TRS:
 {    f(x, y) -> g1(x, x, y),
      f(x, y) -> g1(y, x, x),
      f(x, y) -> g2(x, y, y),
      f(x, y) -> g2(y, y, x),
  g1(x, x, y) -> h(x, y),
  g1(y, x, x) -> h(x, y),
  g2(x, y, y) -> h(x, y),
  g2(y, y, x) -> h(x, y),
      h(x, x) -> x}
 MPO:
  Prec:
   g2 > h, 
   g1 > h, 
   f > g2, 
   f > g1
   empty
  Strict:
   {}
   Weak:
    {}
  Qed