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