YES
Time: 4.574826
TRS:
 {f(x, f(y, a())) -> f(f(f(f(a(), a()), y), h a()), x)}
 DP:
  DP:
   {f#(x, f(y, a())) -> f#(f(f(f(a(), a()), y), h a()), x),
    f#(x, f(y, a())) -> f#(f(f(a(), a()), y), h a()),
    f#(x, f(y, a())) -> f#(f(a(), a()), y),
    f#(x, f(y, a())) -> f#(a(), a())}
  TRS:
  {f(x, f(y, a())) -> f(f(f(f(a(), a()), y), h a()), x)}
  EDG:
   {(f#(x, f(y, a())) -> f#(f(f(f(a(), a()), y), h a()), x), f#(x, f(y, a())) -> f#(a(), a()))
    (f#(x, f(y, a())) -> f#(f(f(f(a(), a()), y), h a()), x), f#(x, f(y, a())) -> f#(f(a(), a()), y))
    (f#(x, f(y, a())) -> f#(f(f(f(a(), a()), y), h a()), x), f#(x, f(y, a())) -> f#(f(f(a(), a()), y), h a()))
    (f#(x, f(y, a())) -> f#(f(f(f(a(), a()), y), h a()), x), f#(x, f(y, a())) -> f#(f(f(f(a(), a()), y), h a()), x))
    (f#(x, f(y, a())) -> f#(f(a(), a()), y), f#(x, f(y, a())) -> f#(f(f(f(a(), a()), y), h a()), x))
    (f#(x, f(y, a())) -> f#(f(a(), a()), y), f#(x, f(y, a())) -> f#(f(f(a(), a()), y), h a()))
    (f#(x, f(y, a())) -> f#(f(a(), a()), y), f#(x, f(y, a())) -> f#(f(a(), a()), y))
    (f#(x, f(y, a())) -> f#(f(a(), a()), y), f#(x, f(y, a())) -> f#(a(), a()))}
   SCCS (1):
    Scc:
     {f#(x, f(y, a())) -> f#(f(f(f(a(), a()), y), h a()), x),
      f#(x, f(y, a())) -> f#(f(a(), a()), y)}
    SCC (2):
     Strict:
      {f#(x, f(y, a())) -> f#(f(f(f(a(), a()), y), h a()), x),
       f#(x, f(y, a())) -> f#(f(a(), a()), y)}
     Weak:
     {f(x, f(y, a())) -> f(f(f(f(a(), a()), y), h a()), x)}
     BOUND:
      Bound: match(-raise)-DP-bounded by 2
      Automaton:
       {     h_1(11) -> 14*
             h_0(10) -> 9*
              h_0(9) -> 9*
              h_0(8) -> 9*
              h_0(7) -> 9*
               a_2() -> 16*
               a_1() -> 11*
               a_0() -> 10*
        f#_2(17, 11) -> 5*
        f#_1(19, 15) -> 5*
        f#_1(15, 12) -> 5*
        f#_1(12, 10) -> 5*
         f#_1(12, 9) -> 5*
         f#_1(12, 8) -> 5*
         f#_1(12, 7) -> 5*
         f#_0(8, 10) -> 5*
          f#_0(8, 9) -> 5*
          f#_0(8, 8) -> 5*
          f#_0(8, 7) -> 5*
          f#_0(7, 8) -> 5*
          f#_0(7, 7) -> 5*
         f_2(16, 16) -> 17*
         f_1(19, 15) -> 13*
         f_1(18, 14) -> 19*
         f_1(15, 12) -> 13*
         f_1(13, 14) -> 15*
         f_1(12, 11) -> 18*
         f_1(12, 10) -> 13*
          f_1(12, 9) -> 13*
          f_1(12, 8) -> 13*
          f_1(12, 7) -> 13*
         f_1(11, 11) -> 12*
         f_0(10, 10) -> 8*
          f_0(10, 9) -> 7*
          f_0(10, 8) -> 7*
          f_0(10, 7) -> 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) -> 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, a())) -> f#(f(f(f(a(), a()), y), h a()), x)}
      EDG:
       {(f#(x, f(y, a())) -> f#(f(f(f(a(), a()), y), h a()), x), f#(x, f(y, a())) -> f#(f(f(f(a(), a()), y), h a()), x))}
       SCCS (1):
        Scc:
         {f#(x, f(y, a())) -> f#(f(f(f(a(), a()), y), h a()), x)}
        SCC (1):
         Strict:
          {f#(x, f(y, a())) -> f#(f(f(f(a(), a()), y), h a()), x)}
         Weak:
         {f(x, f(y, a())) -> f(f(f(f(a(), a()), y), h a()), x)}
         BOUND:
          Bound: match(-raise)-DP-bounded by 1
          Automaton:
           {     h_1(17) -> 20*
                 h_0(16) -> 12*
                 h_0(15) -> 12*
                 h_0(14) -> 13*
                 h_0(13) -> 12*
                 h_0(12) -> 12*
                 h_0(11) -> 12*
                 h_0(10) -> 12*
                   a_1() -> 17*
                   a_0() -> 14*
            f#_1(21, 16) -> 5*
            f#_0(16, 16) -> 5*
            f#_0(16, 15) -> 5*
            f#_0(16, 14) -> 5*
            f#_0(16, 13) -> 5*
            f#_0(16, 12) -> 5*
            f#_0(16, 11) -> 5*
            f#_0(16, 10) -> 5*
             f_1(23, 21) -> 19*
             f_1(22, 20) -> 23*
             f_1(21, 18) -> 19*
             f_1(19, 20) -> 21*
             f_1(18, 17) -> 22*
             f_1(18, 16) -> 19*
             f_1(18, 15) -> 19*
             f_1(18, 14) -> 19*
             f_1(18, 13) -> 19*
             f_1(18, 12) -> 19*
             f_1(18, 11) -> 19*
             f_1(18, 10) -> 19*
             f_1(17, 17) -> 18*
             f_0(16, 16) -> 15 | 10
             f_0(16, 15) -> 10*
             f_0(16, 14) -> 10*
             f_0(16, 13) -> 10*
             f_0(16, 12) -> 10*
             f_0(16, 11) -> 15 | 10
             f_0(16, 10) -> 10*
             f_0(15, 16) -> 10*
             f_0(15, 15) -> 10*
             f_0(15, 14) -> 10*
             f_0(15, 13) -> 16*
             f_0(15, 12) -> 10*
             f_0(15, 11) -> 10*
             f_0(15, 10) -> 10*
             f_0(14, 16) -> 10*
             f_0(14, 15) -> 10*
             f_0(14, 14) -> 11*
             f_0(14, 13) -> 10*
             f_0(14, 12) -> 10*
             f_0(14, 11) -> 10*
             f_0(14, 10) -> 10*
             f_0(13, 16) -> 10*
             f_0(13, 15) -> 10*
             f_0(13, 14) -> 10*
             f_0(13, 13) -> 10*
             f_0(13, 12) -> 10*
             f_0(13, 11) -> 10*
             f_0(13, 10) -> 10*
             f_0(12, 16) -> 10*
             f_0(12, 15) -> 10*
             f_0(12, 14) -> 10*
             f_0(12, 13) -> 10*
             f_0(12, 12) -> 10*
             f_0(12, 11) -> 10*
             f_0(12, 10) -> 10*
             f_0(11, 16) -> 15*
             f_0(11, 15) -> 15*
             f_0(11, 14) -> 15*
             f_0(11, 13) -> 15*
             f_0(11, 12) -> 15*
             f_0(11, 11) -> 15*
             f_0(11, 10) -> 15*
             f_0(10, 16) -> 10*
             f_0(10, 15) -> 10*
             f_0(10, 14) -> 10*
             f_0(10, 13) -> 10*
             f_0(10, 12) -> 10*
             f_0(10, 11) -> 10*
             f_0(10, 10) -> 10*}
          Strict:
           {}
          Qed