(VAR N XS X Y YS ZS V1 V2 X1 X2) (RULES U101(tt,N,XS) -> fst(splitAt(activate(N),activate(XS))) U11(tt,N,XS) -> snd(splitAt(activate(N),activate(XS))) U21(tt,X) -> activate(X) U31(tt,N) -> activate(N) U41(tt,N) -> cons(activate(N),n__natsFrom(n__s(activate(N)))) U51(tt,N,XS) -> head(afterNth(activate(N),activate(XS))) U61(tt,Y) -> activate(Y) U71(tt,XS) -> pair(nil,activate(XS)) U81(tt,N,X,XS) -> U82(splitAt(activate(N),activate(XS)),activate(X)) U82(pair(YS,ZS),X) -> pair(cons(activate(X),YS),ZS) U91(tt,XS) -> activate(XS) afterNth(N,XS) -> U11(and(isNatural(N),n__isLNat(XS)),N,XS) and(tt,X) -> activate(X) fst(pair(X,Y)) -> U21(and(isLNat(X),n__isLNat(Y)),X) head(cons(N,XS)) -> U31(and(isNatural(N),n__isLNat(activate(XS))),N) isLNat(n__nil) -> tt isLNat(n__afterNth(V1,V2)) -> and(isNatural(activate(V1)),n__isLNat(activate(V2))) isLNat(n__cons(V1,V2)) -> and(isNatural(activate(V1)),n__isLNat(activate(V2))) isLNat(n__fst(V1)) -> isPLNat(activate(V1)) isLNat(n__natsFrom(V1)) -> isNatural(activate(V1)) isLNat(n__snd(V1)) -> isPLNat(activate(V1)) isLNat(n__tail(V1)) -> isLNat(activate(V1)) isLNat(n__take(V1,V2)) -> and(isNatural(activate(V1)),n__isLNat(activate(V2))) isNatural(n__0) -> tt isNatural(n__head(V1)) -> isLNat(activate(V1)) isNatural(n__s(V1)) -> isNatural(activate(V1)) isNatural(n__sel(V1,V2)) -> and(isNatural(activate(V1)),n__isLNat(activate(V2))) isPLNat(n__pair(V1,V2)) -> and(isLNat(activate(V1)),n__isLNat(activate(V2))) isPLNat(n__splitAt(V1,V2)) -> and(isNatural(activate(V1)),n__isLNat(activate(V2))) natsFrom(N) -> U41(isNatural(N),N) sel(N,XS) -> U51(and(isNatural(N),n__isLNat(XS)),N,XS) snd(pair(X,Y)) -> U61(and(isLNat(X),n__isLNat(Y)),Y) splitAt(0,XS) -> U71(isLNat(XS),XS) splitAt(s(N),cons(X,XS)) -> U81(and(isNatural(N),n__and(n__isNatural(X),n__isLNat(activate(XS)))),N,X,activate(XS)) tail(cons(N,XS)) -> U91(and(isNatural(N),n__isLNat(activate(XS))),activate(XS)) take(N,XS) -> U101(and(isNatural(N),n__isLNat(XS)),N,XS) natsFrom(X) -> n__natsFrom(X) s(X) -> n__s(X) isLNat(X) -> n__isLNat(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) sel(X1,X2) -> n__sel(X1,X2) pair(X1,X2) -> n__pair(X1,X2) splitAt(X1,X2) -> n__splitAt(X1,X2) and(X1,X2) -> n__and(X1,X2) isNatural(X) -> n__isNatural(X) activate(n__natsFrom(X)) -> natsFrom(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__isLNat(X)) -> isLNat(X) activate(n__nil) -> nil activate(n__afterNth(X1,X2)) -> afterNth(activate(X1),activate(X2)) activate(n__cons(X1,X2)) -> cons(activate(X1),X2) activate(n__fst(X)) -> fst(activate(X)) activate(n__snd(X)) -> snd(activate(X)) activate(n__tail(X)) -> tail(activate(X)) activate(n__take(X1,X2)) -> take(activate(X1),activate(X2)) activate(n__0) -> 0 activate(n__head(X)) -> head(activate(X)) activate(n__sel(X1,X2)) -> sel(activate(X1),activate(X2)) activate(n__pair(X1,X2)) -> pair(activate(X1),activate(X2)) activate(n__splitAt(X1,X2)) -> splitAt(activate(X1),activate(X2)) activate(n__and(X1,X2)) -> and(activate(X1),X2) activate(n__isNatural(X)) -> isNatural(X) activate(X) -> X )