TRS:
 {       f(0()) -> 0(),
      f(s(0())) -> s(0()),
     f(s(s(x))) -> p(h(g(x))),
         g(0()) -> pair(s(0()), s(0())),
        g(s(x)) -> h(g(x)),
           h(x) -> pair(+(p(x), q(x)), p(x)),
  p(pair(x, y)) -> x,
  q(pair(x, y)) -> y,
      +(x, 0()) -> x,
     +(x, s(y)) -> s(+(x, y)),
     f(s(s(x))) -> +(p(g(x)), q(g(x))),
        g(s(x)) -> pair(+(p(g(x)), q(g(x))), p(g(x)))}
 RPO Product:
  Quasi-Precedence:
  h > p, 
  h > +, 
  h > q, 
  f ~ g > q, 
  f ~ g > +, 
  f ~ g > h, 
  f ~ g > p
  empty
  
  Qed


TRS:
 {       f(0()) -> 0(),
      f(s(0())) -> s(0()),
     f(s(s(x))) -> p(h(g(x))),
         g(0()) -> pair(s(0()), s(0())),
        g(s(x)) -> h(g(x)),
           h(x) -> pair(+(p(x), q(x)), p(x)),
  p(pair(x, y)) -> x,
  q(pair(x, y)) -> y,
      +(x, 0()) -> x,
     +(x, s(y)) -> s(+(x, y)),
     f(s(s(x))) -> +(p(g(x)), q(g(x))),
        g(s(x)) -> pair(+(p(g(x)), q(g(x))), p(g(x)))}
 Fail