(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following 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
Q is empty.