YES(?,O(n^1))
TRS:
 {  f f X -> f a b f X,
  f a g X -> b X,
      b X -> a X}
 DUP: We consider a non-duplicating system.
  Trs:
   {  f f X -> f a b f X,
    f a g X -> b X,
        b X -> a X}
  BOUND:
   Bound: match(-raise)-bounded by 4
   Automaton:
    {
      b_3(44) -> 45*
      b_2(37) -> 38*
      b_2(25) -> 26*
      b_1(12) -> 13*
       b_1(9) -> 10*
       b_1(7) -> 8*
       b_0(2) -> 1*
       b_0(1) -> 1*
      a_4(48) -> 49*
      a_3(45) -> 46*
      a_3(39) -> 40*
      a_3(29) -> 30*
      a_2(26) -> 27*
      a_2(22) -> 23*
      a_2(20) -> 21*
      a_2(18) -> 19*
      a_1(13) -> 14*
       a_1(5) -> 6*
       a_1(3) -> 4*
       a_0(2) -> 1*
       a_0(1) -> 1*
       g_0(2) -> 2*
       g_0(1) -> 2*
      f_3(46) -> 47*
      f_3(43) -> 44*
      f_2(41) -> 42*
      f_2(35) -> 36*
      f_2(33) -> 34*
      f_2(27) -> 28*
      f_2(24) -> 25*
      f_1(31) -> 32*
      f_1(16) -> 17*
      f_1(14) -> 15*
      f_1(11) -> 12*
     f_0(2) -> 1*
     f_0(1) -> 1*
         49 -> 45*
         47 -> 34*
         44 -> 48*
         42 -> 37*
         40 -> 38*
         38 -> 26*
         37 -> 39*
         36 -> 25*
         34 -> 25*
         32 -> 12*
         31 -> 41*
         30 -> 26*
         28 -> 37 | 34 | 12
         27 -> 43 | 31
         25 -> 29*
         23 -> 13*
         21 -> 10*
         19 -> 8*
         17 -> 12*
         16 -> 35*
         15 -> 12 | 1
         14 -> 24*
         12 -> 34 | 22 | 1
         11 -> 33*
         10 -> 34 | 12 | 1
          9 -> 20*
          8 -> 34 | 12 | 1
          7 -> 18*
          6 -> 1*
          4 -> 1*
          2 -> 16 | 9 | 5
          1 -> 11 | 7 | 3
    }
   Strict:
    {}
   Qed