YES
Time: 0.020288
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)-DP-bounded by 1
      Automaton:
       {       a_1() -> 14*
               a_0() -> 10*
        f#_1(15, 17) -> 4*
        f#_0(13, 12) -> 4*
        f#_0(12, 10) -> 4*
        f#_0(11, 12) -> 4*
         f_1(14, 16) -> 17*
         f_1(14, 14) -> 16*
         f_1(12, 14) -> 15*
         f_0(13, 13) -> 8*
         f_0(13, 12) -> 11 | 8
         f_0(13, 11) -> 8*
         f_0(13, 10) -> 11*
          f_0(13, 8) -> 8*
         f_0(12, 13) -> 8*
         f_0(12, 12) -> 8*
         f_0(12, 11) -> 8*
         f_0(12, 10) -> 11*
          f_0(12, 8) -> 8*
         f_0(11, 13) -> 8*
         f_0(11, 12) -> 11 | 8
         f_0(11, 11) -> 8*
         f_0(11, 10) -> 11*
          f_0(11, 8) -> 8*
         f_0(10, 13) -> 12*
         f_0(10, 12) -> 8*
         f_0(10, 11) -> 8*
         f_0(10, 10) -> 13*
          f_0(10, 8) -> 8*
          f_0(8, 13) -> 8*
          f_0(8, 12) -> 8*
          f_0(8, 11) -> 8*
          f_0(8, 10) -> 11*
           f_0(8, 8) -> 8*}
      Strict:
       {f#(f(a(), a()), x) -> f#(x, a())}
      EDG:
       {(f#(f(a(), a()), x) -> f#(x, a()), f#(f(a(), a()), x) -> f#(x, a()))}
       SCCS (1):
        Scc:
         {f#(f(a(), a()), x) -> f#(x, a())}
        SCC (1):
         Strict:
          {f#(f(a(), a()), x) -> f#(x, a())}
         Weak:
         {f(f(a(), a()), x) -> f(f(x, a()), f(a(), f(a(), a())))}
         POLY:
          Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
          Interpretation:
           [f](x0, x1) = x0 + x1,
           
           [a] = 1,
           
           [f#](x0, x1) = x0 + x1
          Strict:
           f#(f(a(), a()), x) -> f#(x, a())
           2 + 1x >= 1 + 1x
          Weak:
           
         Qed