(VAR V2 N XS Y X YS ZS V1 X1 X2)
(RULES 
U101(tt,V2) -> U102(isLNat(activate(V2)))
U102(tt) -> tt
U11(tt,N,XS) -> U12(isLNat(activate(XS)),activate(N),activate(XS))
U111(tt) -> tt
U12(tt,N,XS) -> snd(splitAt(activate(N),activate(XS)))
U121(tt) -> tt
U131(tt,V2) -> U132(isLNat(activate(V2)))
U132(tt) -> tt
U141(tt,V2) -> U142(isLNat(activate(V2)))
U142(tt) -> tt
U151(tt,V2) -> U152(isLNat(activate(V2)))
U152(tt) -> tt
U161(tt,N) -> cons(activate(N),n__natsFrom(s(activate(N))))
U171(tt,N,XS) -> U172(isLNat(activate(XS)),activate(N),activate(XS))
U172(tt,N,XS) -> head(afterNth(activate(N),activate(XS)))
U181(tt,Y) -> U182(isLNat(activate(Y)),activate(Y))
U182(tt,Y) -> activate(Y)
U191(tt,XS) -> pair(nil,activate(XS))
U201(tt,N,X,XS) -> U202(isNatural(activate(X)),activate(N),activate(X),activate(XS))
U202(tt,N,X,XS) -> U203(isLNat(activate(XS)),activate(N),activate(X),activate(XS))
U203(tt,N,X,XS) -> U204(splitAt(activate(N),activate(XS)),activate(X))
U204(pair(YS,ZS),X) -> pair(cons(activate(X),YS),ZS)
U21(tt,X,Y) -> U22(isLNat(activate(Y)),activate(X))
U211(tt,XS) -> U212(isLNat(activate(XS)),activate(XS))
U212(tt,XS) -> activate(XS)
U22(tt,X) -> activate(X)
U221(tt,N,XS) -> U222(isLNat(activate(XS)),activate(N),activate(XS))
U222(tt,N,XS) -> fst(splitAt(activate(N),activate(XS)))
U31(tt,N,XS) -> U32(isLNat(activate(XS)),activate(N))
U32(tt,N) -> activate(N)
U41(tt,V2) -> U42(isLNat(activate(V2)))
U42(tt) -> tt
U51(tt,V2) -> U52(isLNat(activate(V2)))
U52(tt) -> tt
U61(tt) -> tt
U71(tt) -> tt
U81(tt) -> tt
U91(tt) -> tt
afterNth(N,XS) -> U11(isNatural(N),N,XS)
fst(pair(X,Y)) -> U21(isLNat(X),X,Y)
head(cons(N,XS)) -> U31(isNatural(N),N,activate(XS))
isLNat(n__nil) -> tt
isLNat(n__afterNth(V1,V2)) -> U41(isNatural(activate(V1)),activate(V2))
isLNat(n__cons(V1,V2)) -> U51(isNatural(activate(V1)),activate(V2))
isLNat(n__fst(V1)) -> U61(isPLNat(activate(V1)))
isLNat(n__natsFrom(V1)) -> U71(isNatural(activate(V1)))
isLNat(n__snd(V1)) -> U81(isPLNat(activate(V1)))
isLNat(n__tail(V1)) -> U91(isLNat(activate(V1)))
isLNat(n__take(V1,V2)) -> U101(isNatural(activate(V1)),activate(V2))
isNatural(n__0) -> tt
isNatural(n__head(V1)) -> U111(isLNat(activate(V1)))
isNatural(n__s(V1)) -> U121(isNatural(activate(V1)))
isNatural(n__sel(V1,V2)) -> U131(isNatural(activate(V1)),activate(V2))
isPLNat(n__pair(V1,V2)) -> U141(isLNat(activate(V1)),activate(V2))
isPLNat(n__splitAt(V1,V2)) -> U151(isNatural(activate(V1)),activate(V2))
natsFrom(N) -> U161(isNatural(N),N)
sel(N,XS) -> U171(isNatural(N),N,XS)
snd(pair(X,Y)) -> U181(isLNat(X),Y)
splitAt(0,XS) -> U191(isLNat(XS),XS)
splitAt(s(N),cons(X,XS)) -> U201(isNatural(N),N,X,activate(XS))
tail(cons(N,XS)) -> U211(isNatural(N),activate(XS))
take(N,XS) -> U221(isNatural(N),N,XS)
natsFrom(X) -> n__natsFrom(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__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
)