(VAR L X X1 X2 )
(RULES 
        active(incr(nil)) -> mark(nil)
        active(incr(cons(X, L))) -> mark(cons(s(X), incr(L)))
        active(adx(nil)) -> mark(nil)
        active(adx(cons(X, L))) -> mark(incr(cons(X, adx(L))))
        active(nats) -> mark(adx(zeros))
        active(zeros) -> mark(cons(0, zeros))
        active(head(cons(X, L))) -> mark(X)
        active(tail(cons(X, L))) -> mark(L)
        active(incr(X)) -> incr(active(X))
        active(cons(X1, X2)) -> cons(active(X1), X2)
        active(s(X)) -> s(active(X))
        active(adx(X)) -> adx(active(X))
        active(head(X)) -> head(active(X))
        active(tail(X)) -> tail(active(X))
        incr(mark(X)) -> mark(incr(X))
        cons(mark(X1), X2) -> mark(cons(X1, X2))
        s(mark(X)) -> mark(s(X))
        adx(mark(X)) -> mark(adx(X))
        head(mark(X)) -> mark(head(X))
        tail(mark(X)) -> mark(tail(X))
        proper(incr(X)) -> incr(proper(X))
        proper(nil) -> ok(nil)
        proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
        proper(s(X)) -> s(proper(X))
        proper(adx(X)) -> adx(proper(X))
        proper(nats) -> ok(nats)
        proper(zeros) -> ok(zeros)
        proper(0) -> ok(0)
        proper(head(X)) -> head(proper(X))
        proper(tail(X)) -> tail(proper(X))
        incr(ok(X)) -> ok(incr(X))
        cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
        s(ok(X)) -> ok(s(X))
        adx(ok(X)) -> ok(adx(X))
        head(ok(X)) -> ok(head(X))
        tail(ok(X)) -> ok(tail(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
        
)