YES
Time: 0.027469
TRS:
 {f(x, f(a(), a())) -> f(f(f(a(), a()), a()), f(x, a()))}
 DP:
  DP:
   {f#(x, f(a(), a())) -> f#(x, a()),
    f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(x, a())),
    f#(x, f(a(), a())) -> f#(f(a(), a()), a())}
  TRS:
  {f(x, f(a(), a())) -> f(f(f(a(), a()), a()), f(x, a()))}
  EDG:
   {(f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(x, a())), f#(x, f(a(), a())) -> f#(x, a()))
    (f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(x, a())), f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(x, a())))
    (f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(x, a())), f#(x, f(a(), a())) -> f#(f(a(), a()), a()))}
   SCCS (1):
    Scc:
     {f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(x, a()))}
    SCC (1):
     Strict:
      {f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(x, a()))}
     Weak:
     {f(x, f(a(), a())) -> f(f(f(a(), a()), a()), f(x, a()))}
     BOUND:
      Bound: match(-raise)-DP-bounded by 1
      Automaton:
       {       a_1() -> 14*
               a_0() -> 10*
        f#_1(16, 17) -> 4*
        f#_0(11, 13) -> 4*
        f#_0(11, 12) -> 4*
        f#_0(11, 11) -> 4*
         f_1(15, 14) -> 16*
         f_1(14, 14) -> 15*
         f_1(11, 14) -> 17*
         f_0(13, 13) -> 8*
         f_0(13, 12) -> 8*
         f_0(13, 11) -> 8*
         f_0(13, 10) -> 11*
          f_0(13, 8) -> 8*
         f_0(12, 13) -> 8*
         f_0(12, 12) -> 8*
         f_0(12, 11) -> 8*
         f_0(12, 10) -> 12*
          f_0(12, 8) -> 8*
         f_0(11, 13) -> 8*
         f_0(11, 12) -> 8*
         f_0(11, 11) -> 8*
         f_0(11, 10) -> 12*
          f_0(11, 8) -> 8*
         f_0(10, 13) -> 8*
         f_0(10, 12) -> 8*
         f_0(10, 11) -> 8*
         f_0(10, 10) -> 13*
          f_0(10, 8) -> 8*
          f_0(8, 13) -> 8*
          f_0(8, 12) -> 8*
          f_0(8, 11) -> 8*
          f_0(8, 10) -> 12*
           f_0(8, 8) -> 8*}
      Strict:
       {}
      Qed