(VAR c x y )
(RULES 
        lt(0, s(x)) -> true
        lt(x, 0) -> false
        lt(s(x), s(y)) -> lt(x, y)
        times(0, y) -> 0
        times(s(x), y) -> plus(y, times(x, y))
        plus(0, y) -> y
        plus(s(x), y) -> s(plus(x, y))
        fac(x) -> loop(x, s(0), s(0))
        loop(x, c, y) -> if(lt(x, c), x, c, y)
        if(false, x, c, y) -> loop(x, s(c), times(y, s(c)))
        if(true, x, c, y) -> y
        
)