(VAR X X1 X2 X3 Y )
(RULES 
        active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
        active(add(0, X)) -> mark(X)
        active(add(s(X), Y)) -> mark(s(add(X, Y)))
        active(prod(0, X)) -> mark(0)
        active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
        active(if(true, X, Y)) -> mark(X)
        active(if(false, X, Y)) -> mark(Y)
        active(zero(0)) -> mark(true)
        active(zero(s(X))) -> mark(false)
        active(p(s(X))) -> mark(X)
        active(fact(X)) -> fact(active(X))
        active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
        active(zero(X)) -> zero(active(X))
        active(s(X)) -> s(active(X))
        active(prod(X1, X2)) -> prod(active(X1), X2)
        active(prod(X1, X2)) -> prod(X1, active(X2))
        active(p(X)) -> p(active(X))
        active(add(X1, X2)) -> add(active(X1), X2)
        active(add(X1, X2)) -> add(X1, active(X2))
        fact(mark(X)) -> mark(fact(X))
        if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
        zero(mark(X)) -> mark(zero(X))
        s(mark(X)) -> mark(s(X))
        prod(mark(X1), X2) -> mark(prod(X1, X2))
        prod(X1, mark(X2)) -> mark(prod(X1, X2))
        p(mark(X)) -> mark(p(X))
        add(mark(X1), X2) -> mark(add(X1, X2))
        add(X1, mark(X2)) -> mark(add(X1, X2))
        proper(fact(X)) -> fact(proper(X))
        proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
        proper(zero(X)) -> zero(proper(X))
        proper(s(X)) -> s(proper(X))
        proper(0) -> ok(0)
        proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
        proper(p(X)) -> p(proper(X))
        proper(add(X1, X2)) -> add(proper(X1), proper(X2))
        proper(true) -> ok(true)
        proper(false) -> ok(false)
        fact(ok(X)) -> ok(fact(X))
        if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
        zero(ok(X)) -> ok(zero(X))
        s(ok(X)) -> ok(s(X))
        prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
        p(ok(X)) -> ok(p(X))
        add(ok(X1), ok(X2)) -> ok(add(X1, X2))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
        
)