(COMMENT
  Example 20 from "Search Techniques for Rational Polynomial Orders"
  (published at AISC '08)
)
(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)
)