YES
TRS:
 {f(f(x, a()), a()) -> f(f(f(a(), a()), f(x, a())), a())}
 DP:
  Strict:
   {f#(f(x, a()), a()) -> f#(f(f(a(), a()), f(x, a())), a()),
    f#(f(x, a()), a()) -> f#(f(a(), a()), f(x, a())),
    f#(f(x, a()), a()) -> f#(a(), a())}
  Weak:
  {f(f(x, a()), a()) -> f(f(f(a(), a()), f(x, a())), a())}
  EDG:
   {(f#(f(x, a()), a()) -> f#(f(f(a(), a()), f(x, a())), a()), f#(f(x, a()), a()) -> f#(f(f(a(), a()), f(x, a())), a()))
    (f#(f(x, a()), a()) -> f#(f(f(a(), a()), f(x, a())), a()), f#(f(x, a()), a()) -> f#(f(a(), a()), f(x, a())))
    (f#(f(x, a()), a()) -> f#(f(f(a(), a()), f(x, a())), a()), f#(f(x, a()), a()) -> f#(a(), a()))}
   SCCS:
    Scc:
     {f#(f(x, a()), a()) -> f#(f(f(a(), a()), f(x, a())), a())}
    SCC:
     Strict:
      {f#(f(x, a()), a()) -> f#(f(f(a(), a()), f(x, a())), a())}
     Weak:
     {f(f(x, a()), a()) -> f(f(f(a(), a()), f(x, a())), a())}
     BOUND:
      Bound: match(-raise)-DP-bounded by 0
      Automaton:
       {       a_0() -> 10*
        f#_0(13, 10) -> 4*
         f_0(13, 13) -> 8*
         f_0(13, 12) -> 8*
         f_0(13, 11) -> 8*
         f_0(13, 10) -> 12*
          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) -> 13*
         f_0(11, 11) -> 13*
         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) -> 11*
          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