YES
Time: 0.005629
TRS:
 {g1(x, x, y) -> h(x, y),
  g1(y, x, x) -> h(x, y),
      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),
  g2(x, y, y) -> h(x, y),
  g2(y, y, x) -> h(x, y),
      h(x, x) -> x}
 BOUND:
  Bound: top(-raise)-bounded by 2
  Automaton:
   {    h_2(1, 1) -> 1*
        h_1(1, 1) -> 1*
        h_0(1, 1) -> 1*
    g2_1(1, 1, 1) -> 1*
    g2_0(1, 1, 1) -> 1*
        f_0(1, 1) -> 1*
    g1_1(1, 1, 1) -> 1*
    g1_0(1, 1, 1) -> 1*}
  Strict:
   {}
  Qed