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