(VAR N X X1 X2 X3 X4 XS YS ZS )
(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)))
        active(natsFrom(X)) -> natsFrom(active(X))
        active(cons(X1, X2)) -> cons(active(X1), X2)
        active(s(X)) -> s(active(X))
        active(fst(X)) -> fst(active(X))
        active(pair(X1, X2)) -> pair(active(X1), X2)
        active(pair(X1, X2)) -> pair(X1, active(X2))
        active(snd(X)) -> snd(active(X))
        active(splitAt(X1, X2)) -> splitAt(active(X1), X2)
        active(splitAt(X1, X2)) -> splitAt(X1, active(X2))
        active(u(X1, X2, X3, X4)) -> u(active(X1), X2, X3, X4)
        active(head(X)) -> head(active(X))
        active(tail(X)) -> tail(active(X))
        active(sel(X1, X2)) -> sel(active(X1), X2)
        active(sel(X1, X2)) -> sel(X1, active(X2))
        active(afterNth(X1, X2)) -> afterNth(active(X1), X2)
        active(afterNth(X1, X2)) -> afterNth(X1, active(X2))
        active(take(X1, X2)) -> take(active(X1), X2)
        active(take(X1, X2)) -> take(X1, active(X2))
        natsFrom(mark(X)) -> mark(natsFrom(X))
        cons(mark(X1), X2) -> mark(cons(X1, X2))
        s(mark(X)) -> mark(s(X))
        fst(mark(X)) -> mark(fst(X))
        pair(mark(X1), X2) -> mark(pair(X1, X2))
        pair(X1, mark(X2)) -> mark(pair(X1, X2))
        snd(mark(X)) -> mark(snd(X))
        splitAt(mark(X1), X2) -> mark(splitAt(X1, X2))
        splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2))
        u(mark(X1), X2, X3, X4) -> mark(u(X1, X2, X3, X4))
        head(mark(X)) -> mark(head(X))
        tail(mark(X)) -> mark(tail(X))
        sel(mark(X1), X2) -> mark(sel(X1, X2))
        sel(X1, mark(X2)) -> mark(sel(X1, X2))
        afterNth(mark(X1), X2) -> mark(afterNth(X1, X2))
        afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2))
        take(mark(X1), X2) -> mark(take(X1, X2))
        take(X1, mark(X2)) -> mark(take(X1, X2))
        proper(natsFrom(X)) -> natsFrom(proper(X))
        proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
        proper(s(X)) -> s(proper(X))
        proper(fst(X)) -> fst(proper(X))
        proper(pair(X1, X2)) -> pair(proper(X1), proper(X2))
        proper(snd(X)) -> snd(proper(X))
        proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2))
        proper(0) -> ok(0)
        proper(nil) -> ok(nil)
        proper(u(X1, X2, X3, X4)) -> u(proper(X1), proper(X2), proper(X3), proper(X4))
        proper(head(X)) -> head(proper(X))
        proper(tail(X)) -> tail(proper(X))
        proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
        proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2))
        proper(take(X1, X2)) -> take(proper(X1), proper(X2))
        natsFrom(ok(X)) -> ok(natsFrom(X))
        cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
        s(ok(X)) -> ok(s(X))
        fst(ok(X)) -> ok(fst(X))
        pair(ok(X1), ok(X2)) -> ok(pair(X1, X2))
        snd(ok(X)) -> ok(snd(X))
        splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2))
        u(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(u(X1, X2, X3, X4))
        head(ok(X)) -> ok(head(X))
        tail(ok(X)) -> ok(tail(X))
        sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
        afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2))
        take(ok(X1), ok(X2)) -> ok(take(X1, X2))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
        
)