YES(?,O(n^1))
TRS:
 {f(a(), f(x, a())) -> f(a(), f(f(a(), x), f(a(), a())))}
 DUP: We consider a non-duplicating system.
  Trs:
   {f(a(), f(x, a())) -> f(a(), f(f(a(), x), f(a(), a())))}
  BOUND:
   Bound: match(-raise)-bounded by 1
   Automaton:
    {
         a_1() -> 2*
         a_0() -> 1*
     f_1(3, 4) -> 5*
     f_1(2, 5) -> 3 | 1
     f_1(2, 2) -> 4*
     f_1(2, 1) -> 3*
     f_0(1, 1) -> 1*
    }
   Strict:
    {}
   Qed