YES
Time: 0.000521
TRS:
 {  f f x -> f c f x,
    f f x -> f d f x,
    g c x -> x,
  g c 1() -> g d 0(),
  g c 0() -> g d 1(),
    g d x -> x}
 DP:
  DP:
   {  f# f x -> f# c f x,
      f# f x -> f# d f x,
    g# c 1() -> g# d 0(),
    g# c 0() -> g# d 1()}
  TRS:
  {  f f x -> f c f x,
     f f x -> f d f x,
     g c x -> x,
   g c 1() -> g d 0(),
   g c 0() -> g d 1(),
     g d x -> x}
  EDG:
   {}
   SCCS (0):
    
    Qed