MAYBE
MAYBE
TRS:
 {
         f(0()) -> 0(),
      f(s(0())) -> s(0()),
     f(s(s(x))) -> p(h(g(x))),
     f(s(s(x))) -> +(p(g(x)), q(g(x))),
  p(pair(x, y)) -> x,
           h(x) -> pair(+(p(x), q(x)), p(x)),
         g(0()) -> pair(s(0()), s(0())),
        g(s(x)) -> h(g(x)),
        g(s(x)) -> pair(+(p(g(x)), q(g(x))), p(g(x))),
      +(x, 0()) -> x,
     +(x, s(y)) -> s(+(x, y)),
  q(pair(x, y)) -> y
 }
 DUP: We consider a duplicating system.
  Trs:
   {
           f(0()) -> 0(),
        f(s(0())) -> s(0()),
       f(s(s(x))) -> p(h(g(x))),
       f(s(s(x))) -> +(p(g(x)), q(g(x))),
    p(pair(x, y)) -> x,
             h(x) -> pair(+(p(x), q(x)), p(x)),
           g(0()) -> pair(s(0()), s(0())),
          g(s(x)) -> h(g(x)),
          g(s(x)) -> pair(+(p(g(x)), q(g(x))), p(g(x))),
        +(x, 0()) -> x,
       +(x, s(y)) -> s(+(x, y)),
    q(pair(x, y)) -> y
   }
  Fail