YES
Time: 0.012286
TRS:
 {f(x, f(a(), a())) -> f(f(f(a(), a()), a()), f(a(), x))}
 DP:
  DP:
   {f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(a(), x)),
    f#(x, f(a(), a())) -> f#(f(a(), a()), a()),
    f#(x, f(a(), a())) -> f#(a(), x)}
  TRS:
  {f(x, f(a(), a())) -> f(f(f(a(), a()), a()), f(a(), x))}
  EDG:
   {(f#(x, f(a(), a())) -> f#(a(), x), f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(a(), x)))
    (f#(x, f(a(), a())) -> f#(a(), x), f#(x, f(a(), a())) -> f#(f(a(), a()), a()))
    (f#(x, f(a(), a())) -> f#(a(), x), f#(x, f(a(), a())) -> f#(a(), x))
    (f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(a(), x)), f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(a(), x)))
    (f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(a(), x)), f#(x, f(a(), a())) -> f#(f(a(), a()), a()))
    (f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(a(), x)), f#(x, f(a(), a())) -> f#(a(), x))}
   SCCS (1):
    Scc:
     {f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(a(), x)),
      f#(x, f(a(), a())) -> f#(a(), x)}
    SCC (2):
     Strict:
      {f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(a(), x)),
       f#(x, f(a(), a())) -> f#(a(), x)}
     Weak:
     {f(x, f(a(), a())) -> f(f(f(a(), a()), a()), f(a(), x))}
     BOUND:
      Bound: match(-raise)-bounded by 2
      Automaton:
       {     a_2() -> 6*
             a_1() -> 2*
             a_0() -> 1*
        f#_2(8, 9) -> 1*
        f#_2(6, 4) -> 1*
        f#_1(4, 5) -> 1*
        f#_1(4, 3) -> 1*
        f#_1(2, 4) -> 1*
        f#_1(2, 2) -> 1*
        f#_1(2, 1) -> 1*
        f#_0(1, 1) -> 1*
         f_2(8, 9) -> 5*
         f_2(7, 6) -> 8*
         f_2(6, 6) -> 7*
         f_2(6, 4) -> 9*
         f_1(4, 5) -> 1*
         f_1(4, 3) -> 5*
         f_1(3, 2) -> 4*
         f_1(2, 4) -> 5*
         f_1(2, 2) -> 3*
         f_1(2, 1) -> 5*
         f_0(1, 1) -> 1*}
      Strict:
       {}
      Qed