YES
Time: 0.021146
TRS:
 {f(f(a(), x), a()) -> f(f(a(), f(a(), f(a(), a()))), x)}
 DP:
  DP:
   {f#(f(a(), x), a()) -> f#(f(a(), f(a(), f(a(), a()))), x),
    f#(f(a(), x), a()) -> f#(a(), f(a(), f(a(), a()))),
    f#(f(a(), x), a()) -> f#(a(), f(a(), a())),
    f#(f(a(), x), a()) -> f#(a(), a())}
  TRS:
  {f(f(a(), x), a()) -> f(f(a(), f(a(), f(a(), a()))), x)}
  EDG:
   {(f#(f(a(), x), a()) -> f#(f(a(), f(a(), f(a(), a()))), x), f#(f(a(), x), a()) -> f#(a(), a()))
    (f#(f(a(), x), a()) -> f#(f(a(), f(a(), f(a(), a()))), x), f#(f(a(), x), a()) -> f#(a(), f(a(), a())))
    (f#(f(a(), x), a()) -> f#(f(a(), f(a(), f(a(), a()))), x), f#(f(a(), x), a()) -> f#(a(), f(a(), f(a(), a()))))
    (f#(f(a(), x), a()) -> f#(f(a(), f(a(), f(a(), a()))), x), f#(f(a(), x), a()) -> f#(f(a(), f(a(), f(a(), a()))), x))}
   SCCS (1):
    Scc:
     {f#(f(a(), x), a()) -> f#(f(a(), f(a(), f(a(), a()))), x)}
    SCC (1):
     Strict:
      {f#(f(a(), x), a()) -> f#(f(a(), f(a(), f(a(), a()))), x)}
     Weak:
     {f(f(a(), x), a()) -> f(f(a(), f(a(), f(a(), a()))), x)}
     BOUND:
      Bound: match(-raise)-DP-bounded by 1
      Automaton:
       {       a_1() -> 13*
               a_0() -> 10*
        f#_1(16, 11) -> 4*
        f#_0(12, 12) -> 4*
        f#_0(12, 11) -> 4*
        f#_0(12, 10) -> 4*
         f#_0(12, 9) -> 4*
         f#_0(12, 8) -> 4*
         f_1(13, 15) -> 16*
         f_1(13, 14) -> 15*
         f_1(13, 13) -> 14*
         f_0(12, 12) -> 8*
         f_0(12, 11) -> 8*
         f_0(12, 10) -> 8*
          f_0(12, 9) -> 8*
          f_0(12, 8) -> 8*
         f_0(11, 12) -> 8*
         f_0(11, 11) -> 8*
         f_0(11, 10) -> 8*
          f_0(11, 9) -> 8*
          f_0(11, 8) -> 8*
         f_0(10, 12) -> 8*
         f_0(10, 11) -> 12*
         f_0(10, 10) -> 9*
          f_0(10, 9) -> 11*
          f_0(10, 8) -> 8*
          f_0(9, 12) -> 8*
          f_0(9, 11) -> 8*
          f_0(9, 10) -> 8*
           f_0(9, 9) -> 8*
           f_0(9, 8) -> 8*
          f_0(8, 12) -> 8*
          f_0(8, 11) -> 8*
          f_0(8, 10) -> 8*
           f_0(8, 9) -> 8*
           f_0(8, 8) -> 8*}
      Strict:
       {}
      Qed