YES
O(n)
TRS:
 {   f(x, x) -> a(),
  f(g(x), y) -> f(x, y)}
 DUP: We consider a non-duplicating system.
  Trs:
   {   f(x, x) -> a(),
    f(g(x), y) -> f(x, y)}
  BOUND:
   Automaton:
    {
        g_0(4) -> 4,
        g_0(3) -> 4,
     f_1(4, 4) -> 3,
     f_1(4, 3) -> 3,
     f_1(3, 4) -> 3,
     f_1(3, 3) -> 3,
     f_0(4, 4) -> 3,
     f_0(4, 3) -> 3,
     f_0(3, 4) -> 3,
     f_0(3, 3) -> 3,
         a_2() -> 3,
         a_1() -> 3,
         a_0() -> 3
    }
   Strict:
    {}
   Qed