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