YES
O(n)
TRS:
 {
       f(f(x)) -> f(c(f(x))),
       f(f(x)) -> f(d(f(x))),
       g(c(x)) -> x,
     g(c(1())) -> g(d(h(0()))),
  g(c(h(0()))) -> g(d(1())),
       g(d(x)) -> x,
       g(h(x)) -> g(x)
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
         f(f(x)) -> f(c(f(x))),
         f(f(x)) -> f(d(f(x))),
         g(c(x)) -> x,
       g(c(1())) -> g(d(h(0()))),
    g(c(h(0()))) -> g(d(1())),
         g(d(x)) -> x,
         g(h(x)) -> g(x)
   }
  BOUND:
   Automaton:
    {
       0_1() -> 18,
       0_0() -> 7,
     h_1(18) -> 19,
      h_0(7) -> 7,
       1_1() -> 10,
       1_0() -> 7,
     g_2(38) -> 39,
     g_1(34) -> 35,
      g_1(8) -> 9,
      g_0(7) -> 7,
     d_2(30) -> 31,
     d_1(16) -> 17,
     d_1(10) -> 11,
      d_0(7) -> 7,
     c_2(25) -> 26,
     c_1(13) -> 14,
      c_0(7) -> 7,
     f_2(26) -> 27,
     f_2(24) -> 25,
     f_1(14) -> 15,
     f_1(12) -> 13,
      f_0(7) -> 7,
          39 -> 9,
          35 -> 7,
          31 -> 26,
          27 -> 13,
          25 -> 30,
          19 -> 10,
          18 -> 38 | 34,
          17 -> 14,
          15 -> 13 | 7,
          14 -> 24,
          13 -> 16,
          11 -> 8,
          10 -> 9,
           9 -> 7,
           7 -> 12 | 9 | 8
    }
   Strict:
    {}
   Qed