(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
a__natsFrom(N) → cons(mark(N), natsFrom(s(N)))
a__fst(pair(XS, YS)) → mark(XS)
a__snd(pair(XS, YS)) → mark(YS)
a__splitAt(0, XS) → pair(nil, mark(XS))
a__splitAt(s(N), cons(X, XS)) → a__u(a__splitAt(mark(N), mark(XS)), N, X, XS)
a__u(pair(YS, ZS), N, X, XS) → pair(cons(mark(X), YS), mark(ZS))
a__head(cons(N, XS)) → mark(N)
a__tail(cons(N, XS)) → mark(XS)
a__sel(N, XS) → a__head(a__afterNth(mark(N), mark(XS)))
a__take(N, XS) → a__fst(a__splitAt(mark(N), mark(XS)))
a__afterNth(N, XS) → a__snd(a__splitAt(mark(N), mark(XS)))
mark(natsFrom(X)) → a__natsFrom(mark(X))
mark(fst(X)) → a__fst(mark(X))
mark(snd(X)) → a__snd(mark(X))
mark(splitAt(X1, X2)) → a__splitAt(mark(X1), mark(X2))
mark(u(X1, X2, X3, X4)) → a__u(mark(X1), X2, X3, X4)
mark(head(X)) → a__head(mark(X))
mark(tail(X)) → a__tail(mark(X))
mark(sel(X1, X2)) → a__sel(mark(X1), mark(X2))
mark(afterNth(X1, X2)) → a__afterNth(mark(X1), mark(X2))
mark(take(X1, X2)) → a__take(mark(X1), mark(X2))
mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))
mark(pair(X1, X2)) → pair(mark(X1), mark(X2))
mark(0) → 0
mark(nil) → nil
a__natsFrom(X) → natsFrom(X)
a__fst(X) → fst(X)
a__snd(X) → snd(X)
a__splitAt(X1, X2) → splitAt(X1, X2)
a__u(X1, X2, X3, X4) → u(X1, X2, X3, X4)
a__head(X) → head(X)
a__tail(X) → tail(X)
a__sel(X1, X2) → sel(X1, X2)
a__afterNth(X1, X2) → afterNth(X1, X2)
a__take(X1, X2) → take(X1, X2)
Q is empty.