(VAR k l x y )
(RULES 
        app(nil, k) -> k
        app(l, nil) -> l
        app(cons(x, l), k) -> cons(x, app(l, k))
        sum(cons(x, nil)) -> cons(x, nil)
        sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l))
        sum(app(l, cons(x, cons(y, k)))) -> sum(app(l, sum(cons(x, cons(y, k)))))
        sum(plus(cons(0, x), cons(y, l))) -> pred(sum(cons(s(x), cons(y, l))))
        pred(cons(s(x), nil)) -> cons(x, nil)
        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)
        
)