YES
TRS:
 {f(a(), b()) -> f(a(), c()),
  f(c(), d()) -> f(b(), d())}
 DP:
  Strict:
   {f#(a(), b()) -> f#(a(), c()),
    f#(c(), d()) -> f#(b(), d())}
  Weak:
  {f(a(), b()) -> f(a(), c()),
   f(c(), d()) -> f(b(), d())}
  EDG:
   {}
   SCCS:
    
    Qed