YES
TRS:
 {f(x, f(a(), a())) -> f(f(f(a(), a()), a()), f(a(), x))}
 DP:
  Strict:
   {f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(a(), x)),
    f#(x, f(a(), a())) -> f#(f(a(), a()), a()),
    f#(x, f(a(), a())) -> f#(a(), x)}
  Weak:
  {f(x, f(a(), a())) -> f(f(f(a(), a()), a()), f(a(), x))}
  EDG:
   {(f#(x, f(a(), a())) -> f#(a(), x), f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(a(), x)))
    (f#(x, f(a(), a())) -> f#(a(), x), f#(x, f(a(), a())) -> f#(f(a(), a()), a()))
    (f#(x, f(a(), a())) -> f#(a(), x), f#(x, f(a(), a())) -> f#(a(), x))
    (f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(a(), x)), f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(a(), x)))
    (f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(a(), x)), f#(x, f(a(), a())) -> f#(f(a(), a()), a()))
    (f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(a(), x)), f#(x, f(a(), a())) -> f#(a(), x))}
   SCCS:
    Scc:
     {f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(a(), x)),
      f#(x, f(a(), a())) -> f#(a(), x)}
    SCC:
     Strict:
      {f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(a(), x)),
       f#(x, f(a(), a())) -> f#(a(), x)}
     Weak:
     {f(x, f(a(), a())) -> f(f(f(a(), a()), a()), f(a(), x))}
     UR:
      {f(x, f(a(), a())) -> f(f(f(a(), a()), a()), f(a(), x))}
      BOUND:
       Bound: match(-raise)-DP-bounded by 1
       Automaton:
        {       a_1() -> 14*
                a_0() -> 10*
         f#_1(16, 17) -> 4*
         f#_0(13, 12) -> 4*
         f#_0(13, 11) -> 4*
         f#_0(10, 13) -> 4*
          f_1(15, 14) -> 16*
          f_1(14, 14) -> 15*
          f_1(14, 13) -> 17*
          f_0(13, 13) -> 8*
          f_0(13, 12) -> 11 | 8
          f_0(13, 11) -> 11 | 8
          f_0(13, 10) -> 8*
           f_0(13, 8) -> 8*
          f_0(12, 13) -> 8*
          f_0(12, 12) -> 8*
          f_0(12, 11) -> 8*
          f_0(12, 10) -> 13*
           f_0(12, 8) -> 8*
          f_0(11, 13) -> 8*
          f_0(11, 12) -> 8*
          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:
        {f#(x, f(a(), a())) -> f#(a(), x)}
       EDG:
        {(f#(x, f(a(), a())) -> f#(a(), x), f#(x, f(a(), a())) -> f#(a(), x))}
        SCCS:
         Scc:
          {f#(x, f(a(), a())) -> f#(a(), x)}
         SCC:
          Strict:
           {f#(x, f(a(), a())) -> f#(a(), x)}
          Weak:
          {f(x, f(a(), a())) -> f(f(f(a(), a()), a()), f(a(), x))}
          POLY:
           Argument Filtering:
            pi(a) = [], pi(f#) = [0,1], pi(f) = []
           Usable Rules:
            {}
           Interpretation:
            [f#](x0, x1) = x0 + x1,
            [f] = 1,
            [a] = 0
           Strict:
            {}
           Weak:
            {f(x, f(a(), a())) -> f(f(f(a(), a()), a()), f(a(), x))}
           Qed