YES
O(n)
TRS:
 {
    f(c(X)) -> X,
  f(c(a())) -> f(d(b())),
  f(c(b())) -> f(d(a())),
     f(a()) -> f(c(a())),
     f(a()) -> f(d(a())),
    f(d(X)) -> X,
    e(g(X)) -> e(X)
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
      f(c(X)) -> X,
    f(c(a())) -> f(d(b())),
    f(c(b())) -> f(d(a())),
       f(a()) -> f(c(a())),
       f(a()) -> f(d(a())),
      f(d(X)) -> X,
      e(g(X)) -> e(X)
   }
  BOUND:
   Automaton:
    {
      g_0(8) -> 8,
      g_0(7) -> 8,
      e_1(9) -> 10,
      e_0(8) -> 7,
      e_0(7) -> 7,
       b_2() -> 19,
       b_1() -> 16,
       b_0() -> 7,
     d_2(19) -> 20,
     d_1(14) -> 15,
      d_0(8) -> 7,
      d_0(7) -> 7,
       a_1() -> 11,
       a_0() -> 7,
     c_1(11) -> 12,
      c_0(8) -> 7,
      c_0(7) -> 7,
     f_2(20) -> 21,
     f_1(12) -> 13,
      f_0(8) -> 7,
      f_0(7) -> 7,
          21 -> 13,
          19 -> 21,
          16 -> 14,
          15 -> 12,
          14 -> 13,
          13 -> 7,
          11 -> 14 | 13,
          10 -> 7,
           8 -> 7,
           7 -> 9
    }
   Strict:
    {}
   Qed