YES
Time: 0.009215
TRS:
 {f(a(), f(x, a())) -> f(f(x, f(f(a(), a()), a())), a())}
 DP:
  DP:
   {f#(a(), f(x, a())) -> f#(x, f(f(a(), a()), a())),
    f#(a(), f(x, a())) -> f#(f(x, f(f(a(), a()), a())), a()),
    f#(a(), f(x, a())) -> f#(f(a(), a()), a()),
    f#(a(), f(x, a())) -> f#(a(), a())}
  TRS:
  {f(a(), f(x, a())) -> f(f(x, f(f(a(), a()), a())), a())}
  EDG:
   {(f#(a(), f(x, a())) -> f#(x, f(f(a(), a()), a())), f#(a(), f(x, a())) -> f#(x, f(f(a(), a()), a())))
    (f#(a(), f(x, a())) -> f#(x, f(f(a(), a()), a())), f#(a(), f(x, a())) -> f#(f(x, f(f(a(), a()), a())), a()))
    (f#(a(), f(x, a())) -> f#(x, f(f(a(), a()), a())), f#(a(), f(x, a())) -> f#(f(a(), a()), a()))
    (f#(a(), f(x, a())) -> f#(x, f(f(a(), a()), a())), f#(a(), f(x, a())) -> f#(a(), a()))}
   SCCS (1):
    Scc:
     {f#(a(), f(x, a())) -> f#(x, f(f(a(), a()), a()))}
    SCC (1):
     Strict:
      {f#(a(), f(x, a())) -> f#(x, f(f(a(), a()), a()))}
     Weak:
     {f(a(), f(x, a())) -> f(f(x, f(f(a(), a()), a())), a())}
     BOUND:
      Bound: match(-raise)-bounded by 1
      Automaton:
       {     a_1() -> 2*
             a_0() -> 1*
        f#_1(5, 4) -> 1*
        f#_1(3, 4) -> 1*
        f#_1(1, 4) -> 1*
        f#_0(1, 1) -> 1*
         f_1(6, 2) -> 5*
         f_1(5, 4) -> 5*
         f_1(5, 2) -> 1*
         f_1(3, 4) -> 6*
         f_1(3, 2) -> 4*
         f_1(2, 2) -> 3*
         f_1(1, 4) -> 5*
         f_0(1, 1) -> 1*}
      Strict:
       {}
      Qed