YES
Time: 0.010754
TRS:
 {f(f(a(), x), a()) -> f(a(), f(f(x, f(a(), a())), a()))}
 DP:
  DP:
   {f#(f(a(), x), a()) -> f#(x, f(a(), a())),
    f#(f(a(), x), a()) -> f#(f(x, f(a(), a())), a()),
    f#(f(a(), x), a()) -> f#(a(), f(f(x, f(a(), a())), a())),
    f#(f(a(), x), a()) -> f#(a(), a())}
  TRS:
  {f(f(a(), x), a()) -> f(a(), f(f(x, f(a(), a())), a()))}
  EDG:
   {(f#(f(a(), x), a()) -> f#(f(x, f(a(), a())), a()), f#(f(a(), x), a()) -> f#(x, f(a(), a())))
    (f#(f(a(), x), a()) -> f#(f(x, f(a(), a())), a()), f#(f(a(), x), a()) -> f#(f(x, f(a(), a())), a()))
    (f#(f(a(), x), a()) -> f#(f(x, f(a(), a())), a()), f#(f(a(), x), a()) -> f#(a(), f(f(x, f(a(), a())), a())))
    (f#(f(a(), x), a()) -> f#(f(x, f(a(), a())), a()), f#(f(a(), x), a()) -> f#(a(), a()))}
   SCCS (1):
    Scc:
     {f#(f(a(), x), a()) -> f#(f(x, f(a(), a())), a())}
    SCC (1):
     Strict:
      {f#(f(a(), x), a()) -> f#(f(x, f(a(), a())), a())}
     Weak:
     {f(f(a(), x), a()) -> f(a(), f(f(x, f(a(), a())), a()))}
     BOUND:
      Bound: match(-raise)-DP-bounded by 1
      Automaton:
       {       a_1() -> 11*
               a_0() -> 9*
        f#_1(13, 11) -> 4*
         f#_0(10, 9) -> 4*
         f_1(11, 11) -> 12*
          f_1(8, 12) -> 13*
         f_0(10, 10) -> 7*
          f_0(10, 9) -> 7*
          f_0(10, 8) -> 10*
          f_0(10, 7) -> 7*
          f_0(9, 10) -> 7*
           f_0(9, 9) -> 8*
           f_0(9, 8) -> 10*
           f_0(9, 7) -> 7*
          f_0(8, 10) -> 7*
           f_0(8, 9) -> 7*
           f_0(8, 8) -> 10*
           f_0(8, 7) -> 7*
          f_0(7, 10) -> 7*
           f_0(7, 9) -> 7*
           f_0(7, 8) -> 10*
           f_0(7, 7) -> 7*}
      Strict:
       {}
      Qed