(VAR x y )
(RULES 
        f(s(x)) -> f(id_inc(c(x, x)))
        f(c(s(x), y)) -> g(c(x, y))
        g(c(s(x), y)) -> g(c(y, x))
        g(c(x, s(y))) -> g(c(y, x))
        g(c(x, x)) -> f(x)
        id_inc(c(x, y)) -> c(id_inc(x), id_inc(y))
        id_inc(s(x)) -> s(id_inc(x))
        id_inc(0) -> 0
        id_inc(0) -> s(0)
        
)