YES
TRS:
 {f(x, f(f(a(), a()), a())) -> f(f(a(), f(a(), a())), x)}
 DP:
  Strict:
   {f#(x, f(f(a(), a()), a())) -> f#(f(a(), f(a(), a())), x),
    f#(x, f(f(a(), a()), a())) -> f#(a(), f(a(), a()))}
  Weak:
  {f(x, f(f(a(), a()), a())) -> f(f(a(), f(a(), a())), x)}
  EDG:
   {(f#(x, f(f(a(), a()), a())) -> f#(f(a(), f(a(), a())), x), f#(x, f(f(a(), a()), a())) -> f#(f(a(), f(a(), a())), x))
    (f#(x, f(f(a(), a()), a())) -> f#(f(a(), f(a(), a())), x), f#(x, f(f(a(), a()), a())) -> f#(a(), f(a(), a())))}
   SCCS:
    Scc:
     {f#(x, f(f(a(), a()), a())) -> f#(f(a(), f(a(), a())), x)}
    SCC:
     Strict:
      {f#(x, f(f(a(), a()), a())) -> f#(f(a(), f(a(), a())), x)}
     Weak:
     {f(x, f(f(a(), a()), a())) -> f(f(a(), f(a(), a())), x)}
     BOUND:
      Bound: match(-raise)-DP-bounded by 1
      Automaton:
       {       a_1() -> 11*
               a_0() -> 9*
        f#_1(13, 10) -> 4*
        f#_0(10, 10) -> 4*
         f#_0(10, 9) -> 4*
         f#_0(10, 8) -> 4*
         f#_0(10, 7) -> 4*
         f_1(11, 12) -> 13*
         f_1(11, 11) -> 12*
         f_0(10, 10) -> 7*
          f_0(10, 9) -> 7*
          f_0(10, 8) -> 7*
          f_0(10, 7) -> 7*
          f_0(9, 10) -> 7*
           f_0(9, 9) -> 8*
           f_0(9, 8) -> 10*
           f_0(9, 7) -> 7*
          f_0(8, 10) -> 7*
           f_0(8, 9) -> 7*
           f_0(8, 8) -> 7*
           f_0(8, 7) -> 7*
          f_0(7, 10) -> 7*
           f_0(7, 9) -> 7*
           f_0(7, 8) -> 7*
           f_0(7, 7) -> 7*}
      Strict:
       {}
      Qed