(VAR N X X1 X2 X3 X4 XS Y YS ZS )
(RULES 
        a__U11(tt, N, X, XS) -> a__U12(a__splitAt(mark(N), mark(XS)), X)
        a__U12(pair(YS, ZS), X) -> pair(cons(mark(X), YS), mark(ZS))
        a__afterNth(N, XS) -> a__snd(a__splitAt(mark(N), mark(XS)))
        a__and(tt, X) -> mark(X)
        a__fst(pair(X, Y)) -> mark(X)
        a__head(cons(N, XS)) -> mark(N)
        a__natsFrom(N) -> cons(mark(N), natsFrom(s(N)))
        a__sel(N, XS) -> a__head(a__afterNth(mark(N), mark(XS)))
        a__snd(pair(X, Y)) -> mark(Y)
        a__splitAt(0, XS) -> pair(nil, mark(XS))
        a__splitAt(s(N), cons(X, XS)) -> a__U11(tt, N, X, XS)
        a__tail(cons(N, XS)) -> mark(XS)
        a__take(N, XS) -> a__fst(a__splitAt(mark(N), mark(XS)))
        mark(U11(X1, X2, X3, X4)) -> a__U11(mark(X1), X2, X3, X4)
        mark(U12(X1, X2)) -> a__U12(mark(X1), X2)
        mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2))
        mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2))
        mark(snd(X)) -> a__snd(mark(X))
        mark(and(X1, X2)) -> a__and(mark(X1), X2)
        mark(fst(X)) -> a__fst(mark(X))
        mark(head(X)) -> a__head(mark(X))
        mark(natsFrom(X)) -> a__natsFrom(mark(X))
        mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
        mark(tail(X)) -> a__tail(mark(X))
        mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
        mark(tt) -> tt
        mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
        mark(cons(X1, X2)) -> cons(mark(X1), X2)
        mark(s(X)) -> s(mark(X))
        mark(0) -> 0
        mark(nil) -> nil
        a__U11(X1, X2, X3, X4) -> U11(X1, X2, X3, X4)
        a__U12(X1, X2) -> U12(X1, X2)
        a__splitAt(X1, X2) -> splitAt(X1, X2)
        a__afterNth(X1, X2) -> afterNth(X1, X2)
        a__snd(X) -> snd(X)
        a__and(X1, X2) -> and(X1, X2)
        a__fst(X) -> fst(X)
        a__head(X) -> head(X)
        a__natsFrom(X) -> natsFrom(X)
        a__sel(X1, X2) -> sel(X1, X2)
        a__tail(X) -> tail(X)
        a__take(X1, X2) -> take(X1, X2)
        
)