(VAR x y )
(RULES 
        minus(x, 0) -> x
        minus(s(x), s(y)) -> minus(x, y)
        double(0) -> 0
        double(s(x)) -> s(s(double(x)))
        plus(s(x), s(y)) -> s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))
        plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x))
        plus(zero, y) -> y
        plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y))))
        id(x) -> x
        if(true, x, y) -> x
        if(false, x, y) -> y
        not(x) -> if(x, false, true)
        gt(s(x), zero) -> true
        gt(zero, y) -> false
        gt(s(x), s(y)) -> gt(x, y)
        
)