(VAR M N X X1 X2 )
(RULES 
        active(and(tt, X)) -> mark(X)
        active(plus(N, 0)) -> mark(N)
        active(plus(N, s(M))) -> mark(s(plus(N, M)))
        active(and(X1, X2)) -> and(active(X1), X2)
        active(plus(X1, X2)) -> plus(active(X1), X2)
        active(plus(X1, X2)) -> plus(X1, active(X2))
        active(s(X)) -> s(active(X))
        and(mark(X1), X2) -> mark(and(X1, X2))
        plus(mark(X1), X2) -> mark(plus(X1, X2))
        plus(X1, mark(X2)) -> mark(plus(X1, X2))
        s(mark(X)) -> mark(s(X))
        proper(and(X1, X2)) -> and(proper(X1), proper(X2))
        proper(tt) -> ok(tt)
        proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
        proper(0) -> ok(0)
        proper(s(X)) -> s(proper(X))
        and(ok(X1), ok(X2)) -> ok(and(X1, X2))
        plus(ok(X1), ok(X2)) -> ok(plus(X1, X2))
        s(ok(X)) -> ok(s(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
        
)