YES
O(n)
TRS:
 {
  f(g(i(a(), b(), b'()), c()), d()) ->
  if(e(), f(.(b(), c()), d'()), f(.(b'(), c()), d'())),
        f(g(h(a(), b()), c()), d()) ->
  if(e(), f(.(b(), g(h(a(), b()), c())), d()), f(c(), d'()))
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
    f(g(i(a(), b(), b'()), c()), d()) ->
    if(e(), f(.(b(), c()), d'()), f(.(b'(), c()), d'())),
          f(g(h(a(), b()), c()), d()) ->
    if(e(), f(.(b(), g(h(a(), b()), c())), d()), f(c(), d'()))
   }
  BOUND:
   Automaton:
    {
          h_1(22, 12) -> 23,
            h_0(1, 1) -> 0,
            h_0(1, 0) -> 0,
            h_0(0, 1) -> 0,
            h_0(0, 0) -> 0,
                d_1() -> 26,
                d_0() -> 0,
                a_1() -> 22,
                a_0() -> 0,
         i_0(1, 1, 1) -> 1,
         i_0(1, 1, 0) -> 1,
         i_0(1, 0, 1) -> 1,
         i_0(1, 0, 0) -> 1,
         i_0(0, 1, 1) -> 1,
         i_0(0, 1, 0) -> 1,
         i_0(0, 0, 1) -> 1,
         i_0(0, 0, 0) -> 1,
          g_1(23, 13) -> 24,
            g_0(1, 1) -> 0,
            g_0(1, 0) -> 0,
            g_0(0, 1) -> 0,
            g_0(0, 0) -> 0,
               b'_1() -> 17,
               b'_0() -> 0,
               d'_1() -> 15,
               d'_0() -> 0,
                c_1() -> 13,
                c_0() -> 0,
                b_1() -> 12,
                b_0() -> 0,
          ._1(17, 13) -> 18,
          ._1(12, 24) -> 25,
          ._1(12, 13) -> 14,
            ._0(1, 1) -> 0,
            ._0(1, 0) -> 0,
            ._0(0, 1) -> 0,
            ._0(0, 0) -> 0,
          f_1(25, 26) -> 27,
          f_1(18, 15) -> 19,
          f_1(14, 15) -> 16,
          f_1(13, 15) -> 28,
            f_0(1, 1) -> 0,
            f_0(1, 0) -> 0,
            f_0(0, 1) -> 0,
            f_0(0, 0) -> 0,
                e_1() -> 11,
                e_0() -> 0,
     if_1(11, 27, 28) -> 0,
     if_1(11, 16, 19) -> 0,
        if_0(1, 1, 1) -> 0,
        if_0(1, 1, 0) -> 0,
        if_0(1, 0, 1) -> 0,
        if_0(1, 0, 0) -> 0,
        if_0(0, 1, 1) -> 0,
        if_0(0, 1, 0) -> 0,
        if_0(0, 0, 1) -> 0,
        if_0(0, 0, 0) -> 0
    }
   Strict:
    {}
   Qed