YES
Time: 0.000958
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}
 DP:
  DP:
   {    f# f x -> f# c f x,
        f# f x -> f# d f x,
      g# c 1() -> g# d h 0(),
    g# c h 0() -> g# d 1(),
        g# h x -> g# x}
  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}
  EDG:
   {(g# h x -> g# x, g# c 1() -> g# d h 0())
    (g# h x -> g# x, g# c h 0() -> g# d 1())
    (g# h x -> g# x, g# h x -> g# x)}
   SCCS (1):
    Scc:
     {g# h x -> g# x}
    SCC (1):
     Strict:
      {g# h x -> g# x}
     Weak:
     {    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}
     SPSC:
      Simple Projection:
       pi(g#) = 0
      Strict:
       {}
      Qed