YES
Trs:
 {f g f -> f g,
    f f -> f g f g f}
 Comment:
  We consider a non-duplicating trs.
  BOUND:
   Automaton:
    {g_3(q89) -> q90,
     g_3(q67) -> q68,
     g_3(q44) -> q45,
     g_3(q39) -> q40,
     g_2(q85) -> q86,
     g_2(q81) -> q82,
     g_2(q65) -> q66,
     g_2(q61) -> q62,
     g_2(q57) -> q58,
     g_2(q37) -> q38,
     g_2(q22) -> q23,
     g_2(q19) -> q20,
     g_1(q52) -> q53,
     g_1(q33) -> q34,
     g_1(q15) -> q16,
      g_1(q3) -> q4,
      g_0(q2) -> q2,
     f_3(q40) -> q41,
     f_2(q75) -> q76,
     f_2(q26) -> q27,
     f_2(q20) -> q21,
     f_1(q71) -> q72,
     f_1(q46) -> q47,
      f_1(q9) -> q10,
      f_1(q4) -> q5,
      f_0(q2) -> q2,
          q90 -> q40,
          q86 -> q20,
          q82 -> q20,
          q76 -> q65,
          q75 -> q89 | q85,
          q72 -> q52,
          q71 -> q81,
          q68 -> q40,
          q66 -> q20,
          q62 -> q20,
          q58 -> q20,
          q53 -> q4,
          q47 -> q33,
          q46 -> q65,
          q45 -> q40,
          q41 -> q21,
          q40 -> q75 | q71 | q67 | q61 | q52,
          q38 -> q20,
          q34 -> q4,
          q27 -> q22,
          q26 -> q57 | q44,
          q23 -> q20,
          q21 -> q5,
          q20 -> q46 | q39 | q37 | q33,
          q16 -> q4,
          q10 -> q3,
           q9 -> q22,
           q5 -> q47 | q27 | q21 | q10 | q2,
           q4 -> q26 | q19 | q15,
           q2 -> q9 | q3}
   Strict:
   {}
   Qed