YES
Time: 0.000698
TRS:
 {g g x -> f x,
  f f x -> g f x}
 DP:
  DP:
   {g# g x -> f# x,
    f# f x -> g# f x}
  TRS:
  {g g x -> f x,
   f f x -> g f x}
  EDG:
   {(g# g x -> f# x, f# f x -> g# f x)
    (f# f x -> g# f x, g# g x -> f# x)}
   SCCS (1):
    Scc:
     {g# g x -> f# x,
      f# f x -> g# f x}
    SCC (2):
     Strict:
      {g# g x -> f# x,
       f# f x -> g# f x}
     Weak:
     {g g x -> f x,
      f f x -> g f x}
     SPSC:
      Simple Projection:
       pi(f#) = 0, pi(g#) = 0
      Strict:
       {f# f x -> g# f x}
      EDG:
       {}
       SCCS (0):
        
        Qed