(VAR x y )
(RULES 
        cond1(true, x, y) -> cond2(gr(x, y), x, y)
        cond2(true, x, y) -> cond1(gr(add(x, y), 0), p(x), y)
        cond2(false, x, y) -> cond3(eq(x, y), x, y)
        cond3(true, x, y) -> cond1(gr(add(x, y), 0), p(x), y)
        cond3(false, x, y) -> cond1(gr(add(x, y), 0), x, p(y))
        gr(0, x) -> false
        gr(s(x), 0) -> true
        gr(s(x), s(y)) -> gr(x, y)
        add(0, x) -> x
        add(s(x), y) -> s(add(x, y))
        eq(0, 0) -> true
        eq(0, s(x)) -> false
        eq(s(x), 0) -> false
        eq(s(x), s(y)) -> eq(x, y)
        p(0) -> 0
        p(s(x)) -> x
        
)