YES
Time: 0.007429
TRS:
 {f(f(a(), x), a()) -> f(a(), f(f(a(), f(a(), a())), x))}
 DP:
  DP:
   {f#(f(a(), x), a()) -> f#(f(a(), f(a(), a())), x),
    f#(f(a(), x), a()) -> f#(a(), f(f(a(), f(a(), a())), x)),
    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(a(), f(f(a(), f(a(), a())), x))}
  EDG:
   {(f#(f(a(), x), a()) -> f#(f(a(), f(a(), a())), x), f#(f(a(), x), a()) -> f#(f(a(), f(a(), a())), x))
    (f#(f(a(), x), a()) -> f#(f(a(), f(a(), a())), x), f#(f(a(), x), a()) -> f#(a(), f(f(a(), f(a(), a())), x)))
    (f#(f(a(), x), a()) -> f#(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(), a())), x), f#(f(a(), x), a()) -> f#(a(), a()))}
   SCCS (1):
    Scc:
     {f#(f(a(), x), a()) -> f#(f(a(), f(a(), a())), x)}
    SCC (1):
     Strict:
      {f#(f(a(), x), a()) -> f#(f(a(), f(a(), a())), x)}
     Weak:
     {f(f(a(), x), a()) -> f(a(), f(f(a(), f(a(), a())), x))}
     BOUND:
      Bound: match(-raise)-bounded by 1
      Automaton:
       {     a_1() -> 2*
             a_0() -> 1*
        f#_1(4, 5) -> 1*
        f#_1(4, 3) -> 1*
        f#_1(4, 1) -> 1*
        f#_0(1, 1) -> 1*
         f_1(4, 5) -> 5*
         f_1(4, 3) -> 6*
         f_1(4, 1) -> 5*
         f_1(2, 6) -> 5*
         f_1(2, 5) -> 1*
         f_1(2, 3) -> 4*
         f_1(2, 2) -> 3*
         f_0(1, 1) -> 1*}
      Strict:
       {}
      Qed