YES
Time: 0.018707
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}
  UR:
   {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)}
    STATUS:
     arrows: 0.500000
     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}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [g](x0) = x0 + 1,
         
         [f](x0) = x0 + 1,
         
         [g#](x0) = x0 + 1,
         
         [f#](x0) = x0 + 1
        Strict:
         f# f x -> g# f x
         2 + 1x >= 2 + 1x
         g# g x -> f# x
         2 + 1x >= 1 + 1x
        Weak:
         f f x -> g f x
         2 + 1x >= 2 + 1x
         g g x -> f x
         2 + 1x >= 1 + 1x
       SCCS (0):