YES
TRS:
 {    f(x, f(y, z)) -> f(f(x, y), z),
  f(f(a(), a()), x) -> f(a(), f(b(), f(a(), x)))}
 DP:
  Strict:
   {    f#(x, f(y, z)) -> f#(x, y),
        f#(x, f(y, z)) -> f#(f(x, y), z),
    f#(f(a(), a()), x) -> f#(a(), x),
    f#(f(a(), a()), x) -> f#(a(), f(b(), f(a(), x))),
    f#(f(a(), a()), x) -> f#(b(), f(a(), x))}
  Weak:
  {    f(x, f(y, z)) -> f(f(x, y), z),
   f(f(a(), a()), x) -> f(a(), f(b(), f(a(), x)))}
  EDG:
   {(f#(x, f(y, z)) -> f#(f(x, y), z), f#(f(a(), a()), x) -> f#(b(), f(a(), x)))
    (f#(x, f(y, z)) -> f#(f(x, y), z), f#(f(a(), a()), x) -> f#(a(), f(b(), f(a(), x))))
    (f#(x, f(y, z)) -> f#(f(x, y), z), f#(f(a(), a()), x) -> f#(a(), x))
    (f#(x, f(y, z)) -> f#(f(x, y), z), f#(x, f(y, z)) -> f#(f(x, y), z))
    (f#(x, f(y, z)) -> f#(f(x, y), z), f#(x, f(y, z)) -> f#(x, y))
    (f#(f(a(), a()), x) -> f#(b(), f(a(), x)), f#(x, f(y, z)) -> f#(f(x, y), z))
    (f#(f(a(), a()), x) -> f#(b(), f(a(), x)), f#(x, f(y, z)) -> f#(x, y))
    (f#(f(a(), a()), x) -> f#(a(), f(b(), f(a(), x))), f#(x, f(y, z)) -> f#(x, y))
    (f#(f(a(), a()), x) -> f#(a(), f(b(), f(a(), x))), f#(x, f(y, z)) -> f#(f(x, y), z))
    (f#(f(a(), a()), x) -> f#(a(), x), f#(x, f(y, z)) -> f#(x, y))
    (f#(f(a(), a()), x) -> f#(a(), x), f#(x, f(y, z)) -> f#(f(x, y), z))
    (f#(x, f(y, z)) -> f#(x, y), f#(x, f(y, z)) -> f#(x, y))
    (f#(x, f(y, z)) -> f#(x, y), f#(x, f(y, z)) -> f#(f(x, y), z))
    (f#(x, f(y, z)) -> f#(x, y), f#(f(a(), a()), x) -> f#(a(), x))
    (f#(x, f(y, z)) -> f#(x, y), f#(f(a(), a()), x) -> f#(a(), f(b(), f(a(), x))))
    (f#(x, f(y, z)) -> f#(x, y), f#(f(a(), a()), x) -> f#(b(), f(a(), x)))}
   SCCS:
    Scc:
     {    f#(x, f(y, z)) -> f#(x, y),
          f#(x, f(y, z)) -> f#(f(x, y), z),
      f#(f(a(), a()), x) -> f#(a(), x),
      f#(f(a(), a()), x) -> f#(a(), f(b(), f(a(), x))),
      f#(f(a(), a()), x) -> f#(b(), f(a(), x))}
    SCC:
     Strict:
      {    f#(x, f(y, z)) -> f#(x, y),
           f#(x, f(y, z)) -> f#(f(x, y), z),
       f#(f(a(), a()), x) -> f#(a(), x),
       f#(f(a(), a()), x) -> f#(a(), f(b(), f(a(), x))),
       f#(f(a(), a()), x) -> f#(b(), f(a(), x))}
     Weak:
     {    f(x, f(y, z)) -> f(f(x, y), z),
      f(f(a(), a()), x) -> f(a(), f(b(), f(a(), x)))}
     POLY:
      Argument Filtering:
       pi(b) = [], pi(a) = [], pi(f#) = [0,1], pi(f) = [0,1]
      Usable Rules:
       {}
      Interpretation:
       [f#](x0, x1) = x0 + x1,
       [f](x0, x1) = x0 + x1,
       [b] = 0,
       [a] = 1
      Strict:
       {    f#(x, f(y, z)) -> f#(x, y),
            f#(x, f(y, z)) -> f#(f(x, y), z),
        f#(f(a(), a()), x) -> f#(a(), f(b(), f(a(), x)))}
      Weak:
       {    f(x, f(y, z)) -> f(f(x, y), z),
        f(f(a(), a()), x) -> f(a(), f(b(), f(a(), x)))}
      EDG:
       {(f#(x, f(y, z)) -> f#(f(x, y), z), f#(f(a(), a()), x) -> f#(a(), f(b(), f(a(), x))))
        (f#(x, f(y, z)) -> f#(f(x, y), z), f#(x, f(y, z)) -> f#(f(x, y), z))
        (f#(x, f(y, z)) -> f#(f(x, y), z), f#(x, f(y, z)) -> f#(x, y))
        (f#(x, f(y, z)) -> f#(x, y), f#(x, f(y, z)) -> f#(x, y))
        (f#(x, f(y, z)) -> f#(x, y), f#(x, f(y, z)) -> f#(f(x, y), z))
        (f#(x, f(y, z)) -> f#(x, y), f#(f(a(), a()), x) -> f#(a(), f(b(), f(a(), x))))
        (f#(f(a(), a()), x) -> f#(a(), f(b(), f(a(), x))), f#(x, f(y, z)) -> f#(x, y))
        (f#(f(a(), a()), x) -> f#(a(), f(b(), f(a(), x))), f#(x, f(y, z)) -> f#(f(x, y), z))}
       SCCS:
        Scc:
         {    f#(x, f(y, z)) -> f#(x, y),
              f#(x, f(y, z)) -> f#(f(x, y), z),
          f#(f(a(), a()), x) -> f#(a(), f(b(), f(a(), x)))}
        SCC:
         Strict:
          {    f#(x, f(y, z)) -> f#(x, y),
               f#(x, f(y, z)) -> f#(f(x, y), z),
           f#(f(a(), a()), x) -> f#(a(), f(b(), f(a(), x)))}
         Weak:
         {    f(x, f(y, z)) -> f(f(x, y), z),
          f(f(a(), a()), x) -> f(a(), f(b(), f(a(), x)))}
         BOUND:
          Bound: match(-raise)-DP-bounded by 1
          Automaton:
           {       b_1() -> 14*
                   b_0() -> 10*
                   a_1() -> 13*
                   a_0() -> 9*
            f#_1(19, 21) -> 5*
            f#_1(19, 20) -> 5*
            f#_1(19, 16) -> 5*
            f#_1(19, 14) -> 5*
            f#_1(19, 12) -> 5*
            f#_1(19, 11) -> 5*
            f#_1(19, 10) -> 5*
             f#_1(19, 9) -> 5*
             f#_1(19, 8) -> 5*
            f#_1(18, 21) -> 5*
            f#_1(18, 20) -> 5*
            f#_1(18, 16) -> 5*
            f#_1(18, 14) -> 5*
            f#_1(18, 12) -> 5*
            f#_1(18, 11) -> 5*
            f#_1(18, 10) -> 5*
             f#_1(18, 9) -> 5*
             f#_1(18, 8) -> 5*
            f#_1(17, 19) -> 5*
            f#_1(17, 18) -> 5*
            f#_1(17, 17) -> 5*
            f#_1(17, 15) -> 5*
            f#_1(17, 13) -> 5*
            f#_1(13, 21) -> 5*
            f#_1(13, 20) -> 5*
            f#_1(13, 16) -> 5*
            f#_1(13, 14) -> 5*
            f#_0(11, 12) -> 5*
            f#_0(11, 11) -> 5*
            f#_0(11, 10) -> 5*
             f#_0(11, 9) -> 5*
             f#_0(11, 8) -> 5*
             f#_0(9, 12) -> 5*
             f#_0(9, 11) -> 5*
             f#_0(9, 10) -> 5*
              f#_0(9, 9) -> 5*
              f#_0(9, 8) -> 5*
             f#_0(8, 12) -> 5*
             f#_0(8, 11) -> 5*
             f#_0(8, 10) -> 5*
              f#_0(8, 9) -> 5*
              f#_0(8, 8) -> 5*
             f_1(21, 21) -> 20*
             f_1(21, 20) -> 20*
             f_1(21, 16) -> 20*
             f_1(21, 14) -> 14*
             f_1(21, 12) -> 20*
             f_1(21, 11) -> 20*
             f_1(21, 10) -> 20*
              f_1(21, 9) -> 20*
              f_1(21, 8) -> 20*
             f_1(20, 21) -> 20*
             f_1(20, 20) -> 20*
             f_1(20, 16) -> 20 | 16
             f_1(20, 14) -> 14*
             f_1(20, 12) -> 20 | 16
             f_1(20, 11) -> 20 | 16
             f_1(20, 10) -> 20 | 16
              f_1(20, 9) -> 20 | 16
              f_1(20, 8) -> 20 | 16
             f_1(19, 21) -> 19*
             f_1(19, 20) -> 19*
             f_1(19, 16) -> 19 | 15
             f_1(19, 14) -> 17*
             f_1(19, 12) -> 19 | 15
             f_1(19, 11) -> 19 | 15
             f_1(19, 10) -> 19 | 15
              f_1(19, 9) -> 19 | 15
              f_1(19, 8) -> 19 | 15
             f_1(18, 21) -> 19*
             f_1(18, 20) -> 19*
             f_1(18, 16) -> 19*
             f_1(18, 14) -> 17*
             f_1(18, 12) -> 19*
             f_1(18, 11) -> 19*
             f_1(18, 10) -> 19*
              f_1(18, 9) -> 19*
              f_1(18, 8) -> 19*
             f_1(17, 19) -> 19*
             f_1(17, 18) -> 19 | 18
             f_1(17, 17) -> 17*
             f_1(17, 15) -> 19 | 15
             f_1(17, 13) -> 19 | 18
             f_1(16, 12) -> 16*
             f_1(16, 11) -> 16*
             f_1(16, 10) -> 16*
              f_1(16, 9) -> 16*
              f_1(16, 8) -> 16*
             f_1(15, 12) -> 15*
             f_1(15, 11) -> 15*
             f_1(15, 10) -> 15*
              f_1(15, 9) -> 15*
              f_1(15, 8) -> 15*
             f_1(14, 19) -> 20*
             f_1(14, 18) -> 21 | 20
             f_1(14, 17) -> 14*
             f_1(14, 15) -> 20 | 16
             f_1(14, 13) -> 21 | 20
             f_1(13, 21) -> 19*
             f_1(13, 20) -> 19*
             f_1(13, 16) -> 19 | 15
             f_1(13, 14) -> 17*
             f_1(13, 12) -> 15*
             f_1(13, 11) -> 15*
             f_1(13, 10) -> 15*
              f_1(13, 9) -> 15*
              f_1(13, 8) -> 15*
             f_0(12, 12) -> 12 | 8
             f_0(12, 11) -> 12 | 8
             f_0(12, 10) -> 12 | 8
              f_0(12, 9) -> 12 | 8
              f_0(12, 8) -> 12 | 8
             f_0(11, 12) -> 11 | 8
             f_0(11, 11) -> 11 | 8
             f_0(11, 10) -> 11 | 8
              f_0(11, 9) -> 11 | 8
              f_0(11, 8) -> 11 | 8
             f_0(10, 12) -> 8*
             f_0(10, 11) -> 12*
             f_0(10, 10) -> 8*
              f_0(10, 9) -> 8*
              f_0(10, 8) -> 8*
              f_0(9, 12) -> 11 | 8
              f_0(9, 11) -> 11*
              f_0(9, 10) -> 11*
               f_0(9, 9) -> 11*
               f_0(9, 8) -> 11*
              f_0(8, 12) -> 12 | 8
              f_0(8, 11) -> 12 | 8
              f_0(8, 10) -> 12 | 8
               f_0(8, 9) -> 12 | 8
               f_0(8, 8) -> 12 | 8}
          Strict:
           {f#(x, f(y, z)) -> f#(x, y),
            f#(x, f(y, z)) -> f#(f(x, y), z)}
          EDG:
           {(f#(x, f(y, z)) -> f#(f(x, y), z), f#(x, f(y, z)) -> f#(f(x, y), z))
            (f#(x, f(y, z)) -> f#(f(x, y), z), f#(x, f(y, z)) -> f#(x, y))
            (f#(x, f(y, z)) -> f#(x, y), f#(x, f(y, z)) -> f#(x, y))
            (f#(x, f(y, z)) -> f#(x, y), f#(x, f(y, z)) -> f#(f(x, y), z))}
           SCCS:
            Scc:
             {f#(x, f(y, z)) -> f#(x, y),
              f#(x, f(y, z)) -> f#(f(x, y), z)}
            SCC:
             Strict:
              {f#(x, f(y, z)) -> f#(x, y),
               f#(x, f(y, z)) -> f#(f(x, y), z)}
             Weak:
             {    f(x, f(y, z)) -> f(f(x, y), z),
              f(f(a(), a()), x) -> f(a(), f(b(), f(a(), x)))}
             SPSC:
              Simple Projection:
               pi(f#) = 1
              Strict:
               {f#(x, f(y, z)) -> f#(f(x, y), z)}
              EDG:
               {(f#(x, f(y, z)) -> f#(f(x, y), z), f#(x, f(y, z)) -> f#(f(x, y), z))}
               SCCS:
                Scc:
                 {f#(x, f(y, z)) -> f#(f(x, y), z)}
                SCC:
                 Strict:
                  {f#(x, f(y, z)) -> f#(f(x, y), z)}
                 Weak:
                 {    f(x, f(y, z)) -> f(f(x, y), z),
                  f(f(a(), a()), x) -> f(a(), f(b(), f(a(), x)))}
                 SPSC:
                  Simple Projection:
                   pi(f#) = 1
                  Strict:
                   {}
                  Qed