YES
O(n)
TRS:
 {f(g(x, y), f(y, y)) -> f(g(y, x), y)}
 DUP: We consider a non-duplicating system.
  Trs:
   {f(g(x, y), f(y, y)) -> f(g(y, x), y)}
  BOUND:
   Automaton:
    {
     g_2(6, 6) -> 6 | 5 | 4 | 3 | 2,
     g_2(6, 4) -> 6 | 5 | 4 | 3 | 2,
     g_2(6, 2) -> 6 | 5 | 4 | 3 | 2,
     g_2(4, 6) -> 6 | 5 | 4 | 3 | 2,
     g_2(4, 4) -> 6 | 5 | 4 | 3 | 2,
     g_2(4, 2) -> 6 | 5 | 4 | 3 | 2,
     g_1(6, 6) -> 4 | 3 | 2,
     g_1(6, 4) -> 4 | 3 | 2,
     g_1(6, 2) -> 4 | 3 | 2,
     g_1(4, 6) -> 4 | 3 | 2,
     g_1(4, 4) -> 4 | 3 | 2,
     g_1(4, 2) -> 4 | 3 | 2,
     g_1(2, 6) -> 4 | 3 | 2,
     g_1(2, 4) -> 4 | 3 | 2,
     g_1(2, 2) -> 4 | 3 | 2,
     g_0(6, 6) -> 2,
     g_0(6, 4) -> 2,
     g_0(6, 2) -> 2,
     g_0(4, 6) -> 2,
     g_0(4, 4) -> 2,
     g_0(4, 2) -> 2,
     g_0(2, 6) -> 2,
     g_0(2, 4) -> 2,
     g_0(2, 2) -> 2,
     f_2(6, 6) -> 2,
     f_2(6, 4) -> 2,
     f_2(5, 6) -> 2,
     f_2(5, 4) -> 2,
     f_1(6, 6) -> 2,
     f_1(6, 4) -> 2,
     f_1(6, 2) -> 2,
     f_1(4, 6) -> 2,
     f_1(4, 4) -> 2,
     f_1(4, 2) -> 2,
     f_1(3, 6) -> 2,
     f_1(3, 4) -> 2,
     f_1(3, 2) -> 2,
     f_0(6, 6) -> 2,
     f_0(6, 4) -> 2,
     f_0(6, 2) -> 2,
     f_0(4, 6) -> 2,
     f_0(4, 4) -> 2,
     f_0(4, 2) -> 2,
     f_0(2, 6) -> 2,
     f_0(2, 4) -> 2,
     f_0(2, 2) -> 2
    }
   Strict:
    {}
   Qed