YES
Time: 0.005474
TRS:
 {f(x, f(a(), a())) -> f(f(x, a()), x)}
 DP:
  DP:
   {f#(x, f(a(), a())) -> f#(x, a()),
    f#(x, f(a(), a())) -> f#(f(x, a()), x)}
  TRS:
  {f(x, f(a(), a())) -> f(f(x, a()), x)}
  EDG:
   {(f#(x, f(a(), a())) -> f#(f(x, a()), x), f#(x, f(a(), a())) -> f#(x, a()))
    (f#(x, f(a(), a())) -> f#(f(x, a()), x), f#(x, f(a(), a())) -> f#(f(x, a()), x))}
   SCCS (1):
    Scc:
     {f#(x, f(a(), a())) -> f#(f(x, a()), x)}
    SCC (1):
     Strict:
      {f#(x, f(a(), a())) -> f#(f(x, a()), x)}
     Weak:
     {f(x, f(a(), a())) -> f(f(x, a()), x)}
     BOUND:
      Bound: top(-raise)-DP-bounded by 2
      Automaton:
       {       a_2() -> 11*
               a_1() -> 9*
               a_0() -> 7*
        f#_2(12, 10) -> 4*
         f#_1(10, 8) -> 4*
          f#_0(8, 8) -> 4*
          f#_0(8, 7) -> 4*
          f#_0(8, 6) -> 4*
         f_2(10, 11) -> 12*
           f_1(8, 9) -> 10*
           f_0(8, 8) -> 6*
           f_0(8, 7) -> 8 | 6
           f_0(8, 6) -> 6*
           f_0(7, 8) -> 6*
           f_0(7, 7) -> 8*
           f_0(7, 6) -> 6*
           f_0(6, 8) -> 6*
           f_0(6, 7) -> 8*
           f_0(6, 6) -> 6*}
      Strict:
       {}
      Qed