YES
Time: 0.238006
TRS:
 {f(f(a(), x), y) -> f(y, f(x, f(a(), f(h a(), a()))))}
 DP:
  DP:
   {f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h a(), a())))),
    f#(f(a(), x), y) -> f#(x, f(a(), f(h a(), a()))),
    f#(f(a(), x), y) -> f#(a(), f(h a(), a())),
    f#(f(a(), x), y) -> f#(h a(), a())}
  TRS:
  {f(f(a(), x), y) -> f(y, f(x, f(a(), f(h a(), a()))))}
  EDG:
   {(f#(f(a(), x), y) -> f#(x, f(a(), f(h a(), a()))), f#(f(a(), x), y) -> f#(h a(), a()))
    (f#(f(a(), x), y) -> f#(x, f(a(), f(h a(), a()))), f#(f(a(), x), y) -> f#(a(), f(h a(), a())))
    (f#(f(a(), x), y) -> f#(x, f(a(), f(h a(), a()))), f#(f(a(), x), y) -> f#(x, f(a(), f(h a(), a()))))
    (f#(f(a(), x), y) -> f#(x, f(a(), f(h a(), a()))), f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h a(), a())))))
    (f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h a(), a())))), f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h a(), a())))))
    (f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h a(), a())))), f#(f(a(), x), y) -> f#(x, f(a(), f(h a(), a()))))
    (f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h a(), a())))), f#(f(a(), x), y) -> f#(a(), f(h a(), a())))
    (f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h a(), a())))), f#(f(a(), x), y) -> f#(h a(), a()))}
   SCCS (1):
    Scc:
     {f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h a(), a())))),
      f#(f(a(), x), y) -> f#(x, f(a(), f(h a(), a())))}
    SCC (2):
     Strict:
      {f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h a(), a())))),
       f#(f(a(), x), y) -> f#(x, f(a(), f(h a(), a())))}
     Weak:
     {f(f(a(), x), y) -> f(y, f(x, f(a(), f(h a(), a()))))}
     BOUND:
      Bound: match(-raise)-DP-bounded by 2
      Automaton:
       {     h_2(20) -> 21*
             h_1(15) -> 16*
             h_0(14) -> 10*
             h_0(13) -> 10*
             h_0(12) -> 11*
             h_0(11) -> 10*
             h_0(10) -> 10*
              h_0(9) -> 10*
               a_2() -> 20*
               a_1() -> 15*
               a_0() -> 12*
        f#_2(17, 23) -> 5*
        f#_1(24, 25) -> 5*
        f#_1(24, 24) -> 5*
        f#_1(19, 24) -> 5*
        f#_1(18, 24) -> 5*
        f#_1(18, 19) -> 5*
        f#_1(18, 18) -> 5*
        f#_1(14, 18) -> 5*
        f#_1(13, 18) -> 5*
        f#_1(12, 18) -> 5*
        f#_1(11, 18) -> 5*
        f#_1(10, 18) -> 5*
         f#_1(9, 18) -> 5*
        f#_0(14, 14) -> 5*
         f#_0(14, 9) -> 5*
        f#_0(13, 14) -> 5*
        f#_0(12, 14) -> 5*
        f#_0(11, 14) -> 5*
        f#_0(10, 14) -> 5*
         f#_0(9, 14) -> 5*
          f#_0(9, 9) -> 5*
         f_2(21, 20) -> 22*
         f_2(20, 22) -> 23*
         f_1(24, 25) -> 19*
         f_1(24, 24) -> 25*
         f_1(19, 24) -> 19*
         f_1(18, 24) -> 25*
         f_1(18, 19) -> 19*
         f_1(18, 18) -> 25*
         f_1(17, 18) -> 24*
         f_1(16, 15) -> 17*
         f_1(15, 17) -> 18*
         f_1(14, 18) -> 19*
         f_1(13, 18) -> 19*
         f_1(12, 18) -> 19*
         f_1(11, 18) -> 19*
         f_1(10, 18) -> 19*
          f_1(9, 18) -> 19*
         f_0(14, 14) -> 9*
         f_0(14, 13) -> 9*
         f_0(14, 12) -> 9*
         f_0(14, 11) -> 9*
         f_0(14, 10) -> 9*
          f_0(14, 9) -> 9*
         f_0(13, 14) -> 9*
         f_0(13, 13) -> 9*
         f_0(13, 12) -> 9*
         f_0(13, 11) -> 9*
         f_0(13, 10) -> 9*
          f_0(13, 9) -> 9*
         f_0(12, 14) -> 9*
         f_0(12, 13) -> 14*
         f_0(12, 12) -> 9*
         f_0(12, 11) -> 9*
         f_0(12, 10) -> 9*
          f_0(12, 9) -> 9*
         f_0(11, 14) -> 9*
         f_0(11, 13) -> 9*
         f_0(11, 12) -> 13*
         f_0(11, 11) -> 9*
         f_0(11, 10) -> 9*
          f_0(11, 9) -> 9*
         f_0(10, 14) -> 9*
         f_0(10, 13) -> 9*
         f_0(10, 12) -> 9*
         f_0(10, 11) -> 9*
         f_0(10, 10) -> 9*
          f_0(10, 9) -> 9*
          f_0(9, 14) -> 9*
          f_0(9, 13) -> 9*
          f_0(9, 12) -> 9*
          f_0(9, 11) -> 9*
          f_0(9, 10) -> 9*
           f_0(9, 9) -> 9*}
      Strict:
       {f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h a(), a()))))}
      EDG:
       {(f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h a(), a())))), f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h a(), a())))))}
       SCCS (1):
        Scc:
         {f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h a(), a()))))}
        SCC (1):
         Strict:
          {f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h a(), a()))))}
         Weak:
         {f(f(a(), x), y) -> f(y, f(x, f(a(), f(h a(), a()))))}
         BOUND:
          Bound: match(-raise)-DP-bounded by 1
          Automaton:
           {     h_1(17) -> 18*
                 h_0(16) -> 11*
                 h_0(15) -> 11*
                 h_0(14) -> 11*
                 h_0(13) -> 12*
                 h_0(12) -> 11*
                 h_0(11) -> 11*
                 h_0(10) -> 11*
                   a_1() -> 17*
                   a_0() -> 13*
            f#_1(21, 21) -> 5*
            f#_1(16, 21) -> 5*
            f#_0(16, 16) -> 5*
            f#_0(15, 16) -> 5*
            f#_0(14, 16) -> 5*
            f#_0(13, 16) -> 5*
            f#_0(12, 16) -> 5*
            f#_0(11, 16) -> 5*
            f#_0(10, 16) -> 5*
             f_1(21, 21) -> 21*
             f_1(20, 21) -> 21*
             f_1(20, 20) -> 21*
             f_1(19, 20) -> 21*
             f_1(18, 17) -> 19*
             f_1(17, 19) -> 20*
             f_1(16, 20) -> 21*
             f_1(15, 20) -> 21*
             f_1(14, 20) -> 21*
             f_1(13, 20) -> 21*
             f_1(12, 20) -> 21*
             f_1(11, 20) -> 21*
             f_1(10, 20) -> 21*
             f_0(16, 16) -> 16 | 10
             f_0(16, 15) -> 16*
             f_0(16, 14) -> 10*
             f_0(16, 13) -> 10*
             f_0(16, 12) -> 10*
             f_0(16, 11) -> 10*
             f_0(16, 10) -> 10*
             f_0(15, 16) -> 16 | 10
             f_0(15, 15) -> 16*
             f_0(15, 14) -> 10*
             f_0(15, 13) -> 10*
             f_0(15, 12) -> 10*
             f_0(15, 11) -> 10*
             f_0(15, 10) -> 10*
             f_0(14, 16) -> 10*
             f_0(14, 15) -> 16*
             f_0(14, 14) -> 10*
             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) -> 16*
             f_0(13, 14) -> 15*
             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) -> 16*
             f_0(12, 14) -> 10*
             f_0(12, 13) -> 14*
             f_0(12, 12) -> 10*
             f_0(12, 11) -> 10*
             f_0(12, 10) -> 10*
             f_0(11, 16) -> 10*
             f_0(11, 15) -> 16*
             f_0(11, 14) -> 10*
             f_0(11, 13) -> 10*
             f_0(11, 12) -> 10*
             f_0(11, 11) -> 10*
             f_0(11, 10) -> 10*
             f_0(10, 16) -> 10*
             f_0(10, 15) -> 16*
             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