297.27 , U183^#(tt()) -> c_67() 957.19/297.27 , U193^#(tt()) -> c_70() 957.19/297.27 , U206^#(tt()) -> c_76() 957.19/297.27 , U232^#(tt()) -> c_84() 957.19/297.27 , U246^#(tt()) -> c_90() 957.19/297.27 , U256^#(tt()) -> c_96() 957.19/297.27 , U262^#(tt()) -> c_98() 957.19/297.27 , U272^#(tt()) -> c_100() 957.19/297.27 , U46^#(tt()) -> c_147() 957.19/297.27 , U56^#(tt()) -> c_153() 957.19/297.27 , U63^#(tt()) -> c_158() 957.19/297.27 , U73^#(tt()) -> c_163() 957.19/297.27 , U83^#(tt()) -> c_166() 957.19/297.27 , U93^#(tt()) -> c_169() } 957.19/297.27 Obligation: 957.19/297.27 runtime complexity 957.19/297.27 Answer: 957.19/297.27 MAYBE 957.19/297.27 957.19/297.27 We estimate the number of application of 957.19/297.27 {4,5,7,10,17,46,49,50,51,53,54,55,56,83,84,88,97,102,103,104,136,140,141,146,147,148} 957.19/297.27 by applications of 957.19/297.27 Pre({4,5,7,10,17,46,49,50,51,53,54,55,56,83,84,88,97,102,103,104,136,140,141,146,147,148}) 957.19/297.27 = 957.19/297.27 {6,8,24,26,27,28,30,32,35,36,38,40,41,42,45,47,48,52,60,61,70,73,74,75,87,92,96,101,114,118,128,135,139,142,143}. 957.19/297.27 Here rules are labeled as follows: 957.19/297.27 957.19/297.27 DPs: 957.19/297.27 { 1: U101^#(tt(), V1, V2) -> 957.19/297.27 c_1(U102^#(isNaturalKind(activate(V1)), 957.19/297.27 activate(V1), 957.19/297.27 activate(V2))) 957.19/297.27 , 2: U102^#(tt(), V1, V2) -> 957.19/297.27 c_2(U103^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.27 , 3: U103^#(tt(), V1, V2) -> 957.19/297.27 c_22(U104^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.27 , 4: isNaturalKind^#(n__head(V1)) -> 957.19/297.27 c_4(U211^#(isLNatKind(activate(V1)))) 957.19/297.27 , 5: isNaturalKind^#(n__s(V1)) -> 957.19/297.27 c_5(U221^#(isNaturalKind(activate(V1)))) 957.19/297.27 , 6: isNaturalKind^#(n__sel(V1, V2)) -> 957.19/297.27 c_6(U231^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.27 , 7: U231^#(tt(), V2) -> c_83(U232^#(isLNatKind(activate(V2)))) 957.19/297.27 , 8: activate^#(X) -> c_7(X) 957.19/297.27 , 9: activate^#(n__natsFrom(X)) -> c_8(natsFrom^#(X)) 957.19/297.27 , 10: activate^#(n__nil()) -> c_9(nil^#()) 957.19/297.27 , 11: activate^#(n__afterNth(X1, X2)) -> c_10(afterNth^#(X1, X2)) 957.19/297.27 , 12: activate^#(n__cons(X1, X2)) -> c_11(cons^#(X1, X2)) 957.19/297.27 , 13: activate^#(n__fst(X)) -> c_12(fst^#(X)) 957.19/297.27 , 14: activate^#(n__snd(X)) -> c_13(snd^#(X)) 957.19/297.27 , 15: activate^#(n__tail(X)) -> c_14(tail^#(X)) 957.19/297.27 , 16: activate^#(n__take(X1, X2)) -> c_15(take^#(X1, X2)) 957.19/297.27 , 17: activate^#(n__0()) -> c_16(0^#()) 957.19/297.27 , 18: activate^#(n__head(X)) -> c_17(head^#(X)) 957.19/297.27 , 19: activate^#(n__s(X)) -> c_18(s^#(X)) 957.19/297.27 , 20: activate^#(n__sel(X1, X2)) -> c_19(sel^#(X1, X2)) 957.19/297.27 , 21: activate^#(n__pair(X1, X2)) -> c_20(pair^#(X1, X2)) 957.19/297.27 , 22: activate^#(n__splitAt(X1, X2)) -> c_21(splitAt^#(X1, X2)) 957.19/297.27 , 23: natsFrom^#(N) -> c_170(U281^#(isNatural(N), N)) 957.19/297.27 , 24: natsFrom^#(X) -> c_171(X) 957.19/297.27 , 25: afterNth^#(N, XS) -> c_111(U11^#(isNatural(N), N, XS)) 957.19/297.27 , 26: afterNth^#(X1, X2) -> c_112(X1, X2) 957.19/297.27 , 27: cons^#(X1, X2) -> c_103(X1, X2) 957.19/297.27 , 28: fst^#(X) -> c_140(X) 957.19/297.27 , 29: fst^#(pair(X, Y)) -> c_141(U21^#(isLNat(X), X, Y)) 957.19/297.27 , 30: snd^#(X) -> c_55(X) 957.19/297.27 , 31: snd^#(pair(X, Y)) -> c_56(U301^#(isLNat(X), X, Y)) 957.19/297.27 , 32: tail^#(X) -> c_175(X) 957.19/297.27 , 33: tail^#(cons(N, XS)) -> 957.19/297.27 c_176(U331^#(isNatural(N), N, activate(XS))) 957.19/297.27 , 34: take^#(N, XS) -> c_177(U341^#(isNatural(N), N, XS)) 957.19/297.27 , 35: take^#(X1, X2) -> c_178(X1, X2) 957.19/297.27 , 36: head^#(X) -> c_109(X) 957.19/297.27 , 37: head^#(cons(N, XS)) -> 957.19/297.27 c_110(U31^#(isNatural(N), N, activate(XS))) 957.19/297.27 , 38: s^#(X) -> c_104(X) 957.19/297.27 , 39: sel^#(N, XS) -> c_172(U291^#(isNatural(N), N, XS)) 957.19/297.27 , 40: sel^#(X1, X2) -> c_173(X1, X2) 957.19/297.27 , 41: pair^#(X1, X2) -> c_121(X1, X2) 957.19/297.27 , 42: splitAt^#(X1, X2) -> c_57(X1, X2) 957.19/297.27 , 43: splitAt^#(s(N), cons(X, XS)) -> 957.19/297.27 c_58(U321^#(isNatural(N), N, X, activate(XS))) 957.19/297.27 , 44: splitAt^#(0(), XS) -> c_59(U311^#(isLNat(XS), XS)) 957.19/297.27 , 45: U104^#(tt(), V1, V2) -> 957.19/297.27 c_31(U105^#(isNatural(activate(V1)), activate(V2))) 957.19/297.27 , 46: isLNatKind^#(n__natsFrom(V1)) -> 957.19/297.27 c_23(U141^#(isNaturalKind(activate(V1)))) 957.19/297.27 , 47: isLNatKind^#(n__afterNth(V1, V2)) -> 957.19/297.27 c_25(U111^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.27 , 48: isLNatKind^#(n__cons(V1, V2)) -> 957.19/297.27 c_26(U121^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.27 , 49: isLNatKind^#(n__fst(V1)) -> 957.19/297.27 c_27(U131^#(isPLNatKind(activate(V1)))) 957.19/297.27 , 50: isLNatKind^#(n__snd(V1)) -> 957.19/297.27 c_28(U151^#(isPLNatKind(activate(V1)))) 957.19/297.27 , 51: isLNatKind^#(n__tail(V1)) -> 957.19/297.27 c_29(U161^#(isLNatKind(activate(V1)))) 957.19/297.27 , 52: isLNatKind^#(n__take(V1, V2)) -> 957.19/297.27 c_30(U171^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.27 , 53: U111^#(tt(), V2) -> c_48(U112^#(isLNatKind(activate(V2)))) 957.19/297.27 , 54: U121^#(tt(), V2) -> c_51(U122^#(isLNatKind(activate(V2)))) 957.19/297.27 , 55: U171^#(tt(), V2) -> c_63(U172^#(isLNatKind(activate(V2)))) 957.19/297.27 , 56: U105^#(tt(), V2) -> c_32(U106^#(isLNat(activate(V2)))) 957.19/297.27 , 57: isNatural^#(n__head(V1)) -> 957.19/297.27 c_34(U181^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.27 , 58: isNatural^#(n__s(V1)) -> 957.19/297.27 c_35(U191^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.27 , 59: isNatural^#(n__sel(V1, V2)) -> 957.19/297.27 c_36(U201^#(isNaturalKind(activate(V1)), 957.19/297.27 activate(V1), 957.19/297.27 activate(V2))) 957.19/297.27 , 60: U181^#(tt(), V1) -> 957.19/297.27 c_65(U182^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.27 , 61: U191^#(tt(), V1) -> 957.19/297.27 c_68(U192^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.28 , 62: U201^#(tt(), V1, V2) -> 957.19/297.28 c_71(U202^#(isNaturalKind(activate(V1)), 957.19/297.28 activate(V1), 957.19/297.28 activate(V2))) 957.19/297.28 , 63: isLNat^#(n__natsFrom(V1)) -> 957.19/297.28 c_38(U71^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.28 , 64: isLNat^#(n__afterNth(V1, V2)) -> 957.19/297.28 c_40(U41^#(isNaturalKind(activate(V1)), 957.19/297.28 activate(V1), 957.19/297.28 activate(V2))) 957.19/297.28 , 65: isLNat^#(n__cons(V1, V2)) -> 957.19/297.28 c_41(U51^#(isNaturalKind(activate(V1)), 957.19/297.28 activate(V1), 957.19/297.28 activate(V2))) 957.19/297.28 , 66: isLNat^#(n__fst(V1)) -> 957.19/297.28 c_42(U61^#(isPLNatKind(activate(V1)), activate(V1))) 957.19/297.28 , 67: isLNat^#(n__snd(V1)) -> 957.19/297.28 c_43(U81^#(isPLNatKind(activate(V1)), activate(V1))) 957.19/297.28 , 68: isLNat^#(n__tail(V1)) -> 957.19/297.28 c_44(U91^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.28 , 69: isLNat^#(n__take(V1, V2)) -> 957.19/297.28 c_45(U101^#(isNaturalKind(activate(V1)), 957.19/297.28 activate(V1), 957.19/297.28 activate(V2))) 957.19/297.28 , 70: U71^#(tt(), V1) -> 957.19/297.28 c_161(U72^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.28 , 71: U41^#(tt(), V1, V2) -> 957.19/297.28 c_142(U42^#(isNaturalKind(activate(V1)), 957.19/297.28 activate(V1), 957.19/297.28 activate(V2))) 957.19/297.28 , 72: U51^#(tt(), V1, V2) -> 957.19/297.28 c_148(U52^#(isNaturalKind(activate(V1)), 957.19/297.28 activate(V1), 957.19/297.28 activate(V2))) 957.19/297.28 , 73: U61^#(tt(), V1) -> 957.19/297.28 c_154(U62^#(isPLNatKind(activate(V1)), activate(V1))) 957.19/297.28 , 74: U81^#(tt(), V1) -> 957.19/297.28 c_164(U82^#(isPLNatKind(activate(V1)), activate(V1))) 957.19/297.28 , 75: U91^#(tt(), V1) -> 957.19/297.28 c_167(U92^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.28 , 76: U11^#(tt(), N, XS) -> 957.19/297.28 c_46(U12^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.19/297.28 , 77: U12^#(tt(), N, XS) -> 957.19/297.28 c_47(U13^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.19/297.28 , 78: U13^#(tt(), N, XS) -> 957.19/297.28 c_50(U14^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.19/297.28 , 79: U14^#(tt(), N, XS) -> 957.19/297.28 c_53(snd^#(splitAt(activate(N), activate(XS)))) 957.19/297.28 , 80: U301^#(tt(), X, Y) -> 957.19/297.28 c_113(U302^#(isLNatKind(activate(X)), activate(Y))) 957.19/297.28 , 81: U321^#(tt(), N, X, XS) -> 957.19/297.28 c_124(U322^#(isNaturalKind(activate(N)), 957.19/297.28 activate(N), 957.19/297.28 activate(X), 957.19/297.28 activate(XS))) 957.19/297.28 , 82: U311^#(tt(), XS) -> 957.19/297.28 c_119(U312^#(isLNatKind(activate(XS)), activate(XS))) 957.19/297.28 , 83: U182^#(tt(), V1) -> c_66(U183^#(isLNat(activate(V1)))) 957.19/297.28 , 84: U192^#(tt(), V1) -> c_69(U193^#(isNatural(activate(V1)))) 957.19/297.28 , 85: U202^#(tt(), V1, V2) -> 957.19/297.28 c_72(U203^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.28 , 86: U203^#(tt(), V1, V2) -> 957.19/297.28 c_73(U204^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.28 , 87: U204^#(tt(), V1, V2) -> 957.19/297.28 c_74(U205^#(isNatural(activate(V1)), activate(V2))) 957.19/297.28 , 88: U205^#(tt(), V2) -> c_75(U206^#(isLNat(activate(V2)))) 957.19/297.28 , 89: U21^#(tt(), X, Y) -> 957.19/297.28 c_77(U22^#(isLNatKind(activate(X)), activate(X), activate(Y))) 957.19/297.28 , 90: U22^#(tt(), X, Y) -> 957.19/297.28 c_78(U23^#(isLNat(activate(Y)), activate(X), activate(Y))) 957.19/297.28 , 91: U23^#(tt(), X, Y) -> 957.19/297.28 c_80(U24^#(isLNatKind(activate(Y)), activate(X))) 957.19/297.28 , 92: U24^#(tt(), X) -> c_82(activate^#(X)) 957.19/297.28 , 93: U241^#(tt(), V1, V2) -> 957.19/297.28 c_85(U242^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.19/297.28 , 94: U242^#(tt(), V1, V2) -> 957.19/297.28 c_86(U243^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.28 , 95: U243^#(tt(), V1, V2) -> 957.19/297.28 c_87(U244^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.28 , 96: U244^#(tt(), V1, V2) -> 957.19/297.28 c_88(U245^#(isLNat(activate(V1)), activate(V2))) 957.19/297.28 , 97: U245^#(tt(), V2) -> c_89(U246^#(isLNat(activate(V2)))) 957.19/297.28 , 98: U251^#(tt(), V1, V2) -> 957.19/297.28 c_91(U252^#(isNaturalKind(activate(V1)), 957.19/297.28 activate(V1), 957.19/297.28 activate(V2))) 957.19/297.28 , 99: U252^#(tt(), V1, V2) -> 957.19/297.28 c_92(U253^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.28 , 100: U253^#(tt(), V1, V2) -> 957.19/297.28 c_93(U254^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.28 , 101: U254^#(tt(), V1, V2) -> 957.19/297.28 c_94(U255^#(isNatural(activate(V1)), activate(V2))) 957.19/297.28 , 102: U255^#(tt(), V2) -> c_95(U256^#(isLNat(activate(V2)))) 957.19/297.28 , 103: U261^#(tt(), V2) -> c_97(U262^#(isLNatKind(activate(V2)))) 957.19/297.28 , 104: U271^#(tt(), V2) -> c_99(U272^#(isLNatKind(activate(V2)))) 957.19/297.28 , 105: U281^#(tt(), N) -> 957.19/297.28 c_101(U282^#(isNaturalKind(activate(N)), activate(N))) 957.19/297.28 , 106: U282^#(tt(), N) -> 957.19/297.28 c_102(cons^#(activate(N), n__natsFrom(s(activate(N))))) 957.19/297.28 , 107: U291^#(tt(), N, XS) -> 957.19/297.28 c_105(U292^#(isNaturalKind(activate(N)), 957.19/297.28 activate(N), 957.19/297.28 activate(XS))) 957.19/297.28 , 108: U292^#(tt(), N, XS) -> 957.19/297.28 c_106(U293^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.19/297.28 , 109: U293^#(tt(), N, XS) -> 957.19/297.28 c_107(U294^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.19/297.28 , 110: U294^#(tt(), N, XS) -> 957.19/297.28 c_108(head^#(afterNth(activate(N), activate(XS)))) 957.19/297.28 , 111: U31^#(tt(), N, XS) -> 957.19/297.28 c_117(U32^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.19/297.28 , 112: U302^#(tt(), Y) -> 957.19/297.28 c_114(U303^#(isLNat(activate(Y)), activate(Y))) 957.19/297.28 , 113: U303^#(tt(), Y) -> 957.19/297.28 c_115(U304^#(isLNatKind(activate(Y)), activate(Y))) 957.19/297.28 , 114: U304^#(tt(), Y) -> c_116(activate^#(Y)) 957.19/297.28 , 115: U32^#(tt(), N, XS) -> 957.19/297.28 c_118(U33^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.19/297.28 , 116: U33^#(tt(), N, XS) -> 957.19/297.28 c_123(U34^#(isLNatKind(activate(XS)), activate(N))) 957.19/297.28 , 117: U312^#(tt(), XS) -> c_120(pair^#(nil(), activate(XS))) 957.19/297.28 , 118: U34^#(tt(), N) -> c_131(activate^#(N)) 957.19/297.28 , 119: U322^#(tt(), N, X, XS) -> 957.19/297.28 c_125(U323^#(isNatural(activate(X)), 957.19/297.28 activate(N), 957.19/297.28 activate(X), 957.19/297.28 activate(XS))) 957.19/297.28 , 120: U323^#(tt(), N, X, XS) -> 957.19/297.28 c_126(U324^#(isNaturalKind(activate(X)), 957.19/297.28 activate(N), 957.19/297.28 activate(X), 957.19/297.28 activate(XS))) 957.19/297.28 , 121: U324^#(tt(), N, X, XS) -> 957.19/297.28 c_127(U325^#(isLNat(activate(XS)), 957.19/297.28 activate(N), 957.19/297.28 activate(X), 957.19/297.28 activate(XS))) 957.19/297.28 , 122: U325^#(tt(), N, X, XS) -> 957.19/297.28 c_128(U326^#(isLNatKind(activate(XS)), 957.19/297.28 activate(N), 957.19/297.28 activate(X), 957.19/297.28 activate(XS))) 957.19/297.28 , 123: U326^#(tt(), N, X, XS) -> 957.19/297.28 c_129(U327^#(splitAt(activate(N), activate(XS)), activate(X))) 957.19/297.28 , 124: U327^#(pair(YS, ZS), X) -> 957.19/297.28 c_130(pair^#(cons(activate(X), YS), ZS)) 957.19/297.28 , 125: U331^#(tt(), N, XS) -> 957.19/297.28 c_132(U332^#(isNaturalKind(activate(N)), activate(XS))) 957.19/297.28 , 126: U332^#(tt(), XS) -> 957.19/297.28 c_133(U333^#(isLNat(activate(XS)), activate(XS))) 957.19/297.28 , 127: U333^#(tt(), XS) -> 957.19/297.28 c_134(U334^#(isLNatKind(activate(XS)), activate(XS))) 957.19/297.28 , 128: U334^#(tt(), XS) -> c_135(activate^#(XS)) 957.19/297.28 , 129: U341^#(tt(), N, XS) -> 957.19/297.28 c_136(U342^#(isNaturalKind(activate(N)), 957.19/297.28 activate(N), 957.19/297.28 activate(XS))) 957.19/297.28 , 130: U342^#(tt(), N, XS) -> 957.19/297.28 c_137(U343^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.19/297.28 , 131: U343^#(tt(), N, XS) -> 957.19/297.28 c_138(U344^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.19/297.28 , 132: U344^#(tt(), N, XS) -> 957.19/297.28 c_139(fst^#(splitAt(activate(N), activate(XS)))) 957.19/297.28 , 133: U42^#(tt(), V1, V2) -> 957.19/297.28 c_143(U43^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.28 , 134: U43^#(tt(), V1, V2) -> 957.19/297.28 c_144(U44^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.28 , 135: U44^#(tt(), V1, V2) -> 957.19/297.28 c_145(U45^#(isNatural(activate(V1)), activate(V2))) 957.19/297.28 , 136: U45^#(tt(), V2) -> c_146(U46^#(isLNat(activate(V2)))) 957.19/297.28 , 137: U52^#(tt(), V1, V2) -> 957.19/297.28 c_149(U53^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.28 , 138: U53^#(tt(), V1, V2) -> 957.19/297.28 c_150(U54^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.28 , 139: U54^#(tt(), V1, V2) -> 957.19/297.28 c_151(U55^#(isNatural(activate(V1)), activate(V2))) 957.19/297.28 , 140: U55^#(tt(), V2) -> c_152(U56^#(isLNat(activate(V2)))) 957.19/297.28 , 141: U62^#(tt(), V1) -> c_155(U63^#(isPLNat(activate(V1)))) 957.19/297.28 , 142: isPLNatKind^#(n__pair(V1, V2)) -> 957.19/297.28 c_156(U261^#(isLNatKind(activate(V1)), activate(V2))) 957.19/297.28 , 143: isPLNatKind^#(n__splitAt(V1, V2)) -> 957.19/297.28 c_157(U271^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.28 , 144: isPLNat^#(n__pair(V1, V2)) -> 957.19/297.28 c_159(U241^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.19/297.28 , 145: isPLNat^#(n__splitAt(V1, V2)) -> 957.19/297.28 c_160(U251^#(isNaturalKind(activate(V1)), 957.19/297.28 activate(V1), 957.19/297.28 activate(V2))) 957.19/297.28 , 146: U72^#(tt(), V1) -> c_162(U73^#(isNatural(activate(V1)))) 957.19/297.28 , 147: U82^#(tt(), V1) -> c_165(U83^#(isPLNat(activate(V1)))) 957.19/297.28 , 148: U92^#(tt(), V1) -> c_168(U93^#(isLNat(activate(V1)))) 957.19/297.28 , 149: isNaturalKind^#(n__0()) -> c_3() 957.19/297.28 , 150: U211^#(tt()) -> c_79() 957.19/297.28 , 151: U221^#(tt()) -> c_81() 957.19/297.28 , 152: nil^#() -> c_122() 957.19/297.28 , 153: 0^#() -> c_174() 957.19/297.28 , 154: isLNatKind^#(n__nil()) -> c_24() 957.19/297.28 , 155: U141^#(tt()) -> c_60() 957.19/297.28 , 156: U131^#(tt()) -> c_54() 957.19/297.28 , 157: U151^#(tt()) -> c_61() 957.19/297.28 , 158: U161^#(tt()) -> c_62() 957.19/297.28 , 159: U106^#(tt()) -> c_37() 957.19/297.28 , 160: isNatural^#(n__0()) -> c_33() 957.19/297.28 , 161: isLNat^#(n__nil()) -> c_39() 957.19/297.28 , 162: U112^#(tt()) -> c_49() 957.19/297.28 , 163: U122^#(tt()) -> c_52() 957.19/297.28 , 164: U172^#(tt()) -> c_64() 957.19/297.28 , 165: U183^#(tt()) -> c_67() 957.19/297.28 , 166: U193^#(tt()) -> c_70() 957.19/297.28 , 167: U206^#(tt()) -> c_76() 957.19/297.28 , 168: U232^#(tt()) -> c_84() 957.19/297.28 , 169: U246^#(tt()) -> c_90() 957.19/297.28 , 170: U256^#(tt()) -> c_96() 957.19/297.28 , 171: U262^#(tt()) -> c_98() 957.19/297.28 , 172: U272^#(tt()) -> c_100() 957.19/297.28 , 173: U46^#(tt()) -> c_147() 957.19/297.28 , 174: U56^#(tt()) -> c_153() 957.19/297.28 , 175: U63^#(tt()) -> c_158() 957.19/297.28 , 176: U73^#(tt()) -> c_163() 957.19/297.28 , 177: U83^#(tt()) -> c_166() 957.19/297.28 , 178: U93^#(tt()) -> c_169() } 957.19/297.28 957.19/297.28 We are left with following problem, upon which TcT provides the 957.19/297.28 certificate MAYBE. 957.19/297.28 957.19/297.28 Strict DPs: 957.19/297.28 { U101^#(tt(), V1, V2) -> 957.19/297.28 c_1(U102^#(isNaturalKind(activate(V1)), 957.19/297.28 activate(V1), 957.19/297.28 activate(V2))) 957.19/297.28 , U102^#(tt(), V1, V2) -> 957.19/297.28 c_2(U103^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.28 , U103^#(tt(), V1, V2) -> 957.19/297.28 c_22(U104^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.28 , isNaturalKind^#(n__sel(V1, V2)) -> 957.19/297.28 c_6(U231^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.28 , activate^#(X) -> c_7(X) 957.19/297.28 , activate^#(n__natsFrom(X)) -> c_8(natsFrom^#(X)) 957.19/297.28 , activate^#(n__afterNth(X1, X2)) -> c_10(afterNth^#(X1, X2)) 957.19/297.28 , activate^#(n__cons(X1, X2)) -> c_11(cons^#(X1, X2)) 957.19/297.28 , activate^#(n__fst(X)) -> c_12(fst^#(X)) 957.19/297.28 , activate^#(n__snd(X)) -> c_13(snd^#(X)) 957.19/297.28 , activate^#(n__tail(X)) -> c_14(tail^#(X)) 957.19/297.28 , activate^#(n__take(X1, X2)) -> c_15(take^#(X1, X2)) 957.19/297.28 , activate^#(n__head(X)) -> c_17(head^#(X)) 957.19/297.28 , activate^#(n__s(X)) -> c_18(s^#(X)) 957.19/297.28 , activate^#(n__sel(X1, X2)) -> c_19(sel^#(X1, X2)) 957.19/297.28 , activate^#(n__pair(X1, X2)) -> c_20(pair^#(X1, X2)) 957.19/297.28 , activate^#(n__splitAt(X1, X2)) -> c_21(splitAt^#(X1, X2)) 957.19/297.28 , natsFrom^#(N) -> c_170(U281^#(isNatural(N), N)) 957.19/297.28 , natsFrom^#(X) -> c_171(X) 957.19/297.28 , afterNth^#(N, XS) -> c_111(U11^#(isNatural(N), N, XS)) 957.19/297.28 , afterNth^#(X1, X2) -> c_112(X1, X2) 957.19/297.28 , cons^#(X1, X2) -> c_103(X1, X2) 957.19/297.28 , fst^#(X) -> c_140(X) 957.19/297.28 , fst^#(pair(X, Y)) -> c_141(U21^#(isLNat(X), X, Y)) 957.19/297.28 , snd^#(X) -> c_55(X) 957.19/297.28 , snd^#(pair(X, Y)) -> c_56(U301^#(isLNat(X), X, Y)) 957.19/297.28 , tail^#(X) -> c_175(X) 957.19/297.28 , tail^#(cons(N, XS)) -> 957.19/297.28 c_176(U331^#(isNatural(N), N, activate(XS))) 957.19/297.28 , take^#(N, XS) -> c_177(U341^#(isNatural(N), N, XS)) 957.19/297.28 , take^#(X1, X2) -> c_178(X1, X2) 957.19/297.28 , head^#(X) -> c_109(X) 957.19/297.28 , head^#(cons(N, XS)) -> 957.19/297.28 c_110(U31^#(isNatural(N), N, activate(XS))) 957.19/297.28 , s^#(X) -> c_104(X) 957.19/297.28 , sel^#(N, XS) -> c_172(U291^#(isNatural(N), N, XS)) 957.19/297.28 , sel^#(X1, X2) -> c_173(X1, X2) 957.19/297.28 , pair^#(X1, X2) -> c_121(X1, X2) 957.19/297.28 , splitAt^#(X1, X2) -> c_57(X1, X2) 957.19/297.28 , splitAt^#(s(N), cons(X, XS)) -> 957.19/297.28 c_58(U321^#(isNatural(N), N, X, activate(XS))) 957.19/297.28 , splitAt^#(0(), XS) -> c_59(U311^#(isLNat(XS), XS)) 957.19/297.28 , U104^#(tt(), V1, V2) -> 957.19/297.28 c_31(U105^#(isNatural(activate(V1)), activate(V2))) 957.19/297.28 , isLNatKind^#(n__afterNth(V1, V2)) -> 957.19/297.28 c_25(U111^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.28 , isLNatKind^#(n__cons(V1, V2)) -> 957.19/297.28 c_26(U121^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.28 , isLNatKind^#(n__take(V1, V2)) -> 957.19/297.28 c_30(U171^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.28 , isNatural^#(n__head(V1)) -> 957.19/297.28 c_34(U181^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.28 , isNatural^#(n__s(V1)) -> 957.19/297.28 c_35(U191^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.28 , isNatural^#(n__sel(V1, V2)) -> 957.19/297.28 c_36(U201^#(isNaturalKind(activate(V1)), 957.19/297.28 activate(V1), 957.19/297.28 activate(V2))) 957.19/297.28 , U181^#(tt(), V1) -> 957.19/297.28 c_65(U182^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.28 , U191^#(tt(), V1) -> 957.19/297.28 c_68(U192^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.28 , U201^#(tt(), V1, V2) -> 957.19/297.28 c_71(U202^#(isNaturalKind(activate(V1)), 957.19/297.28 activate(V1), 957.19/297.28 activate(V2))) 957.19/297.28 , isLNat^#(n__natsFrom(V1)) -> 957.19/297.28 c_38(U71^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.28 , isLNat^#(n__afterNth(V1, V2)) -> 957.19/297.28 c_40(U41^#(isNaturalKind(activate(V1)), 957.19/297.28 activate(V1), 957.19/297.28 activate(V2))) 957.19/297.28 , isLNat^#(n__cons(V1, V2)) -> 957.19/297.28 c_41(U51^#(isNaturalKind(activate(V1)), 957.19/297.28 activate(V1), 957.19/297.28 activate(V2))) 957.19/297.28 , isLNat^#(n__fst(V1)) -> 957.19/297.28 c_42(U61^#(isPLNatKind(activate(V1)), activate(V1))) 957.19/297.28 , isLNat^#(n__snd(V1)) -> 957.19/297.28 c_43(U81^#(isPLNatKind(activate(V1)), activate(V1))) 957.19/297.28 , isLNat^#(n__tail(V1)) -> 957.19/297.28 c_44(U91^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.28 , isLNat^#(n__take(V1, V2)) -> 957.19/297.28 c_45(U101^#(isNaturalKind(activate(V1)), 957.19/297.28 activate(V1), 957.19/297.28 activate(V2))) 957.19/297.28 , U71^#(tt(), V1) -> 957.19/297.28 c_161(U72^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.28 , U41^#(tt(), V1, V2) -> 957.19/297.28 c_142(U42^#(isNaturalKind(activate(V1)), 957.19/297.28 activate(V1), 957.19/297.28 activate(V2))) 957.19/297.28 , U51^#(tt(), V1, V2) -> 957.19/297.28 c_148(U52^#(isNaturalKind(activate(V1)), 957.19/297.28 activate(V1), 957.19/297.28 activate(V2))) 957.19/297.28 , U61^#(tt(), V1) -> 957.19/297.28 c_154(U62^#(isPLNatKind(activate(V1)), activate(V1))) 957.19/297.28 , U81^#(tt(), V1) -> 957.19/297.28 c_164(U82^#(isPLNatKind(activate(V1)), activate(V1))) 957.19/297.28 , U91^#(tt(), V1) -> 957.19/297.28 c_167(U92^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.28 , U11^#(tt(), N, XS) -> 957.19/297.28 c_46(U12^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.19/297.28 , U12^#(tt(), N, XS) -> 957.19/297.28 c_47(U13^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.19/297.28 , U13^#(tt(), N, XS) -> 957.19/297.28 c_50(U14^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.19/297.28 , U14^#(tt(), N, XS) -> 957.19/297.29 c_53(snd^#(splitAt(activate(N), activate(XS)))) 957.19/297.29 , U301^#(tt(), X, Y) -> 957.19/297.29 c_113(U302^#(isLNatKind(activate(X)), activate(Y))) 957.19/297.29 , U321^#(tt(), N, X, XS) -> 957.19/297.29 c_124(U322^#(isNaturalKind(activate(N)), 957.19/297.29 activate(N), 957.19/297.29 activate(X), 957.19/297.29 activate(XS))) 957.19/297.29 , U311^#(tt(), XS) -> 957.19/297.29 c_119(U312^#(isLNatKind(activate(XS)), activate(XS))) 957.19/297.29 , U202^#(tt(), V1, V2) -> 957.19/297.29 c_72(U203^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.29 , U203^#(tt(), V1, V2) -> 957.19/297.29 c_73(U204^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.29 , U204^#(tt(), V1, V2) -> 957.19/297.29 c_74(U205^#(isNatural(activate(V1)), activate(V2))) 957.19/297.29 , U21^#(tt(), X, Y) -> 957.19/297.29 c_77(U22^#(isLNatKind(activate(X)), activate(X), activate(Y))) 957.19/297.29 , U22^#(tt(), X, Y) -> 957.19/297.29 c_78(U23^#(isLNat(activate(Y)), activate(X), activate(Y))) 957.19/297.29 , U23^#(tt(), X, Y) -> 957.19/297.29 c_80(U24^#(isLNatKind(activate(Y)), activate(X))) 957.19/297.29 , U24^#(tt(), X) -> c_82(activate^#(X)) 957.19/297.29 , U241^#(tt(), V1, V2) -> 957.19/297.29 c_85(U242^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.19/297.29 , U242^#(tt(), V1, V2) -> 957.19/297.29 c_86(U243^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.29 , U243^#(tt(), V1, V2) -> 957.19/297.29 c_87(U244^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.29 , U244^#(tt(), V1, V2) -> 957.19/297.29 c_88(U245^#(isLNat(activate(V1)), activate(V2))) 957.19/297.29 , U251^#(tt(), V1, V2) -> 957.19/297.29 c_91(U252^#(isNaturalKind(activate(V1)), 957.19/297.29 activate(V1), 957.19/297.29 activate(V2))) 957.19/297.29 , U252^#(tt(), V1, V2) -> 957.19/297.29 c_92(U253^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.29 , U253^#(tt(), V1, V2) -> 957.19/297.29 c_93(U254^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.29 , U254^#(tt(), V1, V2) -> 957.19/297.29 c_94(U255^#(isNatural(activate(V1)), activate(V2))) 957.19/297.29 , U281^#(tt(), N) -> 957.19/297.29 c_101(U282^#(isNaturalKind(activate(N)), activate(N))) 957.19/297.29 , U282^#(tt(), N) -> 957.19/297.29 c_102(cons^#(activate(N), n__natsFrom(s(activate(N))))) 957.19/297.29 , U291^#(tt(), N, XS) -> 957.19/297.29 c_105(U292^#(isNaturalKind(activate(N)), 957.19/297.29 activate(N), 957.19/297.29 activate(XS))) 957.19/297.29 , U292^#(tt(), N, XS) -> 957.19/297.29 c_106(U293^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.19/297.29 , U293^#(tt(), N, XS) -> 957.19/297.29 c_107(U294^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.19/297.29 , U294^#(tt(), N, XS) -> 957.19/297.29 c_108(head^#(afterNth(activate(N), activate(XS)))) 957.19/297.29 , U31^#(tt(), N, XS) -> 957.19/297.29 c_117(U32^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.19/297.29 , U302^#(tt(), Y) -> 957.19/297.29 c_114(U303^#(isLNat(activate(Y)), activate(Y))) 957.19/297.29 , U303^#(tt(), Y) -> 957.19/297.29 c_115(U304^#(isLNatKind(activate(Y)), activate(Y))) 957.19/297.29 , U304^#(tt(), Y) -> c_116(activate^#(Y)) 957.19/297.29 , U32^#(tt(), N, XS) -> 957.19/297.29 c_118(U33^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.19/297.29 , U33^#(tt(), N, XS) -> 957.19/297.29 c_123(U34^#(isLNatKind(activate(XS)), activate(N))) 957.19/297.29 , U312^#(tt(), XS) -> c_120(pair^#(nil(), activate(XS))) 957.19/297.29 , U34^#(tt(), N) -> c_131(activate^#(N)) 957.19/297.29 , U322^#(tt(), N, X, XS) -> 957.19/297.29 c_125(U323^#(isNatural(activate(X)), 957.19/297.29 activate(N), 957.19/297.29 activate(X), 957.19/297.29 activate(XS))) 957.19/297.29 , U323^#(tt(), N, X, XS) -> 957.19/297.29 c_126(U324^#(isNaturalKind(activate(X)), 957.19/297.29 activate(N), 957.19/297.29 activate(X), 957.19/297.29 activate(XS))) 957.19/297.29 , U324^#(tt(), N, X, XS) -> 957.19/297.29 c_127(U325^#(isLNat(activate(XS)), 957.19/297.29 activate(N), 957.19/297.29 activate(X), 957.19/297.29 activate(XS))) 957.19/297.29 , U325^#(tt(), N, X, XS) -> 957.19/297.29 c_128(U326^#(isLNatKind(activate(XS)), 957.19/297.29 activate(N), 957.19/297.29 activate(X), 957.19/297.29 activate(XS))) 957.19/297.29 , U326^#(tt(), N, X, XS) -> 957.19/297.29 c_129(U327^#(splitAt(activate(N), activate(XS)), activate(X))) 957.19/297.29 , U327^#(pair(YS, ZS), X) -> 957.19/297.29 c_130(pair^#(cons(activate(X), YS), ZS)) 957.19/297.29 , U331^#(tt(), N, XS) -> 957.19/297.29 c_132(U332^#(isNaturalKind(activate(N)), activate(XS))) 957.19/297.29 , U332^#(tt(), XS) -> 957.19/297.29 c_133(U333^#(isLNat(activate(XS)), activate(XS))) 957.19/297.29 , U333^#(tt(), XS) -> 957.19/297.29 c_134(U334^#(isLNatKind(activate(XS)), activate(XS))) 957.19/297.29 , U334^#(tt(), XS) -> c_135(activate^#(XS)) 957.19/297.29 , U341^#(tt(), N, XS) -> 957.19/297.29 c_136(U342^#(isNaturalKind(activate(N)), 957.19/297.29 activate(N), 957.19/297.29 activate(XS))) 957.19/297.29 , U342^#(tt(), N, XS) -> 957.19/297.29 c_137(U343^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.19/297.29 , U343^#(tt(), N, XS) -> 957.19/297.29 c_138(U344^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.19/297.29 , U344^#(tt(), N, XS) -> 957.19/297.29 c_139(fst^#(splitAt(activate(N), activate(XS)))) 957.19/297.29 , U42^#(tt(), V1, V2) -> 957.19/297.29 c_143(U43^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.29 , U43^#(tt(), V1, V2) -> 957.19/297.29 c_144(U44^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.29 , U44^#(tt(), V1, V2) -> 957.19/297.29 c_145(U45^#(isNatural(activate(V1)), activate(V2))) 957.19/297.29 , U52^#(tt(), V1, V2) -> 957.19/297.29 c_149(U53^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.29 , U53^#(tt(), V1, V2) -> 957.19/297.29 c_150(U54^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.29 , U54^#(tt(), V1, V2) -> 957.19/297.29 c_151(U55^#(isNatural(activate(V1)), activate(V2))) 957.19/297.29 , isPLNatKind^#(n__pair(V1, V2)) -> 957.19/297.29 c_156(U261^#(isLNatKind(activate(V1)), activate(V2))) 957.19/297.29 , isPLNatKind^#(n__splitAt(V1, V2)) -> 957.19/297.29 c_157(U271^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.29 , isPLNat^#(n__pair(V1, V2)) -> 957.19/297.29 c_159(U241^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.19/297.29 , isPLNat^#(n__splitAt(V1, V2)) -> 957.19/297.29 c_160(U251^#(isNaturalKind(activate(V1)), 957.19/297.29 activate(V1), 957.19/297.29 activate(V2))) } 957.19/297.29 Strict Trs: 957.19/297.29 { U101(tt(), V1, V2) -> 957.19/297.29 U102(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.29 , U102(tt(), V1, V2) -> 957.19/297.29 U103(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.29 , isNaturalKind(n__0()) -> tt() 957.19/297.29 , isNaturalKind(n__head(V1)) -> U211(isLNatKind(activate(V1))) 957.19/297.29 , isNaturalKind(n__s(V1)) -> U221(isNaturalKind(activate(V1))) 957.19/297.29 , isNaturalKind(n__sel(V1, V2)) -> 957.19/297.29 U231(isNaturalKind(activate(V1)), activate(V2)) 957.19/297.29 , activate(X) -> X 957.19/297.29 , activate(n__natsFrom(X)) -> natsFrom(X) 957.19/297.29 , activate(n__nil()) -> nil() 957.19/297.29 , activate(n__afterNth(X1, X2)) -> afterNth(X1, X2) 957.19/297.29 , activate(n__cons(X1, X2)) -> cons(X1, X2) 957.19/297.29 , activate(n__fst(X)) -> fst(X) 957.19/297.29 , activate(n__snd(X)) -> snd(X) 957.19/297.29 , activate(n__tail(X)) -> tail(X) 957.19/297.29 , activate(n__take(X1, X2)) -> take(X1, X2) 957.19/297.29 , activate(n__0()) -> 0() 957.19/297.29 , activate(n__head(X)) -> head(X) 957.19/297.29 , activate(n__s(X)) -> s(X) 957.19/297.29 , activate(n__sel(X1, X2)) -> sel(X1, X2) 957.19/297.29 , activate(n__pair(X1, X2)) -> pair(X1, X2) 957.19/297.29 , activate(n__splitAt(X1, X2)) -> splitAt(X1, X2) 957.19/297.29 , U103(tt(), V1, V2) -> 957.19/297.29 U104(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.29 , isLNatKind(n__natsFrom(V1)) -> U141(isNaturalKind(activate(V1))) 957.19/297.29 , isLNatKind(n__nil()) -> tt() 957.19/297.29 , isLNatKind(n__afterNth(V1, V2)) -> 957.19/297.29 U111(isNaturalKind(activate(V1)), activate(V2)) 957.19/297.29 , isLNatKind(n__cons(V1, V2)) -> 957.19/297.29 U121(isNaturalKind(activate(V1)), activate(V2)) 957.19/297.29 , isLNatKind(n__fst(V1)) -> U131(isPLNatKind(activate(V1))) 957.19/297.29 , isLNatKind(n__snd(V1)) -> U151(isPLNatKind(activate(V1))) 957.19/297.29 , isLNatKind(n__tail(V1)) -> U161(isLNatKind(activate(V1))) 957.19/297.29 , isLNatKind(n__take(V1, V2)) -> 957.19/297.29 U171(isNaturalKind(activate(V1)), activate(V2)) 957.19/297.29 , U104(tt(), V1, V2) -> U105(isNatural(activate(V1)), activate(V2)) 957.19/297.29 , U105(tt(), V2) -> U106(isLNat(activate(V2))) 957.19/297.29 , isNatural(n__0()) -> tt() 957.19/297.29 , isNatural(n__head(V1)) -> 957.19/297.29 U181(isLNatKind(activate(V1)), activate(V1)) 957.19/297.29 , isNatural(n__s(V1)) -> 957.19/297.29 U191(isNaturalKind(activate(V1)), activate(V1)) 957.19/297.29 , isNatural(n__sel(V1, V2)) -> 957.19/297.29 U201(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.29 , U106(tt()) -> tt() 957.19/297.29 , isLNat(n__natsFrom(V1)) -> 957.19/297.29 U71(isNaturalKind(activate(V1)), activate(V1)) 957.19/297.29 , isLNat(n__nil()) -> tt() 957.19/297.29 , isLNat(n__afterNth(V1, V2)) -> 957.19/297.29 U41(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.29 , isLNat(n__cons(V1, V2)) -> 957.19/297.29 U51(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.29 , isLNat(n__fst(V1)) -> 957.19/297.29 U61(isPLNatKind(activate(V1)), activate(V1)) 957.19/297.29 , isLNat(n__snd(V1)) -> 957.19/297.29 U81(isPLNatKind(activate(V1)), activate(V1)) 957.19/297.29 , isLNat(n__tail(V1)) -> 957.19/297.29 U91(isLNatKind(activate(V1)), activate(V1)) 957.19/297.29 , isLNat(n__take(V1, V2)) -> 957.19/297.29 U101(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.29 , U11(tt(), N, XS) -> 957.19/297.29 U12(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.19/297.29 , U12(tt(), N, XS) -> 957.19/297.29 U13(isLNat(activate(XS)), activate(N), activate(XS)) 957.19/297.29 , U111(tt(), V2) -> U112(isLNatKind(activate(V2))) 957.19/297.29 , U112(tt()) -> tt() 957.19/297.29 , U13(tt(), N, XS) -> 957.19/297.29 U14(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.19/297.29 , U121(tt(), V2) -> U122(isLNatKind(activate(V2))) 957.19/297.29 , U122(tt()) -> tt() 957.19/297.29 , U14(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS))) 957.19/297.29 , U131(tt()) -> tt() 957.19/297.29 , snd(X) -> n__snd(X) 957.19/297.29 , snd(pair(X, Y)) -> U301(isLNat(X), X, Y) 957.19/297.29 , splitAt(X1, X2) -> n__splitAt(X1, X2) 957.19/297.29 , splitAt(s(N), cons(X, XS)) -> 957.19/297.29 U321(isNatural(N), N, X, activate(XS)) 957.19/297.29 , splitAt(0(), XS) -> U311(isLNat(XS), XS) 957.19/297.29 , U141(tt()) -> tt() 957.19/297.29 , U151(tt()) -> tt() 957.19/297.29 , U161(tt()) -> tt() 957.19/297.29 , U171(tt(), V2) -> U172(isLNatKind(activate(V2))) 957.19/297.29 , U172(tt()) -> tt() 957.19/297.29 , U181(tt(), V1) -> U182(isLNatKind(activate(V1)), activate(V1)) 957.19/297.29 , U182(tt(), V1) -> U183(isLNat(activate(V1))) 957.19/297.29 , U183(tt()) -> tt() 957.19/297.29 , U191(tt(), V1) -> U192(isNaturalKind(activate(V1)), activate(V1)) 957.19/297.29 , U192(tt(), V1) -> U193(isNatural(activate(V1))) 957.19/297.29 , U193(tt()) -> tt() 957.19/297.29 , U201(tt(), V1, V2) -> 957.19/297.29 U202(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.29 , U202(tt(), V1, V2) -> 957.19/297.29 U203(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.29 , U203(tt(), V1, V2) -> 957.19/297.29 U204(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.29 , U204(tt(), V1, V2) -> U205(isNatural(activate(V1)), activate(V2)) 957.19/297.29 , U205(tt(), V2) -> U206(isLNat(activate(V2))) 957.19/297.29 , U206(tt()) -> tt() 957.19/297.29 , U21(tt(), X, Y) -> 957.19/297.29 U22(isLNatKind(activate(X)), activate(X), activate(Y)) 957.19/297.29 , U22(tt(), X, Y) -> 957.19/297.29 U23(isLNat(activate(Y)), activate(X), activate(Y)) 957.19/297.29 , U211(tt()) -> tt() 957.19/297.29 , U23(tt(), X, Y) -> U24(isLNatKind(activate(Y)), activate(X)) 957.19/297.29 , U221(tt()) -> tt() 957.19/297.29 , U24(tt(), X) -> activate(X) 957.19/297.29 , U231(tt(), V2) -> U232(isLNatKind(activate(V2))) 957.19/297.29 , U232(tt()) -> tt() 957.19/297.29 , U241(tt(), V1, V2) -> 957.19/297.29 U242(isLNatKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.29 , U242(tt(), V1, V2) -> 957.19/297.29 U243(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.29 , U243(tt(), V1, V2) -> 957.19/297.29 U244(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.29 , U244(tt(), V1, V2) -> U245(isLNat(activate(V1)), activate(V2)) 957.19/297.29 , U245(tt(), V2) -> U246(isLNat(activate(V2))) 957.19/297.29 , U246(tt()) -> tt() 957.19/297.29 , U251(tt(), V1, V2) -> 957.19/297.29 U252(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.29 , U252(tt(), V1, V2) -> 957.19/297.29 U253(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.29 , U253(tt(), V1, V2) -> 957.19/297.29 U254(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.29 , U254(tt(), V1, V2) -> U255(isNatural(activate(V1)), activate(V2)) 957.19/297.29 , U255(tt(), V2) -> U256(isLNat(activate(V2))) 957.19/297.29 , U256(tt()) -> tt() 957.19/297.29 , U261(tt(), V2) -> U262(isLNatKind(activate(V2))) 957.19/297.29 , U262(tt()) -> tt() 957.19/297.29 , U271(tt(), V2) -> U272(isLNatKind(activate(V2))) 957.19/297.29 , U272(tt()) -> tt() 957.19/297.29 , U281(tt(), N) -> U282(isNaturalKind(activate(N)), activate(N)) 957.19/297.29 , U282(tt(), N) -> cons(activate(N), n__natsFrom(s(activate(N)))) 957.19/297.29 , cons(X1, X2) -> n__cons(X1, X2) 957.19/297.29 , s(X) -> n__s(X) 957.19/297.29 , U291(tt(), N, XS) -> 957.19/297.29 U292(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.19/297.29 , U292(tt(), N, XS) -> 957.19/297.29 U293(isLNat(activate(XS)), activate(N), activate(XS)) 957.19/297.29 , U293(tt(), N, XS) -> 957.19/297.29 U294(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.19/297.29 , U294(tt(), N, XS) -> head(afterNth(activate(N), activate(XS))) 957.19/297.29 , head(X) -> n__head(X) 957.19/297.29 , head(cons(N, XS)) -> U31(isNatural(N), N, activate(XS)) 957.19/297.29 , afterNth(N, XS) -> U11(isNatural(N), N, XS) 957.19/297.29 , afterNth(X1, X2) -> n__afterNth(X1, X2) 957.19/297.29 , U301(tt(), X, Y) -> U302(isLNatKind(activate(X)), activate(Y)) 957.19/297.29 , U302(tt(), Y) -> U303(isLNat(activate(Y)), activate(Y)) 957.19/297.29 , U303(tt(), Y) -> U304(isLNatKind(activate(Y)), activate(Y)) 957.19/297.29 , U304(tt(), Y) -> activate(Y) 957.19/297.29 , U31(tt(), N, XS) -> 957.19/297.29 U32(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.19/297.29 , U32(tt(), N, XS) -> 957.19/297.29 U33(isLNat(activate(XS)), activate(N), activate(XS)) 957.19/297.29 , U311(tt(), XS) -> U312(isLNatKind(activate(XS)), activate(XS)) 957.19/297.29 , U312(tt(), XS) -> pair(nil(), activate(XS)) 957.19/297.29 , pair(X1, X2) -> n__pair(X1, X2) 957.19/297.29 , nil() -> n__nil() 957.19/297.29 , U33(tt(), N, XS) -> U34(isLNatKind(activate(XS)), activate(N)) 957.19/297.29 , U321(tt(), N, X, XS) -> 957.19/297.29 U322(isNaturalKind(activate(N)), 957.19/297.29 activate(N), 957.19/297.29 activate(X), 957.19/297.29 activate(XS)) 957.19/297.29 , U322(tt(), N, X, XS) -> 957.19/297.29 U323(isNatural(activate(X)), 957.19/297.29 activate(N), 957.19/297.29 activate(X), 957.19/297.29 activate(XS)) 957.19/297.29 , U323(tt(), N, X, XS) -> 957.19/297.29 U324(isNaturalKind(activate(X)), 957.19/297.29 activate(N), 957.19/297.29 activate(X), 957.19/297.29 activate(XS)) 957.19/297.29 , U324(tt(), N, X, XS) -> 957.19/297.29 U325(isLNat(activate(XS)), activate(N), activate(X), activate(XS)) 957.19/297.29 , U325(tt(), N, X, XS) -> 957.19/297.29 U326(isLNatKind(activate(XS)), 957.19/297.29 activate(N), 957.19/297.29 activate(X), 957.19/297.29 activate(XS)) 957.19/297.29 , U326(tt(), N, X, XS) -> 957.19/297.29 U327(splitAt(activate(N), activate(XS)), activate(X)) 957.19/297.29 , U327(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) 957.19/297.29 , U34(tt(), N) -> activate(N) 957.19/297.29 , U331(tt(), N, XS) -> 957.19/297.29 U332(isNaturalKind(activate(N)), activate(XS)) 957.19/297.29 , U332(tt(), XS) -> U333(isLNat(activate(XS)), activate(XS)) 957.19/297.29 , U333(tt(), XS) -> U334(isLNatKind(activate(XS)), activate(XS)) 957.19/297.29 , U334(tt(), XS) -> activate(XS) 957.19/297.29 , U341(tt(), N, XS) -> 957.19/297.29 U342(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.19/297.29 , U342(tt(), N, XS) -> 957.19/297.29 U343(isLNat(activate(XS)), activate(N), activate(XS)) 957.19/297.29 , U343(tt(), N, XS) -> 957.19/297.29 U344(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.19/297.29 , U344(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS))) 957.19/297.29 , fst(X) -> n__fst(X) 957.19/297.29 , fst(pair(X, Y)) -> U21(isLNat(X), X, Y) 957.19/297.29 , U41(tt(), V1, V2) -> 957.19/297.29 U42(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.29 , U42(tt(), V1, V2) -> 957.19/297.29 U43(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.29 , U43(tt(), V1, V2) -> 957.19/297.29 U44(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.29 , U44(tt(), V1, V2) -> U45(isNatural(activate(V1)), activate(V2)) 957.19/297.29 , U45(tt(), V2) -> U46(isLNat(activate(V2))) 957.19/297.29 , U46(tt()) -> tt() 957.19/297.29 , U51(tt(), V1, V2) -> 957.19/297.29 U52(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.29 , U52(tt(), V1, V2) -> 957.19/297.29 U53(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.29 , U53(tt(), V1, V2) -> 957.19/297.29 U54(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.19/297.29 , U54(tt(), V1, V2) -> U55(isNatural(activate(V1)), activate(V2)) 957.19/297.29 , U55(tt(), V2) -> U56(isLNat(activate(V2))) 957.19/297.29 , U56(tt()) -> tt() 957.19/297.29 , U61(tt(), V1) -> U62(isPLNatKind(activate(V1)), activate(V1)) 957.19/297.29 , U62(tt(), V1) -> U63(isPLNat(activate(V1))) 957.19/297.29 , isPLNatKind(n__pair(V1, V2)) -> 957.19/297.29 U261(isLNatKind(activate(V1)), activate(V2)) 957.19/297.29 , isPLNatKind(n__splitAt(V1, V2)) -> 957.19/297.29 U271(isNaturalKind(activate(V1)), activate(V2)) 957.19/297.29 , U63(tt()) -> tt() 957.19/297.29 , isPLNat(n__pair(V1, V2)) -> 957.19/297.29 U241(isLNatKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.29 , isPLNat(n__splitAt(V1, V2)) -> 957.19/297.29 U251(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.19/297.29 , U71(tt(), V1) -> U72(isNaturalKind(activate(V1)), activate(V1)) 957.19/297.29 , U72(tt(), V1) -> U73(isNatural(activate(V1))) 957.19/297.29 , U73(tt()) -> tt() 957.19/297.29 , U81(tt(), V1) -> U82(isPLNatKind(activate(V1)), activate(V1)) 957.19/297.29 , U82(tt(), V1) -> U83(isPLNat(activate(V1))) 957.19/297.29 , U83(tt()) -> tt() 957.19/297.29 , U91(tt(), V1) -> U92(isLNatKind(activate(V1)), activate(V1)) 957.19/297.29 , U92(tt(), V1) -> U93(isLNat(activate(V1))) 957.19/297.29 , U93(tt()) -> tt() 957.19/297.29 , natsFrom(N) -> U281(isNatural(N), N) 957.19/297.29 , natsFrom(X) -> n__natsFrom(X) 957.19/297.29 , sel(N, XS) -> U291(isNatural(N), N, XS) 957.19/297.29 , sel(X1, X2) -> n__sel(X1, X2) 957.19/297.29 , 0() -> n__0() 957.19/297.29 , tail(X) -> n__tail(X) 957.19/297.29 , tail(cons(N, XS)) -> U331(isNatural(N), N, activate(XS)) 957.19/297.29 , take(N, XS) -> U341(isNatural(N), N, XS) 957.19/297.29 , take(X1, X2) -> n__take(X1, X2) } 957.19/297.29 Weak DPs: 957.19/297.29 { isNaturalKind^#(n__0()) -> c_3() 957.19/297.29 , isNaturalKind^#(n__head(V1)) -> 957.19/297.29 c_4(U211^#(isLNatKind(activate(V1)))) 957.19/297.29 , isNaturalKind^#(n__s(V1)) -> 957.19/297.29 c_5(U221^#(isNaturalKind(activate(V1)))) 957.19/297.29 , U211^#(tt()) -> c_79() 957.19/297.29 , U221^#(tt()) -> c_81() 957.19/297.29 , U231^#(tt(), V2) -> c_83(U232^#(isLNatKind(activate(V2)))) 957.19/297.29 , activate^#(n__nil()) -> c_9(nil^#()) 957.19/297.29 , activate^#(n__0()) -> c_16(0^#()) 957.19/297.29 , nil^#() -> c_122() 957.19/297.29 , 0^#() -> c_174() 957.19/297.29 , isLNatKind^#(n__natsFrom(V1)) -> 957.19/297.29 c_23(U141^#(isNaturalKind(activate(V1)))) 957.19/297.29 , isLNatKind^#(n__nil()) -> c_24() 957.19/297.29 , isLNatKind^#(n__fst(V1)) -> 957.19/297.29 c_27(U131^#(isPLNatKind(activate(V1)))) 957.19/297.29 , isLNatKind^#(n__snd(V1)) -> 957.19/297.29 c_28(U151^#(isPLNatKind(activate(V1)))) 957.19/297.29 , isLNatKind^#(n__tail(V1)) -> 957.19/297.29 c_29(U161^#(isLNatKind(activate(V1)))) 957.19/297.29 , U141^#(tt()) -> c_60() 957.19/297.29 , U111^#(tt(), V2) -> c_48(U112^#(isLNatKind(activate(V2)))) 957.19/297.29 , U121^#(tt(), V2) -> c_51(U122^#(isLNatKind(activate(V2)))) 957.19/297.29 , U131^#(tt()) -> c_54() 957.19/297.29 , U151^#(tt()) -> c_61() 957.19/297.29 , U161^#(tt()) -> c_62() 957.19/297.29 , U171^#(tt(), V2) -> c_63(U172^#(isLNatKind(activate(V2)))) 957.19/297.29 , U105^#(tt(), V2) -> c_32(U106^#(isLNat(activate(V2)))) 957.19/297.29 , U106^#(tt()) -> c_37() 957.19/297.29 , isNatural^#(n__0()) -> c_33() 957.19/297.29 , isLNat^#(n__nil()) -> c_39() 957.19/297.29 , U112^#(tt()) -> c_49() 957.19/297.29 , U122^#(tt()) -> c_52() 957.19/297.29 , U172^#(tt()) -> c_64() 957.19/297.29 , U182^#(tt(), V1) -> c_66(U183^#(isLNat(activate(V1)))) 957.19/297.29 , U183^#(tt()) -> c_67() 957.19/297.29 , U192^#(tt(), V1) -> c_69(U193^#(isNatural(activate(V1)))) 957.19/297.29 , U193^#(tt()) -> c_70() 957.19/297.29 , U205^#(tt(), V2) -> c_75(U206^#(isLNat(activate(V2)))) 957.19/297.29 , U206^#(tt()) -> c_76() 957.19/297.29 , U232^#(tt()) -> c_84() 957.19/297.29 , U245^#(tt(), V2) -> c_89(U246^#(isLNat(activate(V2)))) 957.19/297.29 , U246^#(tt()) -> c_90() 957.19/297.29 , U255^#(tt(), V2) -> c_95(U256^#(isLNat(activate(V2)))) 957.19/297.29 , U256^#(tt()) -> c_96() 957.19/297.29 , U261^#(tt(), V2) -> c_97(U262^#(isLNatKind(activate(V2)))) 957.19/297.29 , U262^#(tt()) -> c_98() 957.19/297.29 , U271^#(tt(), V2) -> c_99(U272^#(isLNatKind(activate(V2)))) 957.19/297.29 , U272^#(tt()) -> c_100() 957.19/297.29 , U45^#(tt(), V2) -> c_146(U46^#(isLNat(activate(V2)))) 957.19/297.29 , U46^#(tt()) -> c_147() 957.19/297.30 , U55^#(tt(), V2) -> c_152(U56^#(isLNat(activate(V2)))) 957.19/297.30 , U56^#(tt()) -> c_153() 957.19/297.30 , U62^#(tt(), V1) -> c_155(U63^#(isPLNat(activate(V1)))) 957.19/297.30 , U63^#(tt()) -> c_158() 957.19/297.30 , U72^#(tt(), V1) -> c_162(U73^#(isNatural(activate(V1)))) 957.19/297.30 , U73^#(tt()) -> c_163() 957.19/297.30 , U82^#(tt(), V1) -> c_165(U83^#(isPLNat(activate(V1)))) 957.19/297.30 , U83^#(tt()) -> c_166() 957.19/297.30 , U92^#(tt(), V1) -> c_168(U93^#(isLNat(activate(V1)))) 957.19/297.30 , U93^#(tt()) -> c_169() } 957.19/297.30 Obligation: 957.19/297.30 runtime complexity 957.19/297.30 Answer: 957.19/297.30 MAYBE 957.19/297.30 957.19/297.30 We estimate the number of application of 957.19/297.30 {4,40,41,42,43,47,48,57,60,61,62,72,80,84,115,118,119,120} by 957.19/297.30 applications of 957.19/297.30 Pre({4,40,41,42,43,47,48,57,60,61,62,72,80,84,115,118,119,120}) = 957.19/297.30 {3,5,19,21,22,23,25,27,30,31,33,35,36,37,44,45,50,53,54,55,71,79,83,114,117}. 957.19/297.30 Here rules are labeled as follows: 957.19/297.30 957.19/297.30 DPs: 957.19/297.30 { 1: U101^#(tt(), V1, V2) -> 957.19/297.30 c_1(U102^#(isNaturalKind(activate(V1)), 957.19/297.30 activate(V1), 957.19/297.30 activate(V2))) 957.19/297.30 , 2: U102^#(tt(), V1, V2) -> 957.19/297.30 c_2(U103^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.30 , 3: U103^#(tt(), V1, V2) -> 957.19/297.30 c_22(U104^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.19/297.30 , 4: isNaturalKind^#(n__sel(V1, V2)) -> 957.19/297.30 c_6(U231^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.30 , 5: activate^#(X) -> c_7(X) 957.19/297.30 , 6: activate^#(n__natsFrom(X)) -> c_8(natsFrom^#(X)) 957.19/297.30 , 7: activate^#(n__afterNth(X1, X2)) -> c_10(afterNth^#(X1, X2)) 957.19/297.30 , 8: activate^#(n__cons(X1, X2)) -> c_11(cons^#(X1, X2)) 957.19/297.30 , 9: activate^#(n__fst(X)) -> c_12(fst^#(X)) 957.19/297.30 , 10: activate^#(n__snd(X)) -> c_13(snd^#(X)) 957.19/297.30 , 11: activate^#(n__tail(X)) -> c_14(tail^#(X)) 957.19/297.30 , 12: activate^#(n__take(X1, X2)) -> c_15(take^#(X1, X2)) 957.19/297.30 , 13: activate^#(n__head(X)) -> c_17(head^#(X)) 957.19/297.30 , 14: activate^#(n__s(X)) -> c_18(s^#(X)) 957.19/297.30 , 15: activate^#(n__sel(X1, X2)) -> c_19(sel^#(X1, X2)) 957.19/297.30 , 16: activate^#(n__pair(X1, X2)) -> c_20(pair^#(X1, X2)) 957.19/297.30 , 17: activate^#(n__splitAt(X1, X2)) -> c_21(splitAt^#(X1, X2)) 957.19/297.30 , 18: natsFrom^#(N) -> c_170(U281^#(isNatural(N), N)) 957.19/297.30 , 19: natsFrom^#(X) -> c_171(X) 957.19/297.30 , 20: afterNth^#(N, XS) -> c_111(U11^#(isNatural(N), N, XS)) 957.19/297.30 , 21: afterNth^#(X1, X2) -> c_112(X1, X2) 957.19/297.30 , 22: cons^#(X1, X2) -> c_103(X1, X2) 957.19/297.30 , 23: fst^#(X) -> c_140(X) 957.19/297.30 , 24: fst^#(pair(X, Y)) -> c_141(U21^#(isLNat(X), X, Y)) 957.19/297.30 , 25: snd^#(X) -> c_55(X) 957.19/297.30 , 26: snd^#(pair(X, Y)) -> c_56(U301^#(isLNat(X), X, Y)) 957.19/297.30 , 27: tail^#(X) -> c_175(X) 957.19/297.30 , 28: tail^#(cons(N, XS)) -> 957.19/297.30 c_176(U331^#(isNatural(N), N, activate(XS))) 957.19/297.30 , 29: take^#(N, XS) -> c_177(U341^#(isNatural(N), N, XS)) 957.19/297.30 , 30: take^#(X1, X2) -> c_178(X1, X2) 957.19/297.30 , 31: head^#(X) -> c_109(X) 957.19/297.30 , 32: head^#(cons(N, XS)) -> 957.19/297.30 c_110(U31^#(isNatural(N), N, activate(XS))) 957.19/297.30 , 33: s^#(X) -> c_104(X) 957.19/297.30 , 34: sel^#(N, XS) -> c_172(U291^#(isNatural(N), N, XS)) 957.19/297.30 , 35: sel^#(X1, X2) -> c_173(X1, X2) 957.19/297.30 , 36: pair^#(X1, X2) -> c_121(X1, X2) 957.19/297.30 , 37: splitAt^#(X1, X2) -> c_57(X1, X2) 957.19/297.30 , 38: splitAt^#(s(N), cons(X, XS)) -> 957.19/297.30 c_58(U321^#(isNatural(N), N, X, activate(XS))) 957.19/297.30 , 39: splitAt^#(0(), XS) -> c_59(U311^#(isLNat(XS), XS)) 957.19/297.30 , 40: U104^#(tt(), V1, V2) -> 957.19/297.30 c_31(U105^#(isNatural(activate(V1)), activate(V2))) 957.19/297.30 , 41: isLNatKind^#(n__afterNth(V1, V2)) -> 957.19/297.30 c_25(U111^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.30 , 42: isLNatKind^#(n__cons(V1, V2)) -> 957.19/297.30 c_26(U121^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.30 , 43: isLNatKind^#(n__take(V1, V2)) -> 957.19/297.30 c_30(U171^#(isNaturalKind(activate(V1)), activate(V2))) 957.19/297.30 , 44: isNatural^#(n__head(V1)) -> 957.19/297.30 c_34(U181^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.30 , 45: isNatural^#(n__s(V1)) -> 957.19/297.30 c_35(U191^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.30 , 46: isNatural^#(n__sel(V1, V2)) -> 957.19/297.30 c_36(U201^#(isNaturalKind(activate(V1)), 957.19/297.30 activate(V1), 957.19/297.30 activate(V2))) 957.19/297.30 , 47: U181^#(tt(), V1) -> 957.19/297.30 c_65(U182^#(isLNatKind(activate(V1)), activate(V1))) 957.19/297.30 , 48: U191^#(tt(), V1) -> 957.19/297.30 c_68(U192^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.30 , 49: U201^#(tt(), V1, V2) -> 957.19/297.30 c_71(U202^#(isNaturalKind(activate(V1)), 957.19/297.30 activate(V1), 957.19/297.30 activate(V2))) 957.19/297.30 , 50: isLNat^#(n__natsFrom(V1)) -> 957.19/297.30 c_38(U71^#(isNaturalKind(activate(V1)), activate(V1))) 957.19/297.30 , 51: isLNat^#(n__afterNth(V1, V2)) -> 957.19/297.30 c_40(U41^#(isNaturalKind(activate(V1)), 957.19/297.30 activate(V1), 957.19/297.30 activate(V2))) 957.19/297.30 , 52: isLNat^#(n__cons(V1, V2)) -> 957.19/297.30 c_41(U51^#(isNaturalKind(activate(V1)), 957.19/297.30 activate(V1), 957.19/297.30 activate(V2))) 957.47/297.30 , 53: isLNat^#(n__fst(V1)) -> 957.47/297.30 c_42(U61^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.30 , 54: isLNat^#(n__snd(V1)) -> 957.47/297.30 c_43(U81^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.30 , 55: isLNat^#(n__tail(V1)) -> 957.47/297.30 c_44(U91^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.30 , 56: isLNat^#(n__take(V1, V2)) -> 957.47/297.30 c_45(U101^#(isNaturalKind(activate(V1)), 957.47/297.30 activate(V1), 957.47/297.30 activate(V2))) 957.47/297.30 , 57: U71^#(tt(), V1) -> 957.47/297.30 c_161(U72^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.30 , 58: U41^#(tt(), V1, V2) -> 957.47/297.30 c_142(U42^#(isNaturalKind(activate(V1)), 957.47/297.30 activate(V1), 957.47/297.30 activate(V2))) 957.47/297.30 , 59: U51^#(tt(), V1, V2) -> 957.47/297.30 c_148(U52^#(isNaturalKind(activate(V1)), 957.47/297.30 activate(V1), 957.47/297.30 activate(V2))) 957.47/297.30 , 60: U61^#(tt(), V1) -> 957.47/297.30 c_154(U62^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.30 , 61: U81^#(tt(), V1) -> 957.47/297.30 c_164(U82^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.30 , 62: U91^#(tt(), V1) -> 957.47/297.30 c_167(U92^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.30 , 63: U11^#(tt(), N, XS) -> 957.47/297.30 c_46(U12^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.47/297.30 , 64: U12^#(tt(), N, XS) -> 957.47/297.30 c_47(U13^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.30 , 65: U13^#(tt(), N, XS) -> 957.47/297.30 c_50(U14^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.30 , 66: U14^#(tt(), N, XS) -> 957.47/297.30 c_53(snd^#(splitAt(activate(N), activate(XS)))) 957.47/297.30 , 67: U301^#(tt(), X, Y) -> 957.47/297.30 c_113(U302^#(isLNatKind(activate(X)), activate(Y))) 957.47/297.30 , 68: U321^#(tt(), N, X, XS) -> 957.47/297.30 c_124(U322^#(isNaturalKind(activate(N)), 957.47/297.30 activate(N), 957.47/297.30 activate(X), 957.47/297.30 activate(XS))) 957.47/297.30 , 69: U311^#(tt(), XS) -> 957.47/297.30 c_119(U312^#(isLNatKind(activate(XS)), activate(XS))) 957.47/297.30 , 70: U202^#(tt(), V1, V2) -> 957.47/297.30 c_72(U203^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.30 , 71: U203^#(tt(), V1, V2) -> 957.47/297.30 c_73(U204^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.30 , 72: U204^#(tt(), V1, V2) -> 957.47/297.30 c_74(U205^#(isNatural(activate(V1)), activate(V2))) 957.47/297.30 , 73: U21^#(tt(), X, Y) -> 957.47/297.30 c_77(U22^#(isLNatKind(activate(X)), activate(X), activate(Y))) 957.47/297.30 , 74: U22^#(tt(), X, Y) -> 957.47/297.30 c_78(U23^#(isLNat(activate(Y)), activate(X), activate(Y))) 957.47/297.30 , 75: U23^#(tt(), X, Y) -> 957.47/297.30 c_80(U24^#(isLNatKind(activate(Y)), activate(X))) 957.47/297.30 , 76: U24^#(tt(), X) -> c_82(activate^#(X)) 957.47/297.30 , 77: U241^#(tt(), V1, V2) -> 957.47/297.30 c_85(U242^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.47/297.30 , 78: U242^#(tt(), V1, V2) -> 957.47/297.30 c_86(U243^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.30 , 79: U243^#(tt(), V1, V2) -> 957.47/297.30 c_87(U244^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.30 , 80: U244^#(tt(), V1, V2) -> 957.47/297.30 c_88(U245^#(isLNat(activate(V1)), activate(V2))) 957.47/297.30 , 81: U251^#(tt(), V1, V2) -> 957.47/297.30 c_91(U252^#(isNaturalKind(activate(V1)), 957.47/297.30 activate(V1), 957.47/297.30 activate(V2))) 957.47/297.30 , 82: U252^#(tt(), V1, V2) -> 957.47/297.30 c_92(U253^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.30 , 83: U253^#(tt(), V1, V2) -> 957.47/297.30 c_93(U254^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.30 , 84: U254^#(tt(), V1, V2) -> 957.47/297.30 c_94(U255^#(isNatural(activate(V1)), activate(V2))) 957.47/297.30 , 85: U281^#(tt(), N) -> 957.47/297.30 c_101(U282^#(isNaturalKind(activate(N)), activate(N))) 957.47/297.30 , 86: U282^#(tt(), N) -> 957.47/297.30 c_102(cons^#(activate(N), n__natsFrom(s(activate(N))))) 957.47/297.30 , 87: U291^#(tt(), N, XS) -> 957.47/297.30 c_105(U292^#(isNaturalKind(activate(N)), 957.47/297.30 activate(N), 957.47/297.30 activate(XS))) 957.47/297.30 , 88: U292^#(tt(), N, XS) -> 957.47/297.30 c_106(U293^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.30 , 89: U293^#(tt(), N, XS) -> 957.47/297.30 c_107(U294^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.30 , 90: U294^#(tt(), N, XS) -> 957.47/297.30 c_108(head^#(afterNth(activate(N), activate(XS)))) 957.47/297.30 , 91: U31^#(tt(), N, XS) -> 957.47/297.30 c_117(U32^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.47/297.30 , 92: U302^#(tt(), Y) -> 957.47/297.30 c_114(U303^#(isLNat(activate(Y)), activate(Y))) 957.47/297.30 , 93: U303^#(tt(), Y) -> 957.47/297.30 c_115(U304^#(isLNatKind(activate(Y)), activate(Y))) 957.47/297.30 , 94: U304^#(tt(), Y) -> c_116(activate^#(Y)) 957.47/297.30 , 95: U32^#(tt(), N, XS) -> 957.47/297.30 c_118(U33^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.30 , 96: U33^#(tt(), N, XS) -> 957.47/297.30 c_123(U34^#(isLNatKind(activate(XS)), activate(N))) 957.47/297.30 , 97: U312^#(tt(), XS) -> c_120(pair^#(nil(), activate(XS))) 957.47/297.30 , 98: U34^#(tt(), N) -> c_131(activate^#(N)) 957.47/297.30 , 99: U322^#(tt(), N, X, XS) -> 957.47/297.30 c_125(U323^#(isNatural(activate(X)), 957.47/297.30 activate(N), 957.47/297.30 activate(X), 957.47/297.30 activate(XS))) 957.47/297.30 , 100: U323^#(tt(), N, X, XS) -> 957.47/297.30 c_126(U324^#(isNaturalKind(activate(X)), 957.47/297.30 activate(N), 957.47/297.30 activate(X), 957.47/297.30 activate(XS))) 957.47/297.30 , 101: U324^#(tt(), N, X, XS) -> 957.47/297.30 c_127(U325^#(isLNat(activate(XS)), 957.47/297.30 activate(N), 957.47/297.30 activate(X), 957.47/297.30 activate(XS))) 957.47/297.30 , 102: U325^#(tt(), N, X, XS) -> 957.47/297.30 c_128(U326^#(isLNatKind(activate(XS)), 957.47/297.30 activate(N), 957.47/297.30 activate(X), 957.47/297.30 activate(XS))) 957.47/297.30 , 103: U326^#(tt(), N, X, XS) -> 957.47/297.30 c_129(U327^#(splitAt(activate(N), activate(XS)), activate(X))) 957.47/297.30 , 104: U327^#(pair(YS, ZS), X) -> 957.47/297.30 c_130(pair^#(cons(activate(X), YS), ZS)) 957.47/297.30 , 105: U331^#(tt(), N, XS) -> 957.47/297.30 c_132(U332^#(isNaturalKind(activate(N)), activate(XS))) 957.47/297.30 , 106: U332^#(tt(), XS) -> 957.47/297.30 c_133(U333^#(isLNat(activate(XS)), activate(XS))) 957.47/297.30 , 107: U333^#(tt(), XS) -> 957.47/297.30 c_134(U334^#(isLNatKind(activate(XS)), activate(XS))) 957.47/297.30 , 108: U334^#(tt(), XS) -> c_135(activate^#(XS)) 957.47/297.30 , 109: U341^#(tt(), N, XS) -> 957.47/297.30 c_136(U342^#(isNaturalKind(activate(N)), 957.47/297.30 activate(N), 957.47/297.30 activate(XS))) 957.47/297.30 , 110: U342^#(tt(), N, XS) -> 957.47/297.30 c_137(U343^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.30 , 111: U343^#(tt(), N, XS) -> 957.47/297.30 c_138(U344^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.30 , 112: U344^#(tt(), N, XS) -> 957.47/297.30 c_139(fst^#(splitAt(activate(N), activate(XS)))) 957.47/297.30 , 113: U42^#(tt(), V1, V2) -> 957.47/297.30 c_143(U43^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.30 , 114: U43^#(tt(), V1, V2) -> 957.47/297.30 c_144(U44^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.30 , 115: U44^#(tt(), V1, V2) -> 957.47/297.30 c_145(U45^#(isNatural(activate(V1)), activate(V2))) 957.47/297.30 , 116: U52^#(tt(), V1, V2) -> 957.47/297.30 c_149(U53^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.30 , 117: U53^#(tt(), V1, V2) -> 957.47/297.30 c_150(U54^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.30 , 118: U54^#(tt(), V1, V2) -> 957.47/297.30 c_151(U55^#(isNatural(activate(V1)), activate(V2))) 957.47/297.30 , 119: isPLNatKind^#(n__pair(V1, V2)) -> 957.47/297.30 c_156(U261^#(isLNatKind(activate(V1)), activate(V2))) 957.47/297.30 , 120: isPLNatKind^#(n__splitAt(V1, V2)) -> 957.47/297.30 c_157(U271^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.30 , 121: isPLNat^#(n__pair(V1, V2)) -> 957.47/297.30 c_159(U241^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.47/297.30 , 122: isPLNat^#(n__splitAt(V1, V2)) -> 957.47/297.30 c_160(U251^#(isNaturalKind(activate(V1)), 957.47/297.30 activate(V1), 957.47/297.30 activate(V2))) 957.47/297.30 , 123: isNaturalKind^#(n__0()) -> c_3() 957.47/297.30 , 124: isNaturalKind^#(n__head(V1)) -> 957.47/297.30 c_4(U211^#(isLNatKind(activate(V1)))) 957.47/297.30 , 125: isNaturalKind^#(n__s(V1)) -> 957.47/297.30 c_5(U221^#(isNaturalKind(activate(V1)))) 957.47/297.30 , 126: U211^#(tt()) -> c_79() 957.47/297.30 , 127: U221^#(tt()) -> c_81() 957.47/297.30 , 128: U231^#(tt(), V2) -> c_83(U232^#(isLNatKind(activate(V2)))) 957.47/297.30 , 129: activate^#(n__nil()) -> c_9(nil^#()) 957.47/297.30 , 130: activate^#(n__0()) -> c_16(0^#()) 957.47/297.30 , 131: nil^#() -> c_122() 957.47/297.30 , 132: 0^#() -> c_174() 957.47/297.30 , 133: isLNatKind^#(n__natsFrom(V1)) -> 957.47/297.30 c_23(U141^#(isNaturalKind(activate(V1)))) 957.47/297.30 , 134: isLNatKind^#(n__nil()) -> c_24() 957.47/297.30 , 135: isLNatKind^#(n__fst(V1)) -> 957.47/297.30 c_27(U131^#(isPLNatKind(activate(V1)))) 957.47/297.30 , 136: isLNatKind^#(n__snd(V1)) -> 957.47/297.30 c_28(U151^#(isPLNatKind(activate(V1)))) 957.47/297.30 , 137: isLNatKind^#(n__tail(V1)) -> 957.47/297.30 c_29(U161^#(isLNatKind(activate(V1)))) 957.47/297.30 , 138: U141^#(tt()) -> c_60() 957.47/297.30 , 139: U111^#(tt(), V2) -> c_48(U112^#(isLNatKind(activate(V2)))) 957.47/297.30 , 140: U121^#(tt(), V2) -> c_51(U122^#(isLNatKind(activate(V2)))) 957.47/297.30 , 141: U131^#(tt()) -> c_54() 957.47/297.30 , 142: U151^#(tt()) -> c_61() 957.47/297.30 , 143: U161^#(tt()) -> c_62() 957.47/297.30 , 144: U171^#(tt(), V2) -> c_63(U172^#(isLNatKind(activate(V2)))) 957.47/297.30 , 145: U105^#(tt(), V2) -> c_32(U106^#(isLNat(activate(V2)))) 957.47/297.30 , 146: U106^#(tt()) -> c_37() 957.47/297.30 , 147: isNatural^#(n__0()) -> c_33() 957.47/297.30 , 148: isLNat^#(n__nil()) -> c_39() 957.47/297.30 , 149: U112^#(tt()) -> c_49() 957.47/297.30 , 150: U122^#(tt()) -> c_52() 957.47/297.30 , 151: U172^#(tt()) -> c_64() 957.47/297.30 , 152: U182^#(tt(), V1) -> c_66(U183^#(isLNat(activate(V1)))) 957.47/297.30 , 153: U183^#(tt()) -> c_67() 957.47/297.30 , 154: U192^#(tt(), V1) -> c_69(U193^#(isNatural(activate(V1)))) 957.47/297.30 , 155: U193^#(tt()) -> c_70() 957.47/297.30 , 156: U205^#(tt(), V2) -> c_75(U206^#(isLNat(activate(V2)))) 957.47/297.30 , 157: U206^#(tt()) -> c_76() 957.47/297.30 , 158: U232^#(tt()) -> c_84() 957.47/297.30 , 159: U245^#(tt(), V2) -> c_89(U246^#(isLNat(activate(V2)))) 957.47/297.30 , 160: U246^#(tt()) -> c_90() 957.47/297.30 , 161: U255^#(tt(), V2) -> c_95(U256^#(isLNat(activate(V2)))) 957.47/297.30 , 162: U256^#(tt()) -> c_96() 957.47/297.30 , 163: U261^#(tt(), V2) -> c_97(U262^#(isLNatKind(activate(V2)))) 957.47/297.30 , 164: U262^#(tt()) -> c_98() 957.47/297.30 , 165: U271^#(tt(), V2) -> c_99(U272^#(isLNatKind(activate(V2)))) 957.47/297.30 , 166: U272^#(tt()) -> c_100() 957.47/297.30 , 167: U45^#(tt(), V2) -> c_146(U46^#(isLNat(activate(V2)))) 957.47/297.30 , 168: U46^#(tt()) -> c_147() 957.47/297.30 , 169: U55^#(tt(), V2) -> c_152(U56^#(isLNat(activate(V2)))) 957.47/297.30 , 170: U56^#(tt()) -> c_153() 957.47/297.30 , 171: U62^#(tt(), V1) -> c_155(U63^#(isPLNat(activate(V1)))) 957.47/297.30 , 172: U63^#(tt()) -> c_158() 957.47/297.30 , 173: U72^#(tt(), V1) -> c_162(U73^#(isNatural(activate(V1)))) 957.47/297.30 , 174: U73^#(tt()) -> c_163() 957.47/297.30 , 175: U82^#(tt(), V1) -> c_165(U83^#(isPLNat(activate(V1)))) 957.47/297.30 , 176: U83^#(tt()) -> c_166() 957.47/297.30 , 177: U92^#(tt(), V1) -> c_168(U93^#(isLNat(activate(V1)))) 957.47/297.30 , 178: U93^#(tt()) -> c_169() } 957.47/297.30 957.47/297.30 We are left with following problem, upon which TcT provides the 957.47/297.30 certificate MAYBE. 957.47/297.30 957.47/297.30 Strict DPs: 957.47/297.30 { U101^#(tt(), V1, V2) -> 957.47/297.30 c_1(U102^#(isNaturalKind(activate(V1)), 957.47/297.30 activate(V1), 957.47/297.30 activate(V2))) 957.47/297.30 , U102^#(tt(), V1, V2) -> 957.47/297.30 c_2(U103^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.30 , U103^#(tt(), V1, V2) -> 957.47/297.30 c_22(U104^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.30 , activate^#(X) -> c_7(X) 957.47/297.30 , activate^#(n__natsFrom(X)) -> c_8(natsFrom^#(X)) 957.47/297.30 , activate^#(n__afterNth(X1, X2)) -> c_10(afterNth^#(X1, X2)) 957.47/297.30 , activate^#(n__cons(X1, X2)) -> c_11(cons^#(X1, X2)) 957.47/297.30 , activate^#(n__fst(X)) -> c_12(fst^#(X)) 957.47/297.30 , activate^#(n__snd(X)) -> c_13(snd^#(X)) 957.47/297.30 , activate^#(n__tail(X)) -> c_14(tail^#(X)) 957.47/297.30 , activate^#(n__take(X1, X2)) -> c_15(take^#(X1, X2)) 957.47/297.30 , activate^#(n__head(X)) -> c_17(head^#(X)) 957.47/297.30 , activate^#(n__s(X)) -> c_18(s^#(X)) 957.47/297.30 , activate^#(n__sel(X1, X2)) -> c_19(sel^#(X1, X2)) 957.47/297.30 , activate^#(n__pair(X1, X2)) -> c_20(pair^#(X1, X2)) 957.47/297.30 , activate^#(n__splitAt(X1, X2)) -> c_21(splitAt^#(X1, X2)) 957.47/297.30 , natsFrom^#(N) -> c_170(U281^#(isNatural(N), N)) 957.47/297.30 , natsFrom^#(X) -> c_171(X) 957.47/297.30 , afterNth^#(N, XS) -> c_111(U11^#(isNatural(N), N, XS)) 957.47/297.30 , afterNth^#(X1, X2) -> c_112(X1, X2) 957.47/297.30 , cons^#(X1, X2) -> c_103(X1, X2) 957.47/297.30 , fst^#(X) -> c_140(X) 957.47/297.30 , fst^#(pair(X, Y)) -> c_141(U21^#(isLNat(X), X, Y)) 957.47/297.30 , snd^#(X) -> c_55(X) 957.47/297.30 , snd^#(pair(X, Y)) -> c_56(U301^#(isLNat(X), X, Y)) 957.47/297.30 , tail^#(X) -> c_175(X) 957.47/297.30 , tail^#(cons(N, XS)) -> 957.47/297.30 c_176(U331^#(isNatural(N), N, activate(XS))) 957.47/297.30 , take^#(N, XS) -> c_177(U341^#(isNatural(N), N, XS)) 957.47/297.30 , take^#(X1, X2) -> c_178(X1, X2) 957.47/297.30 , head^#(X) -> c_109(X) 957.47/297.30 , head^#(cons(N, XS)) -> 957.47/297.30 c_110(U31^#(isNatural(N), N, activate(XS))) 957.47/297.30 , s^#(X) -> c_104(X) 957.47/297.30 , sel^#(N, XS) -> c_172(U291^#(isNatural(N), N, XS)) 957.47/297.30 , sel^#(X1, X2) -> c_173(X1, X2) 957.47/297.30 , pair^#(X1, X2) -> c_121(X1, X2) 957.47/297.30 , splitAt^#(X1, X2) -> c_57(X1, X2) 957.47/297.30 , splitAt^#(s(N), cons(X, XS)) -> 957.47/297.30 c_58(U321^#(isNatural(N), N, X, activate(XS))) 957.47/297.30 , splitAt^#(0(), XS) -> c_59(U311^#(isLNat(XS), XS)) 957.47/297.30 , isNatural^#(n__head(V1)) -> 957.47/297.30 c_34(U181^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.30 , isNatural^#(n__s(V1)) -> 957.47/297.30 c_35(U191^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.30 , isNatural^#(n__sel(V1, V2)) -> 957.47/297.30 c_36(U201^#(isNaturalKind(activate(V1)), 957.47/297.30 activate(V1), 957.47/297.30 activate(V2))) 957.47/297.30 , U201^#(tt(), V1, V2) -> 957.47/297.30 c_71(U202^#(isNaturalKind(activate(V1)), 957.47/297.30 activate(V1), 957.47/297.30 activate(V2))) 957.47/297.30 , isLNat^#(n__natsFrom(V1)) -> 957.47/297.30 c_38(U71^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.30 , isLNat^#(n__afterNth(V1, V2)) -> 957.47/297.30 c_40(U41^#(isNaturalKind(activate(V1)), 957.47/297.30 activate(V1), 957.47/297.30 activate(V2))) 957.47/297.30 , isLNat^#(n__cons(V1, V2)) -> 957.47/297.30 c_41(U51^#(isNaturalKind(activate(V1)), 957.47/297.30 activate(V1), 957.47/297.30 activate(V2))) 957.47/297.30 , isLNat^#(n__fst(V1)) -> 957.47/297.30 c_42(U61^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.30 , isLNat^#(n__snd(V1)) -> 957.47/297.30 c_43(U81^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.30 , isLNat^#(n__tail(V1)) -> 957.47/297.30 c_44(U91^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.30 , isLNat^#(n__take(V1, V2)) -> 957.47/297.30 c_45(U101^#(isNaturalKind(activate(V1)), 957.47/297.30 activate(V1), 957.47/297.30 activate(V2))) 957.47/297.30 , U41^#(tt(), V1, V2) -> 957.47/297.30 c_142(U42^#(isNaturalKind(activate(V1)), 957.47/297.30 activate(V1), 957.47/297.30 activate(V2))) 957.47/297.30 , U51^#(tt(), V1, V2) -> 957.47/297.30 c_148(U52^#(isNaturalKind(activate(V1)), 957.47/297.30 activate(V1), 957.47/297.30 activate(V2))) 957.47/297.30 , U11^#(tt(), N, XS) -> 957.47/297.30 c_46(U12^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.47/297.30 , U12^#(tt(), N, XS) -> 957.47/297.30 c_47(U13^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.30 , U13^#(tt(), N, XS) -> 957.47/297.30 c_50(U14^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.30 , U14^#(tt(), N, XS) -> 957.47/297.30 c_53(snd^#(splitAt(activate(N), activate(XS)))) 957.47/297.30 , U301^#(tt(), X, Y) -> 957.47/297.30 c_113(U302^#(isLNatKind(activate(X)), activate(Y))) 957.47/297.30 , U321^#(tt(), N, X, XS) -> 957.47/297.30 c_124(U322^#(isNaturalKind(activate(N)), 957.47/297.30 activate(N), 957.47/297.30 activate(X), 957.47/297.30 activate(XS))) 957.47/297.30 , U311^#(tt(), XS) -> 957.47/297.30 c_119(U312^#(isLNatKind(activate(XS)), activate(XS))) 957.47/297.30 , U202^#(tt(), V1, V2) -> 957.47/297.30 c_72(U203^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.30 , U203^#(tt(), V1, V2) -> 957.47/297.30 c_73(U204^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.30 , U21^#(tt(), X, Y) -> 957.47/297.30 c_77(U22^#(isLNatKind(activate(X)), activate(X), activate(Y))) 957.47/297.31 , U22^#(tt(), X, Y) -> 957.47/297.31 c_78(U23^#(isLNat(activate(Y)), activate(X), activate(Y))) 957.47/297.31 , U23^#(tt(), X, Y) -> 957.47/297.31 c_80(U24^#(isLNatKind(activate(Y)), activate(X))) 957.47/297.31 , U24^#(tt(), X) -> c_82(activate^#(X)) 957.47/297.31 , U241^#(tt(), V1, V2) -> 957.47/297.31 c_85(U242^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.47/297.31 , U242^#(tt(), V1, V2) -> 957.47/297.31 c_86(U243^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.31 , U243^#(tt(), V1, V2) -> 957.47/297.31 c_87(U244^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.31 , U251^#(tt(), V1, V2) -> 957.47/297.31 c_91(U252^#(isNaturalKind(activate(V1)), 957.47/297.31 activate(V1), 957.47/297.31 activate(V2))) 957.47/297.31 , U252^#(tt(), V1, V2) -> 957.47/297.31 c_92(U253^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.31 , U253^#(tt(), V1, V2) -> 957.47/297.31 c_93(U254^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.31 , U281^#(tt(), N) -> 957.47/297.31 c_101(U282^#(isNaturalKind(activate(N)), activate(N))) 957.47/297.31 , U282^#(tt(), N) -> 957.47/297.31 c_102(cons^#(activate(N), n__natsFrom(s(activate(N))))) 957.47/297.31 , U291^#(tt(), N, XS) -> 957.47/297.31 c_105(U292^#(isNaturalKind(activate(N)), 957.47/297.31 activate(N), 957.47/297.31 activate(XS))) 957.47/297.31 , U292^#(tt(), N, XS) -> 957.47/297.31 c_106(U293^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.31 , U293^#(tt(), N, XS) -> 957.47/297.31 c_107(U294^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.31 , U294^#(tt(), N, XS) -> 957.47/297.31 c_108(head^#(afterNth(activate(N), activate(XS)))) 957.47/297.31 , U31^#(tt(), N, XS) -> 957.47/297.31 c_117(U32^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.47/297.31 , U302^#(tt(), Y) -> 957.47/297.31 c_114(U303^#(isLNat(activate(Y)), activate(Y))) 957.47/297.31 , U303^#(tt(), Y) -> 957.47/297.31 c_115(U304^#(isLNatKind(activate(Y)), activate(Y))) 957.47/297.31 , U304^#(tt(), Y) -> c_116(activate^#(Y)) 957.47/297.31 , U32^#(tt(), N, XS) -> 957.47/297.31 c_118(U33^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.31 , U33^#(tt(), N, XS) -> 957.47/297.31 c_123(U34^#(isLNatKind(activate(XS)), activate(N))) 957.47/297.31 , U312^#(tt(), XS) -> c_120(pair^#(nil(), activate(XS))) 957.47/297.31 , U34^#(tt(), N) -> c_131(activate^#(N)) 957.47/297.31 , U322^#(tt(), N, X, XS) -> 957.47/297.31 c_125(U323^#(isNatural(activate(X)), 957.47/297.31 activate(N), 957.47/297.31 activate(X), 957.47/297.31 activate(XS))) 957.47/297.31 , U323^#(tt(), N, X, XS) -> 957.47/297.31 c_126(U324^#(isNaturalKind(activate(X)), 957.47/297.31 activate(N), 957.47/297.31 activate(X), 957.47/297.31 activate(XS))) 957.47/297.31 , U324^#(tt(), N, X, XS) -> 957.47/297.31 c_127(U325^#(isLNat(activate(XS)), 957.47/297.31 activate(N), 957.47/297.31 activate(X), 957.47/297.31 activate(XS))) 957.47/297.31 , U325^#(tt(), N, X, XS) -> 957.47/297.31 c_128(U326^#(isLNatKind(activate(XS)), 957.47/297.31 activate(N), 957.47/297.31 activate(X), 957.47/297.31 activate(XS))) 957.47/297.31 , U326^#(tt(), N, X, XS) -> 957.47/297.31 c_129(U327^#(splitAt(activate(N), activate(XS)), activate(X))) 957.47/297.31 , U327^#(pair(YS, ZS), X) -> 957.47/297.31 c_130(pair^#(cons(activate(X), YS), ZS)) 957.47/297.31 , U331^#(tt(), N, XS) -> 957.47/297.31 c_132(U332^#(isNaturalKind(activate(N)), activate(XS))) 957.47/297.31 , U332^#(tt(), XS) -> 957.47/297.31 c_133(U333^#(isLNat(activate(XS)), activate(XS))) 957.47/297.31 , U333^#(tt(), XS) -> 957.47/297.31 c_134(U334^#(isLNatKind(activate(XS)), activate(XS))) 957.47/297.31 , U334^#(tt(), XS) -> c_135(activate^#(XS)) 957.47/297.31 , U341^#(tt(), N, XS) -> 957.47/297.31 c_136(U342^#(isNaturalKind(activate(N)), 957.47/297.31 activate(N), 957.47/297.31 activate(XS))) 957.47/297.31 , U342^#(tt(), N, XS) -> 957.47/297.31 c_137(U343^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.31 , U343^#(tt(), N, XS) -> 957.47/297.31 c_138(U344^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.31 , U344^#(tt(), N, XS) -> 957.47/297.31 c_139(fst^#(splitAt(activate(N), activate(XS)))) 957.47/297.31 , U42^#(tt(), V1, V2) -> 957.47/297.31 c_143(U43^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.31 , U43^#(tt(), V1, V2) -> 957.47/297.31 c_144(U44^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.31 , U52^#(tt(), V1, V2) -> 957.47/297.31 c_149(U53^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.31 , U53^#(tt(), V1, V2) -> 957.47/297.31 c_150(U54^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.31 , isPLNat^#(n__pair(V1, V2)) -> 957.47/297.31 c_159(U241^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.47/297.31 , isPLNat^#(n__splitAt(V1, V2)) -> 957.47/297.31 c_160(U251^#(isNaturalKind(activate(V1)), 957.47/297.31 activate(V1), 957.47/297.31 activate(V2))) } 957.47/297.31 Strict Trs: 957.47/297.31 { U101(tt(), V1, V2) -> 957.47/297.31 U102(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.31 , U102(tt(), V1, V2) -> 957.47/297.31 U103(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.31 , isNaturalKind(n__0()) -> tt() 957.47/297.31 , isNaturalKind(n__head(V1)) -> U211(isLNatKind(activate(V1))) 957.47/297.31 , isNaturalKind(n__s(V1)) -> U221(isNaturalKind(activate(V1))) 957.47/297.31 , isNaturalKind(n__sel(V1, V2)) -> 957.47/297.31 U231(isNaturalKind(activate(V1)), activate(V2)) 957.47/297.31 , activate(X) -> X 957.47/297.31 , activate(n__natsFrom(X)) -> natsFrom(X) 957.47/297.31 , activate(n__nil()) -> nil() 957.47/297.31 , activate(n__afterNth(X1, X2)) -> afterNth(X1, X2) 957.47/297.31 , activate(n__cons(X1, X2)) -> cons(X1, X2) 957.47/297.31 , activate(n__fst(X)) -> fst(X) 957.47/297.31 , activate(n__snd(X)) -> snd(X) 957.47/297.31 , activate(n__tail(X)) -> tail(X) 957.47/297.31 , activate(n__take(X1, X2)) -> take(X1, X2) 957.47/297.31 , activate(n__0()) -> 0() 957.47/297.31 , activate(n__head(X)) -> head(X) 957.47/297.31 , activate(n__s(X)) -> s(X) 957.47/297.31 , activate(n__sel(X1, X2)) -> sel(X1, X2) 957.47/297.31 , activate(n__pair(X1, X2)) -> pair(X1, X2) 957.47/297.31 , activate(n__splitAt(X1, X2)) -> splitAt(X1, X2) 957.47/297.31 , U103(tt(), V1, V2) -> 957.47/297.31 U104(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.31 , isLNatKind(n__natsFrom(V1)) -> U141(isNaturalKind(activate(V1))) 957.47/297.31 , isLNatKind(n__nil()) -> tt() 957.47/297.31 , isLNatKind(n__afterNth(V1, V2)) -> 957.47/297.31 U111(isNaturalKind(activate(V1)), activate(V2)) 957.47/297.31 , isLNatKind(n__cons(V1, V2)) -> 957.47/297.31 U121(isNaturalKind(activate(V1)), activate(V2)) 957.47/297.31 , isLNatKind(n__fst(V1)) -> U131(isPLNatKind(activate(V1))) 957.47/297.31 , isLNatKind(n__snd(V1)) -> U151(isPLNatKind(activate(V1))) 957.47/297.31 , isLNatKind(n__tail(V1)) -> U161(isLNatKind(activate(V1))) 957.47/297.31 , isLNatKind(n__take(V1, V2)) -> 957.47/297.31 U171(isNaturalKind(activate(V1)), activate(V2)) 957.47/297.31 , U104(tt(), V1, V2) -> U105(isNatural(activate(V1)), activate(V2)) 957.47/297.31 , U105(tt(), V2) -> U106(isLNat(activate(V2))) 957.47/297.31 , isNatural(n__0()) -> tt() 957.47/297.31 , isNatural(n__head(V1)) -> 957.47/297.31 U181(isLNatKind(activate(V1)), activate(V1)) 957.47/297.31 , isNatural(n__s(V1)) -> 957.47/297.31 U191(isNaturalKind(activate(V1)), activate(V1)) 957.47/297.31 , isNatural(n__sel(V1, V2)) -> 957.47/297.31 U201(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.31 , U106(tt()) -> tt() 957.47/297.31 , isLNat(n__natsFrom(V1)) -> 957.47/297.31 U71(isNaturalKind(activate(V1)), activate(V1)) 957.47/297.31 , isLNat(n__nil()) -> tt() 957.47/297.31 , isLNat(n__afterNth(V1, V2)) -> 957.47/297.31 U41(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.31 , isLNat(n__cons(V1, V2)) -> 957.47/297.31 U51(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.31 , isLNat(n__fst(V1)) -> 957.47/297.31 U61(isPLNatKind(activate(V1)), activate(V1)) 957.47/297.31 , isLNat(n__snd(V1)) -> 957.47/297.31 U81(isPLNatKind(activate(V1)), activate(V1)) 957.47/297.31 , isLNat(n__tail(V1)) -> 957.47/297.31 U91(isLNatKind(activate(V1)), activate(V1)) 957.47/297.31 , isLNat(n__take(V1, V2)) -> 957.47/297.31 U101(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.31 , U11(tt(), N, XS) -> 957.47/297.31 U12(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.47/297.31 , U12(tt(), N, XS) -> 957.47/297.31 U13(isLNat(activate(XS)), activate(N), activate(XS)) 957.47/297.31 , U111(tt(), V2) -> U112(isLNatKind(activate(V2))) 957.47/297.31 , U112(tt()) -> tt() 957.47/297.31 , U13(tt(), N, XS) -> 957.47/297.31 U14(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.47/297.31 , U121(tt(), V2) -> U122(isLNatKind(activate(V2))) 957.47/297.31 , U122(tt()) -> tt() 957.47/297.31 , U14(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS))) 957.47/297.31 , U131(tt()) -> tt() 957.47/297.31 , snd(X) -> n__snd(X) 957.47/297.31 , snd(pair(X, Y)) -> U301(isLNat(X), X, Y) 957.47/297.31 , splitAt(X1, X2) -> n__splitAt(X1, X2) 957.47/297.31 , splitAt(s(N), cons(X, XS)) -> 957.47/297.31 U321(isNatural(N), N, X, activate(XS)) 957.47/297.31 , splitAt(0(), XS) -> U311(isLNat(XS), XS) 957.47/297.31 , U141(tt()) -> tt() 957.47/297.31 , U151(tt()) -> tt() 957.47/297.31 , U161(tt()) -> tt() 957.47/297.31 , U171(tt(), V2) -> U172(isLNatKind(activate(V2))) 957.47/297.31 , U172(tt()) -> tt() 957.47/297.31 , U181(tt(), V1) -> U182(isLNatKind(activate(V1)), activate(V1)) 957.47/297.31 , U182(tt(), V1) -> U183(isLNat(activate(V1))) 957.47/297.31 , U183(tt()) -> tt() 957.47/297.31 , U191(tt(), V1) -> U192(isNaturalKind(activate(V1)), activate(V1)) 957.47/297.31 , U192(tt(), V1) -> U193(isNatural(activate(V1))) 957.47/297.31 , U193(tt()) -> tt() 957.47/297.31 , U201(tt(), V1, V2) -> 957.47/297.31 U202(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.31 , U202(tt(), V1, V2) -> 957.47/297.31 U203(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.31 , U203(tt(), V1, V2) -> 957.47/297.31 U204(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.31 , U204(tt(), V1, V2) -> U205(isNatural(activate(V1)), activate(V2)) 957.47/297.31 , U205(tt(), V2) -> U206(isLNat(activate(V2))) 957.47/297.31 , U206(tt()) -> tt() 957.47/297.31 , U21(tt(), X, Y) -> 957.47/297.31 U22(isLNatKind(activate(X)), activate(X), activate(Y)) 957.47/297.31 , U22(tt(), X, Y) -> 957.47/297.31 U23(isLNat(activate(Y)), activate(X), activate(Y)) 957.47/297.31 , U211(tt()) -> tt() 957.47/297.31 , U23(tt(), X, Y) -> U24(isLNatKind(activate(Y)), activate(X)) 957.47/297.31 , U221(tt()) -> tt() 957.47/297.31 , U24(tt(), X) -> activate(X) 957.47/297.31 , U231(tt(), V2) -> U232(isLNatKind(activate(V2))) 957.47/297.31 , U232(tt()) -> tt() 957.47/297.31 , U241(tt(), V1, V2) -> 957.47/297.31 U242(isLNatKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.31 , U242(tt(), V1, V2) -> 957.47/297.31 U243(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.31 , U243(tt(), V1, V2) -> 957.47/297.31 U244(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.31 , U244(tt(), V1, V2) -> U245(isLNat(activate(V1)), activate(V2)) 957.47/297.31 , U245(tt(), V2) -> U246(isLNat(activate(V2))) 957.47/297.31 , U246(tt()) -> tt() 957.47/297.31 , U251(tt(), V1, V2) -> 957.47/297.31 U252(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.31 , U252(tt(), V1, V2) -> 957.47/297.31 U253(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.31 , U253(tt(), V1, V2) -> 957.47/297.31 U254(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.31 , U254(tt(), V1, V2) -> U255(isNatural(activate(V1)), activate(V2)) 957.47/297.31 , U255(tt(), V2) -> U256(isLNat(activate(V2))) 957.47/297.31 , U256(tt()) -> tt() 957.47/297.31 , U261(tt(), V2) -> U262(isLNatKind(activate(V2))) 957.47/297.31 , U262(tt()) -> tt() 957.47/297.31 , U271(tt(), V2) -> U272(isLNatKind(activate(V2))) 957.47/297.31 , U272(tt()) -> tt() 957.47/297.31 , U281(tt(), N) -> U282(isNaturalKind(activate(N)), activate(N)) 957.47/297.31 , U282(tt(), N) -> cons(activate(N), n__natsFrom(s(activate(N)))) 957.47/297.31 , cons(X1, X2) -> n__cons(X1, X2) 957.47/297.31 , s(X) -> n__s(X) 957.47/297.31 , U291(tt(), N, XS) -> 957.47/297.31 U292(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.47/297.31 , U292(tt(), N, XS) -> 957.47/297.31 U293(isLNat(activate(XS)), activate(N), activate(XS)) 957.47/297.31 , U293(tt(), N, XS) -> 957.47/297.31 U294(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.47/297.31 , U294(tt(), N, XS) -> head(afterNth(activate(N), activate(XS))) 957.47/297.31 , head(X) -> n__head(X) 957.47/297.31 , head(cons(N, XS)) -> U31(isNatural(N), N, activate(XS)) 957.47/297.31 , afterNth(N, XS) -> U11(isNatural(N), N, XS) 957.47/297.31 , afterNth(X1, X2) -> n__afterNth(X1, X2) 957.47/297.31 , U301(tt(), X, Y) -> U302(isLNatKind(activate(X)), activate(Y)) 957.47/297.31 , U302(tt(), Y) -> U303(isLNat(activate(Y)), activate(Y)) 957.47/297.31 , U303(tt(), Y) -> U304(isLNatKind(activate(Y)), activate(Y)) 957.47/297.31 , U304(tt(), Y) -> activate(Y) 957.47/297.31 , U31(tt(), N, XS) -> 957.47/297.31 U32(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.47/297.31 , U32(tt(), N, XS) -> 957.47/297.31 U33(isLNat(activate(XS)), activate(N), activate(XS)) 957.47/297.31 , U311(tt(), XS) -> U312(isLNatKind(activate(XS)), activate(XS)) 957.47/297.31 , U312(tt(), XS) -> pair(nil(), activate(XS)) 957.47/297.31 , pair(X1, X2) -> n__pair(X1, X2) 957.47/297.31 , nil() -> n__nil() 957.47/297.31 , U33(tt(), N, XS) -> U34(isLNatKind(activate(XS)), activate(N)) 957.47/297.31 , U321(tt(), N, X, XS) -> 957.47/297.31 U322(isNaturalKind(activate(N)), 957.47/297.31 activate(N), 957.47/297.31 activate(X), 957.47/297.31 activate(XS)) 957.47/297.31 , U322(tt(), N, X, XS) -> 957.47/297.31 U323(isNatural(activate(X)), 957.47/297.31 activate(N), 957.47/297.31 activate(X), 957.47/297.31 activate(XS)) 957.47/297.31 , U323(tt(), N, X, XS) -> 957.47/297.31 U324(isNaturalKind(activate(X)), 957.47/297.31 activate(N), 957.47/297.31 activate(X), 957.47/297.31 activate(XS)) 957.47/297.31 , U324(tt(), N, X, XS) -> 957.47/297.31 U325(isLNat(activate(XS)), activate(N), activate(X), activate(XS)) 957.47/297.31 , U325(tt(), N, X, XS) -> 957.47/297.31 U326(isLNatKind(activate(XS)), 957.47/297.31 activate(N), 957.47/297.31 activate(X), 957.47/297.31 activate(XS)) 957.47/297.31 , U326(tt(), N, X, XS) -> 957.47/297.31 U327(splitAt(activate(N), activate(XS)), activate(X)) 957.47/297.31 , U327(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) 957.47/297.31 , U34(tt(), N) -> activate(N) 957.47/297.31 , U331(tt(), N, XS) -> 957.47/297.31 U332(isNaturalKind(activate(N)), activate(XS)) 957.47/297.31 , U332(tt(), XS) -> U333(isLNat(activate(XS)), activate(XS)) 957.47/297.31 , U333(tt(), XS) -> U334(isLNatKind(activate(XS)), activate(XS)) 957.47/297.31 , U334(tt(), XS) -> activate(XS) 957.47/297.31 , U341(tt(), N, XS) -> 957.47/297.31 U342(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.47/297.31 , U342(tt(), N, XS) -> 957.47/297.31 U343(isLNat(activate(XS)), activate(N), activate(XS)) 957.47/297.31 , U343(tt(), N, XS) -> 957.47/297.31 U344(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.47/297.31 , U344(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS))) 957.47/297.31 , fst(X) -> n__fst(X) 957.47/297.31 , fst(pair(X, Y)) -> U21(isLNat(X), X, Y) 957.47/297.31 , U41(tt(), V1, V2) -> 957.47/297.31 U42(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.31 , U42(tt(), V1, V2) -> 957.47/297.31 U43(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.31 , U43(tt(), V1, V2) -> 957.47/297.31 U44(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.31 , U44(tt(), V1, V2) -> U45(isNatural(activate(V1)), activate(V2)) 957.47/297.31 , U45(tt(), V2) -> U46(isLNat(activate(V2))) 957.47/297.31 , U46(tt()) -> tt() 957.47/297.31 , U51(tt(), V1, V2) -> 957.47/297.31 U52(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.31 , U52(tt(), V1, V2) -> 957.47/297.31 U53(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.31 , U53(tt(), V1, V2) -> 957.47/297.31 U54(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.31 , U54(tt(), V1, V2) -> U55(isNatural(activate(V1)), activate(V2)) 957.47/297.31 , U55(tt(), V2) -> U56(isLNat(activate(V2))) 957.47/297.31 , U56(tt()) -> tt() 957.47/297.31 , U61(tt(), V1) -> U62(isPLNatKind(activate(V1)), activate(V1)) 957.47/297.31 , U62(tt(), V1) -> U63(isPLNat(activate(V1))) 957.47/297.31 , isPLNatKind(n__pair(V1, V2)) -> 957.47/297.31 U261(isLNatKind(activate(V1)), activate(V2)) 957.47/297.31 , isPLNatKind(n__splitAt(V1, V2)) -> 957.47/297.31 U271(isNaturalKind(activate(V1)), activate(V2)) 957.47/297.31 , U63(tt()) -> tt() 957.47/297.31 , isPLNat(n__pair(V1, V2)) -> 957.47/297.31 U241(isLNatKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.31 , isPLNat(n__splitAt(V1, V2)) -> 957.47/297.31 U251(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.31 , U71(tt(), V1) -> U72(isNaturalKind(activate(V1)), activate(V1)) 957.47/297.31 , U72(tt(), V1) -> U73(isNatural(activate(V1))) 957.47/297.31 , U73(tt()) -> tt() 957.47/297.31 , U81(tt(), V1) -> U82(isPLNatKind(activate(V1)), activate(V1)) 957.47/297.31 , U82(tt(), V1) -> U83(isPLNat(activate(V1))) 957.47/297.31 , U83(tt()) -> tt() 957.47/297.31 , U91(tt(), V1) -> U92(isLNatKind(activate(V1)), activate(V1)) 957.47/297.31 , U92(tt(), V1) -> U93(isLNat(activate(V1))) 957.47/297.31 , U93(tt()) -> tt() 957.47/297.31 , natsFrom(N) -> U281(isNatural(N), N) 957.47/297.31 , natsFrom(X) -> n__natsFrom(X) 957.47/297.31 , sel(N, XS) -> U291(isNatural(N), N, XS) 957.47/297.31 , sel(X1, X2) -> n__sel(X1, X2) 957.47/297.31 , 0() -> n__0() 957.47/297.31 , tail(X) -> n__tail(X) 957.47/297.31 , tail(cons(N, XS)) -> U331(isNatural(N), N, activate(XS)) 957.47/297.31 , take(N, XS) -> U341(isNatural(N), N, XS) 957.47/297.31 , take(X1, X2) -> n__take(X1, X2) } 957.47/297.31 Weak DPs: 957.47/297.31 { isNaturalKind^#(n__0()) -> c_3() 957.47/297.31 , isNaturalKind^#(n__head(V1)) -> 957.47/297.31 c_4(U211^#(isLNatKind(activate(V1)))) 957.47/297.31 , isNaturalKind^#(n__s(V1)) -> 957.47/297.31 c_5(U221^#(isNaturalKind(activate(V1)))) 957.47/297.31 , isNaturalKind^#(n__sel(V1, V2)) -> 957.47/297.31 c_6(U231^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.31 , U211^#(tt()) -> c_79() 957.47/297.31 , U221^#(tt()) -> c_81() 957.47/297.31 , U231^#(tt(), V2) -> c_83(U232^#(isLNatKind(activate(V2)))) 957.47/297.31 , activate^#(n__nil()) -> c_9(nil^#()) 957.47/297.32 , activate^#(n__0()) -> c_16(0^#()) 957.47/297.32 , nil^#() -> c_122() 957.47/297.32 , 0^#() -> c_174() 957.47/297.32 , U104^#(tt(), V1, V2) -> 957.47/297.32 c_31(U105^#(isNatural(activate(V1)), activate(V2))) 957.47/297.32 , isLNatKind^#(n__natsFrom(V1)) -> 957.47/297.32 c_23(U141^#(isNaturalKind(activate(V1)))) 957.47/297.32 , isLNatKind^#(n__nil()) -> c_24() 957.47/297.32 , isLNatKind^#(n__afterNth(V1, V2)) -> 957.47/297.32 c_25(U111^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.32 , isLNatKind^#(n__cons(V1, V2)) -> 957.47/297.32 c_26(U121^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.32 , isLNatKind^#(n__fst(V1)) -> 957.47/297.32 c_27(U131^#(isPLNatKind(activate(V1)))) 957.47/297.32 , isLNatKind^#(n__snd(V1)) -> 957.47/297.32 c_28(U151^#(isPLNatKind(activate(V1)))) 957.47/297.32 , isLNatKind^#(n__tail(V1)) -> 957.47/297.32 c_29(U161^#(isLNatKind(activate(V1)))) 957.47/297.32 , isLNatKind^#(n__take(V1, V2)) -> 957.47/297.32 c_30(U171^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.32 , U141^#(tt()) -> c_60() 957.47/297.32 , U111^#(tt(), V2) -> c_48(U112^#(isLNatKind(activate(V2)))) 957.47/297.32 , U121^#(tt(), V2) -> c_51(U122^#(isLNatKind(activate(V2)))) 957.47/297.32 , U131^#(tt()) -> c_54() 957.47/297.32 , U151^#(tt()) -> c_61() 957.47/297.32 , U161^#(tt()) -> c_62() 957.47/297.32 , U171^#(tt(), V2) -> c_63(U172^#(isLNatKind(activate(V2)))) 957.47/297.32 , U105^#(tt(), V2) -> c_32(U106^#(isLNat(activate(V2)))) 957.47/297.32 , U106^#(tt()) -> c_37() 957.47/297.32 , isNatural^#(n__0()) -> c_33() 957.47/297.32 , U181^#(tt(), V1) -> 957.47/297.32 c_65(U182^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.32 , U191^#(tt(), V1) -> 957.47/297.32 c_68(U192^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.32 , isLNat^#(n__nil()) -> c_39() 957.47/297.32 , U71^#(tt(), V1) -> 957.47/297.32 c_161(U72^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.32 , U61^#(tt(), V1) -> 957.47/297.32 c_154(U62^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.32 , U81^#(tt(), V1) -> 957.47/297.32 c_164(U82^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.32 , U91^#(tt(), V1) -> 957.47/297.32 c_167(U92^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.32 , U112^#(tt()) -> c_49() 957.47/297.32 , U122^#(tt()) -> c_52() 957.47/297.32 , U172^#(tt()) -> c_64() 957.47/297.32 , U182^#(tt(), V1) -> c_66(U183^#(isLNat(activate(V1)))) 957.47/297.32 , U183^#(tt()) -> c_67() 957.47/297.32 , U192^#(tt(), V1) -> c_69(U193^#(isNatural(activate(V1)))) 957.47/297.32 , U193^#(tt()) -> c_70() 957.47/297.32 , U204^#(tt(), V1, V2) -> 957.47/297.32 c_74(U205^#(isNatural(activate(V1)), activate(V2))) 957.47/297.32 , U205^#(tt(), V2) -> c_75(U206^#(isLNat(activate(V2)))) 957.47/297.32 , U206^#(tt()) -> c_76() 957.47/297.32 , U232^#(tt()) -> c_84() 957.47/297.32 , U244^#(tt(), V1, V2) -> 957.47/297.32 c_88(U245^#(isLNat(activate(V1)), activate(V2))) 957.47/297.32 , U245^#(tt(), V2) -> c_89(U246^#(isLNat(activate(V2)))) 957.47/297.32 , U246^#(tt()) -> c_90() 957.47/297.32 , U254^#(tt(), V1, V2) -> 957.47/297.32 c_94(U255^#(isNatural(activate(V1)), activate(V2))) 957.47/297.32 , U255^#(tt(), V2) -> c_95(U256^#(isLNat(activate(V2)))) 957.47/297.32 , U256^#(tt()) -> c_96() 957.47/297.32 , U261^#(tt(), V2) -> c_97(U262^#(isLNatKind(activate(V2)))) 957.47/297.32 , U262^#(tt()) -> c_98() 957.47/297.32 , U271^#(tt(), V2) -> c_99(U272^#(isLNatKind(activate(V2)))) 957.47/297.32 , U272^#(tt()) -> c_100() 957.47/297.32 , U44^#(tt(), V1, V2) -> 957.47/297.32 c_145(U45^#(isNatural(activate(V1)), activate(V2))) 957.47/297.32 , U45^#(tt(), V2) -> c_146(U46^#(isLNat(activate(V2)))) 957.47/297.32 , U46^#(tt()) -> c_147() 957.47/297.32 , U54^#(tt(), V1, V2) -> 957.47/297.32 c_151(U55^#(isNatural(activate(V1)), activate(V2))) 957.47/297.32 , U55^#(tt(), V2) -> c_152(U56^#(isLNat(activate(V2)))) 957.47/297.32 , U56^#(tt()) -> c_153() 957.47/297.32 , U62^#(tt(), V1) -> c_155(U63^#(isPLNat(activate(V1)))) 957.47/297.32 , U63^#(tt()) -> c_158() 957.47/297.32 , isPLNatKind^#(n__pair(V1, V2)) -> 957.47/297.32 c_156(U261^#(isLNatKind(activate(V1)), activate(V2))) 957.47/297.32 , isPLNatKind^#(n__splitAt(V1, V2)) -> 957.47/297.32 c_157(U271^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.32 , U72^#(tt(), V1) -> c_162(U73^#(isNatural(activate(V1)))) 957.47/297.32 , U73^#(tt()) -> c_163() 957.47/297.32 , U82^#(tt(), V1) -> c_165(U83^#(isPLNat(activate(V1)))) 957.47/297.32 , U83^#(tt()) -> c_166() 957.47/297.32 , U92^#(tt(), V1) -> c_168(U93^#(isLNat(activate(V1)))) 957.47/297.32 , U93^#(tt()) -> c_169() } 957.47/297.32 Obligation: 957.47/297.32 runtime complexity 957.47/297.32 Answer: 957.47/297.32 MAYBE 957.47/297.32 957.47/297.32 We estimate the number of application of 957.47/297.32 {3,39,40,43,46,47,48,60,67,70,100,102} by applications of 957.47/297.32 Pre({3,39,40,43,46,47,48,60,67,70,100,102}) = 957.47/297.32 {2,4,18,20,21,22,24,26,29,30,32,34,35,36,59,66,69,99,101}. Here 957.47/297.32 rules are labeled as follows: 957.47/297.32 957.47/297.32 DPs: 957.47/297.32 { 1: U101^#(tt(), V1, V2) -> 957.47/297.32 c_1(U102^#(isNaturalKind(activate(V1)), 957.47/297.32 activate(V1), 957.47/297.32 activate(V2))) 957.47/297.32 , 2: U102^#(tt(), V1, V2) -> 957.47/297.32 c_2(U103^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.32 , 3: U103^#(tt(), V1, V2) -> 957.47/297.32 c_22(U104^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.32 , 4: activate^#(X) -> c_7(X) 957.47/297.32 , 5: activate^#(n__natsFrom(X)) -> c_8(natsFrom^#(X)) 957.47/297.32 , 6: activate^#(n__afterNth(X1, X2)) -> c_10(afterNth^#(X1, X2)) 957.47/297.32 , 7: activate^#(n__cons(X1, X2)) -> c_11(cons^#(X1, X2)) 957.47/297.32 , 8: activate^#(n__fst(X)) -> c_12(fst^#(X)) 957.47/297.32 , 9: activate^#(n__snd(X)) -> c_13(snd^#(X)) 957.47/297.32 , 10: activate^#(n__tail(X)) -> c_14(tail^#(X)) 957.47/297.32 , 11: activate^#(n__take(X1, X2)) -> c_15(take^#(X1, X2)) 957.47/297.32 , 12: activate^#(n__head(X)) -> c_17(head^#(X)) 957.47/297.32 , 13: activate^#(n__s(X)) -> c_18(s^#(X)) 957.47/297.32 , 14: activate^#(n__sel(X1, X2)) -> c_19(sel^#(X1, X2)) 957.47/297.32 , 15: activate^#(n__pair(X1, X2)) -> c_20(pair^#(X1, X2)) 957.47/297.32 , 16: activate^#(n__splitAt(X1, X2)) -> c_21(splitAt^#(X1, X2)) 957.47/297.32 , 17: natsFrom^#(N) -> c_170(U281^#(isNatural(N), N)) 957.47/297.32 , 18: natsFrom^#(X) -> c_171(X) 957.47/297.32 , 19: afterNth^#(N, XS) -> c_111(U11^#(isNatural(N), N, XS)) 957.47/297.32 , 20: afterNth^#(X1, X2) -> c_112(X1, X2) 957.47/297.32 , 21: cons^#(X1, X2) -> c_103(X1, X2) 957.47/297.32 , 22: fst^#(X) -> c_140(X) 957.47/297.32 , 23: fst^#(pair(X, Y)) -> c_141(U21^#(isLNat(X), X, Y)) 957.47/297.32 , 24: snd^#(X) -> c_55(X) 957.47/297.32 , 25: snd^#(pair(X, Y)) -> c_56(U301^#(isLNat(X), X, Y)) 957.47/297.32 , 26: tail^#(X) -> c_175(X) 957.47/297.32 , 27: tail^#(cons(N, XS)) -> 957.47/297.32 c_176(U331^#(isNatural(N), N, activate(XS))) 957.47/297.32 , 28: take^#(N, XS) -> c_177(U341^#(isNatural(N), N, XS)) 957.47/297.32 , 29: take^#(X1, X2) -> c_178(X1, X2) 957.47/297.32 , 30: head^#(X) -> c_109(X) 957.47/297.32 , 31: head^#(cons(N, XS)) -> 957.47/297.32 c_110(U31^#(isNatural(N), N, activate(XS))) 957.47/297.32 , 32: s^#(X) -> c_104(X) 957.47/297.32 , 33: sel^#(N, XS) -> c_172(U291^#(isNatural(N), N, XS)) 957.47/297.32 , 34: sel^#(X1, X2) -> c_173(X1, X2) 957.47/297.32 , 35: pair^#(X1, X2) -> c_121(X1, X2) 957.47/297.32 , 36: splitAt^#(X1, X2) -> c_57(X1, X2) 957.47/297.32 , 37: splitAt^#(s(N), cons(X, XS)) -> 957.47/297.32 c_58(U321^#(isNatural(N), N, X, activate(XS))) 957.47/297.32 , 38: splitAt^#(0(), XS) -> c_59(U311^#(isLNat(XS), XS)) 957.47/297.32 , 39: isNatural^#(n__head(V1)) -> 957.47/297.32 c_34(U181^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.32 , 40: isNatural^#(n__s(V1)) -> 957.47/297.32 c_35(U191^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.32 , 41: isNatural^#(n__sel(V1, V2)) -> 957.47/297.32 c_36(U201^#(isNaturalKind(activate(V1)), 957.47/297.32 activate(V1), 957.47/297.32 activate(V2))) 957.47/297.32 , 42: U201^#(tt(), V1, V2) -> 957.47/297.32 c_71(U202^#(isNaturalKind(activate(V1)), 957.47/297.32 activate(V1), 957.47/297.32 activate(V2))) 957.47/297.32 , 43: isLNat^#(n__natsFrom(V1)) -> 957.47/297.32 c_38(U71^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.32 , 44: isLNat^#(n__afterNth(V1, V2)) -> 957.47/297.32 c_40(U41^#(isNaturalKind(activate(V1)), 957.47/297.32 activate(V1), 957.47/297.32 activate(V2))) 957.47/297.32 , 45: isLNat^#(n__cons(V1, V2)) -> 957.47/297.32 c_41(U51^#(isNaturalKind(activate(V1)), 957.47/297.32 activate(V1), 957.47/297.32 activate(V2))) 957.47/297.32 , 46: isLNat^#(n__fst(V1)) -> 957.47/297.32 c_42(U61^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.32 , 47: isLNat^#(n__snd(V1)) -> 957.47/297.32 c_43(U81^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.32 , 48: isLNat^#(n__tail(V1)) -> 957.47/297.32 c_44(U91^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.32 , 49: isLNat^#(n__take(V1, V2)) -> 957.47/297.32 c_45(U101^#(isNaturalKind(activate(V1)), 957.47/297.32 activate(V1), 957.47/297.32 activate(V2))) 957.47/297.32 , 50: U41^#(tt(), V1, V2) -> 957.47/297.32 c_142(U42^#(isNaturalKind(activate(V1)), 957.47/297.32 activate(V1), 957.47/297.32 activate(V2))) 957.47/297.32 , 51: U51^#(tt(), V1, V2) -> 957.47/297.32 c_148(U52^#(isNaturalKind(activate(V1)), 957.47/297.32 activate(V1), 957.47/297.32 activate(V2))) 957.47/297.32 , 52: U11^#(tt(), N, XS) -> 957.47/297.32 c_46(U12^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.47/297.32 , 53: U12^#(tt(), N, XS) -> 957.47/297.32 c_47(U13^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.32 , 54: U13^#(tt(), N, XS) -> 957.47/297.32 c_50(U14^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.32 , 55: U14^#(tt(), N, XS) -> 957.47/297.32 c_53(snd^#(splitAt(activate(N), activate(XS)))) 957.47/297.32 , 56: U301^#(tt(), X, Y) -> 957.47/297.32 c_113(U302^#(isLNatKind(activate(X)), activate(Y))) 957.47/297.32 , 57: U321^#(tt(), N, X, XS) -> 957.47/297.32 c_124(U322^#(isNaturalKind(activate(N)), 957.47/297.32 activate(N), 957.47/297.32 activate(X), 957.47/297.32 activate(XS))) 957.47/297.32 , 58: U311^#(tt(), XS) -> 957.47/297.32 c_119(U312^#(isLNatKind(activate(XS)), activate(XS))) 957.47/297.32 , 59: U202^#(tt(), V1, V2) -> 957.47/297.32 c_72(U203^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.32 , 60: U203^#(tt(), V1, V2) -> 957.47/297.32 c_73(U204^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.32 , 61: U21^#(tt(), X, Y) -> 957.47/297.32 c_77(U22^#(isLNatKind(activate(X)), activate(X), activate(Y))) 957.47/297.32 , 62: U22^#(tt(), X, Y) -> 957.47/297.32 c_78(U23^#(isLNat(activate(Y)), activate(X), activate(Y))) 957.47/297.32 , 63: U23^#(tt(), X, Y) -> 957.47/297.32 c_80(U24^#(isLNatKind(activate(Y)), activate(X))) 957.47/297.32 , 64: U24^#(tt(), X) -> c_82(activate^#(X)) 957.47/297.32 , 65: U241^#(tt(), V1, V2) -> 957.47/297.32 c_85(U242^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.47/297.32 , 66: U242^#(tt(), V1, V2) -> 957.47/297.32 c_86(U243^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.32 , 67: U243^#(tt(), V1, V2) -> 957.47/297.32 c_87(U244^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.32 , 68: U251^#(tt(), V1, V2) -> 957.47/297.32 c_91(U252^#(isNaturalKind(activate(V1)), 957.47/297.32 activate(V1), 957.47/297.32 activate(V2))) 957.47/297.32 , 69: U252^#(tt(), V1, V2) -> 957.47/297.32 c_92(U253^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.32 , 70: U253^#(tt(), V1, V2) -> 957.47/297.32 c_93(U254^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.32 , 71: U281^#(tt(), N) -> 957.47/297.32 c_101(U282^#(isNaturalKind(activate(N)), activate(N))) 957.47/297.32 , 72: U282^#(tt(), N) -> 957.47/297.32 c_102(cons^#(activate(N), n__natsFrom(s(activate(N))))) 957.47/297.32 , 73: U291^#(tt(), N, XS) -> 957.47/297.32 c_105(U292^#(isNaturalKind(activate(N)), 957.47/297.32 activate(N), 957.47/297.32 activate(XS))) 957.47/297.32 , 74: U292^#(tt(), N, XS) -> 957.47/297.32 c_106(U293^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.32 , 75: U293^#(tt(), N, XS) -> 957.47/297.32 c_107(U294^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.32 , 76: U294^#(tt(), N, XS) -> 957.47/297.32 c_108(head^#(afterNth(activate(N), activate(XS)))) 957.47/297.32 , 77: U31^#(tt(), N, XS) -> 957.47/297.32 c_117(U32^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.47/297.32 , 78: U302^#(tt(), Y) -> 957.47/297.32 c_114(U303^#(isLNat(activate(Y)), activate(Y))) 957.47/297.32 , 79: U303^#(tt(), Y) -> 957.47/297.32 c_115(U304^#(isLNatKind(activate(Y)), activate(Y))) 957.47/297.32 , 80: U304^#(tt(), Y) -> c_116(activate^#(Y)) 957.47/297.32 , 81: U32^#(tt(), N, XS) -> 957.47/297.32 c_118(U33^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.32 , 82: U33^#(tt(), N, XS) -> 957.47/297.32 c_123(U34^#(isLNatKind(activate(XS)), activate(N))) 957.47/297.32 , 83: U312^#(tt(), XS) -> c_120(pair^#(nil(), activate(XS))) 957.47/297.32 , 84: U34^#(tt(), N) -> c_131(activate^#(N)) 957.47/297.32 , 85: U322^#(tt(), N, X, XS) -> 957.47/297.32 c_125(U323^#(isNatural(activate(X)), 957.47/297.32 activate(N), 957.47/297.32 activate(X), 957.47/297.32 activate(XS))) 957.47/297.32 , 86: U323^#(tt(), N, X, XS) -> 957.47/297.32 c_126(U324^#(isNaturalKind(activate(X)), 957.47/297.32 activate(N), 957.47/297.32 activate(X), 957.47/297.32 activate(XS))) 957.47/297.32 , 87: U324^#(tt(), N, X, XS) -> 957.47/297.32 c_127(U325^#(isLNat(activate(XS)), 957.47/297.32 activate(N), 957.47/297.32 activate(X), 957.47/297.32 activate(XS))) 957.47/297.32 , 88: U325^#(tt(), N, X, XS) -> 957.47/297.32 c_128(U326^#(isLNatKind(activate(XS)), 957.47/297.32 activate(N), 957.47/297.32 activate(X), 957.47/297.32 activate(XS))) 957.47/297.32 , 89: U326^#(tt(), N, X, XS) -> 957.47/297.32 c_129(U327^#(splitAt(activate(N), activate(XS)), activate(X))) 957.47/297.32 , 90: U327^#(pair(YS, ZS), X) -> 957.47/297.32 c_130(pair^#(cons(activate(X), YS), ZS)) 957.47/297.32 , 91: U331^#(tt(), N, XS) -> 957.47/297.32 c_132(U332^#(isNaturalKind(activate(N)), activate(XS))) 957.47/297.32 , 92: U332^#(tt(), XS) -> 957.47/297.32 c_133(U333^#(isLNat(activate(XS)), activate(XS))) 957.47/297.32 , 93: U333^#(tt(), XS) -> 957.47/297.32 c_134(U334^#(isLNatKind(activate(XS)), activate(XS))) 957.47/297.32 , 94: U334^#(tt(), XS) -> c_135(activate^#(XS)) 957.47/297.32 , 95: U341^#(tt(), N, XS) -> 957.47/297.32 c_136(U342^#(isNaturalKind(activate(N)), 957.47/297.32 activate(N), 957.47/297.32 activate(XS))) 957.47/297.32 , 96: U342^#(tt(), N, XS) -> 957.47/297.32 c_137(U343^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.32 , 97: U343^#(tt(), N, XS) -> 957.47/297.32 c_138(U344^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.32 , 98: U344^#(tt(), N, XS) -> 957.47/297.32 c_139(fst^#(splitAt(activate(N), activate(XS)))) 957.47/297.32 , 99: U42^#(tt(), V1, V2) -> 957.47/297.32 c_143(U43^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.32 , 100: U43^#(tt(), V1, V2) -> 957.47/297.32 c_144(U44^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.32 , 101: U52^#(tt(), V1, V2) -> 957.47/297.32 c_149(U53^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.32 , 102: U53^#(tt(), V1, V2) -> 957.47/297.32 c_150(U54^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.32 , 103: isPLNat^#(n__pair(V1, V2)) -> 957.47/297.32 c_159(U241^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.47/297.32 , 104: isPLNat^#(n__splitAt(V1, V2)) -> 957.47/297.32 c_160(U251^#(isNaturalKind(activate(V1)), 957.47/297.32 activate(V1), 957.47/297.32 activate(V2))) 957.47/297.32 , 105: isNaturalKind^#(n__0()) -> c_3() 957.47/297.32 , 106: isNaturalKind^#(n__head(V1)) -> 957.47/297.32 c_4(U211^#(isLNatKind(activate(V1)))) 957.47/297.32 , 107: isNaturalKind^#(n__s(V1)) -> 957.47/297.32 c_5(U221^#(isNaturalKind(activate(V1)))) 957.47/297.32 , 108: isNaturalKind^#(n__sel(V1, V2)) -> 957.47/297.32 c_6(U231^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.32 , 109: U211^#(tt()) -> c_79() 957.47/297.32 , 110: U221^#(tt()) -> c_81() 957.47/297.32 , 111: U231^#(tt(), V2) -> c_83(U232^#(isLNatKind(activate(V2)))) 957.47/297.32 , 112: activate^#(n__nil()) -> c_9(nil^#()) 957.47/297.32 , 113: activate^#(n__0()) -> c_16(0^#()) 957.47/297.32 , 114: nil^#() -> c_122() 957.47/297.32 , 115: 0^#() -> c_174() 957.47/297.32 , 116: U104^#(tt(), V1, V2) -> 957.47/297.32 c_31(U105^#(isNatural(activate(V1)), activate(V2))) 957.47/297.32 , 117: isLNatKind^#(n__natsFrom(V1)) -> 957.47/297.32 c_23(U141^#(isNaturalKind(activate(V1)))) 957.47/297.32 , 118: isLNatKind^#(n__nil()) -> c_24() 957.47/297.32 , 119: isLNatKind^#(n__afterNth(V1, V2)) -> 957.47/297.32 c_25(U111^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.32 , 120: isLNatKind^#(n__cons(V1, V2)) -> 957.47/297.32 c_26(U121^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.32 , 121: isLNatKind^#(n__fst(V1)) -> 957.47/297.32 c_27(U131^#(isPLNatKind(activate(V1)))) 957.47/297.32 , 122: isLNatKind^#(n__snd(V1)) -> 957.47/297.32 c_28(U151^#(isPLNatKind(activate(V1)))) 957.47/297.32 , 123: isLNatKind^#(n__tail(V1)) -> 957.47/297.32 c_29(U161^#(isLNatKind(activate(V1)))) 957.47/297.32 , 124: isLNatKind^#(n__take(V1, V2)) -> 957.47/297.32 c_30(U171^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.32 , 125: U141^#(tt()) -> c_60() 957.47/297.32 , 126: U111^#(tt(), V2) -> c_48(U112^#(isLNatKind(activate(V2)))) 957.47/297.32 , 127: U121^#(tt(), V2) -> c_51(U122^#(isLNatKind(activate(V2)))) 957.47/297.32 , 128: U131^#(tt()) -> c_54() 957.47/297.32 , 129: U151^#(tt()) -> c_61() 957.47/297.32 , 130: U161^#(tt()) -> c_62() 957.47/297.32 , 131: U171^#(tt(), V2) -> c_63(U172^#(isLNatKind(activate(V2)))) 957.47/297.32 , 132: U105^#(tt(), V2) -> c_32(U106^#(isLNat(activate(V2)))) 957.47/297.32 , 133: U106^#(tt()) -> c_37() 957.47/297.32 , 134: isNatural^#(n__0()) -> c_33() 957.47/297.32 , 135: U181^#(tt(), V1) -> 957.47/297.32 c_65(U182^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.32 , 136: U191^#(tt(), V1) -> 957.47/297.32 c_68(U192^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.32 , 137: isLNat^#(n__nil()) -> c_39() 957.47/297.32 , 138: U71^#(tt(), V1) -> 957.47/297.32 c_161(U72^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.32 , 139: U61^#(tt(), V1) -> 957.47/297.32 c_154(U62^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.32 , 140: U81^#(tt(), V1) -> 957.47/297.32 c_164(U82^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.32 , 141: U91^#(tt(), V1) -> 957.47/297.32 c_167(U92^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.32 , 142: U112^#(tt()) -> c_49() 957.47/297.32 , 143: U122^#(tt()) -> c_52() 957.47/297.32 , 144: U172^#(tt()) -> c_64() 957.47/297.32 , 145: U182^#(tt(), V1) -> c_66(U183^#(isLNat(activate(V1)))) 957.47/297.32 , 146: U183^#(tt()) -> c_67() 957.47/297.32 , 147: U192^#(tt(), V1) -> c_69(U193^#(isNatural(activate(V1)))) 957.47/297.32 , 148: U193^#(tt()) -> c_70() 957.47/297.32 , 149: U204^#(tt(), V1, V2) -> 957.47/297.32 c_74(U205^#(isNatural(activate(V1)), activate(V2))) 957.47/297.32 , 150: U205^#(tt(), V2) -> c_75(U206^#(isLNat(activate(V2)))) 957.47/297.32 , 151: U206^#(tt()) -> c_76() 957.47/297.32 , 152: U232^#(tt()) -> c_84() 957.47/297.32 , 153: U244^#(tt(), V1, V2) -> 957.47/297.32 c_88(U245^#(isLNat(activate(V1)), activate(V2))) 957.47/297.32 , 154: U245^#(tt(), V2) -> c_89(U246^#(isLNat(activate(V2)))) 957.47/297.32 , 155: U246^#(tt()) -> c_90() 957.47/297.32 , 156: U254^#(tt(), V1, V2) -> 957.47/297.32 c_94(U255^#(isNatural(activate(V1)), activate(V2))) 957.47/297.32 , 157: U255^#(tt(), V2) -> c_95(U256^#(isLNat(activate(V2)))) 957.47/297.32 , 158: U256^#(tt()) -> c_96() 957.47/297.32 , 159: U261^#(tt(), V2) -> c_97(U262^#(isLNatKind(activate(V2)))) 957.47/297.32 , 160: U262^#(tt()) -> c_98() 957.47/297.32 , 161: U271^#(tt(), V2) -> c_99(U272^#(isLNatKind(activate(V2)))) 957.47/297.32 , 162: U272^#(tt()) -> c_100() 957.47/297.32 , 163: U44^#(tt(), V1, V2) -> 957.47/297.32 c_145(U45^#(isNatural(activate(V1)), activate(V2))) 957.47/297.32 , 164: U45^#(tt(), V2) -> c_146(U46^#(isLNat(activate(V2)))) 957.47/297.32 , 165: U46^#(tt()) -> c_147() 957.47/297.32 , 166: U54^#(tt(), V1, V2) -> 957.47/297.32 c_151(U55^#(isNatural(activate(V1)), activate(V2))) 957.47/297.32 , 167: U55^#(tt(), V2) -> c_152(U56^#(isLNat(activate(V2)))) 957.47/297.32 , 168: U56^#(tt()) -> c_153() 957.47/297.32 , 169: U62^#(tt(), V1) -> c_155(U63^#(isPLNat(activate(V1)))) 957.47/297.32 , 170: U63^#(tt()) -> c_158() 957.47/297.32 , 171: isPLNatKind^#(n__pair(V1, V2)) -> 957.47/297.32 c_156(U261^#(isLNatKind(activate(V1)), activate(V2))) 957.47/297.32 , 172: isPLNatKind^#(n__splitAt(V1, V2)) -> 957.47/297.32 c_157(U271^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.32 , 173: U72^#(tt(), V1) -> c_162(U73^#(isNatural(activate(V1)))) 957.47/297.32 , 174: U73^#(tt()) -> c_163() 957.47/297.32 , 175: U82^#(tt(), V1) -> c_165(U83^#(isPLNat(activate(V1)))) 957.47/297.32 , 176: U83^#(tt()) -> c_166() 957.47/297.32 , 177: U92^#(tt(), V1) -> c_168(U93^#(isLNat(activate(V1)))) 957.47/297.32 , 178: U93^#(tt()) -> c_169() } 957.47/297.32 957.47/297.32 We are left with following problem, upon which TcT provides the 957.47/297.32 certificate MAYBE. 957.47/297.32 957.47/297.32 Strict DPs: 957.47/297.32 { U101^#(tt(), V1, V2) -> 957.47/297.32 c_1(U102^#(isNaturalKind(activate(V1)), 957.47/297.32 activate(V1), 957.47/297.32 activate(V2))) 957.47/297.32 , U102^#(tt(), V1, V2) -> 957.47/297.32 c_2(U103^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.32 , activate^#(X) -> c_7(X) 957.47/297.32 , activate^#(n__natsFrom(X)) -> c_8(natsFrom^#(X)) 957.47/297.32 , activate^#(n__afterNth(X1, X2)) -> c_10(afterNth^#(X1, X2)) 957.47/297.32 , activate^#(n__cons(X1, X2)) -> c_11(cons^#(X1, X2)) 957.47/297.32 , activate^#(n__fst(X)) -> c_12(fst^#(X)) 957.47/297.32 , activate^#(n__snd(X)) -> c_13(snd^#(X)) 957.47/297.32 , activate^#(n__tail(X)) -> c_14(tail^#(X)) 957.47/297.32 , activate^#(n__take(X1, X2)) -> c_15(take^#(X1, X2)) 957.47/297.32 , activate^#(n__head(X)) -> c_17(head^#(X)) 957.47/297.32 , activate^#(n__s(X)) -> c_18(s^#(X)) 957.47/297.32 , activate^#(n__sel(X1, X2)) -> c_19(sel^#(X1, X2)) 957.47/297.32 , activate^#(n__pair(X1, X2)) -> c_20(pair^#(X1, X2)) 957.47/297.32 , activate^#(n__splitAt(X1, X2)) -> c_21(splitAt^#(X1, X2)) 957.47/297.32 , natsFrom^#(N) -> c_170(U281^#(isNatural(N), N)) 957.47/297.32 , natsFrom^#(X) -> c_171(X) 957.47/297.32 , afterNth^#(N, XS) -> c_111(U11^#(isNatural(N), N, XS)) 957.47/297.32 , afterNth^#(X1, X2) -> c_112(X1, X2) 957.47/297.32 , cons^#(X1, X2) -> c_103(X1, X2) 957.47/297.32 , fst^#(X) -> c_140(X) 957.47/297.32 , fst^#(pair(X, Y)) -> c_141(U21^#(isLNat(X), X, Y)) 957.47/297.32 , snd^#(X) -> c_55(X) 957.47/297.32 , snd^#(pair(X, Y)) -> c_56(U301^#(isLNat(X), X, Y)) 957.47/297.32 , tail^#(X) -> c_175(X) 957.47/297.32 , tail^#(cons(N, XS)) -> 957.47/297.32 c_176(U331^#(isNatural(N), N, activate(XS))) 957.47/297.32 , take^#(N, XS) -> c_177(U341^#(isNatural(N), N, XS)) 957.47/297.32 , take^#(X1, X2) -> c_178(X1, X2) 957.47/297.32 , head^#(X) -> c_109(X) 957.47/297.32 , head^#(cons(N, XS)) -> 957.47/297.32 c_110(U31^#(isNatural(N), N, activate(XS))) 957.47/297.32 , s^#(X) -> c_104(X) 957.47/297.32 , sel^#(N, XS) -> c_172(U291^#(isNatural(N), N, XS)) 957.47/297.32 , sel^#(X1, X2) -> c_173(X1, X2) 957.47/297.32 , pair^#(X1, X2) -> c_121(X1, X2) 957.47/297.32 , splitAt^#(X1, X2) -> c_57(X1, X2) 957.47/297.32 , splitAt^#(s(N), cons(X, XS)) -> 957.47/297.32 c_58(U321^#(isNatural(N), N, X, activate(XS))) 957.47/297.32 , splitAt^#(0(), XS) -> c_59(U311^#(isLNat(XS), XS)) 957.47/297.32 , isNatural^#(n__sel(V1, V2)) -> 957.47/297.32 c_36(U201^#(isNaturalKind(activate(V1)), 957.47/297.32 activate(V1), 957.47/297.32 activate(V2))) 957.47/297.32 , U201^#(tt(), V1, V2) -> 957.47/297.32 c_71(U202^#(isNaturalKind(activate(V1)), 957.47/297.32 activate(V1), 957.47/297.32 activate(V2))) 957.47/297.32 , isLNat^#(n__afterNth(V1, V2)) -> 957.47/297.32 c_40(U41^#(isNaturalKind(activate(V1)), 957.47/297.32 activate(V1), 957.47/297.32 activate(V2))) 957.47/297.32 , isLNat^#(n__cons(V1, V2)) -> 957.47/297.32 c_41(U51^#(isNaturalKind(activate(V1)), 957.47/297.32 activate(V1), 957.47/297.32 activate(V2))) 957.47/297.32 , isLNat^#(n__take(V1, V2)) -> 957.47/297.32 c_45(U101^#(isNaturalKind(activate(V1)), 957.47/297.32 activate(V1), 957.47/297.32 activate(V2))) 957.47/297.32 , U41^#(tt(), V1, V2) -> 957.47/297.32 c_142(U42^#(isNaturalKind(activate(V1)), 957.47/297.32 activate(V1), 957.47/297.32 activate(V2))) 957.47/297.32 , U51^#(tt(), V1, V2) -> 957.47/297.32 c_148(U52^#(isNaturalKind(activate(V1)), 957.47/297.32 activate(V1), 957.47/297.32 activate(V2))) 957.47/297.32 , U11^#(tt(), N, XS) -> 957.47/297.32 c_46(U12^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.47/297.32 , U12^#(tt(), N, XS) -> 957.47/297.32 c_47(U13^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.32 , U13^#(tt(), N, XS) -> 957.47/297.32 c_50(U14^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.32 , U14^#(tt(), N, XS) -> 957.47/297.32 c_53(snd^#(splitAt(activate(N), activate(XS)))) 957.47/297.32 , U301^#(tt(), X, Y) -> 957.47/297.32 c_113(U302^#(isLNatKind(activate(X)), activate(Y))) 957.47/297.32 , U321^#(tt(), N, X, XS) -> 957.47/297.32 c_124(U322^#(isNaturalKind(activate(N)), 957.47/297.32 activate(N), 957.47/297.32 activate(X), 957.47/297.32 activate(XS))) 957.47/297.32 , U311^#(tt(), XS) -> 957.47/297.32 c_119(U312^#(isLNatKind(activate(XS)), activate(XS))) 957.47/297.32 , U202^#(tt(), V1, V2) -> 957.47/297.32 c_72(U203^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.32 , U21^#(tt(), X, Y) -> 957.47/297.32 c_77(U22^#(isLNatKind(activate(X)), activate(X), activate(Y))) 957.47/297.32 , U22^#(tt(), X, Y) -> 957.47/297.32 c_78(U23^#(isLNat(activate(Y)), activate(X), activate(Y))) 957.47/297.32 , U23^#(tt(), X, Y) -> 957.47/297.32 c_80(U24^#(isLNatKind(activate(Y)), activate(X))) 957.47/297.32 , U24^#(tt(), X) -> c_82(activate^#(X)) 957.47/297.32 , U241^#(tt(), V1, V2) -> 957.47/297.32 c_85(U242^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.47/297.32 , U242^#(tt(), V1, V2) -> 957.47/297.32 c_86(U243^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.32 , U251^#(tt(), V1, V2) -> 957.47/297.33 c_91(U252^#(isNaturalKind(activate(V1)), 957.47/297.33 activate(V1), 957.47/297.33 activate(V2))) 957.47/297.33 , U252^#(tt(), V1, V2) -> 957.47/297.33 c_92(U253^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.33 , U281^#(tt(), N) -> 957.47/297.33 c_101(U282^#(isNaturalKind(activate(N)), activate(N))) 957.47/297.33 , U282^#(tt(), N) -> 957.47/297.33 c_102(cons^#(activate(N), n__natsFrom(s(activate(N))))) 957.47/297.33 , U291^#(tt(), N, XS) -> 957.47/297.33 c_105(U292^#(isNaturalKind(activate(N)), 957.47/297.33 activate(N), 957.47/297.33 activate(XS))) 957.47/297.33 , U292^#(tt(), N, XS) -> 957.47/297.33 c_106(U293^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.33 , U293^#(tt(), N, XS) -> 957.47/297.33 c_107(U294^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.33 , U294^#(tt(), N, XS) -> 957.47/297.33 c_108(head^#(afterNth(activate(N), activate(XS)))) 957.47/297.33 , U31^#(tt(), N, XS) -> 957.47/297.33 c_117(U32^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.47/297.33 , U302^#(tt(), Y) -> 957.47/297.33 c_114(U303^#(isLNat(activate(Y)), activate(Y))) 957.47/297.33 , U303^#(tt(), Y) -> 957.47/297.33 c_115(U304^#(isLNatKind(activate(Y)), activate(Y))) 957.47/297.33 , U304^#(tt(), Y) -> c_116(activate^#(Y)) 957.47/297.33 , U32^#(tt(), N, XS) -> 957.47/297.33 c_118(U33^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.33 , U33^#(tt(), N, XS) -> 957.47/297.33 c_123(U34^#(isLNatKind(activate(XS)), activate(N))) 957.47/297.33 , U312^#(tt(), XS) -> c_120(pair^#(nil(), activate(XS))) 957.47/297.33 , U34^#(tt(), N) -> c_131(activate^#(N)) 957.47/297.33 , U322^#(tt(), N, X, XS) -> 957.47/297.33 c_125(U323^#(isNatural(activate(X)), 957.47/297.33 activate(N), 957.47/297.33 activate(X), 957.47/297.33 activate(XS))) 957.47/297.33 , U323^#(tt(), N, X, XS) -> 957.47/297.33 c_126(U324^#(isNaturalKind(activate(X)), 957.47/297.33 activate(N), 957.47/297.33 activate(X), 957.47/297.33 activate(XS))) 957.47/297.33 , U324^#(tt(), N, X, XS) -> 957.47/297.33 c_127(U325^#(isLNat(activate(XS)), 957.47/297.33 activate(N), 957.47/297.33 activate(X), 957.47/297.33 activate(XS))) 957.47/297.33 , U325^#(tt(), N, X, XS) -> 957.47/297.33 c_128(U326^#(isLNatKind(activate(XS)), 957.47/297.33 activate(N), 957.47/297.33 activate(X), 957.47/297.33 activate(XS))) 957.47/297.33 , U326^#(tt(), N, X, XS) -> 957.47/297.33 c_129(U327^#(splitAt(activate(N), activate(XS)), activate(X))) 957.47/297.33 , U327^#(pair(YS, ZS), X) -> 957.47/297.33 c_130(pair^#(cons(activate(X), YS), ZS)) 957.47/297.33 , U331^#(tt(), N, XS) -> 957.47/297.33 c_132(U332^#(isNaturalKind(activate(N)), activate(XS))) 957.47/297.33 , U332^#(tt(), XS) -> 957.47/297.33 c_133(U333^#(isLNat(activate(XS)), activate(XS))) 957.47/297.33 , U333^#(tt(), XS) -> 957.47/297.33 c_134(U334^#(isLNatKind(activate(XS)), activate(XS))) 957.47/297.33 , U334^#(tt(), XS) -> c_135(activate^#(XS)) 957.47/297.33 , U341^#(tt(), N, XS) -> 957.47/297.33 c_136(U342^#(isNaturalKind(activate(N)), 957.47/297.33 activate(N), 957.47/297.33 activate(XS))) 957.47/297.33 , U342^#(tt(), N, XS) -> 957.47/297.33 c_137(U343^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.33 , U343^#(tt(), N, XS) -> 957.47/297.33 c_138(U344^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.33 , U344^#(tt(), N, XS) -> 957.47/297.33 c_139(fst^#(splitAt(activate(N), activate(XS)))) 957.47/297.33 , U42^#(tt(), V1, V2) -> 957.47/297.33 c_143(U43^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.33 , U52^#(tt(), V1, V2) -> 957.47/297.33 c_149(U53^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.33 , isPLNat^#(n__pair(V1, V2)) -> 957.47/297.33 c_159(U241^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.47/297.33 , isPLNat^#(n__splitAt(V1, V2)) -> 957.47/297.33 c_160(U251^#(isNaturalKind(activate(V1)), 957.47/297.33 activate(V1), 957.47/297.33 activate(V2))) } 957.47/297.33 Strict Trs: 957.47/297.33 { U101(tt(), V1, V2) -> 957.47/297.33 U102(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.33 , U102(tt(), V1, V2) -> 957.47/297.33 U103(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.33 , isNaturalKind(n__0()) -> tt() 957.47/297.33 , isNaturalKind(n__head(V1)) -> U211(isLNatKind(activate(V1))) 957.47/297.33 , isNaturalKind(n__s(V1)) -> U221(isNaturalKind(activate(V1))) 957.47/297.33 , isNaturalKind(n__sel(V1, V2)) -> 957.47/297.33 U231(isNaturalKind(activate(V1)), activate(V2)) 957.47/297.33 , activate(X) -> X 957.47/297.33 , activate(n__natsFrom(X)) -> natsFrom(X) 957.47/297.33 , activate(n__nil()) -> nil() 957.47/297.33 , activate(n__afterNth(X1, X2)) -> afterNth(X1, X2) 957.47/297.33 , activate(n__cons(X1, X2)) -> cons(X1, X2) 957.47/297.33 , activate(n__fst(X)) -> fst(X) 957.47/297.33 , activate(n__snd(X)) -> snd(X) 957.47/297.33 , activate(n__tail(X)) -> tail(X) 957.47/297.33 , activate(n__take(X1, X2)) -> take(X1, X2) 957.47/297.33 , activate(n__0()) -> 0() 957.47/297.33 , activate(n__head(X)) -> head(X) 957.47/297.33 , activate(n__s(X)) -> s(X) 957.47/297.33 , activate(n__sel(X1, X2)) -> sel(X1, X2) 957.47/297.33 , activate(n__pair(X1, X2)) -> pair(X1, X2) 957.47/297.33 , activate(n__splitAt(X1, X2)) -> splitAt(X1, X2) 957.47/297.33 , U103(tt(), V1, V2) -> 957.47/297.33 U104(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.33 , isLNatKind(n__natsFrom(V1)) -> U141(isNaturalKind(activate(V1))) 957.47/297.33 , isLNatKind(n__nil()) -> tt() 957.47/297.33 , isLNatKind(n__afterNth(V1, V2)) -> 957.47/297.33 U111(isNaturalKind(activate(V1)), activate(V2)) 957.47/297.33 , isLNatKind(n__cons(V1, V2)) -> 957.47/297.33 U121(isNaturalKind(activate(V1)), activate(V2)) 957.47/297.33 , isLNatKind(n__fst(V1)) -> U131(isPLNatKind(activate(V1))) 957.47/297.33 , isLNatKind(n__snd(V1)) -> U151(isPLNatKind(activate(V1))) 957.47/297.33 , isLNatKind(n__tail(V1)) -> U161(isLNatKind(activate(V1))) 957.47/297.33 , isLNatKind(n__take(V1, V2)) -> 957.47/297.33 U171(isNaturalKind(activate(V1)), activate(V2)) 957.47/297.33 , U104(tt(), V1, V2) -> U105(isNatural(activate(V1)), activate(V2)) 957.47/297.33 , U105(tt(), V2) -> U106(isLNat(activate(V2))) 957.47/297.33 , isNatural(n__0()) -> tt() 957.47/297.33 , isNatural(n__head(V1)) -> 957.47/297.33 U181(isLNatKind(activate(V1)), activate(V1)) 957.47/297.33 , isNatural(n__s(V1)) -> 957.47/297.33 U191(isNaturalKind(activate(V1)), activate(V1)) 957.47/297.33 , isNatural(n__sel(V1, V2)) -> 957.47/297.33 U201(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.33 , U106(tt()) -> tt() 957.47/297.33 , isLNat(n__natsFrom(V1)) -> 957.47/297.33 U71(isNaturalKind(activate(V1)), activate(V1)) 957.47/297.33 , isLNat(n__nil()) -> tt() 957.47/297.33 , isLNat(n__afterNth(V1, V2)) -> 957.47/297.33 U41(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.33 , isLNat(n__cons(V1, V2)) -> 957.47/297.33 U51(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.33 , isLNat(n__fst(V1)) -> 957.47/297.33 U61(isPLNatKind(activate(V1)), activate(V1)) 957.47/297.33 , isLNat(n__snd(V1)) -> 957.47/297.33 U81(isPLNatKind(activate(V1)), activate(V1)) 957.47/297.33 , isLNat(n__tail(V1)) -> 957.47/297.33 U91(isLNatKind(activate(V1)), activate(V1)) 957.47/297.33 , isLNat(n__take(V1, V2)) -> 957.47/297.33 U101(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.33 , U11(tt(), N, XS) -> 957.47/297.33 U12(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.47/297.33 , U12(tt(), N, XS) -> 957.47/297.33 U13(isLNat(activate(XS)), activate(N), activate(XS)) 957.47/297.33 , U111(tt(), V2) -> U112(isLNatKind(activate(V2))) 957.47/297.33 , U112(tt()) -> tt() 957.47/297.33 , U13(tt(), N, XS) -> 957.47/297.33 U14(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.47/297.33 , U121(tt(), V2) -> U122(isLNatKind(activate(V2))) 957.47/297.33 , U122(tt()) -> tt() 957.47/297.33 , U14(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS))) 957.47/297.33 , U131(tt()) -> tt() 957.47/297.33 , snd(X) -> n__snd(X) 957.47/297.33 , snd(pair(X, Y)) -> U301(isLNat(X), X, Y) 957.47/297.33 , splitAt(X1, X2) -> n__splitAt(X1, X2) 957.47/297.33 , splitAt(s(N), cons(X, XS)) -> 957.47/297.33 U321(isNatural(N), N, X, activate(XS)) 957.47/297.33 , splitAt(0(), XS) -> U311(isLNat(XS), XS) 957.47/297.33 , U141(tt()) -> tt() 957.47/297.33 , U151(tt()) -> tt() 957.47/297.33 , U161(tt()) -> tt() 957.47/297.33 , U171(tt(), V2) -> U172(isLNatKind(activate(V2))) 957.47/297.33 , U172(tt()) -> tt() 957.47/297.33 , U181(tt(), V1) -> U182(isLNatKind(activate(V1)), activate(V1)) 957.47/297.33 , U182(tt(), V1) -> U183(isLNat(activate(V1))) 957.47/297.33 , U183(tt()) -> tt() 957.47/297.33 , U191(tt(), V1) -> U192(isNaturalKind(activate(V1)), activate(V1)) 957.47/297.33 , U192(tt(), V1) -> U193(isNatural(activate(V1))) 957.47/297.33 , U193(tt()) -> tt() 957.47/297.33 , U201(tt(), V1, V2) -> 957.47/297.33 U202(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.33 , U202(tt(), V1, V2) -> 957.47/297.33 U203(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.33 , U203(tt(), V1, V2) -> 957.47/297.33 U204(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.33 , U204(tt(), V1, V2) -> U205(isNatural(activate(V1)), activate(V2)) 957.47/297.33 , U205(tt(), V2) -> U206(isLNat(activate(V2))) 957.47/297.33 , U206(tt()) -> tt() 957.47/297.33 , U21(tt(), X, Y) -> 957.47/297.33 U22(isLNatKind(activate(X)), activate(X), activate(Y)) 957.47/297.33 , U22(tt(), X, Y) -> 957.47/297.33 U23(isLNat(activate(Y)), activate(X), activate(Y)) 957.47/297.33 , U211(tt()) -> tt() 957.47/297.33 , U23(tt(), X, Y) -> U24(isLNatKind(activate(Y)), activate(X)) 957.47/297.33 , U221(tt()) -> tt() 957.47/297.33 , U24(tt(), X) -> activate(X) 957.47/297.33 , U231(tt(), V2) -> U232(isLNatKind(activate(V2))) 957.47/297.33 , U232(tt()) -> tt() 957.47/297.33 , U241(tt(), V1, V2) -> 957.47/297.33 U242(isLNatKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.33 , U242(tt(), V1, V2) -> 957.47/297.33 U243(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.33 , U243(tt(), V1, V2) -> 957.47/297.33 U244(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.33 , U244(tt(), V1, V2) -> U245(isLNat(activate(V1)), activate(V2)) 957.47/297.33 , U245(tt(), V2) -> U246(isLNat(activate(V2))) 957.47/297.33 , U246(tt()) -> tt() 957.47/297.33 , U251(tt(), V1, V2) -> 957.47/297.33 U252(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.33 , U252(tt(), V1, V2) -> 957.47/297.33 U253(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.33 , U253(tt(), V1, V2) -> 957.47/297.33 U254(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.33 , U254(tt(), V1, V2) -> U255(isNatural(activate(V1)), activate(V2)) 957.47/297.33 , U255(tt(), V2) -> U256(isLNat(activate(V2))) 957.47/297.33 , U256(tt()) -> tt() 957.47/297.33 , U261(tt(), V2) -> U262(isLNatKind(activate(V2))) 957.47/297.33 , U262(tt()) -> tt() 957.47/297.33 , U271(tt(), V2) -> U272(isLNatKind(activate(V2))) 957.47/297.33 , U272(tt()) -> tt() 957.47/297.33 , U281(tt(), N) -> U282(isNaturalKind(activate(N)), activate(N)) 957.47/297.33 , U282(tt(), N) -> cons(activate(N), n__natsFrom(s(activate(N)))) 957.47/297.33 , cons(X1, X2) -> n__cons(X1, X2) 957.47/297.33 , s(X) -> n__s(X) 957.47/297.33 , U291(tt(), N, XS) -> 957.47/297.33 U292(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.47/297.33 , U292(tt(), N, XS) -> 957.47/297.33 U293(isLNat(activate(XS)), activate(N), activate(XS)) 957.47/297.33 , U293(tt(), N, XS) -> 957.47/297.33 U294(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.47/297.33 , U294(tt(), N, XS) -> head(afterNth(activate(N), activate(XS))) 957.47/297.33 , head(X) -> n__head(X) 957.47/297.33 , head(cons(N, XS)) -> U31(isNatural(N), N, activate(XS)) 957.47/297.33 , afterNth(N, XS) -> U11(isNatural(N), N, XS) 957.47/297.33 , afterNth(X1, X2) -> n__afterNth(X1, X2) 957.47/297.33 , U301(tt(), X, Y) -> U302(isLNatKind(activate(X)), activate(Y)) 957.47/297.33 , U302(tt(), Y) -> U303(isLNat(activate(Y)), activate(Y)) 957.47/297.33 , U303(tt(), Y) -> U304(isLNatKind(activate(Y)), activate(Y)) 957.47/297.33 , U304(tt(), Y) -> activate(Y) 957.47/297.33 , U31(tt(), N, XS) -> 957.47/297.33 U32(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.47/297.33 , U32(tt(), N, XS) -> 957.47/297.33 U33(isLNat(activate(XS)), activate(N), activate(XS)) 957.47/297.33 , U311(tt(), XS) -> U312(isLNatKind(activate(XS)), activate(XS)) 957.47/297.33 , U312(tt(), XS) -> pair(nil(), activate(XS)) 957.47/297.33 , pair(X1, X2) -> n__pair(X1, X2) 957.47/297.33 , nil() -> n__nil() 957.47/297.33 , U33(tt(), N, XS) -> U34(isLNatKind(activate(XS)), activate(N)) 957.47/297.33 , U321(tt(), N, X, XS) -> 957.47/297.33 U322(isNaturalKind(activate(N)), 957.47/297.33 activate(N), 957.47/297.33 activate(X), 957.47/297.33 activate(XS)) 957.47/297.33 , U322(tt(), N, X, XS) -> 957.47/297.33 U323(isNatural(activate(X)), 957.47/297.33 activate(N), 957.47/297.33 activate(X), 957.47/297.33 activate(XS)) 957.47/297.33 , U323(tt(), N, X, XS) -> 957.47/297.33 U324(isNaturalKind(activate(X)), 957.47/297.33 activate(N), 957.47/297.33 activate(X), 957.47/297.33 activate(XS)) 957.47/297.33 , U324(tt(), N, X, XS) -> 957.47/297.33 U325(isLNat(activate(XS)), activate(N), activate(X), activate(XS)) 957.47/297.33 , U325(tt(), N, X, XS) -> 957.47/297.33 U326(isLNatKind(activate(XS)), 957.47/297.33 activate(N), 957.47/297.33 activate(X), 957.47/297.33 activate(XS)) 957.47/297.33 , U326(tt(), N, X, XS) -> 957.47/297.33 U327(splitAt(activate(N), activate(XS)), activate(X)) 957.47/297.33 , U327(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) 957.47/297.33 , U34(tt(), N) -> activate(N) 957.47/297.33 , U331(tt(), N, XS) -> 957.47/297.33 U332(isNaturalKind(activate(N)), activate(XS)) 957.47/297.33 , U332(tt(), XS) -> U333(isLNat(activate(XS)), activate(XS)) 957.47/297.33 , U333(tt(), XS) -> U334(isLNatKind(activate(XS)), activate(XS)) 957.47/297.33 , U334(tt(), XS) -> activate(XS) 957.47/297.33 , U341(tt(), N, XS) -> 957.47/297.33 U342(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.47/297.33 , U342(tt(), N, XS) -> 957.47/297.33 U343(isLNat(activate(XS)), activate(N), activate(XS)) 957.47/297.33 , U343(tt(), N, XS) -> 957.47/297.33 U344(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.47/297.33 , U344(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS))) 957.47/297.33 , fst(X) -> n__fst(X) 957.47/297.33 , fst(pair(X, Y)) -> U21(isLNat(X), X, Y) 957.47/297.33 , U41(tt(), V1, V2) -> 957.47/297.33 U42(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.33 , U42(tt(), V1, V2) -> 957.47/297.33 U43(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.33 , U43(tt(), V1, V2) -> 957.47/297.33 U44(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.33 , U44(tt(), V1, V2) -> U45(isNatural(activate(V1)), activate(V2)) 957.47/297.33 , U45(tt(), V2) -> U46(isLNat(activate(V2))) 957.47/297.33 , U46(tt()) -> tt() 957.47/297.33 , U51(tt(), V1, V2) -> 957.47/297.33 U52(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.33 , U52(tt(), V1, V2) -> 957.47/297.33 U53(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.33 , U53(tt(), V1, V2) -> 957.47/297.33 U54(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.33 , U54(tt(), V1, V2) -> U55(isNatural(activate(V1)), activate(V2)) 957.47/297.33 , U55(tt(), V2) -> U56(isLNat(activate(V2))) 957.47/297.33 , U56(tt()) -> tt() 957.47/297.33 , U61(tt(), V1) -> U62(isPLNatKind(activate(V1)), activate(V1)) 957.47/297.33 , U62(tt(), V1) -> U63(isPLNat(activate(V1))) 957.47/297.33 , isPLNatKind(n__pair(V1, V2)) -> 957.47/297.33 U261(isLNatKind(activate(V1)), activate(V2)) 957.47/297.33 , isPLNatKind(n__splitAt(V1, V2)) -> 957.47/297.33 U271(isNaturalKind(activate(V1)), activate(V2)) 957.47/297.33 , U63(tt()) -> tt() 957.47/297.33 , isPLNat(n__pair(V1, V2)) -> 957.47/297.33 U241(isLNatKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.33 , isPLNat(n__splitAt(V1, V2)) -> 957.47/297.33 U251(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.33 , U71(tt(), V1) -> U72(isNaturalKind(activate(V1)), activate(V1)) 957.47/297.33 , U72(tt(), V1) -> U73(isNatural(activate(V1))) 957.47/297.33 , U73(tt()) -> tt() 957.47/297.33 , U81(tt(), V1) -> U82(isPLNatKind(activate(V1)), activate(V1)) 957.47/297.33 , U82(tt(), V1) -> U83(isPLNat(activate(V1))) 957.47/297.33 , U83(tt()) -> tt() 957.47/297.33 , U91(tt(), V1) -> U92(isLNatKind(activate(V1)), activate(V1)) 957.47/297.33 , U92(tt(), V1) -> U93(isLNat(activate(V1))) 957.47/297.33 , U93(tt()) -> tt() 957.47/297.33 , natsFrom(N) -> U281(isNatural(N), N) 957.47/297.33 , natsFrom(X) -> n__natsFrom(X) 957.47/297.33 , sel(N, XS) -> U291(isNatural(N), N, XS) 957.47/297.33 , sel(X1, X2) -> n__sel(X1, X2) 957.47/297.33 , 0() -> n__0() 957.47/297.33 , tail(X) -> n__tail(X) 957.47/297.33 , tail(cons(N, XS)) -> U331(isNatural(N), N, activate(XS)) 957.47/297.33 , take(N, XS) -> U341(isNatural(N), N, XS) 957.47/297.33 , take(X1, X2) -> n__take(X1, X2) } 957.47/297.33 Weak DPs: 957.47/297.33 { U103^#(tt(), V1, V2) -> 957.47/297.33 c_22(U104^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.33 , isNaturalKind^#(n__0()) -> c_3() 957.47/297.33 , isNaturalKind^#(n__head(V1)) -> 957.47/297.33 c_4(U211^#(isLNatKind(activate(V1)))) 957.47/297.33 , isNaturalKind^#(n__s(V1)) -> 957.47/297.33 c_5(U221^#(isNaturalKind(activate(V1)))) 957.47/297.33 , isNaturalKind^#(n__sel(V1, V2)) -> 957.47/297.33 c_6(U231^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.33 , U211^#(tt()) -> c_79() 957.47/297.33 , U221^#(tt()) -> c_81() 957.47/297.33 , U231^#(tt(), V2) -> c_83(U232^#(isLNatKind(activate(V2)))) 957.47/297.33 , activate^#(n__nil()) -> c_9(nil^#()) 957.47/297.33 , activate^#(n__0()) -> c_16(0^#()) 957.47/297.33 , nil^#() -> c_122() 957.47/297.33 , 0^#() -> c_174() 957.47/297.33 , U104^#(tt(), V1, V2) -> 957.47/297.33 c_31(U105^#(isNatural(activate(V1)), activate(V2))) 957.47/297.33 , isLNatKind^#(n__natsFrom(V1)) -> 957.47/297.33 c_23(U141^#(isNaturalKind(activate(V1)))) 957.47/297.33 , isLNatKind^#(n__nil()) -> c_24() 957.47/297.33 , isLNatKind^#(n__afterNth(V1, V2)) -> 957.47/297.33 c_25(U111^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.33 , isLNatKind^#(n__cons(V1, V2)) -> 957.47/297.33 c_26(U121^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.33 , isLNatKind^#(n__fst(V1)) -> 957.47/297.33 c_27(U131^#(isPLNatKind(activate(V1)))) 957.47/297.33 , isLNatKind^#(n__snd(V1)) -> 957.47/297.33 c_28(U151^#(isPLNatKind(activate(V1)))) 957.47/297.33 , isLNatKind^#(n__tail(V1)) -> 957.47/297.33 c_29(U161^#(isLNatKind(activate(V1)))) 957.47/297.33 , isLNatKind^#(n__take(V1, V2)) -> 957.47/297.34 c_30(U171^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.34 , U141^#(tt()) -> c_60() 957.47/297.34 , U111^#(tt(), V2) -> c_48(U112^#(isLNatKind(activate(V2)))) 957.47/297.34 , U121^#(tt(), V2) -> c_51(U122^#(isLNatKind(activate(V2)))) 957.47/297.34 , U131^#(tt()) -> c_54() 957.47/297.34 , U151^#(tt()) -> c_61() 957.47/297.34 , U161^#(tt()) -> c_62() 957.47/297.34 , U171^#(tt(), V2) -> c_63(U172^#(isLNatKind(activate(V2)))) 957.47/297.34 , U105^#(tt(), V2) -> c_32(U106^#(isLNat(activate(V2)))) 957.47/297.34 , U106^#(tt()) -> c_37() 957.47/297.34 , isNatural^#(n__0()) -> c_33() 957.47/297.34 , isNatural^#(n__head(V1)) -> 957.47/297.34 c_34(U181^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.34 , isNatural^#(n__s(V1)) -> 957.47/297.34 c_35(U191^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.34 , U181^#(tt(), V1) -> 957.47/297.34 c_65(U182^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.34 , U191^#(tt(), V1) -> 957.47/297.34 c_68(U192^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.34 , isLNat^#(n__natsFrom(V1)) -> 957.47/297.34 c_38(U71^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.34 , isLNat^#(n__nil()) -> c_39() 957.47/297.34 , isLNat^#(n__fst(V1)) -> 957.47/297.34 c_42(U61^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.34 , isLNat^#(n__snd(V1)) -> 957.47/297.34 c_43(U81^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.34 , isLNat^#(n__tail(V1)) -> 957.47/297.34 c_44(U91^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.34 , U71^#(tt(), V1) -> 957.47/297.34 c_161(U72^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.34 , U61^#(tt(), V1) -> 957.47/297.34 c_154(U62^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.34 , U81^#(tt(), V1) -> 957.47/297.34 c_164(U82^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.34 , U91^#(tt(), V1) -> 957.47/297.34 c_167(U92^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.34 , U112^#(tt()) -> c_49() 957.47/297.34 , U122^#(tt()) -> c_52() 957.47/297.34 , U172^#(tt()) -> c_64() 957.47/297.34 , U182^#(tt(), V1) -> c_66(U183^#(isLNat(activate(V1)))) 957.47/297.34 , U183^#(tt()) -> c_67() 957.47/297.34 , U192^#(tt(), V1) -> c_69(U193^#(isNatural(activate(V1)))) 957.47/297.34 , U193^#(tt()) -> c_70() 957.47/297.34 , U203^#(tt(), V1, V2) -> 957.47/297.34 c_73(U204^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.34 , U204^#(tt(), V1, V2) -> 957.47/297.34 c_74(U205^#(isNatural(activate(V1)), activate(V2))) 957.47/297.34 , U205^#(tt(), V2) -> c_75(U206^#(isLNat(activate(V2)))) 957.47/297.34 , U206^#(tt()) -> c_76() 957.47/297.34 , U232^#(tt()) -> c_84() 957.47/297.34 , U243^#(tt(), V1, V2) -> 957.47/297.34 c_87(U244^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.34 , U244^#(tt(), V1, V2) -> 957.47/297.34 c_88(U245^#(isLNat(activate(V1)), activate(V2))) 957.47/297.34 , U245^#(tt(), V2) -> c_89(U246^#(isLNat(activate(V2)))) 957.47/297.34 , U246^#(tt()) -> c_90() 957.47/297.34 , U253^#(tt(), V1, V2) -> 957.47/297.34 c_93(U254^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.34 , U254^#(tt(), V1, V2) -> 957.47/297.34 c_94(U255^#(isNatural(activate(V1)), activate(V2))) 957.47/297.34 , U255^#(tt(), V2) -> c_95(U256^#(isLNat(activate(V2)))) 957.47/297.34 , U256^#(tt()) -> c_96() 957.47/297.34 , U261^#(tt(), V2) -> c_97(U262^#(isLNatKind(activate(V2)))) 957.47/297.34 , U262^#(tt()) -> c_98() 957.47/297.34 , U271^#(tt(), V2) -> c_99(U272^#(isLNatKind(activate(V2)))) 957.47/297.34 , U272^#(tt()) -> c_100() 957.47/297.34 , U43^#(tt(), V1, V2) -> 957.47/297.34 c_144(U44^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.34 , U44^#(tt(), V1, V2) -> 957.47/297.34 c_145(U45^#(isNatural(activate(V1)), activate(V2))) 957.47/297.34 , U45^#(tt(), V2) -> c_146(U46^#(isLNat(activate(V2)))) 957.47/297.34 , U46^#(tt()) -> c_147() 957.47/297.34 , U53^#(tt(), V1, V2) -> 957.47/297.34 c_150(U54^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.34 , U54^#(tt(), V1, V2) -> 957.47/297.34 c_151(U55^#(isNatural(activate(V1)), activate(V2))) 957.47/297.34 , U55^#(tt(), V2) -> c_152(U56^#(isLNat(activate(V2)))) 957.47/297.34 , U56^#(tt()) -> c_153() 957.47/297.34 , U62^#(tt(), V1) -> c_155(U63^#(isPLNat(activate(V1)))) 957.47/297.34 , U63^#(tt()) -> c_158() 957.47/297.34 , isPLNatKind^#(n__pair(V1, V2)) -> 957.47/297.34 c_156(U261^#(isLNatKind(activate(V1)), activate(V2))) 957.47/297.34 , isPLNatKind^#(n__splitAt(V1, V2)) -> 957.47/297.34 c_157(U271^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.34 , U72^#(tt(), V1) -> c_162(U73^#(isNatural(activate(V1)))) 957.47/297.34 , U73^#(tt()) -> c_163() 957.47/297.34 , U82^#(tt(), V1) -> c_165(U83^#(isPLNat(activate(V1)))) 957.47/297.34 , U83^#(tt()) -> c_166() 957.47/297.34 , U92^#(tt(), V1) -> c_168(U93^#(isLNat(activate(V1)))) 957.47/297.34 , U93^#(tt()) -> c_169() } 957.47/297.34 Obligation: 957.47/297.34 runtime complexity 957.47/297.34 Answer: 957.47/297.34 MAYBE 957.47/297.34 957.47/297.34 We estimate the number of application of {2,52,58,60,89,90} by 957.47/297.34 applications of Pre({2,52,58,60,89,90}) = 957.47/297.34 {1,3,17,19,20,21,23,25,28,29,31,33,34,35,39,43,44,57,59}. Here 957.47/297.34 rules are labeled as follows: 957.47/297.34 957.47/297.34 DPs: 957.47/297.34 { 1: U101^#(tt(), V1, V2) -> 957.47/297.34 c_1(U102^#(isNaturalKind(activate(V1)), 957.47/297.34 activate(V1), 957.47/297.34 activate(V2))) 957.47/297.34 , 2: U102^#(tt(), V1, V2) -> 957.47/297.34 c_2(U103^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.34 , 3: activate^#(X) -> c_7(X) 957.47/297.34 , 4: activate^#(n__natsFrom(X)) -> c_8(natsFrom^#(X)) 957.47/297.34 , 5: activate^#(n__afterNth(X1, X2)) -> c_10(afterNth^#(X1, X2)) 957.47/297.34 , 6: activate^#(n__cons(X1, X2)) -> c_11(cons^#(X1, X2)) 957.47/297.34 , 7: activate^#(n__fst(X)) -> c_12(fst^#(X)) 957.47/297.34 , 8: activate^#(n__snd(X)) -> c_13(snd^#(X)) 957.47/297.34 , 9: activate^#(n__tail(X)) -> c_14(tail^#(X)) 957.47/297.34 , 10: activate^#(n__take(X1, X2)) -> c_15(take^#(X1, X2)) 957.47/297.34 , 11: activate^#(n__head(X)) -> c_17(head^#(X)) 957.47/297.34 , 12: activate^#(n__s(X)) -> c_18(s^#(X)) 957.47/297.34 , 13: activate^#(n__sel(X1, X2)) -> c_19(sel^#(X1, X2)) 957.47/297.34 , 14: activate^#(n__pair(X1, X2)) -> c_20(pair^#(X1, X2)) 957.47/297.34 , 15: activate^#(n__splitAt(X1, X2)) -> c_21(splitAt^#(X1, X2)) 957.47/297.34 , 16: natsFrom^#(N) -> c_170(U281^#(isNatural(N), N)) 957.47/297.34 , 17: natsFrom^#(X) -> c_171(X) 957.47/297.34 , 18: afterNth^#(N, XS) -> c_111(U11^#(isNatural(N), N, XS)) 957.47/297.34 , 19: afterNth^#(X1, X2) -> c_112(X1, X2) 957.47/297.34 , 20: cons^#(X1, X2) -> c_103(X1, X2) 957.47/297.34 , 21: fst^#(X) -> c_140(X) 957.47/297.34 , 22: fst^#(pair(X, Y)) -> c_141(U21^#(isLNat(X), X, Y)) 957.47/297.34 , 23: snd^#(X) -> c_55(X) 957.47/297.34 , 24: snd^#(pair(X, Y)) -> c_56(U301^#(isLNat(X), X, Y)) 957.47/297.34 , 25: tail^#(X) -> c_175(X) 957.47/297.34 , 26: tail^#(cons(N, XS)) -> 957.47/297.34 c_176(U331^#(isNatural(N), N, activate(XS))) 957.47/297.34 , 27: take^#(N, XS) -> c_177(U341^#(isNatural(N), N, XS)) 957.47/297.34 , 28: take^#(X1, X2) -> c_178(X1, X2) 957.47/297.34 , 29: head^#(X) -> c_109(X) 957.47/297.34 , 30: head^#(cons(N, XS)) -> 957.47/297.34 c_110(U31^#(isNatural(N), N, activate(XS))) 957.47/297.34 , 31: s^#(X) -> c_104(X) 957.47/297.34 , 32: sel^#(N, XS) -> c_172(U291^#(isNatural(N), N, XS)) 957.47/297.34 , 33: sel^#(X1, X2) -> c_173(X1, X2) 957.47/297.34 , 34: pair^#(X1, X2) -> c_121(X1, X2) 957.47/297.34 , 35: splitAt^#(X1, X2) -> c_57(X1, X2) 957.47/297.34 , 36: splitAt^#(s(N), cons(X, XS)) -> 957.47/297.34 c_58(U321^#(isNatural(N), N, X, activate(XS))) 957.47/297.34 , 37: splitAt^#(0(), XS) -> c_59(U311^#(isLNat(XS), XS)) 957.47/297.34 , 38: isNatural^#(n__sel(V1, V2)) -> 957.47/297.34 c_36(U201^#(isNaturalKind(activate(V1)), 957.47/297.34 activate(V1), 957.47/297.34 activate(V2))) 957.47/297.34 , 39: U201^#(tt(), V1, V2) -> 957.47/297.34 c_71(U202^#(isNaturalKind(activate(V1)), 957.47/297.34 activate(V1), 957.47/297.34 activate(V2))) 957.47/297.34 , 40: isLNat^#(n__afterNth(V1, V2)) -> 957.47/297.34 c_40(U41^#(isNaturalKind(activate(V1)), 957.47/297.34 activate(V1), 957.47/297.34 activate(V2))) 957.47/297.34 , 41: isLNat^#(n__cons(V1, V2)) -> 957.47/297.34 c_41(U51^#(isNaturalKind(activate(V1)), 957.47/297.34 activate(V1), 957.47/297.34 activate(V2))) 957.47/297.34 , 42: isLNat^#(n__take(V1, V2)) -> 957.47/297.34 c_45(U101^#(isNaturalKind(activate(V1)), 957.47/297.34 activate(V1), 957.47/297.34 activate(V2))) 957.47/297.34 , 43: U41^#(tt(), V1, V2) -> 957.47/297.34 c_142(U42^#(isNaturalKind(activate(V1)), 957.47/297.34 activate(V1), 957.47/297.34 activate(V2))) 957.47/297.34 , 44: U51^#(tt(), V1, V2) -> 957.47/297.34 c_148(U52^#(isNaturalKind(activate(V1)), 957.47/297.34 activate(V1), 957.47/297.34 activate(V2))) 957.47/297.34 , 45: U11^#(tt(), N, XS) -> 957.47/297.34 c_46(U12^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.47/297.34 , 46: U12^#(tt(), N, XS) -> 957.47/297.34 c_47(U13^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.34 , 47: U13^#(tt(), N, XS) -> 957.47/297.34 c_50(U14^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.34 , 48: U14^#(tt(), N, XS) -> 957.47/297.34 c_53(snd^#(splitAt(activate(N), activate(XS)))) 957.47/297.34 , 49: U301^#(tt(), X, Y) -> 957.47/297.34 c_113(U302^#(isLNatKind(activate(X)), activate(Y))) 957.47/297.34 , 50: U321^#(tt(), N, X, XS) -> 957.47/297.34 c_124(U322^#(isNaturalKind(activate(N)), 957.47/297.34 activate(N), 957.47/297.34 activate(X), 957.47/297.34 activate(XS))) 957.47/297.34 , 51: U311^#(tt(), XS) -> 957.47/297.34 c_119(U312^#(isLNatKind(activate(XS)), activate(XS))) 957.47/297.34 , 52: U202^#(tt(), V1, V2) -> 957.47/297.34 c_72(U203^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.34 , 53: U21^#(tt(), X, Y) -> 957.47/297.34 c_77(U22^#(isLNatKind(activate(X)), activate(X), activate(Y))) 957.47/297.34 , 54: U22^#(tt(), X, Y) -> 957.47/297.34 c_78(U23^#(isLNat(activate(Y)), activate(X), activate(Y))) 957.47/297.34 , 55: U23^#(tt(), X, Y) -> 957.47/297.34 c_80(U24^#(isLNatKind(activate(Y)), activate(X))) 957.47/297.34 , 56: U24^#(tt(), X) -> c_82(activate^#(X)) 957.47/297.34 , 57: U241^#(tt(), V1, V2) -> 957.47/297.34 c_85(U242^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.47/297.34 , 58: U242^#(tt(), V1, V2) -> 957.47/297.34 c_86(U243^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.34 , 59: U251^#(tt(), V1, V2) -> 957.47/297.34 c_91(U252^#(isNaturalKind(activate(V1)), 957.47/297.34 activate(V1), 957.47/297.34 activate(V2))) 957.47/297.34 , 60: U252^#(tt(), V1, V2) -> 957.47/297.34 c_92(U253^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.34 , 61: U281^#(tt(), N) -> 957.47/297.34 c_101(U282^#(isNaturalKind(activate(N)), activate(N))) 957.47/297.34 , 62: U282^#(tt(), N) -> 957.47/297.34 c_102(cons^#(activate(N), n__natsFrom(s(activate(N))))) 957.47/297.34 , 63: U291^#(tt(), N, XS) -> 957.47/297.34 c_105(U292^#(isNaturalKind(activate(N)), 957.47/297.34 activate(N), 957.47/297.34 activate(XS))) 957.47/297.34 , 64: U292^#(tt(), N, XS) -> 957.47/297.34 c_106(U293^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.34 , 65: U293^#(tt(), N, XS) -> 957.47/297.34 c_107(U294^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.34 , 66: U294^#(tt(), N, XS) -> 957.47/297.34 c_108(head^#(afterNth(activate(N), activate(XS)))) 957.47/297.34 , 67: U31^#(tt(), N, XS) -> 957.47/297.34 c_117(U32^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.47/297.34 , 68: U302^#(tt(), Y) -> 957.47/297.34 c_114(U303^#(isLNat(activate(Y)), activate(Y))) 957.47/297.34 , 69: U303^#(tt(), Y) -> 957.47/297.34 c_115(U304^#(isLNatKind(activate(Y)), activate(Y))) 957.47/297.34 , 70: U304^#(tt(), Y) -> c_116(activate^#(Y)) 957.47/297.34 , 71: U32^#(tt(), N, XS) -> 957.47/297.34 c_118(U33^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.34 , 72: U33^#(tt(), N, XS) -> 957.47/297.34 c_123(U34^#(isLNatKind(activate(XS)), activate(N))) 957.47/297.34 , 73: U312^#(tt(), XS) -> c_120(pair^#(nil(), activate(XS))) 957.47/297.34 , 74: U34^#(tt(), N) -> c_131(activate^#(N)) 957.47/297.34 , 75: U322^#(tt(), N, X, XS) -> 957.47/297.34 c_125(U323^#(isNatural(activate(X)), 957.47/297.34 activate(N), 957.47/297.34 activate(X), 957.47/297.34 activate(XS))) 957.47/297.34 , 76: U323^#(tt(), N, X, XS) -> 957.47/297.34 c_126(U324^#(isNaturalKind(activate(X)), 957.47/297.34 activate(N), 957.47/297.34 activate(X), 957.47/297.34 activate(XS))) 957.47/297.34 , 77: U324^#(tt(), N, X, XS) -> 957.47/297.34 c_127(U325^#(isLNat(activate(XS)), 957.47/297.34 activate(N), 957.47/297.34 activate(X), 957.47/297.34 activate(XS))) 957.47/297.34 , 78: U325^#(tt(), N, X, XS) -> 957.47/297.34 c_128(U326^#(isLNatKind(activate(XS)), 957.47/297.34 activate(N), 957.47/297.34 activate(X), 957.47/297.34 activate(XS))) 957.47/297.34 , 79: U326^#(tt(), N, X, XS) -> 957.47/297.34 c_129(U327^#(splitAt(activate(N), activate(XS)), activate(X))) 957.47/297.34 , 80: U327^#(pair(YS, ZS), X) -> 957.47/297.34 c_130(pair^#(cons(activate(X), YS), ZS)) 957.47/297.34 , 81: U331^#(tt(), N, XS) -> 957.47/297.34 c_132(U332^#(isNaturalKind(activate(N)), activate(XS))) 957.47/297.34 , 82: U332^#(tt(), XS) -> 957.47/297.34 c_133(U333^#(isLNat(activate(XS)), activate(XS))) 957.47/297.34 , 83: U333^#(tt(), XS) -> 957.47/297.34 c_134(U334^#(isLNatKind(activate(XS)), activate(XS))) 957.47/297.34 , 84: U334^#(tt(), XS) -> c_135(activate^#(XS)) 957.47/297.34 , 85: U341^#(tt(), N, XS) -> 957.47/297.34 c_136(U342^#(isNaturalKind(activate(N)), 957.47/297.34 activate(N), 957.47/297.34 activate(XS))) 957.47/297.34 , 86: U342^#(tt(), N, XS) -> 957.47/297.34 c_137(U343^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.34 , 87: U343^#(tt(), N, XS) -> 957.47/297.34 c_138(U344^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.34 , 88: U344^#(tt(), N, XS) -> 957.47/297.34 c_139(fst^#(splitAt(activate(N), activate(XS)))) 957.47/297.34 , 89: U42^#(tt(), V1, V2) -> 957.47/297.34 c_143(U43^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.34 , 90: U52^#(tt(), V1, V2) -> 957.47/297.34 c_149(U53^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.34 , 91: isPLNat^#(n__pair(V1, V2)) -> 957.47/297.34 c_159(U241^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.47/297.34 , 92: isPLNat^#(n__splitAt(V1, V2)) -> 957.47/297.34 c_160(U251^#(isNaturalKind(activate(V1)), 957.47/297.34 activate(V1), 957.47/297.34 activate(V2))) 957.47/297.34 , 93: U103^#(tt(), V1, V2) -> 957.47/297.34 c_22(U104^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.34 , 94: isNaturalKind^#(n__0()) -> c_3() 957.47/297.34 , 95: isNaturalKind^#(n__head(V1)) -> 957.47/297.34 c_4(U211^#(isLNatKind(activate(V1)))) 957.47/297.34 , 96: isNaturalKind^#(n__s(V1)) -> 957.47/297.34 c_5(U221^#(isNaturalKind(activate(V1)))) 957.47/297.34 , 97: isNaturalKind^#(n__sel(V1, V2)) -> 957.47/297.34 c_6(U231^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.34 , 98: U211^#(tt()) -> c_79() 957.47/297.34 , 99: U221^#(tt()) -> c_81() 957.47/297.34 , 100: U231^#(tt(), V2) -> c_83(U232^#(isLNatKind(activate(V2)))) 957.47/297.34 , 101: activate^#(n__nil()) -> c_9(nil^#()) 957.47/297.34 , 102: activate^#(n__0()) -> c_16(0^#()) 957.47/297.34 , 103: nil^#() -> c_122() 957.47/297.34 , 104: 0^#() -> c_174() 957.47/297.34 , 105: U104^#(tt(), V1, V2) -> 957.47/297.34 c_31(U105^#(isNatural(activate(V1)), activate(V2))) 957.47/297.34 , 106: isLNatKind^#(n__natsFrom(V1)) -> 957.47/297.34 c_23(U141^#(isNaturalKind(activate(V1)))) 957.47/297.34 , 107: isLNatKind^#(n__nil()) -> c_24() 957.47/297.34 , 108: isLNatKind^#(n__afterNth(V1, V2)) -> 957.47/297.34 c_25(U111^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.34 , 109: isLNatKind^#(n__cons(V1, V2)) -> 957.47/297.34 c_26(U121^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.34 , 110: isLNatKind^#(n__fst(V1)) -> 957.47/297.34 c_27(U131^#(isPLNatKind(activate(V1)))) 957.47/297.34 , 111: isLNatKind^#(n__snd(V1)) -> 957.47/297.34 c_28(U151^#(isPLNatKind(activate(V1)))) 957.47/297.34 , 112: isLNatKind^#(n__tail(V1)) -> 957.47/297.34 c_29(U161^#(isLNatKind(activate(V1)))) 957.47/297.34 , 113: isLNatKind^#(n__take(V1, V2)) -> 957.47/297.34 c_30(U171^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.34 , 114: U141^#(tt()) -> c_60() 957.47/297.34 , 115: U111^#(tt(), V2) -> c_48(U112^#(isLNatKind(activate(V2)))) 957.47/297.34 , 116: U121^#(tt(), V2) -> c_51(U122^#(isLNatKind(activate(V2)))) 957.47/297.34 , 117: U131^#(tt()) -> c_54() 957.47/297.34 , 118: U151^#(tt()) -> c_61() 957.47/297.34 , 119: U161^#(tt()) -> c_62() 957.47/297.34 , 120: U171^#(tt(), V2) -> c_63(U172^#(isLNatKind(activate(V2)))) 957.47/297.34 , 121: U105^#(tt(), V2) -> c_32(U106^#(isLNat(activate(V2)))) 957.47/297.34 , 122: U106^#(tt()) -> c_37() 957.47/297.34 , 123: isNatural^#(n__0()) -> c_33() 957.47/297.34 , 124: isNatural^#(n__head(V1)) -> 957.47/297.34 c_34(U181^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.34 , 125: isNatural^#(n__s(V1)) -> 957.47/297.34 c_35(U191^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.34 , 126: U181^#(tt(), V1) -> 957.47/297.34 c_65(U182^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.34 , 127: U191^#(tt(), V1) -> 957.47/297.34 c_68(U192^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.34 , 128: isLNat^#(n__natsFrom(V1)) -> 957.47/297.34 c_38(U71^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.34 , 129: isLNat^#(n__nil()) -> c_39() 957.47/297.34 , 130: isLNat^#(n__fst(V1)) -> 957.47/297.34 c_42(U61^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.34 , 131: isLNat^#(n__snd(V1)) -> 957.47/297.34 c_43(U81^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.34 , 132: isLNat^#(n__tail(V1)) -> 957.47/297.34 c_44(U91^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.34 , 133: U71^#(tt(), V1) -> 957.47/297.34 c_161(U72^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.34 , 134: U61^#(tt(), V1) -> 957.47/297.34 c_154(U62^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.34 , 135: U81^#(tt(), V1) -> 957.47/297.34 c_164(U82^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.34 , 136: U91^#(tt(), V1) -> 957.47/297.34 c_167(U92^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.34 , 137: U112^#(tt()) -> c_49() 957.47/297.34 , 138: U122^#(tt()) -> c_52() 957.47/297.34 , 139: U172^#(tt()) -> c_64() 957.47/297.34 , 140: U182^#(tt(), V1) -> c_66(U183^#(isLNat(activate(V1)))) 957.47/297.34 , 141: U183^#(tt()) -> c_67() 957.47/297.34 , 142: U192^#(tt(), V1) -> c_69(U193^#(isNatural(activate(V1)))) 957.47/297.34 , 143: U193^#(tt()) -> c_70() 957.47/297.34 , 144: U203^#(tt(), V1, V2) -> 957.47/297.34 c_73(U204^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.34 , 145: U204^#(tt(), V1, V2) -> 957.47/297.34 c_74(U205^#(isNatural(activate(V1)), activate(V2))) 957.47/297.34 , 146: U205^#(tt(), V2) -> c_75(U206^#(isLNat(activate(V2)))) 957.47/297.34 , 147: U206^#(tt()) -> c_76() 957.47/297.34 , 148: U232^#(tt()) -> c_84() 957.47/297.34 , 149: U243^#(tt(), V1, V2) -> 957.47/297.34 c_87(U244^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.34 , 150: U244^#(tt(), V1, V2) -> 957.47/297.34 c_88(U245^#(isLNat(activate(V1)), activate(V2))) 957.47/297.34 , 151: U245^#(tt(), V2) -> c_89(U246^#(isLNat(activate(V2)))) 957.47/297.34 , 152: U246^#(tt()) -> c_90() 957.47/297.34 , 153: U253^#(tt(), V1, V2) -> 957.47/297.34 c_93(U254^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.34 , 154: U254^#(tt(), V1, V2) -> 957.47/297.34 c_94(U255^#(isNatural(activate(V1)), activate(V2))) 957.47/297.34 , 155: U255^#(tt(), V2) -> c_95(U256^#(isLNat(activate(V2)))) 957.47/297.34 , 156: U256^#(tt()) -> c_96() 957.47/297.34 , 157: U261^#(tt(), V2) -> c_97(U262^#(isLNatKind(activate(V2)))) 957.47/297.34 , 158: U262^#(tt()) -> c_98() 957.47/297.34 , 159: U271^#(tt(), V2) -> c_99(U272^#(isLNatKind(activate(V2)))) 957.47/297.34 , 160: U272^#(tt()) -> c_100() 957.47/297.34 , 161: U43^#(tt(), V1, V2) -> 957.47/297.34 c_144(U44^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.34 , 162: U44^#(tt(), V1, V2) -> 957.47/297.34 c_145(U45^#(isNatural(activate(V1)), activate(V2))) 957.47/297.34 , 163: U45^#(tt(), V2) -> c_146(U46^#(isLNat(activate(V2)))) 957.47/297.34 , 164: U46^#(tt()) -> c_147() 957.47/297.34 , 165: U53^#(tt(), V1, V2) -> 957.47/297.34 c_150(U54^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.34 , 166: U54^#(tt(), V1, V2) -> 957.47/297.34 c_151(U55^#(isNatural(activate(V1)), activate(V2))) 957.47/297.34 , 167: U55^#(tt(), V2) -> c_152(U56^#(isLNat(activate(V2)))) 957.47/297.34 , 168: U56^#(tt()) -> c_153() 957.47/297.34 , 169: U62^#(tt(), V1) -> c_155(U63^#(isPLNat(activate(V1)))) 957.47/297.34 , 170: U63^#(tt()) -> c_158() 957.47/297.34 , 171: isPLNatKind^#(n__pair(V1, V2)) -> 957.47/297.34 c_156(U261^#(isLNatKind(activate(V1)), activate(V2))) 957.47/297.34 , 172: isPLNatKind^#(n__splitAt(V1, V2)) -> 957.47/297.34 c_157(U271^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.34 , 173: U72^#(tt(), V1) -> c_162(U73^#(isNatural(activate(V1)))) 957.47/297.34 , 174: U73^#(tt()) -> c_163() 957.47/297.34 , 175: U82^#(tt(), V1) -> c_165(U83^#(isPLNat(activate(V1)))) 957.47/297.34 , 176: U83^#(tt()) -> c_166() 957.47/297.34 , 177: U92^#(tt(), V1) -> c_168(U93^#(isLNat(activate(V1)))) 957.47/297.34 , 178: U93^#(tt()) -> c_169() } 957.47/297.34 957.47/297.34 We are left with following problem, upon which TcT provides the 957.47/297.34 certificate MAYBE. 957.47/297.34 957.47/297.34 Strict DPs: 957.47/297.34 { U101^#(tt(), V1, V2) -> 957.47/297.34 c_1(U102^#(isNaturalKind(activate(V1)), 957.47/297.34 activate(V1), 957.47/297.34 activate(V2))) 957.47/297.34 , activate^#(X) -> c_7(X) 957.47/297.34 , activate^#(n__natsFrom(X)) -> c_8(natsFrom^#(X)) 957.47/297.34 , activate^#(n__afterNth(X1, X2)) -> c_10(afterNth^#(X1, X2)) 957.47/297.34 , activate^#(n__cons(X1, X2)) -> c_11(cons^#(X1, X2)) 957.47/297.34 , activate^#(n__fst(X)) -> c_12(fst^#(X)) 957.47/297.34 , activate^#(n__snd(X)) -> c_13(snd^#(X)) 957.47/297.34 , activate^#(n__tail(X)) -> c_14(tail^#(X)) 957.47/297.34 , activate^#(n__take(X1, X2)) -> c_15(take^#(X1, X2)) 957.47/297.34 , activate^#(n__head(X)) -> c_17(head^#(X)) 957.47/297.34 , activate^#(n__s(X)) -> c_18(s^#(X)) 957.47/297.34 , activate^#(n__sel(X1, X2)) -> c_19(sel^#(X1, X2)) 957.47/297.34 , activate^#(n__pair(X1, X2)) -> c_20(pair^#(X1, X2)) 957.47/297.34 , activate^#(n__splitAt(X1, X2)) -> c_21(splitAt^#(X1, X2)) 957.47/297.34 , natsFrom^#(N) -> c_170(U281^#(isNatural(N), N)) 957.47/297.34 , natsFrom^#(X) -> c_171(X) 957.47/297.34 , afterNth^#(N, XS) -> c_111(U11^#(isNatural(N), N, XS)) 957.47/297.34 , afterNth^#(X1, X2) -> c_112(X1, X2) 957.47/297.34 , cons^#(X1, X2) -> c_103(X1, X2) 957.47/297.34 , fst^#(X) -> c_140(X) 957.47/297.34 , fst^#(pair(X, Y)) -> c_141(U21^#(isLNat(X), X, Y)) 957.47/297.34 , snd^#(X) -> c_55(X) 957.47/297.34 , snd^#(pair(X, Y)) -> c_56(U301^#(isLNat(X), X, Y)) 957.47/297.34 , tail^#(X) -> c_175(X) 957.47/297.34 , tail^#(cons(N, XS)) -> 957.47/297.34 c_176(U331^#(isNatural(N), N, activate(XS))) 957.47/297.34 , take^#(N, XS) -> c_177(U341^#(isNatural(N), N, XS)) 957.47/297.34 , take^#(X1, X2) -> c_178(X1, X2) 957.47/297.34 , head^#(X) -> c_109(X) 957.47/297.34 , head^#(cons(N, XS)) -> 957.47/297.34 c_110(U31^#(isNatural(N), N, activate(XS))) 957.47/297.34 , s^#(X) -> c_104(X) 957.47/297.34 , sel^#(N, XS) -> c_172(U291^#(isNatural(N), N, XS)) 957.47/297.34 , sel^#(X1, X2) -> c_173(X1, X2) 957.47/297.34 , pair^#(X1, X2) -> c_121(X1, X2) 957.47/297.34 , splitAt^#(X1, X2) -> c_57(X1, X2) 957.47/297.34 , splitAt^#(s(N), cons(X, XS)) -> 957.47/297.34 c_58(U321^#(isNatural(N), N, X, activate(XS))) 957.47/297.34 , splitAt^#(0(), XS) -> c_59(U311^#(isLNat(XS), XS)) 957.47/297.34 , isNatural^#(n__sel(V1, V2)) -> 957.47/297.34 c_36(U201^#(isNaturalKind(activate(V1)), 957.47/297.34 activate(V1), 957.47/297.34 activate(V2))) 957.47/297.34 , U201^#(tt(), V1, V2) -> 957.47/297.34 c_71(U202^#(isNaturalKind(activate(V1)), 957.47/297.34 activate(V1), 957.47/297.34 activate(V2))) 957.47/297.34 , isLNat^#(n__afterNth(V1, V2)) -> 957.47/297.34 c_40(U41^#(isNaturalKind(activate(V1)), 957.47/297.34 activate(V1), 957.47/297.34 activate(V2))) 957.47/297.34 , isLNat^#(n__cons(V1, V2)) -> 957.47/297.34 c_41(U51^#(isNaturalKind(activate(V1)), 957.47/297.34 activate(V1), 957.47/297.34 activate(V2))) 957.47/297.34 , isLNat^#(n__take(V1, V2)) -> 957.47/297.34 c_45(U101^#(isNaturalKind(activate(V1)), 957.47/297.34 activate(V1), 957.47/297.34 activate(V2))) 957.47/297.34 , U41^#(tt(), V1, V2) -> 957.47/297.34 c_142(U42^#(isNaturalKind(activate(V1)), 957.47/297.34 activate(V1), 957.47/297.34 activate(V2))) 957.47/297.34 , U51^#(tt(), V1, V2) -> 957.47/297.34 c_148(U52^#(isNaturalKind(activate(V1)), 957.47/297.34 activate(V1), 957.47/297.34 activate(V2))) 957.47/297.34 , U11^#(tt(), N, XS) -> 957.47/297.34 c_46(U12^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.47/297.34 , U12^#(tt(), N, XS) -> 957.47/297.34 c_47(U13^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.34 , U13^#(tt(), N, XS) -> 957.47/297.34 c_50(U14^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.34 , U14^#(tt(), N, XS) -> 957.47/297.34 c_53(snd^#(splitAt(activate(N), activate(XS)))) 957.47/297.34 , U301^#(tt(), X, Y) -> 957.47/297.34 c_113(U302^#(isLNatKind(activate(X)), activate(Y))) 957.47/297.34 , U321^#(tt(), N, X, XS) -> 957.47/297.34 c_124(U322^#(isNaturalKind(activate(N)), 957.47/297.34 activate(N), 957.47/297.34 activate(X), 957.47/297.34 activate(XS))) 957.47/297.34 , U311^#(tt(), XS) -> 957.47/297.34 c_119(U312^#(isLNatKind(activate(XS)), activate(XS))) 957.47/297.34 , U21^#(tt(), X, Y) -> 957.47/297.34 c_77(U22^#(isLNatKind(activate(X)), activate(X), activate(Y))) 957.47/297.34 , U22^#(tt(), X, Y) -> 957.47/297.34 c_78(U23^#(isLNat(activate(Y)), activate(X), activate(Y))) 957.47/297.34 , U23^#(tt(), X, Y) -> 957.47/297.34 c_80(U24^#(isLNatKind(activate(Y)), activate(X))) 957.47/297.34 , U24^#(tt(), X) -> c_82(activate^#(X)) 957.47/297.34 , U241^#(tt(), V1, V2) -> 957.47/297.34 c_85(U242^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.47/297.34 , U251^#(tt(), V1, V2) -> 957.47/297.34 c_91(U252^#(isNaturalKind(activate(V1)), 957.47/297.34 activate(V1), 957.47/297.35 activate(V2))) 957.47/297.35 , U281^#(tt(), N) -> 957.47/297.35 c_101(U282^#(isNaturalKind(activate(N)), activate(N))) 957.47/297.35 , U282^#(tt(), N) -> 957.47/297.35 c_102(cons^#(activate(N), n__natsFrom(s(activate(N))))) 957.47/297.35 , U291^#(tt(), N, XS) -> 957.47/297.35 c_105(U292^#(isNaturalKind(activate(N)), 957.47/297.35 activate(N), 957.47/297.35 activate(XS))) 957.47/297.35 , U292^#(tt(), N, XS) -> 957.47/297.35 c_106(U293^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.35 , U293^#(tt(), N, XS) -> 957.47/297.35 c_107(U294^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.35 , U294^#(tt(), N, XS) -> 957.47/297.35 c_108(head^#(afterNth(activate(N), activate(XS)))) 957.47/297.35 , U31^#(tt(), N, XS) -> 957.47/297.35 c_117(U32^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.47/297.35 , U302^#(tt(), Y) -> 957.47/297.35 c_114(U303^#(isLNat(activate(Y)), activate(Y))) 957.47/297.35 , U303^#(tt(), Y) -> 957.47/297.35 c_115(U304^#(isLNatKind(activate(Y)), activate(Y))) 957.47/297.35 , U304^#(tt(), Y) -> c_116(activate^#(Y)) 957.47/297.35 , U32^#(tt(), N, XS) -> 957.47/297.35 c_118(U33^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.35 , U33^#(tt(), N, XS) -> 957.47/297.35 c_123(U34^#(isLNatKind(activate(XS)), activate(N))) 957.47/297.35 , U312^#(tt(), XS) -> c_120(pair^#(nil(), activate(XS))) 957.47/297.35 , U34^#(tt(), N) -> c_131(activate^#(N)) 957.47/297.35 , U322^#(tt(), N, X, XS) -> 957.47/297.35 c_125(U323^#(isNatural(activate(X)), 957.47/297.35 activate(N), 957.47/297.35 activate(X), 957.47/297.35 activate(XS))) 957.47/297.35 , U323^#(tt(), N, X, XS) -> 957.47/297.35 c_126(U324^#(isNaturalKind(activate(X)), 957.47/297.35 activate(N), 957.47/297.35 activate(X), 957.47/297.35 activate(XS))) 957.47/297.35 , U324^#(tt(), N, X, XS) -> 957.47/297.35 c_127(U325^#(isLNat(activate(XS)), 957.47/297.35 activate(N), 957.47/297.35 activate(X), 957.47/297.35 activate(XS))) 957.47/297.35 , U325^#(tt(), N, X, XS) -> 957.47/297.35 c_128(U326^#(isLNatKind(activate(XS)), 957.47/297.35 activate(N), 957.47/297.35 activate(X), 957.47/297.35 activate(XS))) 957.47/297.35 , U326^#(tt(), N, X, XS) -> 957.47/297.35 c_129(U327^#(splitAt(activate(N), activate(XS)), activate(X))) 957.47/297.35 , U327^#(pair(YS, ZS), X) -> 957.47/297.35 c_130(pair^#(cons(activate(X), YS), ZS)) 957.47/297.35 , U331^#(tt(), N, XS) -> 957.47/297.35 c_132(U332^#(isNaturalKind(activate(N)), activate(XS))) 957.47/297.35 , U332^#(tt(), XS) -> 957.47/297.35 c_133(U333^#(isLNat(activate(XS)), activate(XS))) 957.47/297.35 , U333^#(tt(), XS) -> 957.47/297.35 c_134(U334^#(isLNatKind(activate(XS)), activate(XS))) 957.47/297.35 , U334^#(tt(), XS) -> c_135(activate^#(XS)) 957.47/297.35 , U341^#(tt(), N, XS) -> 957.47/297.35 c_136(U342^#(isNaturalKind(activate(N)), 957.47/297.35 activate(N), 957.47/297.35 activate(XS))) 957.47/297.35 , U342^#(tt(), N, XS) -> 957.47/297.35 c_137(U343^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.35 , U343^#(tt(), N, XS) -> 957.47/297.35 c_138(U344^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.35 , U344^#(tt(), N, XS) -> 957.47/297.35 c_139(fst^#(splitAt(activate(N), activate(XS)))) 957.47/297.35 , isPLNat^#(n__pair(V1, V2)) -> 957.47/297.35 c_159(U241^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.47/297.35 , isPLNat^#(n__splitAt(V1, V2)) -> 957.47/297.35 c_160(U251^#(isNaturalKind(activate(V1)), 957.47/297.35 activate(V1), 957.47/297.35 activate(V2))) } 957.47/297.35 Strict Trs: 957.47/297.35 { U101(tt(), V1, V2) -> 957.47/297.35 U102(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.35 , U102(tt(), V1, V2) -> 957.47/297.35 U103(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.35 , isNaturalKind(n__0()) -> tt() 957.47/297.35 , isNaturalKind(n__head(V1)) -> U211(isLNatKind(activate(V1))) 957.47/297.35 , isNaturalKind(n__s(V1)) -> U221(isNaturalKind(activate(V1))) 957.47/297.35 , isNaturalKind(n__sel(V1, V2)) -> 957.47/297.35 U231(isNaturalKind(activate(V1)), activate(V2)) 957.47/297.35 , activate(X) -> X 957.47/297.35 , activate(n__natsFrom(X)) -> natsFrom(X) 957.47/297.35 , activate(n__nil()) -> nil() 957.47/297.35 , activate(n__afterNth(X1, X2)) -> afterNth(X1, X2) 957.47/297.35 , activate(n__cons(X1, X2)) -> cons(X1, X2) 957.47/297.35 , activate(n__fst(X)) -> fst(X) 957.47/297.35 , activate(n__snd(X)) -> snd(X) 957.47/297.35 , activate(n__tail(X)) -> tail(X) 957.47/297.35 , activate(n__take(X1, X2)) -> take(X1, X2) 957.47/297.35 , activate(n__0()) -> 0() 957.47/297.35 , activate(n__head(X)) -> head(X) 957.47/297.35 , activate(n__s(X)) -> s(X) 957.47/297.35 , activate(n__sel(X1, X2)) -> sel(X1, X2) 957.47/297.35 , activate(n__pair(X1, X2)) -> pair(X1, X2) 957.47/297.35 , activate(n__splitAt(X1, X2)) -> splitAt(X1, X2) 957.47/297.35 , U103(tt(), V1, V2) -> 957.47/297.35 U104(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.35 , isLNatKind(n__natsFrom(V1)) -> U141(isNaturalKind(activate(V1))) 957.47/297.35 , isLNatKind(n__nil()) -> tt() 957.47/297.35 , isLNatKind(n__afterNth(V1, V2)) -> 957.47/297.35 U111(isNaturalKind(activate(V1)), activate(V2)) 957.47/297.35 , isLNatKind(n__cons(V1, V2)) -> 957.47/297.35 U121(isNaturalKind(activate(V1)), activate(V2)) 957.47/297.35 , isLNatKind(n__fst(V1)) -> U131(isPLNatKind(activate(V1))) 957.47/297.35 , isLNatKind(n__snd(V1)) -> U151(isPLNatKind(activate(V1))) 957.47/297.35 , isLNatKind(n__tail(V1)) -> U161(isLNatKind(activate(V1))) 957.47/297.35 , isLNatKind(n__take(V1, V2)) -> 957.47/297.35 U171(isNaturalKind(activate(V1)), activate(V2)) 957.47/297.35 , U104(tt(), V1, V2) -> U105(isNatural(activate(V1)), activate(V2)) 957.47/297.35 , U105(tt(), V2) -> U106(isLNat(activate(V2))) 957.47/297.35 , isNatural(n__0()) -> tt() 957.47/297.35 , isNatural(n__head(V1)) -> 957.47/297.35 U181(isLNatKind(activate(V1)), activate(V1)) 957.47/297.35 , isNatural(n__s(V1)) -> 957.47/297.35 U191(isNaturalKind(activate(V1)), activate(V1)) 957.47/297.35 , isNatural(n__sel(V1, V2)) -> 957.47/297.35 U201(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.35 , U106(tt()) -> tt() 957.47/297.35 , isLNat(n__natsFrom(V1)) -> 957.47/297.35 U71(isNaturalKind(activate(V1)), activate(V1)) 957.47/297.35 , isLNat(n__nil()) -> tt() 957.47/297.35 , isLNat(n__afterNth(V1, V2)) -> 957.47/297.35 U41(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.35 , isLNat(n__cons(V1, V2)) -> 957.47/297.35 U51(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.35 , isLNat(n__fst(V1)) -> 957.47/297.35 U61(isPLNatKind(activate(V1)), activate(V1)) 957.47/297.35 , isLNat(n__snd(V1)) -> 957.47/297.35 U81(isPLNatKind(activate(V1)), activate(V1)) 957.47/297.35 , isLNat(n__tail(V1)) -> 957.47/297.35 U91(isLNatKind(activate(V1)), activate(V1)) 957.47/297.35 , isLNat(n__take(V1, V2)) -> 957.47/297.35 U101(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.35 , U11(tt(), N, XS) -> 957.47/297.35 U12(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.47/297.35 , U12(tt(), N, XS) -> 957.47/297.35 U13(isLNat(activate(XS)), activate(N), activate(XS)) 957.47/297.35 , U111(tt(), V2) -> U112(isLNatKind(activate(V2))) 957.47/297.35 , U112(tt()) -> tt() 957.47/297.35 , U13(tt(), N, XS) -> 957.47/297.35 U14(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.47/297.35 , U121(tt(), V2) -> U122(isLNatKind(activate(V2))) 957.47/297.35 , U122(tt()) -> tt() 957.47/297.35 , U14(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS))) 957.47/297.35 , U131(tt()) -> tt() 957.47/297.35 , snd(X) -> n__snd(X) 957.47/297.35 , snd(pair(X, Y)) -> U301(isLNat(X), X, Y) 957.47/297.35 , splitAt(X1, X2) -> n__splitAt(X1, X2) 957.47/297.35 , splitAt(s(N), cons(X, XS)) -> 957.47/297.35 U321(isNatural(N), N, X, activate(XS)) 957.47/297.35 , splitAt(0(), XS) -> U311(isLNat(XS), XS) 957.47/297.35 , U141(tt()) -> tt() 957.47/297.35 , U151(tt()) -> tt() 957.47/297.35 , U161(tt()) -> tt() 957.47/297.35 , U171(tt(), V2) -> U172(isLNatKind(activate(V2))) 957.47/297.35 , U172(tt()) -> tt() 957.47/297.35 , U181(tt(), V1) -> U182(isLNatKind(activate(V1)), activate(V1)) 957.47/297.35 , U182(tt(), V1) -> U183(isLNat(activate(V1))) 957.47/297.35 , U183(tt()) -> tt() 957.47/297.35 , U191(tt(), V1) -> U192(isNaturalKind(activate(V1)), activate(V1)) 957.47/297.35 , U192(tt(), V1) -> U193(isNatural(activate(V1))) 957.47/297.35 , U193(tt()) -> tt() 957.47/297.35 , U201(tt(), V1, V2) -> 957.47/297.35 U202(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.35 , U202(tt(), V1, V2) -> 957.47/297.35 U203(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.35 , U203(tt(), V1, V2) -> 957.47/297.35 U204(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.35 , U204(tt(), V1, V2) -> U205(isNatural(activate(V1)), activate(V2)) 957.47/297.35 , U205(tt(), V2) -> U206(isLNat(activate(V2))) 957.47/297.35 , U206(tt()) -> tt() 957.47/297.35 , U21(tt(), X, Y) -> 957.47/297.35 U22(isLNatKind(activate(X)), activate(X), activate(Y)) 957.47/297.35 , U22(tt(), X, Y) -> 957.47/297.35 U23(isLNat(activate(Y)), activate(X), activate(Y)) 957.47/297.35 , U211(tt()) -> tt() 957.47/297.35 , U23(tt(), X, Y) -> U24(isLNatKind(activate(Y)), activate(X)) 957.47/297.35 , U221(tt()) -> tt() 957.47/297.35 , U24(tt(), X) -> activate(X) 957.47/297.35 , U231(tt(), V2) -> U232(isLNatKind(activate(V2))) 957.47/297.35 , U232(tt()) -> tt() 957.47/297.35 , U241(tt(), V1, V2) -> 957.47/297.35 U242(isLNatKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.35 , U242(tt(), V1, V2) -> 957.47/297.35 U243(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.35 , U243(tt(), V1, V2) -> 957.47/297.35 U244(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.35 , U244(tt(), V1, V2) -> U245(isLNat(activate(V1)), activate(V2)) 957.47/297.35 , U245(tt(), V2) -> U246(isLNat(activate(V2))) 957.47/297.35 , U246(tt()) -> tt() 957.47/297.35 , U251(tt(), V1, V2) -> 957.47/297.35 U252(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.35 , U252(tt(), V1, V2) -> 957.47/297.35 U253(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.35 , U253(tt(), V1, V2) -> 957.47/297.35 U254(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.35 , U254(tt(), V1, V2) -> U255(isNatural(activate(V1)), activate(V2)) 957.47/297.35 , U255(tt(), V2) -> U256(isLNat(activate(V2))) 957.47/297.35 , U256(tt()) -> tt() 957.47/297.35 , U261(tt(), V2) -> U262(isLNatKind(activate(V2))) 957.47/297.35 , U262(tt()) -> tt() 957.47/297.35 , U271(tt(), V2) -> U272(isLNatKind(activate(V2))) 957.47/297.35 , U272(tt()) -> tt() 957.47/297.35 , U281(tt(), N) -> U282(isNaturalKind(activate(N)), activate(N)) 957.47/297.35 , U282(tt(), N) -> cons(activate(N), n__natsFrom(s(activate(N)))) 957.47/297.35 , cons(X1, X2) -> n__cons(X1, X2) 957.47/297.35 , s(X) -> n__s(X) 957.47/297.35 , U291(tt(), N, XS) -> 957.47/297.35 U292(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.47/297.35 , U292(tt(), N, XS) -> 957.47/297.35 U293(isLNat(activate(XS)), activate(N), activate(XS)) 957.47/297.35 , U293(tt(), N, XS) -> 957.47/297.35 U294(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.47/297.35 , U294(tt(), N, XS) -> head(afterNth(activate(N), activate(XS))) 957.47/297.35 , head(X) -> n__head(X) 957.47/297.35 , head(cons(N, XS)) -> U31(isNatural(N), N, activate(XS)) 957.47/297.35 , afterNth(N, XS) -> U11(isNatural(N), N, XS) 957.47/297.35 , afterNth(X1, X2) -> n__afterNth(X1, X2) 957.47/297.35 , U301(tt(), X, Y) -> U302(isLNatKind(activate(X)), activate(Y)) 957.47/297.35 , U302(tt(), Y) -> U303(isLNat(activate(Y)), activate(Y)) 957.47/297.35 , U303(tt(), Y) -> U304(isLNatKind(activate(Y)), activate(Y)) 957.47/297.35 , U304(tt(), Y) -> activate(Y) 957.47/297.35 , U31(tt(), N, XS) -> 957.47/297.35 U32(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.47/297.35 , U32(tt(), N, XS) -> 957.47/297.35 U33(isLNat(activate(XS)), activate(N), activate(XS)) 957.47/297.35 , U311(tt(), XS) -> U312(isLNatKind(activate(XS)), activate(XS)) 957.47/297.35 , U312(tt(), XS) -> pair(nil(), activate(XS)) 957.47/297.35 , pair(X1, X2) -> n__pair(X1, X2) 957.47/297.35 , nil() -> n__nil() 957.47/297.35 , U33(tt(), N, XS) -> U34(isLNatKind(activate(XS)), activate(N)) 957.47/297.35 , U321(tt(), N, X, XS) -> 957.47/297.35 U322(isNaturalKind(activate(N)), 957.47/297.35 activate(N), 957.47/297.35 activate(X), 957.47/297.35 activate(XS)) 957.47/297.35 , U322(tt(), N, X, XS) -> 957.47/297.35 U323(isNatural(activate(X)), 957.47/297.35 activate(N), 957.47/297.35 activate(X), 957.47/297.35 activate(XS)) 957.47/297.35 , U323(tt(), N, X, XS) -> 957.47/297.35 U324(isNaturalKind(activate(X)), 957.47/297.35 activate(N), 957.47/297.35 activate(X), 957.47/297.35 activate(XS)) 957.47/297.35 , U324(tt(), N, X, XS) -> 957.47/297.35 U325(isLNat(activate(XS)), activate(N), activate(X), activate(XS)) 957.47/297.35 , U325(tt(), N, X, XS) -> 957.47/297.35 U326(isLNatKind(activate(XS)), 957.47/297.35 activate(N), 957.47/297.35 activate(X), 957.47/297.35 activate(XS)) 957.47/297.35 , U326(tt(), N, X, XS) -> 957.47/297.35 U327(splitAt(activate(N), activate(XS)), activate(X)) 957.47/297.35 , U327(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) 957.47/297.35 , U34(tt(), N) -> activate(N) 957.47/297.35 , U331(tt(), N, XS) -> 957.47/297.35 U332(isNaturalKind(activate(N)), activate(XS)) 957.47/297.35 , U332(tt(), XS) -> U333(isLNat(activate(XS)), activate(XS)) 957.47/297.35 , U333(tt(), XS) -> U334(isLNatKind(activate(XS)), activate(XS)) 957.47/297.35 , U334(tt(), XS) -> activate(XS) 957.47/297.35 , U341(tt(), N, XS) -> 957.47/297.35 U342(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.47/297.35 , U342(tt(), N, XS) -> 957.47/297.35 U343(isLNat(activate(XS)), activate(N), activate(XS)) 957.47/297.35 , U343(tt(), N, XS) -> 957.47/297.35 U344(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.47/297.35 , U344(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS))) 957.47/297.35 , fst(X) -> n__fst(X) 957.47/297.35 , fst(pair(X, Y)) -> U21(isLNat(X), X, Y) 957.47/297.35 , U41(tt(), V1, V2) -> 957.47/297.35 U42(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.35 , U42(tt(), V1, V2) -> 957.47/297.35 U43(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.35 , U43(tt(), V1, V2) -> 957.47/297.35 U44(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.35 , U44(tt(), V1, V2) -> U45(isNatural(activate(V1)), activate(V2)) 957.47/297.35 , U45(tt(), V2) -> U46(isLNat(activate(V2))) 957.47/297.35 , U46(tt()) -> tt() 957.47/297.35 , U51(tt(), V1, V2) -> 957.47/297.35 U52(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.35 , U52(tt(), V1, V2) -> 957.47/297.35 U53(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.35 , U53(tt(), V1, V2) -> 957.47/297.35 U54(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.35 , U54(tt(), V1, V2) -> U55(isNatural(activate(V1)), activate(V2)) 957.47/297.35 , U55(tt(), V2) -> U56(isLNat(activate(V2))) 957.47/297.35 , U56(tt()) -> tt() 957.47/297.35 , U61(tt(), V1) -> U62(isPLNatKind(activate(V1)), activate(V1)) 957.47/297.35 , U62(tt(), V1) -> U63(isPLNat(activate(V1))) 957.47/297.35 , isPLNatKind(n__pair(V1, V2)) -> 957.47/297.35 U261(isLNatKind(activate(V1)), activate(V2)) 957.47/297.35 , isPLNatKind(n__splitAt(V1, V2)) -> 957.47/297.35 U271(isNaturalKind(activate(V1)), activate(V2)) 957.47/297.35 , U63(tt()) -> tt() 957.47/297.35 , isPLNat(n__pair(V1, V2)) -> 957.47/297.35 U241(isLNatKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.35 , isPLNat(n__splitAt(V1, V2)) -> 957.47/297.35 U251(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.35 , U71(tt(), V1) -> U72(isNaturalKind(activate(V1)), activate(V1)) 957.47/297.35 , U72(tt(), V1) -> U73(isNatural(activate(V1))) 957.47/297.35 , U73(tt()) -> tt() 957.47/297.35 , U81(tt(), V1) -> U82(isPLNatKind(activate(V1)), activate(V1)) 957.47/297.35 , U82(tt(), V1) -> U83(isPLNat(activate(V1))) 957.47/297.35 , U83(tt()) -> tt() 957.47/297.35 , U91(tt(), V1) -> U92(isLNatKind(activate(V1)), activate(V1)) 957.47/297.35 , U92(tt(), V1) -> U93(isLNat(activate(V1))) 957.47/297.35 , U93(tt()) -> tt() 957.47/297.35 , natsFrom(N) -> U281(isNatural(N), N) 957.47/297.35 , natsFrom(X) -> n__natsFrom(X) 957.47/297.35 , sel(N, XS) -> U291(isNatural(N), N, XS) 957.47/297.35 , sel(X1, X2) -> n__sel(X1, X2) 957.47/297.35 , 0() -> n__0() 957.47/297.35 , tail(X) -> n__tail(X) 957.47/297.35 , tail(cons(N, XS)) -> U331(isNatural(N), N, activate(XS)) 957.47/297.35 , take(N, XS) -> U341(isNatural(N), N, XS) 957.47/297.35 , take(X1, X2) -> n__take(X1, X2) } 957.47/297.35 Weak DPs: 957.47/297.35 { U102^#(tt(), V1, V2) -> 957.47/297.35 c_2(U103^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.35 , U103^#(tt(), V1, V2) -> 957.47/297.35 c_22(U104^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.35 , isNaturalKind^#(n__0()) -> c_3() 957.47/297.35 , isNaturalKind^#(n__head(V1)) -> 957.47/297.35 c_4(U211^#(isLNatKind(activate(V1)))) 957.47/297.35 , isNaturalKind^#(n__s(V1)) -> 957.47/297.35 c_5(U221^#(isNaturalKind(activate(V1)))) 957.47/297.35 , isNaturalKind^#(n__sel(V1, V2)) -> 957.47/297.35 c_6(U231^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.35 , U211^#(tt()) -> c_79() 957.47/297.35 , U221^#(tt()) -> c_81() 957.47/297.35 , U231^#(tt(), V2) -> c_83(U232^#(isLNatKind(activate(V2)))) 957.47/297.35 , activate^#(n__nil()) -> c_9(nil^#()) 957.47/297.35 , activate^#(n__0()) -> c_16(0^#()) 957.47/297.35 , nil^#() -> c_122() 957.47/297.35 , 0^#() -> c_174() 957.47/297.35 , U104^#(tt(), V1, V2) -> 957.47/297.35 c_31(U105^#(isNatural(activate(V1)), activate(V2))) 957.47/297.35 , isLNatKind^#(n__natsFrom(V1)) -> 957.47/297.35 c_23(U141^#(isNaturalKind(activate(V1)))) 957.47/297.35 , isLNatKind^#(n__nil()) -> c_24() 957.47/297.35 , isLNatKind^#(n__afterNth(V1, V2)) -> 957.47/297.35 c_25(U111^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.35 , isLNatKind^#(n__cons(V1, V2)) -> 957.47/297.35 c_26(U121^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.35 , isLNatKind^#(n__fst(V1)) -> 957.47/297.35 c_27(U131^#(isPLNatKind(activate(V1)))) 957.47/297.35 , isLNatKind^#(n__snd(V1)) -> 957.47/297.35 c_28(U151^#(isPLNatKind(activate(V1)))) 957.47/297.35 , isLNatKind^#(n__tail(V1)) -> 957.47/297.35 c_29(U161^#(isLNatKind(activate(V1)))) 957.47/297.35 , isLNatKind^#(n__take(V1, V2)) -> 957.47/297.35 c_30(U171^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.35 , U141^#(tt()) -> c_60() 957.47/297.35 , U111^#(tt(), V2) -> c_48(U112^#(isLNatKind(activate(V2)))) 957.47/297.35 , U121^#(tt(), V2) -> c_51(U122^#(isLNatKind(activate(V2)))) 957.47/297.35 , U131^#(tt()) -> c_54() 957.47/297.35 , U151^#(tt()) -> c_61() 957.47/297.36 , U161^#(tt()) -> c_62() 957.47/297.36 , U171^#(tt(), V2) -> c_63(U172^#(isLNatKind(activate(V2)))) 957.47/297.36 , U105^#(tt(), V2) -> c_32(U106^#(isLNat(activate(V2)))) 957.47/297.36 , U106^#(tt()) -> c_37() 957.47/297.36 , isNatural^#(n__0()) -> c_33() 957.47/297.36 , isNatural^#(n__head(V1)) -> 957.47/297.36 c_34(U181^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.36 , isNatural^#(n__s(V1)) -> 957.47/297.36 c_35(U191^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.36 , U181^#(tt(), V1) -> 957.47/297.36 c_65(U182^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.36 , U191^#(tt(), V1) -> 957.47/297.36 c_68(U192^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.36 , isLNat^#(n__natsFrom(V1)) -> 957.47/297.36 c_38(U71^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.36 , isLNat^#(n__nil()) -> c_39() 957.47/297.36 , isLNat^#(n__fst(V1)) -> 957.47/297.36 c_42(U61^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.36 , isLNat^#(n__snd(V1)) -> 957.47/297.36 c_43(U81^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.36 , isLNat^#(n__tail(V1)) -> 957.47/297.36 c_44(U91^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.36 , U71^#(tt(), V1) -> 957.47/297.36 c_161(U72^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.36 , U61^#(tt(), V1) -> 957.47/297.36 c_154(U62^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.36 , U81^#(tt(), V1) -> 957.47/297.36 c_164(U82^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.36 , U91^#(tt(), V1) -> 957.47/297.36 c_167(U92^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.36 , U112^#(tt()) -> c_49() 957.47/297.36 , U122^#(tt()) -> c_52() 957.47/297.36 , U172^#(tt()) -> c_64() 957.47/297.36 , U182^#(tt(), V1) -> c_66(U183^#(isLNat(activate(V1)))) 957.47/297.36 , U183^#(tt()) -> c_67() 957.47/297.36 , U192^#(tt(), V1) -> c_69(U193^#(isNatural(activate(V1)))) 957.47/297.36 , U193^#(tt()) -> c_70() 957.47/297.36 , U202^#(tt(), V1, V2) -> 957.47/297.36 c_72(U203^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.36 , U203^#(tt(), V1, V2) -> 957.47/297.36 c_73(U204^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.36 , U204^#(tt(), V1, V2) -> 957.47/297.36 c_74(U205^#(isNatural(activate(V1)), activate(V2))) 957.47/297.36 , U205^#(tt(), V2) -> c_75(U206^#(isLNat(activate(V2)))) 957.47/297.36 , U206^#(tt()) -> c_76() 957.47/297.36 , U232^#(tt()) -> c_84() 957.47/297.36 , U242^#(tt(), V1, V2) -> 957.47/297.36 c_86(U243^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.36 , U243^#(tt(), V1, V2) -> 957.47/297.36 c_87(U244^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.36 , U244^#(tt(), V1, V2) -> 957.47/297.36 c_88(U245^#(isLNat(activate(V1)), activate(V2))) 957.47/297.36 , U245^#(tt(), V2) -> c_89(U246^#(isLNat(activate(V2)))) 957.47/297.36 , U246^#(tt()) -> c_90() 957.47/297.36 , U252^#(tt(), V1, V2) -> 957.47/297.36 c_92(U253^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.36 , U253^#(tt(), V1, V2) -> 957.47/297.36 c_93(U254^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.36 , U254^#(tt(), V1, V2) -> 957.47/297.36 c_94(U255^#(isNatural(activate(V1)), activate(V2))) 957.47/297.36 , U255^#(tt(), V2) -> c_95(U256^#(isLNat(activate(V2)))) 957.47/297.36 , U256^#(tt()) -> c_96() 957.47/297.36 , U261^#(tt(), V2) -> c_97(U262^#(isLNatKind(activate(V2)))) 957.47/297.36 , U262^#(tt()) -> c_98() 957.47/297.36 , U271^#(tt(), V2) -> c_99(U272^#(isLNatKind(activate(V2)))) 957.47/297.36 , U272^#(tt()) -> c_100() 957.47/297.36 , U42^#(tt(), V1, V2) -> 957.47/297.36 c_143(U43^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.36 , U43^#(tt(), V1, V2) -> 957.47/297.36 c_144(U44^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.36 , U44^#(tt(), V1, V2) -> 957.47/297.36 c_145(U45^#(isNatural(activate(V1)), activate(V2))) 957.47/297.36 , U45^#(tt(), V2) -> c_146(U46^#(isLNat(activate(V2)))) 957.47/297.36 , U46^#(tt()) -> c_147() 957.47/297.36 , U52^#(tt(), V1, V2) -> 957.47/297.36 c_149(U53^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.36 , U53^#(tt(), V1, V2) -> 957.47/297.36 c_150(U54^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.36 , U54^#(tt(), V1, V2) -> 957.47/297.36 c_151(U55^#(isNatural(activate(V1)), activate(V2))) 957.47/297.36 , U55^#(tt(), V2) -> c_152(U56^#(isLNat(activate(V2)))) 957.47/297.36 , U56^#(tt()) -> c_153() 957.47/297.36 , U62^#(tt(), V1) -> c_155(U63^#(isPLNat(activate(V1)))) 957.47/297.36 , U63^#(tt()) -> c_158() 957.47/297.36 , isPLNatKind^#(n__pair(V1, V2)) -> 957.47/297.36 c_156(U261^#(isLNatKind(activate(V1)), activate(V2))) 957.47/297.36 , isPLNatKind^#(n__splitAt(V1, V2)) -> 957.47/297.36 c_157(U271^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.36 , U72^#(tt(), V1) -> c_162(U73^#(isNatural(activate(V1)))) 957.47/297.36 , U73^#(tt()) -> c_163() 957.47/297.36 , U82^#(tt(), V1) -> c_165(U83^#(isPLNat(activate(V1)))) 957.47/297.36 , U83^#(tt()) -> c_166() 957.47/297.36 , U92^#(tt(), V1) -> c_168(U93^#(isLNat(activate(V1)))) 957.47/297.36 , U93^#(tt()) -> c_169() } 957.47/297.36 Obligation: 957.47/297.36 runtime complexity 957.47/297.36 Answer: 957.47/297.36 MAYBE 957.47/297.36 957.47/297.36 We estimate the number of application of {1,38,42,43,55,56} by 957.47/297.36 applications of Pre({1,38,42,43,55,56}) = 957.47/297.36 {2,16,18,19,20,22,24,27,28,30,32,33,34,37,39,40,41,85,86}. Here 957.47/297.36 rules are labeled as follows: 957.47/297.36 957.47/297.36 DPs: 957.47/297.36 { 1: U101^#(tt(), V1, V2) -> 957.47/297.36 c_1(U102^#(isNaturalKind(activate(V1)), 957.47/297.36 activate(V1), 957.47/297.36 activate(V2))) 957.47/297.36 , 2: activate^#(X) -> c_7(X) 957.47/297.36 , 3: activate^#(n__natsFrom(X)) -> c_8(natsFrom^#(X)) 957.47/297.36 , 4: activate^#(n__afterNth(X1, X2)) -> c_10(afterNth^#(X1, X2)) 957.47/297.36 , 5: activate^#(n__cons(X1, X2)) -> c_11(cons^#(X1, X2)) 957.47/297.36 , 6: activate^#(n__fst(X)) -> c_12(fst^#(X)) 957.47/297.36 , 7: activate^#(n__snd(X)) -> c_13(snd^#(X)) 957.47/297.36 , 8: activate^#(n__tail(X)) -> c_14(tail^#(X)) 957.47/297.36 , 9: activate^#(n__take(X1, X2)) -> c_15(take^#(X1, X2)) 957.47/297.36 , 10: activate^#(n__head(X)) -> c_17(head^#(X)) 957.47/297.36 , 11: activate^#(n__s(X)) -> c_18(s^#(X)) 957.47/297.36 , 12: activate^#(n__sel(X1, X2)) -> c_19(sel^#(X1, X2)) 957.47/297.36 , 13: activate^#(n__pair(X1, X2)) -> c_20(pair^#(X1, X2)) 957.47/297.36 , 14: activate^#(n__splitAt(X1, X2)) -> c_21(splitAt^#(X1, X2)) 957.47/297.36 , 15: natsFrom^#(N) -> c_170(U281^#(isNatural(N), N)) 957.47/297.36 , 16: natsFrom^#(X) -> c_171(X) 957.47/297.36 , 17: afterNth^#(N, XS) -> c_111(U11^#(isNatural(N), N, XS)) 957.47/297.36 , 18: afterNth^#(X1, X2) -> c_112(X1, X2) 957.47/297.36 , 19: cons^#(X1, X2) -> c_103(X1, X2) 957.47/297.36 , 20: fst^#(X) -> c_140(X) 957.47/297.36 , 21: fst^#(pair(X, Y)) -> c_141(U21^#(isLNat(X), X, Y)) 957.47/297.36 , 22: snd^#(X) -> c_55(X) 957.47/297.36 , 23: snd^#(pair(X, Y)) -> c_56(U301^#(isLNat(X), X, Y)) 957.47/297.36 , 24: tail^#(X) -> c_175(X) 957.47/297.36 , 25: tail^#(cons(N, XS)) -> 957.47/297.36 c_176(U331^#(isNatural(N), N, activate(XS))) 957.47/297.36 , 26: take^#(N, XS) -> c_177(U341^#(isNatural(N), N, XS)) 957.47/297.36 , 27: take^#(X1, X2) -> c_178(X1, X2) 957.47/297.36 , 28: head^#(X) -> c_109(X) 957.47/297.36 , 29: head^#(cons(N, XS)) -> 957.47/297.36 c_110(U31^#(isNatural(N), N, activate(XS))) 957.47/297.36 , 30: s^#(X) -> c_104(X) 957.47/297.36 , 31: sel^#(N, XS) -> c_172(U291^#(isNatural(N), N, XS)) 957.47/297.36 , 32: sel^#(X1, X2) -> c_173(X1, X2) 957.47/297.36 , 33: pair^#(X1, X2) -> c_121(X1, X2) 957.47/297.36 , 34: splitAt^#(X1, X2) -> c_57(X1, X2) 957.47/297.36 , 35: splitAt^#(s(N), cons(X, XS)) -> 957.47/297.36 c_58(U321^#(isNatural(N), N, X, activate(XS))) 957.47/297.36 , 36: splitAt^#(0(), XS) -> c_59(U311^#(isLNat(XS), XS)) 957.47/297.36 , 37: isNatural^#(n__sel(V1, V2)) -> 957.47/297.36 c_36(U201^#(isNaturalKind(activate(V1)), 957.47/297.36 activate(V1), 957.47/297.36 activate(V2))) 957.47/297.36 , 38: U201^#(tt(), V1, V2) -> 957.47/297.36 c_71(U202^#(isNaturalKind(activate(V1)), 957.47/297.36 activate(V1), 957.47/297.36 activate(V2))) 957.47/297.36 , 39: isLNat^#(n__afterNth(V1, V2)) -> 957.47/297.36 c_40(U41^#(isNaturalKind(activate(V1)), 957.47/297.36 activate(V1), 957.47/297.36 activate(V2))) 957.47/297.36 , 40: isLNat^#(n__cons(V1, V2)) -> 957.47/297.36 c_41(U51^#(isNaturalKind(activate(V1)), 957.47/297.36 activate(V1), 957.47/297.36 activate(V2))) 957.47/297.36 , 41: isLNat^#(n__take(V1, V2)) -> 957.47/297.36 c_45(U101^#(isNaturalKind(activate(V1)), 957.47/297.36 activate(V1), 957.47/297.36 activate(V2))) 957.47/297.36 , 42: U41^#(tt(), V1, V2) -> 957.47/297.36 c_142(U42^#(isNaturalKind(activate(V1)), 957.47/297.36 activate(V1), 957.47/297.36 activate(V2))) 957.47/297.36 , 43: U51^#(tt(), V1, V2) -> 957.47/297.36 c_148(U52^#(isNaturalKind(activate(V1)), 957.47/297.36 activate(V1), 957.47/297.36 activate(V2))) 957.47/297.36 , 44: U11^#(tt(), N, XS) -> 957.47/297.36 c_46(U12^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.47/297.36 , 45: U12^#(tt(), N, XS) -> 957.47/297.36 c_47(U13^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.36 , 46: U13^#(tt(), N, XS) -> 957.47/297.36 c_50(U14^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.36 , 47: U14^#(tt(), N, XS) -> 957.47/297.36 c_53(snd^#(splitAt(activate(N), activate(XS)))) 957.47/297.36 , 48: U301^#(tt(), X, Y) -> 957.47/297.36 c_113(U302^#(isLNatKind(activate(X)), activate(Y))) 957.47/297.36 , 49: U321^#(tt(), N, X, XS) -> 957.47/297.36 c_124(U322^#(isNaturalKind(activate(N)), 957.47/297.36 activate(N), 957.47/297.36 activate(X), 957.47/297.36 activate(XS))) 957.47/297.36 , 50: U311^#(tt(), XS) -> 957.47/297.36 c_119(U312^#(isLNatKind(activate(XS)), activate(XS))) 957.47/297.36 , 51: U21^#(tt(), X, Y) -> 957.47/297.36 c_77(U22^#(isLNatKind(activate(X)), activate(X), activate(Y))) 957.47/297.36 , 52: U22^#(tt(), X, Y) -> 957.47/297.36 c_78(U23^#(isLNat(activate(Y)), activate(X), activate(Y))) 957.47/297.36 , 53: U23^#(tt(), X, Y) -> 957.47/297.36 c_80(U24^#(isLNatKind(activate(Y)), activate(X))) 957.47/297.36 , 54: U24^#(tt(), X) -> c_82(activate^#(X)) 957.47/297.36 , 55: U241^#(tt(), V1, V2) -> 957.47/297.36 c_85(U242^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.47/297.36 , 56: U251^#(tt(), V1, V2) -> 957.47/297.36 c_91(U252^#(isNaturalKind(activate(V1)), 957.47/297.36 activate(V1), 957.47/297.36 activate(V2))) 957.47/297.36 , 57: U281^#(tt(), N) -> 957.47/297.36 c_101(U282^#(isNaturalKind(activate(N)), activate(N))) 957.47/297.36 , 58: U282^#(tt(), N) -> 957.47/297.36 c_102(cons^#(activate(N), n__natsFrom(s(activate(N))))) 957.47/297.36 , 59: U291^#(tt(), N, XS) -> 957.47/297.36 c_105(U292^#(isNaturalKind(activate(N)), 957.47/297.36 activate(N), 957.47/297.36 activate(XS))) 957.47/297.36 , 60: U292^#(tt(), N, XS) -> 957.47/297.36 c_106(U293^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.36 , 61: U293^#(tt(), N, XS) -> 957.47/297.36 c_107(U294^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.36 , 62: U294^#(tt(), N, XS) -> 957.47/297.36 c_108(head^#(afterNth(activate(N), activate(XS)))) 957.47/297.36 , 63: U31^#(tt(), N, XS) -> 957.47/297.36 c_117(U32^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.47/297.36 , 64: U302^#(tt(), Y) -> 957.47/297.36 c_114(U303^#(isLNat(activate(Y)), activate(Y))) 957.47/297.36 , 65: U303^#(tt(), Y) -> 957.47/297.36 c_115(U304^#(isLNatKind(activate(Y)), activate(Y))) 957.47/297.36 , 66: U304^#(tt(), Y) -> c_116(activate^#(Y)) 957.47/297.36 , 67: U32^#(tt(), N, XS) -> 957.47/297.36 c_118(U33^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.36 , 68: U33^#(tt(), N, XS) -> 957.47/297.36 c_123(U34^#(isLNatKind(activate(XS)), activate(N))) 957.47/297.36 , 69: U312^#(tt(), XS) -> c_120(pair^#(nil(), activate(XS))) 957.47/297.36 , 70: U34^#(tt(), N) -> c_131(activate^#(N)) 957.47/297.36 , 71: U322^#(tt(), N, X, XS) -> 957.47/297.36 c_125(U323^#(isNatural(activate(X)), 957.47/297.36 activate(N), 957.47/297.36 activate(X), 957.47/297.36 activate(XS))) 957.47/297.36 , 72: U323^#(tt(), N, X, XS) -> 957.47/297.36 c_126(U324^#(isNaturalKind(activate(X)), 957.47/297.36 activate(N), 957.47/297.36 activate(X), 957.47/297.36 activate(XS))) 957.47/297.36 , 73: U324^#(tt(), N, X, XS) -> 957.47/297.36 c_127(U325^#(isLNat(activate(XS)), 957.47/297.36 activate(N), 957.47/297.36 activate(X), 957.47/297.36 activate(XS))) 957.47/297.36 , 74: U325^#(tt(), N, X, XS) -> 957.47/297.36 c_128(U326^#(isLNatKind(activate(XS)), 957.47/297.36 activate(N), 957.47/297.36 activate(X), 957.47/297.36 activate(XS))) 957.47/297.36 , 75: U326^#(tt(), N, X, XS) -> 957.47/297.36 c_129(U327^#(splitAt(activate(N), activate(XS)), activate(X))) 957.47/297.36 , 76: U327^#(pair(YS, ZS), X) -> 957.47/297.36 c_130(pair^#(cons(activate(X), YS), ZS)) 957.47/297.36 , 77: U331^#(tt(), N, XS) -> 957.47/297.36 c_132(U332^#(isNaturalKind(activate(N)), activate(XS))) 957.47/297.36 , 78: U332^#(tt(), XS) -> 957.47/297.36 c_133(U333^#(isLNat(activate(XS)), activate(XS))) 957.47/297.36 , 79: U333^#(tt(), XS) -> 957.47/297.36 c_134(U334^#(isLNatKind(activate(XS)), activate(XS))) 957.47/297.36 , 80: U334^#(tt(), XS) -> c_135(activate^#(XS)) 957.47/297.36 , 81: U341^#(tt(), N, XS) -> 957.47/297.36 c_136(U342^#(isNaturalKind(activate(N)), 957.47/297.36 activate(N), 957.47/297.36 activate(XS))) 957.47/297.36 , 82: U342^#(tt(), N, XS) -> 957.47/297.36 c_137(U343^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.36 , 83: U343^#(tt(), N, XS) -> 957.47/297.36 c_138(U344^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.36 , 84: U344^#(tt(), N, XS) -> 957.47/297.36 c_139(fst^#(splitAt(activate(N), activate(XS)))) 957.47/297.36 , 85: isPLNat^#(n__pair(V1, V2)) -> 957.47/297.36 c_159(U241^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.47/297.36 , 86: isPLNat^#(n__splitAt(V1, V2)) -> 957.47/297.36 c_160(U251^#(isNaturalKind(activate(V1)), 957.47/297.36 activate(V1), 957.47/297.36 activate(V2))) 957.47/297.36 , 87: U102^#(tt(), V1, V2) -> 957.47/297.36 c_2(U103^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.36 , 88: U103^#(tt(), V1, V2) -> 957.47/297.36 c_22(U104^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.36 , 89: isNaturalKind^#(n__0()) -> c_3() 957.47/297.36 , 90: isNaturalKind^#(n__head(V1)) -> 957.47/297.36 c_4(U211^#(isLNatKind(activate(V1)))) 957.47/297.36 , 91: isNaturalKind^#(n__s(V1)) -> 957.47/297.36 c_5(U221^#(isNaturalKind(activate(V1)))) 957.47/297.36 , 92: isNaturalKind^#(n__sel(V1, V2)) -> 957.47/297.36 c_6(U231^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.36 , 93: U211^#(tt()) -> c_79() 957.47/297.36 , 94: U221^#(tt()) -> c_81() 957.47/297.36 , 95: U231^#(tt(), V2) -> c_83(U232^#(isLNatKind(activate(V2)))) 957.47/297.36 , 96: activate^#(n__nil()) -> c_9(nil^#()) 957.47/297.36 , 97: activate^#(n__0()) -> c_16(0^#()) 957.47/297.36 , 98: nil^#() -> c_122() 957.47/297.36 , 99: 0^#() -> c_174() 957.47/297.36 , 100: U104^#(tt(), V1, V2) -> 957.47/297.36 c_31(U105^#(isNatural(activate(V1)), activate(V2))) 957.47/297.36 , 101: isLNatKind^#(n__natsFrom(V1)) -> 957.47/297.36 c_23(U141^#(isNaturalKind(activate(V1)))) 957.47/297.36 , 102: isLNatKind^#(n__nil()) -> c_24() 957.47/297.36 , 103: isLNatKind^#(n__afterNth(V1, V2)) -> 957.47/297.36 c_25(U111^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.36 , 104: isLNatKind^#(n__cons(V1, V2)) -> 957.47/297.36 c_26(U121^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.36 , 105: isLNatKind^#(n__fst(V1)) -> 957.47/297.36 c_27(U131^#(isPLNatKind(activate(V1)))) 957.47/297.36 , 106: isLNatKind^#(n__snd(V1)) -> 957.47/297.36 c_28(U151^#(isPLNatKind(activate(V1)))) 957.47/297.36 , 107: isLNatKind^#(n__tail(V1)) -> 957.47/297.36 c_29(U161^#(isLNatKind(activate(V1)))) 957.47/297.36 , 108: isLNatKind^#(n__take(V1, V2)) -> 957.47/297.36 c_30(U171^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.36 , 109: U141^#(tt()) -> c_60() 957.47/297.36 , 110: U111^#(tt(), V2) -> c_48(U112^#(isLNatKind(activate(V2)))) 957.47/297.36 , 111: U121^#(tt(), V2) -> c_51(U122^#(isLNatKind(activate(V2)))) 957.47/297.36 , 112: U131^#(tt()) -> c_54() 957.47/297.36 , 113: U151^#(tt()) -> c_61() 957.47/297.36 , 114: U161^#(tt()) -> c_62() 957.47/297.36 , 115: U171^#(tt(), V2) -> c_63(U172^#(isLNatKind(activate(V2)))) 957.47/297.36 , 116: U105^#(tt(), V2) -> c_32(U106^#(isLNat(activate(V2)))) 957.47/297.36 , 117: U106^#(tt()) -> c_37() 957.47/297.36 , 118: isNatural^#(n__0()) -> c_33() 957.47/297.36 , 119: isNatural^#(n__head(V1)) -> 957.47/297.36 c_34(U181^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.36 , 120: isNatural^#(n__s(V1)) -> 957.47/297.36 c_35(U191^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.36 , 121: U181^#(tt(), V1) -> 957.47/297.36 c_65(U182^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.36 , 122: U191^#(tt(), V1) -> 957.47/297.36 c_68(U192^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.36 , 123: isLNat^#(n__natsFrom(V1)) -> 957.47/297.36 c_38(U71^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.36 , 124: isLNat^#(n__nil()) -> c_39() 957.47/297.36 , 125: isLNat^#(n__fst(V1)) -> 957.47/297.36 c_42(U61^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.36 , 126: isLNat^#(n__snd(V1)) -> 957.47/297.36 c_43(U81^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.37 , 127: isLNat^#(n__tail(V1)) -> 957.47/297.37 c_44(U91^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.37 , 128: U71^#(tt(), V1) -> 957.47/297.37 c_161(U72^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.37 , 129: U61^#(tt(), V1) -> 957.47/297.37 c_154(U62^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.37 , 130: U81^#(tt(), V1) -> 957.47/297.37 c_164(U82^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.37 , 131: U91^#(tt(), V1) -> 957.47/297.37 c_167(U92^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.37 , 132: U112^#(tt()) -> c_49() 957.47/297.37 , 133: U122^#(tt()) -> c_52() 957.47/297.37 , 134: U172^#(tt()) -> c_64() 957.47/297.37 , 135: U182^#(tt(), V1) -> c_66(U183^#(isLNat(activate(V1)))) 957.47/297.37 , 136: U183^#(tt()) -> c_67() 957.47/297.37 , 137: U192^#(tt(), V1) -> c_69(U193^#(isNatural(activate(V1)))) 957.47/297.37 , 138: U193^#(tt()) -> c_70() 957.47/297.37 , 139: U202^#(tt(), V1, V2) -> 957.47/297.37 c_72(U203^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.37 , 140: U203^#(tt(), V1, V2) -> 957.47/297.37 c_73(U204^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.37 , 141: U204^#(tt(), V1, V2) -> 957.47/297.37 c_74(U205^#(isNatural(activate(V1)), activate(V2))) 957.47/297.37 , 142: U205^#(tt(), V2) -> c_75(U206^#(isLNat(activate(V2)))) 957.47/297.37 , 143: U206^#(tt()) -> c_76() 957.47/297.37 , 144: U232^#(tt()) -> c_84() 957.47/297.37 , 145: U242^#(tt(), V1, V2) -> 957.47/297.37 c_86(U243^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.37 , 146: U243^#(tt(), V1, V2) -> 957.47/297.37 c_87(U244^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.37 , 147: U244^#(tt(), V1, V2) -> 957.47/297.37 c_88(U245^#(isLNat(activate(V1)), activate(V2))) 957.47/297.37 , 148: U245^#(tt(), V2) -> c_89(U246^#(isLNat(activate(V2)))) 957.47/297.37 , 149: U246^#(tt()) -> c_90() 957.47/297.37 , 150: U252^#(tt(), V1, V2) -> 957.47/297.37 c_92(U253^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.37 , 151: U253^#(tt(), V1, V2) -> 957.47/297.37 c_93(U254^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.37 , 152: U254^#(tt(), V1, V2) -> 957.47/297.37 c_94(U255^#(isNatural(activate(V1)), activate(V2))) 957.47/297.37 , 153: U255^#(tt(), V2) -> c_95(U256^#(isLNat(activate(V2)))) 957.47/297.37 , 154: U256^#(tt()) -> c_96() 957.47/297.37 , 155: U261^#(tt(), V2) -> c_97(U262^#(isLNatKind(activate(V2)))) 957.47/297.37 , 156: U262^#(tt()) -> c_98() 957.47/297.37 , 157: U271^#(tt(), V2) -> c_99(U272^#(isLNatKind(activate(V2)))) 957.47/297.37 , 158: U272^#(tt()) -> c_100() 957.47/297.37 , 159: U42^#(tt(), V1, V2) -> 957.47/297.37 c_143(U43^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.37 , 160: U43^#(tt(), V1, V2) -> 957.47/297.37 c_144(U44^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.37 , 161: U44^#(tt(), V1, V2) -> 957.47/297.37 c_145(U45^#(isNatural(activate(V1)), activate(V2))) 957.47/297.37 , 162: U45^#(tt(), V2) -> c_146(U46^#(isLNat(activate(V2)))) 957.47/297.37 , 163: U46^#(tt()) -> c_147() 957.47/297.37 , 164: U52^#(tt(), V1, V2) -> 957.47/297.37 c_149(U53^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.37 , 165: U53^#(tt(), V1, V2) -> 957.47/297.37 c_150(U54^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.37 , 166: U54^#(tt(), V1, V2) -> 957.47/297.37 c_151(U55^#(isNatural(activate(V1)), activate(V2))) 957.47/297.37 , 167: U55^#(tt(), V2) -> c_152(U56^#(isLNat(activate(V2)))) 957.47/297.37 , 168: U56^#(tt()) -> c_153() 957.47/297.37 , 169: U62^#(tt(), V1) -> c_155(U63^#(isPLNat(activate(V1)))) 957.47/297.37 , 170: U63^#(tt()) -> c_158() 957.47/297.37 , 171: isPLNatKind^#(n__pair(V1, V2)) -> 957.47/297.37 c_156(U261^#(isLNatKind(activate(V1)), activate(V2))) 957.47/297.37 , 172: isPLNatKind^#(n__splitAt(V1, V2)) -> 957.47/297.37 c_157(U271^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.37 , 173: U72^#(tt(), V1) -> c_162(U73^#(isNatural(activate(V1)))) 957.47/297.37 , 174: U73^#(tt()) -> c_163() 957.47/297.37 , 175: U82^#(tt(), V1) -> c_165(U83^#(isPLNat(activate(V1)))) 957.47/297.37 , 176: U83^#(tt()) -> c_166() 957.47/297.37 , 177: U92^#(tt(), V1) -> c_168(U93^#(isLNat(activate(V1)))) 957.47/297.37 , 178: U93^#(tt()) -> c_169() } 957.47/297.37 957.47/297.37 We are left with following problem, upon which TcT provides the 957.47/297.37 certificate MAYBE. 957.47/297.37 957.47/297.37 Strict DPs: 957.47/297.37 { activate^#(X) -> c_7(X) 957.47/297.37 , activate^#(n__natsFrom(X)) -> c_8(natsFrom^#(X)) 957.47/297.37 , activate^#(n__afterNth(X1, X2)) -> c_10(afterNth^#(X1, X2)) 957.47/297.37 , activate^#(n__cons(X1, X2)) -> c_11(cons^#(X1, X2)) 957.47/297.37 , activate^#(n__fst(X)) -> c_12(fst^#(X)) 957.47/297.37 , activate^#(n__snd(X)) -> c_13(snd^#(X)) 957.47/297.37 , activate^#(n__tail(X)) -> c_14(tail^#(X)) 957.47/297.37 , activate^#(n__take(X1, X2)) -> c_15(take^#(X1, X2)) 957.47/297.37 , activate^#(n__head(X)) -> c_17(head^#(X)) 957.47/297.37 , activate^#(n__s(X)) -> c_18(s^#(X)) 957.47/297.37 , activate^#(n__sel(X1, X2)) -> c_19(sel^#(X1, X2)) 957.47/297.37 , activate^#(n__pair(X1, X2)) -> c_20(pair^#(X1, X2)) 957.47/297.37 , activate^#(n__splitAt(X1, X2)) -> c_21(splitAt^#(X1, X2)) 957.47/297.37 , natsFrom^#(N) -> c_170(U281^#(isNatural(N), N)) 957.47/297.37 , natsFrom^#(X) -> c_171(X) 957.47/297.37 , afterNth^#(N, XS) -> c_111(U11^#(isNatural(N), N, XS)) 957.47/297.37 , afterNth^#(X1, X2) -> c_112(X1, X2) 957.47/297.37 , cons^#(X1, X2) -> c_103(X1, X2) 957.47/297.37 , fst^#(X) -> c_140(X) 957.47/297.37 , fst^#(pair(X, Y)) -> c_141(U21^#(isLNat(X), X, Y)) 957.47/297.37 , snd^#(X) -> c_55(X) 957.47/297.37 , snd^#(pair(X, Y)) -> c_56(U301^#(isLNat(X), X, Y)) 957.47/297.37 , tail^#(X) -> c_175(X) 957.47/297.37 , tail^#(cons(N, XS)) -> 957.47/297.37 c_176(U331^#(isNatural(N), N, activate(XS))) 957.47/297.37 , take^#(N, XS) -> c_177(U341^#(isNatural(N), N, XS)) 957.47/297.37 , take^#(X1, X2) -> c_178(X1, X2) 957.47/297.37 , head^#(X) -> c_109(X) 957.47/297.37 , head^#(cons(N, XS)) -> 957.47/297.37 c_110(U31^#(isNatural(N), N, activate(XS))) 957.47/297.37 , s^#(X) -> c_104(X) 957.47/297.37 , sel^#(N, XS) -> c_172(U291^#(isNatural(N), N, XS)) 957.47/297.37 , sel^#(X1, X2) -> c_173(X1, X2) 957.47/297.37 , pair^#(X1, X2) -> c_121(X1, X2) 957.47/297.37 , splitAt^#(X1, X2) -> c_57(X1, X2) 957.47/297.37 , splitAt^#(s(N), cons(X, XS)) -> 957.47/297.37 c_58(U321^#(isNatural(N), N, X, activate(XS))) 957.47/297.37 , splitAt^#(0(), XS) -> c_59(U311^#(isLNat(XS), XS)) 957.47/297.37 , isNatural^#(n__sel(V1, V2)) -> 957.47/297.37 c_36(U201^#(isNaturalKind(activate(V1)), 957.47/297.37 activate(V1), 957.47/297.37 activate(V2))) 957.47/297.37 , isLNat^#(n__afterNth(V1, V2)) -> 957.47/297.37 c_40(U41^#(isNaturalKind(activate(V1)), 957.47/297.37 activate(V1), 957.47/297.37 activate(V2))) 957.47/297.37 , isLNat^#(n__cons(V1, V2)) -> 957.47/297.37 c_41(U51^#(isNaturalKind(activate(V1)), 957.47/297.37 activate(V1), 957.47/297.37 activate(V2))) 957.47/297.37 , isLNat^#(n__take(V1, V2)) -> 957.47/297.37 c_45(U101^#(isNaturalKind(activate(V1)), 957.47/297.37 activate(V1), 957.47/297.37 activate(V2))) 957.47/297.37 , U11^#(tt(), N, XS) -> 957.47/297.37 c_46(U12^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.47/297.37 , U12^#(tt(), N, XS) -> 957.47/297.37 c_47(U13^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.37 , U13^#(tt(), N, XS) -> 957.47/297.37 c_50(U14^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.37 , U14^#(tt(), N, XS) -> 957.47/297.37 c_53(snd^#(splitAt(activate(N), activate(XS)))) 957.47/297.37 , U301^#(tt(), X, Y) -> 957.47/297.37 c_113(U302^#(isLNatKind(activate(X)), activate(Y))) 957.47/297.37 , U321^#(tt(), N, X, XS) -> 957.47/297.37 c_124(U322^#(isNaturalKind(activate(N)), 957.47/297.37 activate(N), 957.47/297.37 activate(X), 957.47/297.37 activate(XS))) 957.47/297.37 , U311^#(tt(), XS) -> 957.47/297.37 c_119(U312^#(isLNatKind(activate(XS)), activate(XS))) 957.47/297.37 , U21^#(tt(), X, Y) -> 957.47/297.37 c_77(U22^#(isLNatKind(activate(X)), activate(X), activate(Y))) 957.47/297.37 , U22^#(tt(), X, Y) -> 957.47/297.37 c_78(U23^#(isLNat(activate(Y)), activate(X), activate(Y))) 957.47/297.37 , U23^#(tt(), X, Y) -> 957.47/297.37 c_80(U24^#(isLNatKind(activate(Y)), activate(X))) 957.47/297.37 , U24^#(tt(), X) -> c_82(activate^#(X)) 957.47/297.37 , U281^#(tt(), N) -> 957.47/297.37 c_101(U282^#(isNaturalKind(activate(N)), activate(N))) 957.47/297.37 , U282^#(tt(), N) -> 957.47/297.37 c_102(cons^#(activate(N), n__natsFrom(s(activate(N))))) 957.47/297.37 , U291^#(tt(), N, XS) -> 957.47/297.37 c_105(U292^#(isNaturalKind(activate(N)), 957.47/297.37 activate(N), 957.47/297.37 activate(XS))) 957.47/297.37 , U292^#(tt(), N, XS) -> 957.47/297.37 c_106(U293^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.37 , U293^#(tt(), N, XS) -> 957.47/297.37 c_107(U294^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.37 , U294^#(tt(), N, XS) -> 957.47/297.37 c_108(head^#(afterNth(activate(N), activate(XS)))) 957.47/297.37 , U31^#(tt(), N, XS) -> 957.47/297.37 c_117(U32^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.47/297.37 , U302^#(tt(), Y) -> 957.47/297.37 c_114(U303^#(isLNat(activate(Y)), activate(Y))) 957.47/297.37 , U303^#(tt(), Y) -> 957.47/297.37 c_115(U304^#(isLNatKind(activate(Y)), activate(Y))) 957.47/297.37 , U304^#(tt(), Y) -> c_116(activate^#(Y)) 957.47/297.37 , U32^#(tt(), N, XS) -> 957.47/297.37 c_118(U33^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.37 , U33^#(tt(), N, XS) -> 957.47/297.37 c_123(U34^#(isLNatKind(activate(XS)), activate(N))) 957.47/297.37 , U312^#(tt(), XS) -> c_120(pair^#(nil(), activate(XS))) 957.47/297.37 , U34^#(tt(), N) -> c_131(activate^#(N)) 957.47/297.37 , U322^#(tt(), N, X, XS) -> 957.47/297.37 c_125(U323^#(isNatural(activate(X)), 957.47/297.37 activate(N), 957.47/297.37 activate(X), 957.47/297.37 activate(XS))) 957.47/297.37 , U323^#(tt(), N, X, XS) -> 957.47/297.37 c_126(U324^#(isNaturalKind(activate(X)), 957.47/297.37 activate(N), 957.47/297.37 activate(X), 957.47/297.37 activate(XS))) 957.47/297.37 , U324^#(tt(), N, X, XS) -> 957.47/297.37 c_127(U325^#(isLNat(activate(XS)), 957.47/297.37 activate(N), 957.47/297.37 activate(X), 957.47/297.37 activate(XS))) 957.47/297.37 , U325^#(tt(), N, X, XS) -> 957.47/297.37 c_128(U326^#(isLNatKind(activate(XS)), 957.47/297.37 activate(N), 957.47/297.37 activate(X), 957.47/297.37 activate(XS))) 957.47/297.37 , U326^#(tt(), N, X, XS) -> 957.47/297.37 c_129(U327^#(splitAt(activate(N), activate(XS)), activate(X))) 957.47/297.37 , U327^#(pair(YS, ZS), X) -> 957.47/297.37 c_130(pair^#(cons(activate(X), YS), ZS)) 957.47/297.37 , U331^#(tt(), N, XS) -> 957.47/297.37 c_132(U332^#(isNaturalKind(activate(N)), activate(XS))) 957.47/297.37 , U332^#(tt(), XS) -> 957.47/297.37 c_133(U333^#(isLNat(activate(XS)), activate(XS))) 957.47/297.37 , U333^#(tt(), XS) -> 957.47/297.37 c_134(U334^#(isLNatKind(activate(XS)), activate(XS))) 957.47/297.37 , U334^#(tt(), XS) -> c_135(activate^#(XS)) 957.47/297.37 , U341^#(tt(), N, XS) -> 957.47/297.37 c_136(U342^#(isNaturalKind(activate(N)), 957.47/297.37 activate(N), 957.47/297.37 activate(XS))) 957.47/297.37 , U342^#(tt(), N, XS) -> 957.47/297.37 c_137(U343^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.37 , U343^#(tt(), N, XS) -> 957.47/297.37 c_138(U344^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.37 , U344^#(tt(), N, XS) -> 957.47/297.37 c_139(fst^#(splitAt(activate(N), activate(XS)))) 957.47/297.37 , isPLNat^#(n__pair(V1, V2)) -> 957.47/297.37 c_159(U241^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.47/297.37 , isPLNat^#(n__splitAt(V1, V2)) -> 957.47/297.37 c_160(U251^#(isNaturalKind(activate(V1)), 957.47/297.37 activate(V1), 957.47/297.37 activate(V2))) } 957.47/297.37 Strict Trs: 957.47/297.37 { U101(tt(), V1, V2) -> 957.47/297.37 U102(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.37 , U102(tt(), V1, V2) -> 957.47/297.37 U103(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.37 , isNaturalKind(n__0()) -> tt() 957.47/297.37 , isNaturalKind(n__head(V1)) -> U211(isLNatKind(activate(V1))) 957.47/297.37 , isNaturalKind(n__s(V1)) -> U221(isNaturalKind(activate(V1))) 957.47/297.37 , isNaturalKind(n__sel(V1, V2)) -> 957.47/297.37 U231(isNaturalKind(activate(V1)), activate(V2)) 957.47/297.37 , activate(X) -> X 957.47/297.37 , activate(n__natsFrom(X)) -> natsFrom(X) 957.47/297.37 , activate(n__nil()) -> nil() 957.47/297.37 , activate(n__afterNth(X1, X2)) -> afterNth(X1, X2) 957.47/297.37 , activate(n__cons(X1, X2)) -> cons(X1, X2) 957.47/297.37 , activate(n__fst(X)) -> fst(X) 957.47/297.37 , activate(n__snd(X)) -> snd(X) 957.47/297.37 , activate(n__tail(X)) -> tail(X) 957.47/297.37 , activate(n__take(X1, X2)) -> take(X1, X2) 957.47/297.37 , activate(n__0()) -> 0() 957.47/297.37 , activate(n__head(X)) -> head(X) 957.47/297.37 , activate(n__s(X)) -> s(X) 957.47/297.37 , activate(n__sel(X1, X2)) -> sel(X1, X2) 957.47/297.37 , activate(n__pair(X1, X2)) -> pair(X1, X2) 957.47/297.37 , activate(n__splitAt(X1, X2)) -> splitAt(X1, X2) 957.47/297.37 , U103(tt(), V1, V2) -> 957.47/297.37 U104(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.37 , isLNatKind(n__natsFrom(V1)) -> U141(isNaturalKind(activate(V1))) 957.47/297.37 , isLNatKind(n__nil()) -> tt() 957.47/297.37 , isLNatKind(n__afterNth(V1, V2)) -> 957.47/297.37 U111(isNaturalKind(activate(V1)), activate(V2)) 957.47/297.37 , isLNatKind(n__cons(V1, V2)) -> 957.47/297.37 U121(isNaturalKind(activate(V1)), activate(V2)) 957.47/297.37 , isLNatKind(n__fst(V1)) -> U131(isPLNatKind(activate(V1))) 957.47/297.37 , isLNatKind(n__snd(V1)) -> U151(isPLNatKind(activate(V1))) 957.47/297.37 , isLNatKind(n__tail(V1)) -> U161(isLNatKind(activate(V1))) 957.47/297.37 , isLNatKind(n__take(V1, V2)) -> 957.47/297.37 U171(isNaturalKind(activate(V1)), activate(V2)) 957.47/297.37 , U104(tt(), V1, V2) -> U105(isNatural(activate(V1)), activate(V2)) 957.47/297.37 , U105(tt(), V2) -> U106(isLNat(activate(V2))) 957.47/297.37 , isNatural(n__0()) -> tt() 957.47/297.37 , isNatural(n__head(V1)) -> 957.47/297.37 U181(isLNatKind(activate(V1)), activate(V1)) 957.47/297.37 , isNatural(n__s(V1)) -> 957.47/297.37 U191(isNaturalKind(activate(V1)), activate(V1)) 957.47/297.37 , isNatural(n__sel(V1, V2)) -> 957.47/297.37 U201(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.37 , U106(tt()) -> tt() 957.47/297.37 , isLNat(n__natsFrom(V1)) -> 957.47/297.37 U71(isNaturalKind(activate(V1)), activate(V1)) 957.47/297.37 , isLNat(n__nil()) -> tt() 957.47/297.37 , isLNat(n__afterNth(V1, V2)) -> 957.47/297.37 U41(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.37 , isLNat(n__cons(V1, V2)) -> 957.47/297.37 U51(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.37 , isLNat(n__fst(V1)) -> 957.47/297.37 U61(isPLNatKind(activate(V1)), activate(V1)) 957.47/297.37 , isLNat(n__snd(V1)) -> 957.47/297.37 U81(isPLNatKind(activate(V1)), activate(V1)) 957.47/297.37 , isLNat(n__tail(V1)) -> 957.47/297.37 U91(isLNatKind(activate(V1)), activate(V1)) 957.47/297.37 , isLNat(n__take(V1, V2)) -> 957.47/297.37 U101(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.37 , U11(tt(), N, XS) -> 957.47/297.37 U12(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.47/297.37 , U12(tt(), N, XS) -> 957.47/297.37 U13(isLNat(activate(XS)), activate(N), activate(XS)) 957.47/297.37 , U111(tt(), V2) -> U112(isLNatKind(activate(V2))) 957.47/297.37 , U112(tt()) -> tt() 957.47/297.37 , U13(tt(), N, XS) -> 957.47/297.37 U14(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.47/297.37 , U121(tt(), V2) -> U122(isLNatKind(activate(V2))) 957.47/297.37 , U122(tt()) -> tt() 957.47/297.37 , U14(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS))) 957.47/297.37 , U131(tt()) -> tt() 957.47/297.37 , snd(X) -> n__snd(X) 957.47/297.37 , snd(pair(X, Y)) -> U301(isLNat(X), X, Y) 957.47/297.37 , splitAt(X1, X2) -> n__splitAt(X1, X2) 957.47/297.37 , splitAt(s(N), cons(X, XS)) -> 957.47/297.37 U321(isNatural(N), N, X, activate(XS)) 957.47/297.37 , splitAt(0(), XS) -> U311(isLNat(XS), XS) 957.47/297.37 , U141(tt()) -> tt() 957.47/297.37 , U151(tt()) -> tt() 957.47/297.37 , U161(tt()) -> tt() 957.47/297.37 , U171(tt(), V2) -> U172(isLNatKind(activate(V2))) 957.47/297.37 , U172(tt()) -> tt() 957.47/297.37 , U181(tt(), V1) -> U182(isLNatKind(activate(V1)), activate(V1)) 957.47/297.37 , U182(tt(), V1) -> U183(isLNat(activate(V1))) 957.47/297.37 , U183(tt()) -> tt() 957.47/297.37 , U191(tt(), V1) -> U192(isNaturalKind(activate(V1)), activate(V1)) 957.47/297.37 , U192(tt(), V1) -> U193(isNatural(activate(V1))) 957.47/297.37 , U193(tt()) -> tt() 957.47/297.37 , U201(tt(), V1, V2) -> 957.47/297.37 U202(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.37 , U202(tt(), V1, V2) -> 957.47/297.37 U203(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.37 , U203(tt(), V1, V2) -> 957.47/297.37 U204(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.37 , U204(tt(), V1, V2) -> U205(isNatural(activate(V1)), activate(V2)) 957.47/297.37 , U205(tt(), V2) -> U206(isLNat(activate(V2))) 957.47/297.37 , U206(tt()) -> tt() 957.47/297.37 , U21(tt(), X, Y) -> 957.47/297.37 U22(isLNatKind(activate(X)), activate(X), activate(Y)) 957.47/297.37 , U22(tt(), X, Y) -> 957.47/297.37 U23(isLNat(activate(Y)), activate(X), activate(Y)) 957.47/297.37 , U211(tt()) -> tt() 957.47/297.37 , U23(tt(), X, Y) -> U24(isLNatKind(activate(Y)), activate(X)) 957.47/297.37 , U221(tt()) -> tt() 957.47/297.37 , U24(tt(), X) -> activate(X) 957.47/297.37 , U231(tt(), V2) -> U232(isLNatKind(activate(V2))) 957.47/297.37 , U232(tt()) -> tt() 957.47/297.37 , U241(tt(), V1, V2) -> 957.47/297.37 U242(isLNatKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.37 , U242(tt(), V1, V2) -> 957.47/297.37 U243(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.37 , U243(tt(), V1, V2) -> 957.47/297.37 U244(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.37 , U244(tt(), V1, V2) -> U245(isLNat(activate(V1)), activate(V2)) 957.47/297.37 , U245(tt(), V2) -> U246(isLNat(activate(V2))) 957.47/297.37 , U246(tt()) -> tt() 957.47/297.37 , U251(tt(), V1, V2) -> 957.47/297.37 U252(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.37 , U252(tt(), V1, V2) -> 957.47/297.37 U253(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.37 , U253(tt(), V1, V2) -> 957.47/297.37 U254(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.37 , U254(tt(), V1, V2) -> U255(isNatural(activate(V1)), activate(V2)) 957.47/297.37 , U255(tt(), V2) -> U256(isLNat(activate(V2))) 957.47/297.37 , U256(tt()) -> tt() 957.47/297.37 , U261(tt(), V2) -> U262(isLNatKind(activate(V2))) 957.47/297.37 , U262(tt()) -> tt() 957.47/297.37 , U271(tt(), V2) -> U272(isLNatKind(activate(V2))) 957.47/297.37 , U272(tt()) -> tt() 957.47/297.37 , U281(tt(), N) -> U282(isNaturalKind(activate(N)), activate(N)) 957.47/297.37 , U282(tt(), N) -> cons(activate(N), n__natsFrom(s(activate(N)))) 957.47/297.37 , cons(X1, X2) -> n__cons(X1, X2) 957.47/297.37 , s(X) -> n__s(X) 957.47/297.37 , U291(tt(), N, XS) -> 957.47/297.37 U292(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.47/297.37 , U292(tt(), N, XS) -> 957.47/297.37 U293(isLNat(activate(XS)), activate(N), activate(XS)) 957.47/297.37 , U293(tt(), N, XS) -> 957.47/297.37 U294(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.47/297.37 , U294(tt(), N, XS) -> head(afterNth(activate(N), activate(XS))) 957.47/297.37 , head(X) -> n__head(X) 957.47/297.37 , head(cons(N, XS)) -> U31(isNatural(N), N, activate(XS)) 957.47/297.37 , afterNth(N, XS) -> U11(isNatural(N), N, XS) 957.47/297.37 , afterNth(X1, X2) -> n__afterNth(X1, X2) 957.47/297.37 , U301(tt(), X, Y) -> U302(isLNatKind(activate(X)), activate(Y)) 957.47/297.37 , U302(tt(), Y) -> U303(isLNat(activate(Y)), activate(Y)) 957.47/297.37 , U303(tt(), Y) -> U304(isLNatKind(activate(Y)), activate(Y)) 957.47/297.37 , U304(tt(), Y) -> activate(Y) 957.47/297.37 , U31(tt(), N, XS) -> 957.47/297.37 U32(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.47/297.37 , U32(tt(), N, XS) -> 957.47/297.37 U33(isLNat(activate(XS)), activate(N), activate(XS)) 957.47/297.37 , U311(tt(), XS) -> U312(isLNatKind(activate(XS)), activate(XS)) 957.47/297.37 , U312(tt(), XS) -> pair(nil(), activate(XS)) 957.47/297.37 , pair(X1, X2) -> n__pair(X1, X2) 957.47/297.37 , nil() -> n__nil() 957.47/297.37 , U33(tt(), N, XS) -> U34(isLNatKind(activate(XS)), activate(N)) 957.47/297.37 , U321(tt(), N, X, XS) -> 957.47/297.37 U322(isNaturalKind(activate(N)), 957.47/297.37 activate(N), 957.47/297.37 activate(X), 957.47/297.37 activate(XS)) 957.47/297.37 , U322(tt(), N, X, XS) -> 957.47/297.37 U323(isNatural(activate(X)), 957.47/297.37 activate(N), 957.47/297.37 activate(X), 957.47/297.37 activate(XS)) 957.47/297.37 , U323(tt(), N, X, XS) -> 957.47/297.37 U324(isNaturalKind(activate(X)), 957.47/297.37 activate(N), 957.47/297.37 activate(X), 957.47/297.37 activate(XS)) 957.47/297.37 , U324(tt(), N, X, XS) -> 957.47/297.37 U325(isLNat(activate(XS)), activate(N), activate(X), activate(XS)) 957.47/297.37 , U325(tt(), N, X, XS) -> 957.47/297.37 U326(isLNatKind(activate(XS)), 957.47/297.37 activate(N), 957.47/297.37 activate(X), 957.47/297.37 activate(XS)) 957.47/297.37 , U326(tt(), N, X, XS) -> 957.47/297.37 U327(splitAt(activate(N), activate(XS)), activate(X)) 957.47/297.37 , U327(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) 957.47/297.37 , U34(tt(), N) -> activate(N) 957.47/297.37 , U331(tt(), N, XS) -> 957.47/297.37 U332(isNaturalKind(activate(N)), activate(XS)) 957.47/297.37 , U332(tt(), XS) -> U333(isLNat(activate(XS)), activate(XS)) 957.47/297.37 , U333(tt(), XS) -> U334(isLNatKind(activate(XS)), activate(XS)) 957.47/297.37 , U334(tt(), XS) -> activate(XS) 957.47/297.38 , U341(tt(), N, XS) -> 957.47/297.38 U342(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.47/297.38 , U342(tt(), N, XS) -> 957.47/297.38 U343(isLNat(activate(XS)), activate(N), activate(XS)) 957.47/297.38 , U343(tt(), N, XS) -> 957.47/297.38 U344(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.47/297.38 , U344(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS))) 957.47/297.38 , fst(X) -> n__fst(X) 957.47/297.38 , fst(pair(X, Y)) -> U21(isLNat(X), X, Y) 957.47/297.38 , U41(tt(), V1, V2) -> 957.47/297.38 U42(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.38 , U42(tt(), V1, V2) -> 957.47/297.38 U43(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.38 , U43(tt(), V1, V2) -> 957.47/297.38 U44(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.38 , U44(tt(), V1, V2) -> U45(isNatural(activate(V1)), activate(V2)) 957.47/297.38 , U45(tt(), V2) -> U46(isLNat(activate(V2))) 957.47/297.38 , U46(tt()) -> tt() 957.47/297.38 , U51(tt(), V1, V2) -> 957.47/297.38 U52(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.38 , U52(tt(), V1, V2) -> 957.47/297.38 U53(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.38 , U53(tt(), V1, V2) -> 957.47/297.38 U54(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.38 , U54(tt(), V1, V2) -> U55(isNatural(activate(V1)), activate(V2)) 957.47/297.38 , U55(tt(), V2) -> U56(isLNat(activate(V2))) 957.47/297.38 , U56(tt()) -> tt() 957.47/297.38 , U61(tt(), V1) -> U62(isPLNatKind(activate(V1)), activate(V1)) 957.47/297.38 , U62(tt(), V1) -> U63(isPLNat(activate(V1))) 957.47/297.38 , isPLNatKind(n__pair(V1, V2)) -> 957.47/297.38 U261(isLNatKind(activate(V1)), activate(V2)) 957.47/297.38 , isPLNatKind(n__splitAt(V1, V2)) -> 957.47/297.38 U271(isNaturalKind(activate(V1)), activate(V2)) 957.47/297.38 , U63(tt()) -> tt() 957.47/297.38 , isPLNat(n__pair(V1, V2)) -> 957.47/297.38 U241(isLNatKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.38 , isPLNat(n__splitAt(V1, V2)) -> 957.47/297.38 U251(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.38 , U71(tt(), V1) -> U72(isNaturalKind(activate(V1)), activate(V1)) 957.47/297.38 , U72(tt(), V1) -> U73(isNatural(activate(V1))) 957.47/297.38 , U73(tt()) -> tt() 957.47/297.38 , U81(tt(), V1) -> U82(isPLNatKind(activate(V1)), activate(V1)) 957.47/297.38 , U82(tt(), V1) -> U83(isPLNat(activate(V1))) 957.47/297.38 , U83(tt()) -> tt() 957.47/297.38 , U91(tt(), V1) -> U92(isLNatKind(activate(V1)), activate(V1)) 957.47/297.38 , U92(tt(), V1) -> U93(isLNat(activate(V1))) 957.47/297.38 , U93(tt()) -> tt() 957.47/297.38 , natsFrom(N) -> U281(isNatural(N), N) 957.47/297.38 , natsFrom(X) -> n__natsFrom(X) 957.47/297.38 , sel(N, XS) -> U291(isNatural(N), N, XS) 957.47/297.38 , sel(X1, X2) -> n__sel(X1, X2) 957.47/297.38 , 0() -> n__0() 957.47/297.38 , tail(X) -> n__tail(X) 957.47/297.38 , tail(cons(N, XS)) -> U331(isNatural(N), N, activate(XS)) 957.47/297.38 , take(N, XS) -> U341(isNatural(N), N, XS) 957.47/297.38 , take(X1, X2) -> n__take(X1, X2) } 957.47/297.38 Weak DPs: 957.47/297.38 { U101^#(tt(), V1, V2) -> 957.47/297.38 c_1(U102^#(isNaturalKind(activate(V1)), 957.47/297.38 activate(V1), 957.47/297.38 activate(V2))) 957.47/297.38 , U102^#(tt(), V1, V2) -> 957.47/297.38 c_2(U103^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.38 , U103^#(tt(), V1, V2) -> 957.47/297.38 c_22(U104^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.38 , isNaturalKind^#(n__0()) -> c_3() 957.47/297.38 , isNaturalKind^#(n__head(V1)) -> 957.47/297.38 c_4(U211^#(isLNatKind(activate(V1)))) 957.47/297.38 , isNaturalKind^#(n__s(V1)) -> 957.47/297.38 c_5(U221^#(isNaturalKind(activate(V1)))) 957.47/297.38 , isNaturalKind^#(n__sel(V1, V2)) -> 957.47/297.38 c_6(U231^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.38 , U211^#(tt()) -> c_79() 957.47/297.38 , U221^#(tt()) -> c_81() 957.47/297.38 , U231^#(tt(), V2) -> c_83(U232^#(isLNatKind(activate(V2)))) 957.47/297.38 , activate^#(n__nil()) -> c_9(nil^#()) 957.47/297.38 , activate^#(n__0()) -> c_16(0^#()) 957.47/297.38 , nil^#() -> c_122() 957.47/297.38 , 0^#() -> c_174() 957.47/297.38 , U104^#(tt(), V1, V2) -> 957.47/297.38 c_31(U105^#(isNatural(activate(V1)), activate(V2))) 957.47/297.38 , isLNatKind^#(n__natsFrom(V1)) -> 957.47/297.38 c_23(U141^#(isNaturalKind(activate(V1)))) 957.47/297.38 , isLNatKind^#(n__nil()) -> c_24() 957.47/297.38 , isLNatKind^#(n__afterNth(V1, V2)) -> 957.47/297.38 c_25(U111^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.38 , isLNatKind^#(n__cons(V1, V2)) -> 957.47/297.38 c_26(U121^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.38 , isLNatKind^#(n__fst(V1)) -> 957.47/297.38 c_27(U131^#(isPLNatKind(activate(V1)))) 957.47/297.38 , isLNatKind^#(n__snd(V1)) -> 957.47/297.38 c_28(U151^#(isPLNatKind(activate(V1)))) 957.47/297.38 , isLNatKind^#(n__tail(V1)) -> 957.47/297.38 c_29(U161^#(isLNatKind(activate(V1)))) 957.47/297.38 , isLNatKind^#(n__take(V1, V2)) -> 957.47/297.38 c_30(U171^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.38 , U141^#(tt()) -> c_60() 957.47/297.38 , U111^#(tt(), V2) -> c_48(U112^#(isLNatKind(activate(V2)))) 957.47/297.38 , U121^#(tt(), V2) -> c_51(U122^#(isLNatKind(activate(V2)))) 957.47/297.38 , U131^#(tt()) -> c_54() 957.47/297.38 , U151^#(tt()) -> c_61() 957.47/297.38 , U161^#(tt()) -> c_62() 957.47/297.38 , U171^#(tt(), V2) -> c_63(U172^#(isLNatKind(activate(V2)))) 957.47/297.38 , U105^#(tt(), V2) -> c_32(U106^#(isLNat(activate(V2)))) 957.47/297.38 , U106^#(tt()) -> c_37() 957.47/297.38 , isNatural^#(n__0()) -> c_33() 957.47/297.38 , isNatural^#(n__head(V1)) -> 957.47/297.38 c_34(U181^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.38 , isNatural^#(n__s(V1)) -> 957.47/297.38 c_35(U191^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.38 , U181^#(tt(), V1) -> 957.47/297.38 c_65(U182^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.38 , U191^#(tt(), V1) -> 957.47/297.38 c_68(U192^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.38 , U201^#(tt(), V1, V2) -> 957.47/297.38 c_71(U202^#(isNaturalKind(activate(V1)), 957.47/297.38 activate(V1), 957.47/297.38 activate(V2))) 957.47/297.38 , isLNat^#(n__natsFrom(V1)) -> 957.47/297.38 c_38(U71^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.38 , isLNat^#(n__nil()) -> c_39() 957.47/297.38 , isLNat^#(n__fst(V1)) -> 957.47/297.38 c_42(U61^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.38 , isLNat^#(n__snd(V1)) -> 957.47/297.38 c_43(U81^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.38 , isLNat^#(n__tail(V1)) -> 957.47/297.38 c_44(U91^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.38 , U71^#(tt(), V1) -> 957.47/297.38 c_161(U72^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.38 , U41^#(tt(), V1, V2) -> 957.47/297.38 c_142(U42^#(isNaturalKind(activate(V1)), 957.47/297.38 activate(V1), 957.47/297.38 activate(V2))) 957.47/297.38 , U51^#(tt(), V1, V2) -> 957.47/297.38 c_148(U52^#(isNaturalKind(activate(V1)), 957.47/297.38 activate(V1), 957.47/297.38 activate(V2))) 957.47/297.38 , U61^#(tt(), V1) -> 957.47/297.38 c_154(U62^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.38 , U81^#(tt(), V1) -> 957.47/297.38 c_164(U82^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.38 , U91^#(tt(), V1) -> 957.47/297.38 c_167(U92^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.38 , U112^#(tt()) -> c_49() 957.47/297.38 , U122^#(tt()) -> c_52() 957.47/297.38 , U172^#(tt()) -> c_64() 957.47/297.38 , U182^#(tt(), V1) -> c_66(U183^#(isLNat(activate(V1)))) 957.47/297.38 , U183^#(tt()) -> c_67() 957.47/297.38 , U192^#(tt(), V1) -> c_69(U193^#(isNatural(activate(V1)))) 957.47/297.38 , U193^#(tt()) -> c_70() 957.47/297.38 , U202^#(tt(), V1, V2) -> 957.47/297.38 c_72(U203^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.38 , U203^#(tt(), V1, V2) -> 957.47/297.38 c_73(U204^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.38 , U204^#(tt(), V1, V2) -> 957.47/297.38 c_74(U205^#(isNatural(activate(V1)), activate(V2))) 957.47/297.38 , U205^#(tt(), V2) -> c_75(U206^#(isLNat(activate(V2)))) 957.47/297.38 , U206^#(tt()) -> c_76() 957.47/297.38 , U232^#(tt()) -> c_84() 957.47/297.38 , U241^#(tt(), V1, V2) -> 957.47/297.38 c_85(U242^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.47/297.38 , U242^#(tt(), V1, V2) -> 957.47/297.38 c_86(U243^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.38 , U243^#(tt(), V1, V2) -> 957.47/297.38 c_87(U244^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.38 , U244^#(tt(), V1, V2) -> 957.47/297.38 c_88(U245^#(isLNat(activate(V1)), activate(V2))) 957.47/297.38 , U245^#(tt(), V2) -> c_89(U246^#(isLNat(activate(V2)))) 957.47/297.38 , U246^#(tt()) -> c_90() 957.47/297.38 , U251^#(tt(), V1, V2) -> 957.47/297.38 c_91(U252^#(isNaturalKind(activate(V1)), 957.47/297.38 activate(V1), 957.47/297.38 activate(V2))) 957.47/297.38 , U252^#(tt(), V1, V2) -> 957.47/297.38 c_92(U253^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.38 , U253^#(tt(), V1, V2) -> 957.47/297.38 c_93(U254^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.38 , U254^#(tt(), V1, V2) -> 957.47/297.38 c_94(U255^#(isNatural(activate(V1)), activate(V2))) 957.47/297.38 , U255^#(tt(), V2) -> c_95(U256^#(isLNat(activate(V2)))) 957.47/297.38 , U256^#(tt()) -> c_96() 957.47/297.38 , U261^#(tt(), V2) -> c_97(U262^#(isLNatKind(activate(V2)))) 957.47/297.38 , U262^#(tt()) -> c_98() 957.47/297.38 , U271^#(tt(), V2) -> c_99(U272^#(isLNatKind(activate(V2)))) 957.47/297.38 , U272^#(tt()) -> c_100() 957.47/297.38 , U42^#(tt(), V1, V2) -> 957.47/297.38 c_143(U43^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.38 , U43^#(tt(), V1, V2) -> 957.47/297.38 c_144(U44^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.38 , U44^#(tt(), V1, V2) -> 957.47/297.38 c_145(U45^#(isNatural(activate(V1)), activate(V2))) 957.47/297.38 , U45^#(tt(), V2) -> c_146(U46^#(isLNat(activate(V2)))) 957.47/297.38 , U46^#(tt()) -> c_147() 957.47/297.38 , U52^#(tt(), V1, V2) -> 957.47/297.38 c_149(U53^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.38 , U53^#(tt(), V1, V2) -> 957.47/297.38 c_150(U54^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.38 , U54^#(tt(), V1, V2) -> 957.47/297.38 c_151(U55^#(isNatural(activate(V1)), activate(V2))) 957.47/297.38 , U55^#(tt(), V2) -> c_152(U56^#(isLNat(activate(V2)))) 957.47/297.38 , U56^#(tt()) -> c_153() 957.47/297.38 , U62^#(tt(), V1) -> c_155(U63^#(isPLNat(activate(V1)))) 957.47/297.38 , U63^#(tt()) -> c_158() 957.47/297.38 , isPLNatKind^#(n__pair(V1, V2)) -> 957.47/297.38 c_156(U261^#(isLNatKind(activate(V1)), activate(V2))) 957.47/297.38 , isPLNatKind^#(n__splitAt(V1, V2)) -> 957.47/297.38 c_157(U271^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.38 , U72^#(tt(), V1) -> c_162(U73^#(isNatural(activate(V1)))) 957.47/297.38 , U73^#(tt()) -> c_163() 957.47/297.38 , U82^#(tt(), V1) -> c_165(U83^#(isPLNat(activate(V1)))) 957.47/297.38 , U83^#(tt()) -> c_166() 957.47/297.38 , U92^#(tt(), V1) -> c_168(U93^#(isLNat(activate(V1)))) 957.47/297.38 , U93^#(tt()) -> c_169() } 957.47/297.38 Obligation: 957.47/297.38 runtime complexity 957.47/297.38 Answer: 957.47/297.38 MAYBE 957.47/297.38 957.47/297.38 We estimate the number of application of {36,37,38,39,79,80} by 957.47/297.38 applications of Pre({36,37,38,39,79,80}) = 957.47/297.38 {1,15,17,18,19,21,23,26,27,29,31,32,33}. Here rules are labeled as 957.47/297.38 follows: 957.47/297.38 957.47/297.38 DPs: 957.47/297.38 { 1: activate^#(X) -> c_7(X) 957.47/297.38 , 2: activate^#(n__natsFrom(X)) -> c_8(natsFrom^#(X)) 957.47/297.38 , 3: activate^#(n__afterNth(X1, X2)) -> c_10(afterNth^#(X1, X2)) 957.47/297.38 , 4: activate^#(n__cons(X1, X2)) -> c_11(cons^#(X1, X2)) 957.47/297.38 , 5: activate^#(n__fst(X)) -> c_12(fst^#(X)) 957.47/297.38 , 6: activate^#(n__snd(X)) -> c_13(snd^#(X)) 957.47/297.38 , 7: activate^#(n__tail(X)) -> c_14(tail^#(X)) 957.47/297.38 , 8: activate^#(n__take(X1, X2)) -> c_15(take^#(X1, X2)) 957.47/297.38 , 9: activate^#(n__head(X)) -> c_17(head^#(X)) 957.47/297.38 , 10: activate^#(n__s(X)) -> c_18(s^#(X)) 957.47/297.38 , 11: activate^#(n__sel(X1, X2)) -> c_19(sel^#(X1, X2)) 957.47/297.38 , 12: activate^#(n__pair(X1, X2)) -> c_20(pair^#(X1, X2)) 957.47/297.38 , 13: activate^#(n__splitAt(X1, X2)) -> c_21(splitAt^#(X1, X2)) 957.47/297.38 , 14: natsFrom^#(N) -> c_170(U281^#(isNatural(N), N)) 957.47/297.38 , 15: natsFrom^#(X) -> c_171(X) 957.47/297.38 , 16: afterNth^#(N, XS) -> c_111(U11^#(isNatural(N), N, XS)) 957.47/297.38 , 17: afterNth^#(X1, X2) -> c_112(X1, X2) 957.47/297.38 , 18: cons^#(X1, X2) -> c_103(X1, X2) 957.47/297.38 , 19: fst^#(X) -> c_140(X) 957.47/297.38 , 20: fst^#(pair(X, Y)) -> c_141(U21^#(isLNat(X), X, Y)) 957.47/297.38 , 21: snd^#(X) -> c_55(X) 957.47/297.38 , 22: snd^#(pair(X, Y)) -> c_56(U301^#(isLNat(X), X, Y)) 957.47/297.38 , 23: tail^#(X) -> c_175(X) 957.47/297.38 , 24: tail^#(cons(N, XS)) -> 957.47/297.38 c_176(U331^#(isNatural(N), N, activate(XS))) 957.47/297.38 , 25: take^#(N, XS) -> c_177(U341^#(isNatural(N), N, XS)) 957.47/297.38 , 26: take^#(X1, X2) -> c_178(X1, X2) 957.47/297.38 , 27: head^#(X) -> c_109(X) 957.47/297.38 , 28: head^#(cons(N, XS)) -> 957.47/297.38 c_110(U31^#(isNatural(N), N, activate(XS))) 957.47/297.38 , 29: s^#(X) -> c_104(X) 957.47/297.38 , 30: sel^#(N, XS) -> c_172(U291^#(isNatural(N), N, XS)) 957.47/297.38 , 31: sel^#(X1, X2) -> c_173(X1, X2) 957.47/297.38 , 32: pair^#(X1, X2) -> c_121(X1, X2) 957.47/297.38 , 33: splitAt^#(X1, X2) -> c_57(X1, X2) 957.47/297.38 , 34: splitAt^#(s(N), cons(X, XS)) -> 957.47/297.38 c_58(U321^#(isNatural(N), N, X, activate(XS))) 957.47/297.38 , 35: splitAt^#(0(), XS) -> c_59(U311^#(isLNat(XS), XS)) 957.47/297.38 , 36: isNatural^#(n__sel(V1, V2)) -> 957.47/297.38 c_36(U201^#(isNaturalKind(activate(V1)), 957.47/297.38 activate(V1), 957.47/297.38 activate(V2))) 957.47/297.38 , 37: isLNat^#(n__afterNth(V1, V2)) -> 957.47/297.38 c_40(U41^#(isNaturalKind(activate(V1)), 957.47/297.38 activate(V1), 957.47/297.38 activate(V2))) 957.47/297.38 , 38: isLNat^#(n__cons(V1, V2)) -> 957.47/297.38 c_41(U51^#(isNaturalKind(activate(V1)), 957.47/297.38 activate(V1), 957.47/297.38 activate(V2))) 957.47/297.38 , 39: isLNat^#(n__take(V1, V2)) -> 957.47/297.38 c_45(U101^#(isNaturalKind(activate(V1)), 957.47/297.38 activate(V1), 957.47/297.38 activate(V2))) 957.47/297.38 , 40: U11^#(tt(), N, XS) -> 957.47/297.38 c_46(U12^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.47/297.38 , 41: U12^#(tt(), N, XS) -> 957.47/297.38 c_47(U13^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.38 , 42: U13^#(tt(), N, XS) -> 957.47/297.38 c_50(U14^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.38 , 43: U14^#(tt(), N, XS) -> 957.47/297.38 c_53(snd^#(splitAt(activate(N), activate(XS)))) 957.47/297.38 , 44: U301^#(tt(), X, Y) -> 957.47/297.38 c_113(U302^#(isLNatKind(activate(X)), activate(Y))) 957.47/297.38 , 45: U321^#(tt(), N, X, XS) -> 957.47/297.38 c_124(U322^#(isNaturalKind(activate(N)), 957.47/297.38 activate(N), 957.47/297.38 activate(X), 957.47/297.38 activate(XS))) 957.47/297.38 , 46: U311^#(tt(), XS) -> 957.47/297.38 c_119(U312^#(isLNatKind(activate(XS)), activate(XS))) 957.47/297.38 , 47: U21^#(tt(), X, Y) -> 957.47/297.38 c_77(U22^#(isLNatKind(activate(X)), activate(X), activate(Y))) 957.47/297.38 , 48: U22^#(tt(), X, Y) -> 957.47/297.38 c_78(U23^#(isLNat(activate(Y)), activate(X), activate(Y))) 957.47/297.38 , 49: U23^#(tt(), X, Y) -> 957.47/297.38 c_80(U24^#(isLNatKind(activate(Y)), activate(X))) 957.47/297.38 , 50: U24^#(tt(), X) -> c_82(activate^#(X)) 957.47/297.38 , 51: U281^#(tt(), N) -> 957.47/297.38 c_101(U282^#(isNaturalKind(activate(N)), activate(N))) 957.47/297.38 , 52: U282^#(tt(), N) -> 957.47/297.38 c_102(cons^#(activate(N), n__natsFrom(s(activate(N))))) 957.47/297.38 , 53: U291^#(tt(), N, XS) -> 957.47/297.38 c_105(U292^#(isNaturalKind(activate(N)), 957.47/297.38 activate(N), 957.47/297.38 activate(XS))) 957.47/297.38 , 54: U292^#(tt(), N, XS) -> 957.47/297.38 c_106(U293^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.38 , 55: U293^#(tt(), N, XS) -> 957.47/297.38 c_107(U294^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.38 , 56: U294^#(tt(), N, XS) -> 957.47/297.38 c_108(head^#(afterNth(activate(N), activate(XS)))) 957.47/297.38 , 57: U31^#(tt(), N, XS) -> 957.47/297.38 c_117(U32^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.47/297.38 , 58: U302^#(tt(), Y) -> 957.47/297.38 c_114(U303^#(isLNat(activate(Y)), activate(Y))) 957.47/297.38 , 59: U303^#(tt(), Y) -> 957.47/297.38 c_115(U304^#(isLNatKind(activate(Y)), activate(Y))) 957.47/297.38 , 60: U304^#(tt(), Y) -> c_116(activate^#(Y)) 957.47/297.38 , 61: U32^#(tt(), N, XS) -> 957.47/297.38 c_118(U33^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.38 , 62: U33^#(tt(), N, XS) -> 957.47/297.38 c_123(U34^#(isLNatKind(activate(XS)), activate(N))) 957.47/297.38 , 63: U312^#(tt(), XS) -> c_120(pair^#(nil(), activate(XS))) 957.47/297.38 , 64: U34^#(tt(), N) -> c_131(activate^#(N)) 957.47/297.38 , 65: U322^#(tt(), N, X, XS) -> 957.47/297.38 c_125(U323^#(isNatural(activate(X)), 957.47/297.38 activate(N), 957.47/297.38 activate(X), 957.47/297.38 activate(XS))) 957.47/297.38 , 66: U323^#(tt(), N, X, XS) -> 957.47/297.38 c_126(U324^#(isNaturalKind(activate(X)), 957.47/297.38 activate(N), 957.47/297.38 activate(X), 957.47/297.38 activate(XS))) 957.47/297.38 , 67: U324^#(tt(), N, X, XS) -> 957.47/297.38 c_127(U325^#(isLNat(activate(XS)), 957.47/297.38 activate(N), 957.47/297.38 activate(X), 957.47/297.38 activate(XS))) 957.47/297.38 , 68: U325^#(tt(), N, X, XS) -> 957.47/297.38 c_128(U326^#(isLNatKind(activate(XS)), 957.47/297.38 activate(N), 957.47/297.38 activate(X), 957.47/297.38 activate(XS))) 957.47/297.38 , 69: U326^#(tt(), N, X, XS) -> 957.47/297.38 c_129(U327^#(splitAt(activate(N), activate(XS)), activate(X))) 957.47/297.38 , 70: U327^#(pair(YS, ZS), X) -> 957.47/297.38 c_130(pair^#(cons(activate(X), YS), ZS)) 957.47/297.38 , 71: U331^#(tt(), N, XS) -> 957.47/297.38 c_132(U332^#(isNaturalKind(activate(N)), activate(XS))) 957.47/297.38 , 72: U332^#(tt(), XS) -> 957.47/297.38 c_133(U333^#(isLNat(activate(XS)), activate(XS))) 957.47/297.38 , 73: U333^#(tt(), XS) -> 957.47/297.38 c_134(U334^#(isLNatKind(activate(XS)), activate(XS))) 957.47/297.38 , 74: U334^#(tt(), XS) -> c_135(activate^#(XS)) 957.47/297.38 , 75: U341^#(tt(), N, XS) -> 957.47/297.38 c_136(U342^#(isNaturalKind(activate(N)), 957.47/297.38 activate(N), 957.47/297.38 activate(XS))) 957.47/297.38 , 76: U342^#(tt(), N, XS) -> 957.47/297.38 c_137(U343^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.38 , 77: U343^#(tt(), N, XS) -> 957.47/297.38 c_138(U344^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.38 , 78: U344^#(tt(), N, XS) -> 957.47/297.38 c_139(fst^#(splitAt(activate(N), activate(XS)))) 957.47/297.38 , 79: isPLNat^#(n__pair(V1, V2)) -> 957.47/297.38 c_159(U241^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.47/297.38 , 80: isPLNat^#(n__splitAt(V1, V2)) -> 957.47/297.38 c_160(U251^#(isNaturalKind(activate(V1)), 957.47/297.38 activate(V1), 957.47/297.38 activate(V2))) 957.47/297.38 , 81: U101^#(tt(), V1, V2) -> 957.47/297.38 c_1(U102^#(isNaturalKind(activate(V1)), 957.47/297.38 activate(V1), 957.47/297.38 activate(V2))) 957.47/297.38 , 82: U102^#(tt(), V1, V2) -> 957.47/297.38 c_2(U103^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.38 , 83: U103^#(tt(), V1, V2) -> 957.47/297.38 c_22(U104^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.38 , 84: isNaturalKind^#(n__0()) -> c_3() 957.47/297.38 , 85: isNaturalKind^#(n__head(V1)) -> 957.47/297.38 c_4(U211^#(isLNatKind(activate(V1)))) 957.47/297.38 , 86: isNaturalKind^#(n__s(V1)) -> 957.47/297.38 c_5(U221^#(isNaturalKind(activate(V1)))) 957.47/297.38 , 87: isNaturalKind^#(n__sel(V1, V2)) -> 957.47/297.38 c_6(U231^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.38 , 88: U211^#(tt()) -> c_79() 957.47/297.38 , 89: U221^#(tt()) -> c_81() 957.47/297.38 , 90: U231^#(tt(), V2) -> c_83(U232^#(isLNatKind(activate(V2)))) 957.47/297.38 , 91: activate^#(n__nil()) -> c_9(nil^#()) 957.47/297.38 , 92: activate^#(n__0()) -> c_16(0^#()) 957.47/297.38 , 93: nil^#() -> c_122() 957.47/297.38 , 94: 0^#() -> c_174() 957.47/297.38 , 95: U104^#(tt(), V1, V2) -> 957.47/297.38 c_31(U105^#(isNatural(activate(V1)), activate(V2))) 957.47/297.38 , 96: isLNatKind^#(n__natsFrom(V1)) -> 957.47/297.38 c_23(U141^#(isNaturalKind(activate(V1)))) 957.47/297.38 , 97: isLNatKind^#(n__nil()) -> c_24() 957.47/297.38 , 98: isLNatKind^#(n__afterNth(V1, V2)) -> 957.47/297.38 c_25(U111^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.38 , 99: isLNatKind^#(n__cons(V1, V2)) -> 957.47/297.38 c_26(U121^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.38 , 100: isLNatKind^#(n__fst(V1)) -> 957.47/297.38 c_27(U131^#(isPLNatKind(activate(V1)))) 957.47/297.38 , 101: isLNatKind^#(n__snd(V1)) -> 957.47/297.38 c_28(U151^#(isPLNatKind(activate(V1)))) 957.47/297.38 , 102: isLNatKind^#(n__tail(V1)) -> 957.47/297.38 c_29(U161^#(isLNatKind(activate(V1)))) 957.47/297.38 , 103: isLNatKind^#(n__take(V1, V2)) -> 957.47/297.38 c_30(U171^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.38 , 104: U141^#(tt()) -> c_60() 957.47/297.38 , 105: U111^#(tt(), V2) -> c_48(U112^#(isLNatKind(activate(V2)))) 957.47/297.38 , 106: U121^#(tt(), V2) -> c_51(U122^#(isLNatKind(activate(V2)))) 957.47/297.38 , 107: U131^#(tt()) -> c_54() 957.47/297.38 , 108: U151^#(tt()) -> c_61() 957.47/297.38 , 109: U161^#(tt()) -> c_62() 957.47/297.38 , 110: U171^#(tt(), V2) -> c_63(U172^#(isLNatKind(activate(V2)))) 957.47/297.38 , 111: U105^#(tt(), V2) -> c_32(U106^#(isLNat(activate(V2)))) 957.47/297.38 , 112: U106^#(tt()) -> c_37() 957.47/297.38 , 113: isNatural^#(n__0()) -> c_33() 957.47/297.38 , 114: isNatural^#(n__head(V1)) -> 957.47/297.38 c_34(U181^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.38 , 115: isNatural^#(n__s(V1)) -> 957.47/297.38 c_35(U191^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.38 , 116: U181^#(tt(), V1) -> 957.47/297.38 c_65(U182^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.38 , 117: U191^#(tt(), V1) -> 957.47/297.38 c_68(U192^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.38 , 118: U201^#(tt(), V1, V2) -> 957.47/297.38 c_71(U202^#(isNaturalKind(activate(V1)), 957.47/297.38 activate(V1), 957.47/297.38 activate(V2))) 957.47/297.38 , 119: isLNat^#(n__natsFrom(V1)) -> 957.47/297.38 c_38(U71^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.38 , 120: isLNat^#(n__nil()) -> c_39() 957.47/297.38 , 121: isLNat^#(n__fst(V1)) -> 957.47/297.38 c_42(U61^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.38 , 122: isLNat^#(n__snd(V1)) -> 957.47/297.38 c_43(U81^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.38 , 123: isLNat^#(n__tail(V1)) -> 957.47/297.38 c_44(U91^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.38 , 124: U71^#(tt(), V1) -> 957.47/297.38 c_161(U72^#(isNaturalKind(activate(V1)), activate(V1))) 957.47/297.38 , 125: U41^#(tt(), V1, V2) -> 957.47/297.38 c_142(U42^#(isNaturalKind(activate(V1)), 957.47/297.38 activate(V1), 957.47/297.38 activate(V2))) 957.47/297.38 , 126: U51^#(tt(), V1, V2) -> 957.47/297.39 c_148(U52^#(isNaturalKind(activate(V1)), 957.47/297.39 activate(V1), 957.47/297.39 activate(V2))) 957.47/297.39 , 127: U61^#(tt(), V1) -> 957.47/297.39 c_154(U62^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.39 , 128: U81^#(tt(), V1) -> 957.47/297.39 c_164(U82^#(isPLNatKind(activate(V1)), activate(V1))) 957.47/297.39 , 129: U91^#(tt(), V1) -> 957.47/297.39 c_167(U92^#(isLNatKind(activate(V1)), activate(V1))) 957.47/297.39 , 130: U112^#(tt()) -> c_49() 957.47/297.39 , 131: U122^#(tt()) -> c_52() 957.47/297.39 , 132: U172^#(tt()) -> c_64() 957.47/297.39 , 133: U182^#(tt(), V1) -> c_66(U183^#(isLNat(activate(V1)))) 957.47/297.39 , 134: U183^#(tt()) -> c_67() 957.47/297.39 , 135: U192^#(tt(), V1) -> c_69(U193^#(isNatural(activate(V1)))) 957.47/297.39 , 136: U193^#(tt()) -> c_70() 957.47/297.39 , 137: U202^#(tt(), V1, V2) -> 957.47/297.39 c_72(U203^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.39 , 138: U203^#(tt(), V1, V2) -> 957.47/297.39 c_73(U204^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.39 , 139: U204^#(tt(), V1, V2) -> 957.47/297.39 c_74(U205^#(isNatural(activate(V1)), activate(V2))) 957.47/297.39 , 140: U205^#(tt(), V2) -> c_75(U206^#(isLNat(activate(V2)))) 957.47/297.39 , 141: U206^#(tt()) -> c_76() 957.47/297.39 , 142: U232^#(tt()) -> c_84() 957.47/297.39 , 143: U241^#(tt(), V1, V2) -> 957.47/297.39 c_85(U242^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.47/297.39 , 144: U242^#(tt(), V1, V2) -> 957.47/297.39 c_86(U243^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.39 , 145: U243^#(tt(), V1, V2) -> 957.47/297.39 c_87(U244^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.39 , 146: U244^#(tt(), V1, V2) -> 957.47/297.39 c_88(U245^#(isLNat(activate(V1)), activate(V2))) 957.47/297.39 , 147: U245^#(tt(), V2) -> c_89(U246^#(isLNat(activate(V2)))) 957.47/297.39 , 148: U246^#(tt()) -> c_90() 957.47/297.39 , 149: U251^#(tt(), V1, V2) -> 957.47/297.39 c_91(U252^#(isNaturalKind(activate(V1)), 957.47/297.39 activate(V1), 957.47/297.39 activate(V2))) 957.47/297.39 , 150: U252^#(tt(), V1, V2) -> 957.47/297.39 c_92(U253^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.39 , 151: U253^#(tt(), V1, V2) -> 957.47/297.39 c_93(U254^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.39 , 152: U254^#(tt(), V1, V2) -> 957.47/297.39 c_94(U255^#(isNatural(activate(V1)), activate(V2))) 957.47/297.39 , 153: U255^#(tt(), V2) -> c_95(U256^#(isLNat(activate(V2)))) 957.47/297.39 , 154: U256^#(tt()) -> c_96() 957.47/297.39 , 155: U261^#(tt(), V2) -> c_97(U262^#(isLNatKind(activate(V2)))) 957.47/297.39 , 156: U262^#(tt()) -> c_98() 957.47/297.39 , 157: U271^#(tt(), V2) -> c_99(U272^#(isLNatKind(activate(V2)))) 957.47/297.39 , 158: U272^#(tt()) -> c_100() 957.47/297.39 , 159: U42^#(tt(), V1, V2) -> 957.47/297.39 c_143(U43^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.39 , 160: U43^#(tt(), V1, V2) -> 957.47/297.39 c_144(U44^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.39 , 161: U44^#(tt(), V1, V2) -> 957.47/297.39 c_145(U45^#(isNatural(activate(V1)), activate(V2))) 957.47/297.39 , 162: U45^#(tt(), V2) -> c_146(U46^#(isLNat(activate(V2)))) 957.47/297.39 , 163: U46^#(tt()) -> c_147() 957.47/297.39 , 164: U52^#(tt(), V1, V2) -> 957.47/297.39 c_149(U53^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.39 , 165: U53^#(tt(), V1, V2) -> 957.47/297.39 c_150(U54^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.39 , 166: U54^#(tt(), V1, V2) -> 957.47/297.39 c_151(U55^#(isNatural(activate(V1)), activate(V2))) 957.47/297.39 , 167: U55^#(tt(), V2) -> c_152(U56^#(isLNat(activate(V2)))) 957.47/297.39 , 168: U56^#(tt()) -> c_153() 957.47/297.39 , 169: U62^#(tt(), V1) -> c_155(U63^#(isPLNat(activate(V1)))) 957.47/297.39 , 170: U63^#(tt()) -> c_158() 957.47/297.39 , 171: isPLNatKind^#(n__pair(V1, V2)) -> 957.47/297.39 c_156(U261^#(isLNatKind(activate(V1)), activate(V2))) 957.47/297.39 , 172: isPLNatKind^#(n__splitAt(V1, V2)) -> 957.47/297.39 c_157(U271^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.39 , 173: U72^#(tt(), V1) -> c_162(U73^#(isNatural(activate(V1)))) 957.47/297.39 , 174: U73^#(tt()) -> c_163() 957.47/297.39 , 175: U82^#(tt(), V1) -> c_165(U83^#(isPLNat(activate(V1)))) 957.47/297.39 , 176: U83^#(tt()) -> c_166() 957.47/297.39 , 177: U92^#(tt(), V1) -> c_168(U93^#(isLNat(activate(V1)))) 957.47/297.39 , 178: U93^#(tt()) -> c_169() } 957.47/297.39 957.47/297.39 We are left with following problem, upon which TcT provides the 957.47/297.39 certificate MAYBE. 957.47/297.39 957.47/297.39 Strict DPs: 957.47/297.39 { activate^#(X) -> c_7(X) 957.47/297.39 , activate^#(n__natsFrom(X)) -> c_8(natsFrom^#(X)) 957.47/297.39 , activate^#(n__afterNth(X1, X2)) -> c_10(afterNth^#(X1, X2)) 957.47/297.39 , activate^#(n__cons(X1, X2)) -> c_11(cons^#(X1, X2)) 957.47/297.39 , activate^#(n__fst(X)) -> c_12(fst^#(X)) 957.47/297.39 , activate^#(n__snd(X)) -> c_13(snd^#(X)) 957.47/297.39 , activate^#(n__tail(X)) -> c_14(tail^#(X)) 957.47/297.39 , activate^#(n__take(X1, X2)) -> c_15(take^#(X1, X2)) 957.47/297.39 , activate^#(n__head(X)) -> c_17(head^#(X)) 957.47/297.39 , activate^#(n__s(X)) -> c_18(s^#(X)) 957.47/297.39 , activate^#(n__sel(X1, X2)) -> c_19(sel^#(X1, X2)) 957.47/297.39 , activate^#(n__pair(X1, X2)) -> c_20(pair^#(X1, X2)) 957.47/297.39 , activate^#(n__splitAt(X1, X2)) -> c_21(splitAt^#(X1, X2)) 957.47/297.39 , natsFrom^#(N) -> c_170(U281^#(isNatural(N), N)) 957.47/297.39 , natsFrom^#(X) -> c_171(X) 957.47/297.39 , afterNth^#(N, XS) -> c_111(U11^#(isNatural(N), N, XS)) 957.47/297.39 , afterNth^#(X1, X2) -> c_112(X1, X2) 957.47/297.39 , cons^#(X1, X2) -> c_103(X1, X2) 957.47/297.39 , fst^#(X) -> c_140(X) 957.47/297.39 , fst^#(pair(X, Y)) -> c_141(U21^#(isLNat(X), X, Y)) 957.47/297.39 , snd^#(X) -> c_55(X) 957.47/297.39 , snd^#(pair(X, Y)) -> c_56(U301^#(isLNat(X), X, Y)) 957.47/297.39 , tail^#(X) -> c_175(X) 957.47/297.39 , tail^#(cons(N, XS)) -> 957.47/297.39 c_176(U331^#(isNatural(N), N, activate(XS))) 957.47/297.39 , take^#(N, XS) -> c_177(U341^#(isNatural(N), N, XS)) 957.47/297.39 , take^#(X1, X2) -> c_178(X1, X2) 957.47/297.39 , head^#(X) -> c_109(X) 957.47/297.39 , head^#(cons(N, XS)) -> 957.47/297.39 c_110(U31^#(isNatural(N), N, activate(XS))) 957.47/297.39 , s^#(X) -> c_104(X) 957.47/297.39 , sel^#(N, XS) -> c_172(U291^#(isNatural(N), N, XS)) 957.47/297.39 , sel^#(X1, X2) -> c_173(X1, X2) 957.47/297.39 , pair^#(X1, X2) -> c_121(X1, X2) 957.47/297.39 , splitAt^#(X1, X2) -> c_57(X1, X2) 957.47/297.39 , splitAt^#(s(N), cons(X, XS)) -> 957.47/297.39 c_58(U321^#(isNatural(N), N, X, activate(XS))) 957.47/297.39 , splitAt^#(0(), XS) -> c_59(U311^#(isLNat(XS), XS)) 957.47/297.39 , U11^#(tt(), N, XS) -> 957.47/297.39 c_46(U12^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.47/297.39 , U12^#(tt(), N, XS) -> 957.47/297.39 c_47(U13^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.39 , U13^#(tt(), N, XS) -> 957.47/297.39 c_50(U14^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.39 , U14^#(tt(), N, XS) -> 957.47/297.39 c_53(snd^#(splitAt(activate(N), activate(XS)))) 957.47/297.39 , U301^#(tt(), X, Y) -> 957.47/297.39 c_113(U302^#(isLNatKind(activate(X)), activate(Y))) 957.47/297.39 , U321^#(tt(), N, X, XS) -> 957.47/297.39 c_124(U322^#(isNaturalKind(activate(N)), 957.47/297.39 activate(N), 957.47/297.39 activate(X), 957.47/297.39 activate(XS))) 957.47/297.39 , U311^#(tt(), XS) -> 957.47/297.39 c_119(U312^#(isLNatKind(activate(XS)), activate(XS))) 957.47/297.39 , U21^#(tt(), X, Y) -> 957.47/297.39 c_77(U22^#(isLNatKind(activate(X)), activate(X), activate(Y))) 957.47/297.39 , U22^#(tt(), X, Y) -> 957.47/297.39 c_78(U23^#(isLNat(activate(Y)), activate(X), activate(Y))) 957.47/297.39 , U23^#(tt(), X, Y) -> 957.47/297.39 c_80(U24^#(isLNatKind(activate(Y)), activate(X))) 957.47/297.39 , U24^#(tt(), X) -> c_82(activate^#(X)) 957.47/297.39 , U281^#(tt(), N) -> 957.47/297.39 c_101(U282^#(isNaturalKind(activate(N)), activate(N))) 957.47/297.39 , U282^#(tt(), N) -> 957.47/297.39 c_102(cons^#(activate(N), n__natsFrom(s(activate(N))))) 957.47/297.39 , U291^#(tt(), N, XS) -> 957.47/297.39 c_105(U292^#(isNaturalKind(activate(N)), 957.47/297.39 activate(N), 957.47/297.39 activate(XS))) 957.47/297.39 , U292^#(tt(), N, XS) -> 957.47/297.39 c_106(U293^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.39 , U293^#(tt(), N, XS) -> 957.47/297.39 c_107(U294^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.39 , U294^#(tt(), N, XS) -> 957.47/297.39 c_108(head^#(afterNth(activate(N), activate(XS)))) 957.47/297.39 , U31^#(tt(), N, XS) -> 957.47/297.39 c_117(U32^#(isNaturalKind(activate(N)), activate(N), activate(XS))) 957.47/297.39 , U302^#(tt(), Y) -> 957.47/297.39 c_114(U303^#(isLNat(activate(Y)), activate(Y))) 957.47/297.39 , U303^#(tt(), Y) -> 957.47/297.39 c_115(U304^#(isLNatKind(activate(Y)), activate(Y))) 957.47/297.39 , U304^#(tt(), Y) -> c_116(activate^#(Y)) 957.47/297.39 , U32^#(tt(), N, XS) -> 957.47/297.39 c_118(U33^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.39 , U33^#(tt(), N, XS) -> 957.47/297.39 c_123(U34^#(isLNatKind(activate(XS)), activate(N))) 957.47/297.39 , U312^#(tt(), XS) -> c_120(pair^#(nil(), activate(XS))) 957.47/297.39 , U34^#(tt(), N) -> c_131(activate^#(N)) 957.47/297.39 , U322^#(tt(), N, X, XS) -> 957.47/297.39 c_125(U323^#(isNatural(activate(X)), 957.47/297.39 activate(N), 957.47/297.39 activate(X), 957.47/297.39 activate(XS))) 957.47/297.39 , U323^#(tt(), N, X, XS) -> 957.47/297.39 c_126(U324^#(isNaturalKind(activate(X)), 957.47/297.39 activate(N), 957.47/297.39 activate(X), 957.47/297.39 activate(XS))) 957.47/297.39 , U324^#(tt(), N, X, XS) -> 957.47/297.39 c_127(U325^#(isLNat(activate(XS)), 957.47/297.39 activate(N), 957.47/297.39 activate(X), 957.47/297.39 activate(XS))) 957.47/297.39 , U325^#(tt(), N, X, XS) -> 957.47/297.39 c_128(U326^#(isLNatKind(activate(XS)), 957.47/297.39 activate(N), 957.47/297.39 activate(X), 957.47/297.39 activate(XS))) 957.47/297.39 , U326^#(tt(), N, X, XS) -> 957.47/297.39 c_129(U327^#(splitAt(activate(N), activate(XS)), activate(X))) 957.47/297.39 , U327^#(pair(YS, ZS), X) -> 957.47/297.39 c_130(pair^#(cons(activate(X), YS), ZS)) 957.47/297.39 , U331^#(tt(), N, XS) -> 957.47/297.39 c_132(U332^#(isNaturalKind(activate(N)), activate(XS))) 957.47/297.39 , U332^#(tt(), XS) -> 957.47/297.39 c_133(U333^#(isLNat(activate(XS)), activate(XS))) 957.47/297.39 , U333^#(tt(), XS) -> 957.47/297.39 c_134(U334^#(isLNatKind(activate(XS)), activate(XS))) 957.47/297.39 , U334^#(tt(), XS) -> c_135(activate^#(XS)) 957.47/297.39 , U341^#(tt(), N, XS) -> 957.47/297.39 c_136(U342^#(isNaturalKind(activate(N)), 957.47/297.39 activate(N), 957.47/297.39 activate(XS))) 957.47/297.39 , U342^#(tt(), N, XS) -> 957.47/297.39 c_137(U343^#(isLNat(activate(XS)), activate(N), activate(XS))) 957.47/297.39 , U343^#(tt(), N, XS) -> 957.47/297.39 c_138(U344^#(isLNatKind(activate(XS)), activate(N), activate(XS))) 957.47/297.39 , U344^#(tt(), N, XS) -> 957.47/297.39 c_139(fst^#(splitAt(activate(N), activate(XS)))) } 957.47/297.39 Strict Trs: 957.47/297.39 { U101(tt(), V1, V2) -> 957.47/297.39 U102(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.39 , U102(tt(), V1, V2) -> 957.47/297.39 U103(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.39 , isNaturalKind(n__0()) -> tt() 957.47/297.39 , isNaturalKind(n__head(V1)) -> U211(isLNatKind(activate(V1))) 957.47/297.39 , isNaturalKind(n__s(V1)) -> U221(isNaturalKind(activate(V1))) 957.47/297.39 , isNaturalKind(n__sel(V1, V2)) -> 957.47/297.39 U231(isNaturalKind(activate(V1)), activate(V2)) 957.47/297.39 , activate(X) -> X 957.47/297.39 , activate(n__natsFrom(X)) -> natsFrom(X) 957.47/297.39 , activate(n__nil()) -> nil() 957.47/297.39 , activate(n__afterNth(X1, X2)) -> afterNth(X1, X2) 957.47/297.39 , activate(n__cons(X1, X2)) -> cons(X1, X2) 957.47/297.39 , activate(n__fst(X)) -> fst(X) 957.47/297.39 , activate(n__snd(X)) -> snd(X) 957.47/297.39 , activate(n__tail(X)) -> tail(X) 957.47/297.39 , activate(n__take(X1, X2)) -> take(X1, X2) 957.47/297.39 , activate(n__0()) -> 0() 957.47/297.39 , activate(n__head(X)) -> head(X) 957.47/297.39 , activate(n__s(X)) -> s(X) 957.47/297.39 , activate(n__sel(X1, X2)) -> sel(X1, X2) 957.47/297.39 , activate(n__pair(X1, X2)) -> pair(X1, X2) 957.47/297.39 , activate(n__splitAt(X1, X2)) -> splitAt(X1, X2) 957.47/297.39 , U103(tt(), V1, V2) -> 957.47/297.39 U104(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.39 , isLNatKind(n__natsFrom(V1)) -> U141(isNaturalKind(activate(V1))) 957.47/297.39 , isLNatKind(n__nil()) -> tt() 957.47/297.39 , isLNatKind(n__afterNth(V1, V2)) -> 957.47/297.39 U111(isNaturalKind(activate(V1)), activate(V2)) 957.47/297.39 , isLNatKind(n__cons(V1, V2)) -> 957.47/297.39 U121(isNaturalKind(activate(V1)), activate(V2)) 957.47/297.39 , isLNatKind(n__fst(V1)) -> U131(isPLNatKind(activate(V1))) 957.47/297.39 , isLNatKind(n__snd(V1)) -> U151(isPLNatKind(activate(V1))) 957.47/297.39 , isLNatKind(n__tail(V1)) -> U161(isLNatKind(activate(V1))) 957.47/297.39 , isLNatKind(n__take(V1, V2)) -> 957.47/297.39 U171(isNaturalKind(activate(V1)), activate(V2)) 957.47/297.39 , U104(tt(), V1, V2) -> U105(isNatural(activate(V1)), activate(V2)) 957.47/297.39 , U105(tt(), V2) -> U106(isLNat(activate(V2))) 957.47/297.39 , isNatural(n__0()) -> tt() 957.47/297.39 , isNatural(n__head(V1)) -> 957.47/297.39 U181(isLNatKind(activate(V1)), activate(V1)) 957.47/297.39 , isNatural(n__s(V1)) -> 957.47/297.39 U191(isNaturalKind(activate(V1)), activate(V1)) 957.47/297.39 , isNatural(n__sel(V1, V2)) -> 957.47/297.39 U201(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.39 , U106(tt()) -> tt() 957.47/297.39 , isLNat(n__natsFrom(V1)) -> 957.47/297.39 U71(isNaturalKind(activate(V1)), activate(V1)) 957.47/297.39 , isLNat(n__nil()) -> tt() 957.47/297.39 , isLNat(n__afterNth(V1, V2)) -> 957.47/297.39 U41(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.39 , isLNat(n__cons(V1, V2)) -> 957.47/297.39 U51(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.39 , isLNat(n__fst(V1)) -> 957.47/297.39 U61(isPLNatKind(activate(V1)), activate(V1)) 957.47/297.39 , isLNat(n__snd(V1)) -> 957.47/297.39 U81(isPLNatKind(activate(V1)), activate(V1)) 957.47/297.39 , isLNat(n__tail(V1)) -> 957.47/297.39 U91(isLNatKind(activate(V1)), activate(V1)) 957.47/297.39 , isLNat(n__take(V1, V2)) -> 957.47/297.39 U101(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.39 , U11(tt(), N, XS) -> 957.47/297.39 U12(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.47/297.39 , U12(tt(), N, XS) -> 957.47/297.39 U13(isLNat(activate(XS)), activate(N), activate(XS)) 957.47/297.39 , U111(tt(), V2) -> U112(isLNatKind(activate(V2))) 957.47/297.39 , U112(tt()) -> tt() 957.47/297.39 , U13(tt(), N, XS) -> 957.47/297.39 U14(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.47/297.39 , U121(tt(), V2) -> U122(isLNatKind(activate(V2))) 957.47/297.39 , U122(tt()) -> tt() 957.47/297.39 , U14(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS))) 957.47/297.39 , U131(tt()) -> tt() 957.47/297.39 , snd(X) -> n__snd(X) 957.47/297.39 , snd(pair(X, Y)) -> U301(isLNat(X), X, Y) 957.47/297.39 , splitAt(X1, X2) -> n__splitAt(X1, X2) 957.47/297.39 , splitAt(s(N), cons(X, XS)) -> 957.47/297.39 U321(isNatural(N), N, X, activate(XS)) 957.47/297.39 , splitAt(0(), XS) -> U311(isLNat(XS), XS) 957.47/297.39 , U141(tt()) -> tt() 957.47/297.39 , U151(tt()) -> tt() 957.47/297.39 , U161(tt()) -> tt() 957.47/297.39 , U171(tt(), V2) -> U172(isLNatKind(activate(V2))) 957.47/297.39 , U172(tt()) -> tt() 957.47/297.39 , U181(tt(), V1) -> U182(isLNatKind(activate(V1)), activate(V1)) 957.47/297.39 , U182(tt(), V1) -> U183(isLNat(activate(V1))) 957.47/297.39 , U183(tt()) -> tt() 957.47/297.39 , U191(tt(), V1) -> U192(isNaturalKind(activate(V1)), activate(V1)) 957.47/297.39 , U192(tt(), V1) -> U193(isNatural(activate(V1))) 957.47/297.39 , U193(tt()) -> tt() 957.47/297.39 , U201(tt(), V1, V2) -> 957.47/297.39 U202(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.39 , U202(tt(), V1, V2) -> 957.47/297.39 U203(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.39 , U203(tt(), V1, V2) -> 957.47/297.39 U204(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.39 , U204(tt(), V1, V2) -> U205(isNatural(activate(V1)), activate(V2)) 957.47/297.39 , U205(tt(), V2) -> U206(isLNat(activate(V2))) 957.47/297.39 , U206(tt()) -> tt() 957.47/297.39 , U21(tt(), X, Y) -> 957.47/297.39 U22(isLNatKind(activate(X)), activate(X), activate(Y)) 957.47/297.39 , U22(tt(), X, Y) -> 957.47/297.39 U23(isLNat(activate(Y)), activate(X), activate(Y)) 957.47/297.39 , U211(tt()) -> tt() 957.47/297.39 , U23(tt(), X, Y) -> U24(isLNatKind(activate(Y)), activate(X)) 957.47/297.39 , U221(tt()) -> tt() 957.47/297.39 , U24(tt(), X) -> activate(X) 957.47/297.39 , U231(tt(), V2) -> U232(isLNatKind(activate(V2))) 957.47/297.39 , U232(tt()) -> tt() 957.47/297.39 , U241(tt(), V1, V2) -> 957.47/297.39 U242(isLNatKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.39 , U242(tt(), V1, V2) -> 957.47/297.39 U243(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.39 , U243(tt(), V1, V2) -> 957.47/297.39 U244(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.39 , U244(tt(), V1, V2) -> U245(isLNat(activate(V1)), activate(V2)) 957.47/297.39 , U245(tt(), V2) -> U246(isLNat(activate(V2))) 957.47/297.39 , U246(tt()) -> tt() 957.47/297.39 , U251(tt(), V1, V2) -> 957.47/297.39 U252(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.39 , U252(tt(), V1, V2) -> 957.47/297.39 U253(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.39 , U253(tt(), V1, V2) -> 957.47/297.39 U254(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.39 , U254(tt(), V1, V2) -> U255(isNatural(activate(V1)), activate(V2)) 957.47/297.39 , U255(tt(), V2) -> U256(isLNat(activate(V2))) 957.47/297.39 , U256(tt()) -> tt() 957.47/297.39 , U261(tt(), V2) -> U262(isLNatKind(activate(V2))) 957.47/297.39 , U262(tt()) -> tt() 957.47/297.39 , U271(tt(), V2) -> U272(isLNatKind(activate(V2))) 957.47/297.39 , U272(tt()) -> tt() 957.47/297.39 , U281(tt(), N) -> U282(isNaturalKind(activate(N)), activate(N)) 957.47/297.39 , U282(tt(), N) -> cons(activate(N), n__natsFrom(s(activate(N)))) 957.47/297.40 , cons(X1, X2) -> n__cons(X1, X2) 957.47/297.40 , s(X) -> n__s(X) 957.47/297.40 , U291(tt(), N, XS) -> 957.47/297.40 U292(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.47/297.40 , U292(tt(), N, XS) -> 957.47/297.40 U293(isLNat(activate(XS)), activate(N), activate(XS)) 957.47/297.40 , U293(tt(), N, XS) -> 957.47/297.40 U294(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.47/297.40 , U294(tt(), N, XS) -> head(afterNth(activate(N), activate(XS))) 957.47/297.40 , head(X) -> n__head(X) 957.47/297.40 , head(cons(N, XS)) -> U31(isNatural(N), N, activate(XS)) 957.47/297.40 , afterNth(N, XS) -> U11(isNatural(N), N, XS) 957.47/297.40 , afterNth(X1, X2) -> n__afterNth(X1, X2) 957.47/297.40 , U301(tt(), X, Y) -> U302(isLNatKind(activate(X)), activate(Y)) 957.47/297.40 , U302(tt(), Y) -> U303(isLNat(activate(Y)), activate(Y)) 957.47/297.40 , U303(tt(), Y) -> U304(isLNatKind(activate(Y)), activate(Y)) 957.47/297.40 , U304(tt(), Y) -> activate(Y) 957.47/297.40 , U31(tt(), N, XS) -> 957.47/297.40 U32(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.47/297.40 , U32(tt(), N, XS) -> 957.47/297.40 U33(isLNat(activate(XS)), activate(N), activate(XS)) 957.47/297.40 , U311(tt(), XS) -> U312(isLNatKind(activate(XS)), activate(XS)) 957.47/297.40 , U312(tt(), XS) -> pair(nil(), activate(XS)) 957.47/297.40 , pair(X1, X2) -> n__pair(X1, X2) 957.47/297.40 , nil() -> n__nil() 957.47/297.40 , U33(tt(), N, XS) -> U34(isLNatKind(activate(XS)), activate(N)) 957.47/297.40 , U321(tt(), N, X, XS) -> 957.47/297.40 U322(isNaturalKind(activate(N)), 957.47/297.40 activate(N), 957.47/297.40 activate(X), 957.47/297.40 activate(XS)) 957.47/297.40 , U322(tt(), N, X, XS) -> 957.47/297.40 U323(isNatural(activate(X)), 957.47/297.40 activate(N), 957.47/297.40 activate(X), 957.47/297.40 activate(XS)) 957.47/297.40 , U323(tt(), N, X, XS) -> 957.47/297.40 U324(isNaturalKind(activate(X)), 957.47/297.40 activate(N), 957.47/297.40 activate(X), 957.47/297.40 activate(XS)) 957.47/297.40 , U324(tt(), N, X, XS) -> 957.47/297.40 U325(isLNat(activate(XS)), activate(N), activate(X), activate(XS)) 957.47/297.40 , U325(tt(), N, X, XS) -> 957.47/297.40 U326(isLNatKind(activate(XS)), 957.47/297.40 activate(N), 957.47/297.40 activate(X), 957.47/297.40 activate(XS)) 957.47/297.40 , U326(tt(), N, X, XS) -> 957.47/297.40 U327(splitAt(activate(N), activate(XS)), activate(X)) 957.47/297.40 , U327(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) 957.47/297.40 , U34(tt(), N) -> activate(N) 957.47/297.40 , U331(tt(), N, XS) -> 957.47/297.40 U332(isNaturalKind(activate(N)), activate(XS)) 957.47/297.40 , U332(tt(), XS) -> U333(isLNat(activate(XS)), activate(XS)) 957.47/297.40 , U333(tt(), XS) -> U334(isLNatKind(activate(XS)), activate(XS)) 957.47/297.40 , U334(tt(), XS) -> activate(XS) 957.47/297.40 , U341(tt(), N, XS) -> 957.47/297.40 U342(isNaturalKind(activate(N)), activate(N), activate(XS)) 957.47/297.40 , U342(tt(), N, XS) -> 957.47/297.40 U343(isLNat(activate(XS)), activate(N), activate(XS)) 957.47/297.40 , U343(tt(), N, XS) -> 957.47/297.40 U344(isLNatKind(activate(XS)), activate(N), activate(XS)) 957.47/297.40 , U344(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS))) 957.47/297.40 , fst(X) -> n__fst(X) 957.47/297.40 , fst(pair(X, Y)) -> U21(isLNat(X), X, Y) 957.47/297.40 , U41(tt(), V1, V2) -> 957.47/297.40 U42(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.40 , U42(tt(), V1, V2) -> 957.47/297.40 U43(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.40 , U43(tt(), V1, V2) -> 957.47/297.40 U44(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.40 , U44(tt(), V1, V2) -> U45(isNatural(activate(V1)), activate(V2)) 957.47/297.40 , U45(tt(), V2) -> U46(isLNat(activate(V2))) 957.47/297.40 , U46(tt()) -> tt() 957.47/297.40 , U51(tt(), V1, V2) -> 957.47/297.40 U52(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.40 , U52(tt(), V1, V2) -> 957.47/297.40 U53(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.40 , U53(tt(), V1, V2) -> 957.47/297.40 U54(isLNatKind(activate(V2)), activate(V1), activate(V2)) 957.47/297.40 , U54(tt(), V1, V2) -> U55(isNatural(activate(V1)), activate(V2)) 957.47/297.40 , U55(tt(), V2) -> U56(isLNat(activate(V2))) 957.47/297.40 , U56(tt()) -> tt() 957.47/297.40 , U61(tt(), V1) -> U62(isPLNatKind(activate(V1)), activate(V1)) 957.47/297.40 , U62(tt(), V1) -> U63(isPLNat(activate(V1))) 957.47/297.40 , isPLNatKind(n__pair(V1, V2)) -> 957.47/297.40 U261(isLNatKind(activate(V1)), activate(V2)) 957.47/297.40 , isPLNatKind(n__splitAt(V1, V2)) -> 957.47/297.40 U271(isNaturalKind(activate(V1)), activate(V2)) 957.47/297.40 , U63(tt()) -> tt() 957.47/297.40 , isPLNat(n__pair(V1, V2)) -> 957.47/297.40 U241(isLNatKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.40 , isPLNat(n__splitAt(V1, V2)) -> 957.47/297.40 U251(isNaturalKind(activate(V1)), activate(V1), activate(V2)) 957.47/297.40 , U71(tt(), V1) -> U72(isNaturalKind(activate(V1)), activate(V1)) 957.47/297.40 , U72(tt(), V1) -> U73(isNatural(activate(V1))) 957.47/297.40 , U73(tt()) -> tt() 957.47/297.40 , U81(tt(), V1) -> U82(isPLNatKind(activate(V1)), activate(V1)) 957.47/297.40 , U82(tt(), V1) -> U83(isPLNat(activate(V1))) 957.47/297.40 , U83(tt()) -> tt() 957.47/297.40 , U91(tt(), V1) -> U92(isLNatKind(activate(V1)), activate(V1)) 957.47/297.40 , U92(tt(), V1) -> U93(isLNat(activate(V1))) 957.47/297.40 , U93(tt()) -> tt() 957.47/297.40 , natsFrom(N) -> U281(isNatural(N), N) 957.47/297.40 , natsFrom(X) -> n__natsFrom(X) 957.47/297.40 , sel(N, XS) -> U291(isNatural(N), N, XS) 957.47/297.40 , sel(X1, X2) -> n__sel(X1, X2) 957.47/297.40 , 0() -> n__0() 957.47/297.40 , tail(X) -> n__tail(X) 957.47/297.40 , tail(cons(N, XS)) -> U331(isNatural(N), N, activate(XS)) 957.47/297.40 , take(N, XS) -> U341(isNatural(N), N, XS) 957.47/297.40 , take(X1, X2) -> n__take(X1, X2) } 957.47/297.40 Weak DPs: 957.47/297.40 { U101^#(tt(), V1, V2) -> 957.47/297.40 c_1(U102^#(isNaturalKind(activate(V1)), 957.47/297.40 activate(V1), 957.47/297.40 activate(V2))) 957.47/297.40 , U102^#(tt(), V1, V2) -> 957.47/297.40 c_2(U103^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.40 , U103^#(tt(), V1, V2) -> 957.47/297.40 c_22(U104^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.47/297.40 , isNaturalKind^#(n__0()) -> c_3() 957.47/297.40 , isNaturalKind^#(n__head(V1)) -> 957.47/297.40 c_4(U211^#(isLNatKind(activate(V1)))) 957.47/297.40 , isNaturalKind^#(n__s(V1)) -> 957.47/297.40 c_5(U221^#(isNaturalKind(activate(V1)))) 957.47/297.40 , isNaturalKind^#(n__sel(V1, V2)) -> 957.47/297.40 c_6(U231^#(isNaturalKind(activate(V1)), activate(V2))) 957.47/297.40 , U211^#(tt()) -> c_79() 957.47/297.40 , U221^#(tt()) -> c_81() 957.47/297.40 , U231^#(tt(), V2) -> c_83(U232^#(isLNatKind(activate(V2)))) 957.47/297.40 , activate^#(n__nil()) -> c_9(nil^#()) 957.47/297.40 , activate^#(n__0()) -> c_16(0^#()) 957.47/297.40 , nil^#() -> c_122() 957.47/297.40 , 0^#() -> c_174() 957.47/297.40 , U104^#(tt(), V1, V2) -> 957.47/297.40 c_31(U105^#(isNatural(activate(V1)), activate(V2))) 957.47/297.40 , isLNatKind^#(n__natsFrom(V1)) -> 957.72/297.40 c_23(U141^#(isNaturalKind(activate(V1)))) 957.72/297.40 , isLNatKind^#(n__nil()) -> c_24() 957.72/297.40 , isLNatKind^#(n__afterNth(V1, V2)) -> 957.72/297.40 c_25(U111^#(isNaturalKind(activate(V1)), activate(V2))) 957.72/297.40 , isLNatKind^#(n__cons(V1, V2)) -> 957.72/297.40 c_26(U121^#(isNaturalKind(activate(V1)), activate(V2))) 957.72/297.40 , isLNatKind^#(n__fst(V1)) -> 957.72/297.40 c_27(U131^#(isPLNatKind(activate(V1)))) 957.72/297.40 , isLNatKind^#(n__snd(V1)) -> 957.72/297.40 c_28(U151^#(isPLNatKind(activate(V1)))) 957.72/297.40 , isLNatKind^#(n__tail(V1)) -> 957.72/297.40 c_29(U161^#(isLNatKind(activate(V1)))) 957.72/297.40 , isLNatKind^#(n__take(V1, V2)) -> 957.72/297.40 c_30(U171^#(isNaturalKind(activate(V1)), activate(V2))) 957.72/297.40 , U141^#(tt()) -> c_60() 957.72/297.40 , U111^#(tt(), V2) -> c_48(U112^#(isLNatKind(activate(V2)))) 957.72/297.40 , U121^#(tt(), V2) -> c_51(U122^#(isLNatKind(activate(V2)))) 957.72/297.40 , U131^#(tt()) -> c_54() 957.72/297.40 , U151^#(tt()) -> c_61() 957.72/297.40 , U161^#(tt()) -> c_62() 957.72/297.40 , U171^#(tt(), V2) -> c_63(U172^#(isLNatKind(activate(V2)))) 957.72/297.40 , U105^#(tt(), V2) -> c_32(U106^#(isLNat(activate(V2)))) 957.72/297.40 , U106^#(tt()) -> c_37() 957.72/297.40 , isNatural^#(n__0()) -> c_33() 957.72/297.40 , isNatural^#(n__head(V1)) -> 957.72/297.40 c_34(U181^#(isLNatKind(activate(V1)), activate(V1))) 957.72/297.40 , isNatural^#(n__s(V1)) -> 957.72/297.40 c_35(U191^#(isNaturalKind(activate(V1)), activate(V1))) 957.72/297.40 , isNatural^#(n__sel(V1, V2)) -> 957.72/297.40 c_36(U201^#(isNaturalKind(activate(V1)), 957.72/297.40 activate(V1), 957.72/297.40 activate(V2))) 957.72/297.40 , U181^#(tt(), V1) -> 957.72/297.40 c_65(U182^#(isLNatKind(activate(V1)), activate(V1))) 957.72/297.40 , U191^#(tt(), V1) -> 957.72/297.40 c_68(U192^#(isNaturalKind(activate(V1)), activate(V1))) 957.72/297.40 , U201^#(tt(), V1, V2) -> 957.72/297.40 c_71(U202^#(isNaturalKind(activate(V1)), 957.72/297.40 activate(V1), 957.72/297.40 activate(V2))) 957.72/297.40 , isLNat^#(n__natsFrom(V1)) -> 957.72/297.40 c_38(U71^#(isNaturalKind(activate(V1)), activate(V1))) 957.72/297.40 , isLNat^#(n__nil()) -> c_39() 957.72/297.40 , isLNat^#(n__afterNth(V1, V2)) -> 957.72/297.40 c_40(U41^#(isNaturalKind(activate(V1)), 957.72/297.40 activate(V1), 957.72/297.40 activate(V2))) 957.72/297.40 , isLNat^#(n__cons(V1, V2)) -> 957.72/297.40 c_41(U51^#(isNaturalKind(activate(V1)), 957.72/297.40 activate(V1), 957.72/297.40 activate(V2))) 957.72/297.40 , isLNat^#(n__fst(V1)) -> 957.72/297.40 c_42(U61^#(isPLNatKind(activate(V1)), activate(V1))) 957.72/297.40 , isLNat^#(n__snd(V1)) -> 957.72/297.40 c_43(U81^#(isPLNatKind(activate(V1)), activate(V1))) 957.72/297.40 , isLNat^#(n__tail(V1)) -> 957.72/297.40 c_44(U91^#(isLNatKind(activate(V1)), activate(V1))) 957.72/297.40 , isLNat^#(n__take(V1, V2)) -> 957.72/297.40 c_45(U101^#(isNaturalKind(activate(V1)), 957.72/297.40 activate(V1), 957.72/297.40 activate(V2))) 957.72/297.40 , U71^#(tt(), V1) -> 957.72/297.40 c_161(U72^#(isNaturalKind(activate(V1)), activate(V1))) 957.72/297.40 , U41^#(tt(), V1, V2) -> 957.72/297.40 c_142(U42^#(isNaturalKind(activate(V1)), 957.72/297.40 activate(V1), 957.72/297.40 activate(V2))) 957.72/297.40 , U51^#(tt(), V1, V2) -> 957.72/297.40 c_148(U52^#(isNaturalKind(activate(V1)), 957.72/297.40 activate(V1), 957.72/297.40 activate(V2))) 957.72/297.40 , U61^#(tt(), V1) -> 957.72/297.40 c_154(U62^#(isPLNatKind(activate(V1)), activate(V1))) 957.72/297.40 , U81^#(tt(), V1) -> 957.72/297.40 c_164(U82^#(isPLNatKind(activate(V1)), activate(V1))) 957.72/297.40 , U91^#(tt(), V1) -> 957.72/297.40 c_167(U92^#(isLNatKind(activate(V1)), activate(V1))) 957.72/297.40 , U112^#(tt()) -> c_49() 957.72/297.40 , U122^#(tt()) -> c_52() 957.72/297.40 , U172^#(tt()) -> c_64() 957.72/297.40 , U182^#(tt(), V1) -> c_66(U183^#(isLNat(activate(V1)))) 957.72/297.40 , U183^#(tt()) -> c_67() 957.72/297.40 , U192^#(tt(), V1) -> c_69(U193^#(isNatural(activate(V1)))) 957.72/297.40 , U193^#(tt()) -> c_70() 957.72/297.40 , U202^#(tt(), V1, V2) -> 957.72/297.40 c_72(U203^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.72/297.40 , U203^#(tt(), V1, V2) -> 957.72/297.40 c_73(U204^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.72/297.40 , U204^#(tt(), V1, V2) -> 957.72/297.40 c_74(U205^#(isNatural(activate(V1)), activate(V2))) 957.72/297.40 , U205^#(tt(), V2) -> c_75(U206^#(isLNat(activate(V2)))) 957.72/297.40 , U206^#(tt()) -> c_76() 957.72/297.40 , U232^#(tt()) -> c_84() 957.72/297.40 , U241^#(tt(), V1, V2) -> 957.72/297.40 c_85(U242^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.72/297.40 , U242^#(tt(), V1, V2) -> 957.72/297.40 c_86(U243^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.72/297.40 , U243^#(tt(), V1, V2) -> 957.72/297.40 c_87(U244^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.72/297.40 , U244^#(tt(), V1, V2) -> 957.72/297.40 c_88(U245^#(isLNat(activate(V1)), activate(V2))) 957.72/297.40 , U245^#(tt(), V2) -> c_89(U246^#(isLNat(activate(V2)))) 957.72/297.40 , U246^#(tt()) -> c_90() 957.72/297.40 , U251^#(tt(), V1, V2) -> 957.72/297.40 c_91(U252^#(isNaturalKind(activate(V1)), 957.72/297.40 activate(V1), 957.72/297.40 activate(V2))) 957.72/297.40 , U252^#(tt(), V1, V2) -> 957.72/297.40 c_92(U253^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.72/297.40 , U253^#(tt(), V1, V2) -> 957.72/297.40 c_93(U254^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.72/297.40 , U254^#(tt(), V1, V2) -> 957.72/297.40 c_94(U255^#(isNatural(activate(V1)), activate(V2))) 957.72/297.40 , U255^#(tt(), V2) -> c_95(U256^#(isLNat(activate(V2)))) 957.72/297.40 , U256^#(tt()) -> c_96() 957.72/297.40 , U261^#(tt(), V2) -> c_97(U262^#(isLNatKind(activate(V2)))) 957.72/297.40 , U262^#(tt()) -> c_98() 957.72/297.40 , U271^#(tt(), V2) -> c_99(U272^#(isLNatKind(activate(V2)))) 957.72/297.40 , U272^#(tt()) -> c_100() 957.72/297.40 , U42^#(tt(), V1, V2) -> 957.72/297.40 c_143(U43^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.72/297.40 , U43^#(tt(), V1, V2) -> 957.72/297.40 c_144(U44^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.72/297.40 , U44^#(tt(), V1, V2) -> 957.72/297.40 c_145(U45^#(isNatural(activate(V1)), activate(V2))) 957.72/297.40 , U45^#(tt(), V2) -> c_146(U46^#(isLNat(activate(V2)))) 957.72/297.40 , U46^#(tt()) -> c_147() 957.72/297.40 , U52^#(tt(), V1, V2) -> 957.72/297.40 c_149(U53^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.72/297.40 , U53^#(tt(), V1, V2) -> 957.72/297.40 c_150(U54^#(isLNatKind(activate(V2)), activate(V1), activate(V2))) 957.72/297.40 , U54^#(tt(), V1, V2) -> 957.72/297.40 c_151(U55^#(isNatural(activate(V1)), activate(V2))) 957.72/297.40 , U55^#(tt(), V2) -> c_152(U56^#(isLNat(activate(V2)))) 957.72/297.40 , U56^#(tt()) -> c_153() 957.72/297.40 , U62^#(tt(), V1) -> c_155(U63^#(isPLNat(activate(V1)))) 957.72/297.40 , U63^#(tt()) -> c_158() 957.72/297.40 , isPLNatKind^#(n__pair(V1, V2)) -> 957.72/297.40 c_156(U261^#(isLNatKind(activate(V1)), activate(V2))) 957.72/297.40 , isPLNatKind^#(n__splitAt(V1, V2)) -> 957.72/297.40 c_157(U271^#(isNaturalKind(activate(V1)), activate(V2))) 957.72/297.40 , isPLNat^#(n__pair(V1, V2)) -> 957.72/297.40 c_159(U241^#(isLNatKind(activate(V1)), activate(V1), activate(V2))) 957.72/297.40 , isPLNat^#(n__splitAt(V1, V2)) -> 957.72/297.40 c_160(U251^#(isNaturalKind(activate(V1)), 957.72/297.40 activate(V1), 957.72/297.40 activate(V2))) 957.72/297.40 , U72^#(tt(), V1) -> c_162(U73^#(isNatural(activate(V1)))) 957.72/297.40 , U73^#(tt()) -> c_163() 957.72/297.40 , U82^#(tt(), V1) -> c_165(U83^#(isPLNat(activate(V1)))) 957.72/297.40 , U83^#(tt()) -> c_166() 957.72/297.40 , U92^#(tt(), V1) -> c_168(U93^#(isLNat(activate(V1)))) 957.72/297.40 , U93^#(tt()) -> c_169() } 957.72/297.40 Obligation: 957.72/297.40 runtime complexity 957.72/297.40 Answer: 957.72/297.40 MAYBE 957.72/297.40 957.72/297.40 Empty strict component of the problem is NOT empty. 957.72/297.40 957.72/297.40 957.72/297.40 Arrrr.. 957.72/297.40 EOF