(VAR N X XS Y YS ZS )
(RULES 
        U11(tt, N, X, XS) -> U12(splitAt(activate(N), activate(XS)), activate(X))
        U12(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS)
        afterNth(N, XS) -> snd(splitAt(N, XS))
        and(tt, X) -> activate(X)
        fst(pair(X, Y)) -> X
        head(cons(N, XS)) -> N
        natsFrom(N) -> cons(N, n__natsFrom(n__s(N)))
        sel(N, XS) -> head(afterNth(N, XS))
        snd(pair(X, Y)) -> Y
        splitAt(0, XS) -> pair(nil, XS)
        splitAt(s(N), cons(X, XS)) -> U11(tt, N, X, activate(XS))
        tail(cons(N, XS)) -> activate(XS)
        take(N, XS) -> fst(splitAt(N, XS))
        natsFrom(X) -> n__natsFrom(X)
        s(X) -> n__s(X)
        activate(n__natsFrom(X)) -> natsFrom(activate(X))
        activate(n__s(X)) -> s(activate(X))
        activate(X) -> X
        
)