YES
Time: 0.010706
TRS:
 {f(f(a(), a()), x) -> f(f(x, a()), f(a(), f(a(), a())))}
 DP:
  DP:
   {f#(f(a(), a()), x) -> f#(x, a()),
    f#(f(a(), a()), x) -> f#(f(x, a()), f(a(), f(a(), a()))),
    f#(f(a(), a()), x) -> f#(a(), f(a(), a()))}
  TRS:
  {f(f(a(), a()), x) -> f(f(x, a()), f(a(), f(a(), a())))}
  EDG:
   {(f#(f(a(), a()), x) -> f#(x, a()), f#(f(a(), a()), x) -> f#(a(), f(a(), a())))
    (f#(f(a(), a()), x) -> f#(x, a()), f#(f(a(), a()), x) -> f#(f(x, a()), f(a(), f(a(), a()))))
    (f#(f(a(), a()), x) -> f#(x, a()), f#(f(a(), a()), x) -> f#(x, a()))
    (f#(f(a(), a()), x) -> f#(f(x, a()), f(a(), f(a(), a()))), f#(f(a(), a()), x) -> f#(x, a()))
    (f#(f(a(), a()), x) -> f#(f(x, a()), f(a(), f(a(), a()))), f#(f(a(), a()), x) -> f#(f(x, a()), f(a(), f(a(), a()))))
    (f#(f(a(), a()), x) -> f#(f(x, a()), f(a(), f(a(), a()))), f#(f(a(), a()), x) -> f#(a(), f(a(), a())))}
   SCCS (1):
    Scc:
     {f#(f(a(), a()), x) -> f#(x, a()),
      f#(f(a(), a()), x) -> f#(f(x, a()), f(a(), f(a(), a())))}
    SCC (2):
     Strict:
      {f#(f(a(), a()), x) -> f#(x, a()),
       f#(f(a(), a()), x) -> f#(f(x, a()), f(a(), f(a(), a())))}
     Weak:
     {f(f(a(), a()), x) -> f(f(x, a()), f(a(), f(a(), a())))}
     BOUND:
      Bound: match(-raise)-bounded by 2
      Automaton:
       {     a_2() -> 6*
             a_1() -> 2*
             a_0() -> 1*
        f#_2(7, 9) -> 1*
        f#_2(5, 6) -> 1*
        f#_1(5, 2) -> 1*
        f#_1(4, 5) -> 1*
        f#_1(3, 5) -> 1*
        f#_1(2, 2) -> 1*
        f#_1(1, 2) -> 1*
        f#_0(1, 1) -> 1*
         f_2(7, 9) -> 3*
         f_2(6, 8) -> 9*
         f_2(6, 6) -> 8*
         f_2(5, 6) -> 7*
         f_1(5, 2) -> 3*
         f_1(4, 5) -> 3*
         f_1(3, 5) -> 1*
         f_1(2, 4) -> 5*
         f_1(2, 2) -> 4*
         f_1(1, 2) -> 3*
         f_0(1, 1) -> 1*}
      Strict:
       {}
      Qed