(VAR N V1 V2 X X1 X2 XS Y YS ZS ) (RULES U101(tt, V1, V2) -> U102(isNatural(activate(V1)), activate(V2)) U102(tt, V2) -> U103(isLNat(activate(V2))) U103(tt) -> tt U11(tt, N, XS) -> snd(splitAt(activate(N), activate(XS))) U111(tt, V1) -> U112(isLNat(activate(V1))) U112(tt) -> tt U121(tt, V1) -> U122(isNatural(activate(V1))) U122(tt) -> tt U131(tt, V1, V2) -> U132(isNatural(activate(V1)), activate(V2)) U132(tt, V2) -> U133(isLNat(activate(V2))) U133(tt) -> tt U141(tt, V1, V2) -> U142(isLNat(activate(V1)), activate(V2)) U142(tt, V2) -> U143(isLNat(activate(V2))) U143(tt) -> tt U151(tt, V1, V2) -> U152(isNatural(activate(V1)), activate(V2)) U152(tt, V2) -> U153(isLNat(activate(V2))) U153(tt) -> tt U161(tt, N) -> cons(activate(N), n__natsFrom(s(activate(N)))) U171(tt, N, XS) -> head(afterNth(activate(N), activate(XS))) U181(tt, Y) -> activate(Y) U191(tt, XS) -> pair(nil, activate(XS)) U201(tt, N, X, XS) -> U202(splitAt(activate(N), activate(XS)), activate(X)) U202(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) U21(tt, X) -> activate(X) U211(tt, XS) -> activate(XS) U221(tt, N, XS) -> fst(splitAt(activate(N), activate(XS))) U31(tt, N) -> activate(N) U41(tt, V1, V2) -> U42(isNatural(activate(V1)), activate(V2)) U42(tt, V2) -> U43(isLNat(activate(V2))) U43(tt) -> tt U51(tt, V1, V2) -> U52(isNatural(activate(V1)), activate(V2)) U52(tt, V2) -> U53(isLNat(activate(V2))) U53(tt) -> tt U61(tt, V1) -> U62(isPLNat(activate(V1))) U62(tt) -> tt U71(tt, V1) -> U72(isNatural(activate(V1))) U72(tt) -> tt U81(tt, V1) -> U82(isPLNat(activate(V1))) U82(tt) -> tt U91(tt, V1) -> U92(isLNat(activate(V1))) U92(tt) -> tt afterNth(N, XS) -> U11(and(and(isNatural(N), n__isNaturalKind(N)), n__and(isLNat(XS), n__isLNatKind(XS))), N, XS) and(tt, X) -> activate(X) fst(pair(X, Y)) -> U21(and(and(isLNat(X), n__isLNatKind(X)), n__and(isLNat(Y), n__isLNatKind(Y))), X) head(cons(N, XS)) -> U31(and(and(isNatural(N), n__isNaturalKind(N)), n__and(isLNat(activate(XS)), n__isLNatKind(activate(XS)))), N) isLNat(n__nil) -> tt isLNat(n__afterNth(V1, V2)) -> U41(and(isNaturalKind(activate(V1)), n__isLNatKind(activate(V2))), activate(V1), activate(V2)) isLNat(n__cons(V1, V2)) -> U51(and(isNaturalKind(activate(V1)), n__isLNatKind(activate(V2))), activate(V1), activate(V2)) isLNat(n__fst(V1)) -> U61(isPLNatKind(activate(V1)), activate(V1)) isLNat(n__natsFrom(V1)) -> U71(isNaturalKind(activate(V1)), activate(V1)) isLNat(n__snd(V1)) -> U81(isPLNatKind(activate(V1)), activate(V1)) isLNat(n__tail(V1)) -> U91(isLNatKind(activate(V1)), activate(V1)) isLNat(n__take(V1, V2)) -> U101(and(isNaturalKind(activate(V1)), n__isLNatKind(activate(V2))), activate(V1), activate(V2)) isLNatKind(n__nil) -> tt isLNatKind(n__afterNth(V1, V2)) -> and(isNaturalKind(activate(V1)), n__isLNatKind(activate(V2))) isLNatKind(n__cons(V1, V2)) -> and(isNaturalKind(activate(V1)), n__isLNatKind(activate(V2))) isLNatKind(n__fst(V1)) -> isPLNatKind(activate(V1)) isLNatKind(n__natsFrom(V1)) -> isNaturalKind(activate(V1)) isLNatKind(n__snd(V1)) -> isPLNatKind(activate(V1)) isLNatKind(n__tail(V1)) -> isLNatKind(activate(V1)) isLNatKind(n__take(V1, V2)) -> and(isNaturalKind(activate(V1)), n__isLNatKind(activate(V2))) isNatural(n__0) -> tt isNatural(n__head(V1)) -> U111(isLNatKind(activate(V1)), activate(V1)) isNatural(n__s(V1)) -> U121(isNaturalKind(activate(V1)), activate(V1)) isNatural(n__sel(V1, V2)) -> U131(and(isNaturalKind(activate(V1)), n__isLNatKind(activate(V2))), activate(V1), activate(V2)) isNaturalKind(n__0) -> tt isNaturalKind(n__head(V1)) -> isLNatKind(activate(V1)) isNaturalKind(n__s(V1)) -> isNaturalKind(activate(V1)) isNaturalKind(n__sel(V1, V2)) -> and(isNaturalKind(activate(V1)), n__isLNatKind(activate(V2))) isPLNat(n__pair(V1, V2)) -> U141(and(isLNatKind(activate(V1)), n__isLNatKind(activate(V2))), activate(V1), activate(V2)) isPLNat(n__splitAt(V1, V2)) -> U151(and(isNaturalKind(activate(V1)), n__isLNatKind(activate(V2))), activate(V1), activate(V2)) isPLNatKind(n__pair(V1, V2)) -> and(isLNatKind(activate(V1)), n__isLNatKind(activate(V2))) isPLNatKind(n__splitAt(V1, V2)) -> and(isNaturalKind(activate(V1)), n__isLNatKind(activate(V2))) natsFrom(N) -> U161(and(isNatural(N), n__isNaturalKind(N)), N) sel(N, XS) -> U171(and(and(isNatural(N), n__isNaturalKind(N)), n__and(isLNat(XS), n__isLNatKind(XS))), N, XS) snd(pair(X, Y)) -> U181(and(and(isLNat(X), n__isLNatKind(X)), n__and(isLNat(Y), n__isLNatKind(Y))), Y) splitAt(0, XS) -> U191(and(isLNat(XS), n__isLNatKind(XS)), XS) splitAt(s(N), cons(X, XS)) -> U201(and(and(isNatural(N), n__isNaturalKind(N)), n__and(and(isNatural(X), n__isNaturalKind(X)), n__and(isLNat(activate(XS)), n__isLNatKind(activate(XS))))), N, X, activate(XS)) tail(cons(N, XS)) -> U211(and(and(isNatural(N), n__isNaturalKind(N)), n__and(isLNat(activate(XS)), n__isLNatKind(activate(XS)))), activate(XS)) take(N, XS) -> U221(and(and(isNatural(N), n__isNaturalKind(N)), n__and(isLNat(XS), n__isLNatKind(XS))), N, XS) natsFrom(X) -> n__natsFrom(X) isNaturalKind(X) -> n__isNaturalKind(X) and(X1, X2) -> n__and(X1, X2) isLNatKind(X) -> n__isLNatKind(X) nil -> n__nil afterNth(X1, X2) -> n__afterNth(X1, X2) cons(X1, X2) -> n__cons(X1, X2) fst(X) -> n__fst(X) snd(X) -> n__snd(X) tail(X) -> n__tail(X) take(X1, X2) -> n__take(X1, X2) 0 -> n__0 head(X) -> n__head(X) s(X) -> n__s(X) sel(X1, X2) -> n__sel(X1, X2) pair(X1, X2) -> n__pair(X1, X2) splitAt(X1, X2) -> n__splitAt(X1, X2) activate(n__natsFrom(X)) -> natsFrom(X) activate(n__isNaturalKind(X)) -> isNaturalKind(X) activate(n__and(X1, X2)) -> and(X1, X2) activate(n__isLNatKind(X)) -> isLNatKind(X) activate(n__nil) -> nil activate(n__afterNth(X1, X2)) -> afterNth(X1, X2) activate(n__cons(X1, X2)) -> cons(X1, X2) activate(n__fst(X)) -> fst(X) activate(n__snd(X)) -> snd(X) activate(n__tail(X)) -> tail(X) activate(n__take(X1, X2)) -> take(X1, X2) activate(n__0) -> 0 activate(n__head(X)) -> head(X) activate(n__s(X)) -> s(X) activate(n__sel(X1, X2)) -> sel(X1, X2) activate(n__pair(X1, X2)) -> pair(X1, X2) activate(n__splitAt(X1, X2)) -> splitAt(X1, X2) activate(X) -> X )