YES
TRS:
 {    f(x, f(y, z)) -> f(f(x, y), z),
  f(f(a(), b()), x) -> f(a(), f(a(), x)),
  f(f(b(), a()), x) -> f(b(), f(b(), x))}
 DP:
  Strict:
   {    f#(x, f(y, z)) -> f#(x, y),
        f#(x, f(y, z)) -> f#(f(x, y), z),
    f#(f(a(), b()), x) -> f#(a(), x),
    f#(f(a(), b()), x) -> f#(a(), f(a(), x)),
    f#(f(b(), a()), x) -> f#(b(), x),
    f#(f(b(), a()), x) -> f#(b(), f(b(), x))}
  Weak:
  {    f(x, f(y, z)) -> f(f(x, y), z),
   f(f(a(), b()), x) -> f(a(), f(a(), x)),
   f(f(b(), a()), x) -> f(b(), f(b(), x))}
  EDG:
   {(f#(f(b(), a()), x) -> f#(b(), f(b(), x)), f#(x, f(y, z)) -> f#(f(x, y), z))
    (f#(f(b(), a()), x) -> f#(b(), f(b(), x)), f#(x, f(y, z)) -> f#(x, y))
    (f#(x, f(y, z)) -> f#(f(x, y), z), f#(f(b(), a()), x) -> f#(b(), f(b(), x)))
    (f#(x, f(y, z)) -> f#(f(x, y), z), f#(f(b(), a()), x) -> f#(b(), x))
    (f#(x, f(y, z)) -> f#(f(x, y), z), f#(f(a(), b()), x) -> f#(a(), f(a(), x)))
    (f#(x, f(y, z)) -> f#(f(x, y), z), f#(f(a(), b()), 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(b(), a()), x) -> f#(b(), x), f#(x, f(y, z)) -> f#(f(x, y), z))
    (f#(f(b(), a()), x) -> f#(b(), x), f#(x, f(y, z)) -> f#(x, y))
    (f#(f(a(), b()), x) -> f#(a(), x), f#(x, f(y, z)) -> f#(x, y))
    (f#(f(a(), b()), 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(), b()), x) -> f#(a(), x))
    (f#(x, f(y, z)) -> f#(x, y), f#(f(a(), b()), x) -> f#(a(), f(a(), x)))
    (f#(x, f(y, z)) -> f#(x, y), f#(f(b(), a()), x) -> f#(b(), x))
    (f#(x, f(y, z)) -> f#(x, y), f#(f(b(), a()), x) -> f#(b(), f(b(), x)))
    (f#(f(a(), b()), x) -> f#(a(), f(a(), x)), f#(x, f(y, z)) -> f#(x, y))
    (f#(f(a(), b()), x) -> f#(a(), 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(), b()), x) -> f#(a(), x),
      f#(f(a(), b()), x) -> f#(a(), f(a(), x)),
      f#(f(b(), a()), x) -> f#(b(), x),
      f#(f(b(), a()), x) -> f#(b(), f(b(), x))}
    SCC:
     Strict:
      {    f#(x, f(y, z)) -> f#(x, y),
           f#(x, f(y, z)) -> f#(f(x, y), z),
       f#(f(a(), b()), x) -> f#(a(), x),
       f#(f(a(), b()), x) -> f#(a(), f(a(), x)),
       f#(f(b(), a()), x) -> f#(b(), x),
       f#(f(b(), a()), x) -> f#(b(), f(b(), x))}
     Weak:
     {    f(x, f(y, z)) -> f(f(x, y), z),
      f(f(a(), b()), x) -> f(a(), f(a(), x)),
      f(f(b(), a()), x) -> f(b(), f(b(), 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 + 1,
       [b] = 0,
       [a] = 0
      Strict:
       {    f#(x, f(y, z)) -> f#(f(x, y), z),
        f#(f(a(), b()), x) -> f#(a(), f(a(), x)),
        f#(f(b(), a()), x) -> f#(b(), f(b(), x))}
      Weak:
       {    f(x, f(y, z)) -> f(f(x, y), z),
        f(f(a(), b()), x) -> f(a(), f(a(), x)),
        f(f(b(), a()), x) -> f(b(), f(b(), x))}
      EDG:
       {(f#(f(a(), b()), x) -> f#(a(), f(a(), x)), f#(x, f(y, z)) -> f#(f(x, y), z))
        (f#(f(b(), a()), x) -> f#(b(), f(b(), 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#(f(x, y), z), f#(f(a(), b()), x) -> f#(a(), f(a(), x)))
        (f#(x, f(y, z)) -> f#(f(x, y), z), f#(f(b(), a()), x) -> f#(b(), f(b(), x)))}
       SCCS:
        Scc:
         {    f#(x, f(y, z)) -> f#(f(x, y), z),
          f#(f(a(), b()), x) -> f#(a(), f(a(), x)),
          f#(f(b(), a()), x) -> f#(b(), f(b(), x))}
        SCC:
         Strict:
          {    f#(x, f(y, z)) -> f#(f(x, y), z),
           f#(f(a(), b()), x) -> f#(a(), f(a(), x)),
           f#(f(b(), a()), x) -> f#(b(), f(b(), x))}
         Weak:
         {    f(x, f(y, z)) -> f(f(x, y), z),
          f(f(a(), b()), x) -> f(a(), f(a(), x)),
          f(f(b(), a()), x) -> f(b(), f(b(), x))}
         BOUND:
          Bound: match(-raise)-DP-bounded by 1
          Automaton:
           {       b_0() -> 9*
                   a_1() -> 11*
                   a_0() -> 8*
            f#_1(13, 12) -> 5*
            f#_1(13, 10) -> 5*
             f#_1(13, 9) -> 5*
             f#_1(13, 8) -> 5*
             f#_1(13, 7) -> 5*
            f#_1(11, 12) -> 5*
            f#_0(10, 10) -> 5*
             f#_0(10, 9) -> 5*
             f#_0(10, 8) -> 5*
             f#_0(10, 7) -> 5*
              f#_0(9, 7) -> 5*
             f#_0(8, 10) -> 5*
             f#_0(7, 10) -> 5*
              f#_0(7, 9) -> 5*
              f#_0(7, 8) -> 5*
              f#_0(7, 7) -> 5*
             f_1(13, 13) -> 13*
             f_1(13, 12) -> 13 | 12
             f_1(13, 11) -> 13*
             f_1(13, 10) -> 13 | 12
              f_1(13, 9) -> 13 | 12
              f_1(13, 8) -> 13 | 12
              f_1(13, 7) -> 13 | 12
             f_1(12, 10) -> 12*
              f_1(12, 9) -> 12*
              f_1(12, 8) -> 12*
              f_1(12, 7) -> 12*
             f_1(11, 13) -> 13*
             f_1(11, 12) -> 13 | 12
             f_1(11, 11) -> 13*
             f_1(11, 10) -> 12*
              f_1(11, 9) -> 12*
              f_1(11, 8) -> 12*
              f_1(11, 7) -> 12*
             f_0(10, 10) -> 10 | 7
              f_0(10, 9) -> 10 | 7
              f_0(10, 8) -> 10 | 7
              f_0(10, 7) -> 10 | 7
              f_0(9, 10) -> 7*
               f_0(9, 9) -> 7*
               f_0(9, 8) -> 7*
               f_0(9, 7) -> 7*
              f_0(8, 10) -> 10 | 7
               f_0(8, 9) -> 10*
               f_0(8, 8) -> 10*
               f_0(8, 7) -> 10*
              f_0(7, 10) -> 7*
               f_0(7, 9) -> 7*
               f_0(7, 8) -> 7*
               f_0(7, 7) -> 7*}
          Strict:
           {    f#(x, f(y, z)) -> f#(f(x, y), z),
            f#(f(b(), a()), x) -> f#(b(), f(b(), x))}
          EDG:
           {(f#(x, f(y, z)) -> f#(f(x, y), z), f#(f(b(), a()), x) -> f#(b(), f(b(), x)))
            (f#(x, f(y, z)) -> f#(f(x, y), z), f#(x, f(y, z)) -> f#(f(x, y), z))
            (f#(f(b(), a()), x) -> f#(b(), f(b(), x)), f#(x, f(y, z)) -> f#(f(x, y), z))}
           SCCS:
            Scc:
             {    f#(x, f(y, z)) -> f#(f(x, y), z),
              f#(f(b(), a()), x) -> f#(b(), f(b(), x))}
            SCC:
             Strict:
              {    f#(x, f(y, z)) -> f#(f(x, y), z),
               f#(f(b(), a()), x) -> f#(b(), f(b(), x))}
             Weak:
             {    f(x, f(y, z)) -> f(f(x, y), z),
              f(f(a(), b()), x) -> f(a(), f(a(), x)),
              f(f(b(), a()), x) -> f(b(), f(b(), x))}
             BOUND:
              Bound: match(-raise)-DP-bounded by 1
              Automaton:
               {       b_1() -> 11*
                       b_0() -> 9*
                       a_0() -> 8*
                f#_1(13, 12) -> 5*
                f#_1(13, 10) -> 5*
                 f#_1(13, 9) -> 5*
                 f#_1(13, 8) -> 5*
                 f#_1(13, 7) -> 5*
                f#_1(11, 12) -> 5*
                f#_0(10, 10) -> 5*
                 f#_0(10, 9) -> 5*
                 f#_0(10, 8) -> 5*
                 f#_0(10, 7) -> 5*
                 f#_0(9, 10) -> 5*
                 f#_0(7, 10) -> 5*
                  f#_0(7, 9) -> 5*
                  f#_0(7, 8) -> 5*
                  f#_0(7, 7) -> 5*
                 f_1(13, 13) -> 13*
                 f_1(13, 12) -> 13 | 12
                 f_1(13, 11) -> 13*
                 f_1(13, 10) -> 13 | 12
                  f_1(13, 9) -> 13 | 12
                  f_1(13, 8) -> 13 | 12
                  f_1(13, 7) -> 13 | 12
                 f_1(12, 10) -> 12*
                  f_1(12, 9) -> 12*
                  f_1(12, 8) -> 12*
                  f_1(12, 7) -> 12*
                 f_1(11, 13) -> 13*
                 f_1(11, 12) -> 13 | 12
                 f_1(11, 11) -> 13*
                 f_1(11, 10) -> 12*
                  f_1(11, 9) -> 12*
                  f_1(11, 8) -> 12*
                  f_1(11, 7) -> 12*
                 f_0(10, 10) -> 10 | 7
                  f_0(10, 9) -> 10 | 7
                  f_0(10, 8) -> 10 | 7
                  f_0(10, 7) -> 10 | 7
                  f_0(9, 10) -> 10 | 7
                   f_0(9, 9) -> 10*
                   f_0(9, 8) -> 10*
                   f_0(9, 7) -> 10*
                  f_0(8, 10) -> 7*
                   f_0(8, 9) -> 7*
                   f_0(8, 8) -> 7*
                   f_0(8, 7) -> 7*
                  f_0(7, 10) -> 7*
                   f_0(7, 9) -> 7*
                   f_0(7, 8) -> 7*
                   f_0(7, 7) -> 7*}
              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(), b()), x) -> f(a(), f(a(), x)),
                  f(f(b(), a()), x) -> f(b(), f(b(), x))}
                 SPSC:
                  Simple Projection:
                   pi(f#) = 1
                  Strict:
                   {}
                  Qed