YES
O(n)
TRS:
 {f(a(), b()) -> f(a(), c()),
  f(c(), d()) -> f(b(), d())}
 DUP: We consider a non-duplicating system.
  Trs:
   {f(a(), b()) -> f(a(), c()),
    f(c(), d()) -> f(b(), d())}
  BOUND:
   Automaton:
    {
         d_1() -> 7,
         d_0() -> 5,
         b_1() -> 6,
         b_0() -> 5,
         c_1() -> 7,
         c_0() -> 5,
         a_1() -> 6,
         a_0() -> 5,
     f_1(6, 7) -> 5,
     f_0(5, 5) -> 5
    }
   Strict:
    {}
   Qed