YES
Time: 0.012502
TRS:
 {f(a(), f(a(), x)) -> f(a(), f(f(a(), x), f(a(), a())))}
 DP:
  DP:
   {f#(a(), f(a(), x)) -> f#(f(a(), x), f(a(), a())),
    f#(a(), f(a(), x)) -> f#(a(), f(f(a(), x), f(a(), a()))),
    f#(a(), f(a(), x)) -> f#(a(), a())}
  TRS:
  {f(a(), f(a(), x)) -> f(a(), f(f(a(), x), f(a(), a())))}
  EDG:
   {(f#(a(), f(a(), x)) -> f#(a(), f(f(a(), x), f(a(), a()))), f#(a(), f(a(), x)) -> f#(f(a(), x), f(a(), a())))
    (f#(a(), f(a(), x)) -> f#(a(), f(f(a(), x), f(a(), a()))), f#(a(), f(a(), x)) -> f#(a(), f(f(a(), x), f(a(), a()))))
    (f#(a(), f(a(), x)) -> f#(a(), f(f(a(), x), f(a(), a()))), f#(a(), f(a(), x)) -> f#(a(), a()))}
   SCCS (1):
    Scc:
     {f#(a(), f(a(), x)) -> f#(a(), f(f(a(), x), f(a(), a())))}
    SCC (1):
     Strict:
      {f#(a(), f(a(), x)) -> f#(a(), f(f(a(), x), f(a(), a())))}
     Weak:
     {f(a(), f(a(), x)) -> f(a(), f(f(a(), x), f(a(), a())))}
     BOUND:
      Bound: match(-raise)-DP-bounded by 0
      Automaton:
       {       a_0() -> 10*
        f#_0(10, 13) -> 4*
         f_0(13, 13) -> 8*
         f_0(13, 12) -> 8*
         f_0(13, 11) -> 8*
         f_0(13, 10) -> 8*
          f_0(13, 8) -> 8*
         f_0(12, 13) -> 8*
         f_0(12, 12) -> 13*
         f_0(12, 11) -> 8*
         f_0(12, 10) -> 8*
          f_0(12, 8) -> 8*
         f_0(11, 13) -> 8*
         f_0(11, 12) -> 13*
         f_0(11, 11) -> 8*
         f_0(11, 10) -> 8*
          f_0(11, 8) -> 8*
         f_0(10, 13) -> 11*
         f_0(10, 12) -> 11*
         f_0(10, 11) -> 11*
         f_0(10, 10) -> 12*
          f_0(10, 8) -> 11*
          f_0(8, 13) -> 8*
          f_0(8, 12) -> 8*
          f_0(8, 11) -> 8*
          f_0(8, 10) -> 8*
           f_0(8, 8) -> 8*}
      Strict:
       {}
      Qed