(VAR V1 V2 N XS Y X YS ZS X1 X2) (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(n__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(n__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(n__isLNat(Y),n__isLNatKind(Y))),X) head(cons(N,XS)) -> U31(and(and(isNatural(N),n__isNaturalKind(N)),n__and(n__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(n__isLNat(XS),n__isLNatKind(XS))),N,XS) snd(pair(X,Y)) -> U181(and(and(isLNat(X),n__isLNatKind(X)),n__and(n__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(n__and(n__isNatural(X),n__isNaturalKind(X)),n__and(n__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(n__isLNat(activate(XS)),n__isLNatKind(activate(XS)))),activate(XS)) take(N,XS) -> U221(and(and(isNatural(N),n__isNaturalKind(N)),n__and(n__isLNat(XS),n__isLNatKind(XS))),N,XS) natsFrom(X) -> n__natsFrom(X) s(X) -> n__s(X) isNaturalKind(X) -> n__isNaturalKind(X) and(X1,X2) -> n__and(X1,X2) isLNat(X) -> n__isLNat(X) 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) sel(X1,X2) -> n__sel(X1,X2) pair(X1,X2) -> n__pair(X1,X2) splitAt(X1,X2) -> n__splitAt(X1,X2) isNatural(X) -> n__isNatural(X) activate(n__natsFrom(X)) -> natsFrom(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__isNaturalKind(X)) -> isNaturalKind(X) activate(n__and(X1,X2)) -> and(activate(X1),X2) activate(n__isLNat(X)) -> isLNat(X) activate(n__isLNatKind(X)) -> isLNatKind(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__isNatural(X)) -> isNatural(X) activate(X) -> X )