(VAR X X1 X2 X3 Y )
(RULES 
        active(p(0)) -> mark(0)
        active(p(s(X))) -> mark(X)
        active(leq(0, Y)) -> mark(true)
        active(leq(s(X), 0)) -> mark(false)
        active(leq(s(X), s(Y))) -> mark(leq(X, Y))
        active(if(true, X, Y)) -> mark(X)
        active(if(false, X, Y)) -> mark(Y)
        active(diff(X, Y)) -> mark(if(leq(X, Y), 0, s(diff(p(X), Y))))
        active(p(X)) -> p(active(X))
        active(s(X)) -> s(active(X))
        active(leq(X1, X2)) -> leq(active(X1), X2)
        active(leq(X1, X2)) -> leq(X1, active(X2))
        active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
        active(diff(X1, X2)) -> diff(active(X1), X2)
        active(diff(X1, X2)) -> diff(X1, active(X2))
        p(mark(X)) -> mark(p(X))
        s(mark(X)) -> mark(s(X))
        leq(mark(X1), X2) -> mark(leq(X1, X2))
        leq(X1, mark(X2)) -> mark(leq(X1, X2))
        if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
        diff(mark(X1), X2) -> mark(diff(X1, X2))
        diff(X1, mark(X2)) -> mark(diff(X1, X2))
        proper(p(X)) -> p(proper(X))
        proper(0) -> ok(0)
        proper(s(X)) -> s(proper(X))
        proper(leq(X1, X2)) -> leq(proper(X1), proper(X2))
        proper(true) -> ok(true)
        proper(false) -> ok(false)
        proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
        proper(diff(X1, X2)) -> diff(proper(X1), proper(X2))
        p(ok(X)) -> ok(p(X))
        s(ok(X)) -> ok(s(X))
        leq(ok(X1), ok(X2)) -> ok(leq(X1, X2))
        if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
        diff(ok(X1), ok(X2)) -> ok(diff(X1, X2))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
        
)