YES
Time: 0.011960
TRS:
 {        f g x -> g f f x,
          f h x -> h g x,
  f'(s x, y, y) -> f'(y, x, s x)}
 DP:
  DP:
   {        f# g x -> f# x,
            f# g x -> f# f x,
    f'#(s x, y, y) -> f'#(y, x, s x)}
  TRS:
  {        f g x -> g f f x,
           f h x -> h g x,
   f'(s x, y, y) -> f'(y, x, s x)}
  EDG:
   {(f'#(s x, y, y) -> f'#(y, x, s x), f'#(s x, y, y) -> f'#(y, x, s x))
    (f# g x -> f# f x, f# g x -> f# x)
    (f# g x -> f# f x, f# g x -> f# f x)
    (f# g x -> f# x, f# g x -> f# x)
    (f# g x -> f# x, f# g x -> f# f x)}
   STATUS:
    arrows: 0.444444
    SCCS (2):
     Scc:
      {f'#(s x, y, y) -> f'#(y, x, s x)}
     Scc:
      {f# g x -> f# x,
       f# g x -> f# f x}
     
     SCC (1):
      Strict:
       {f'#(s x, y, y) -> f'#(y, x, s x)}
      Weak:
      {        f g x -> g f f x,
               f h x -> h g x,
       f'(s x, y, y) -> f'(y, x, s x)}
      POLY:
       Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
       Interpretation:
        [f'](x0, x1, x2) = x0,
        
        [g](x0) = x0 + 1,
        
        [f](x0) = x0 + 1,
        
        [h](x0) = x0 + 1,
        
        [s](x0) = x0 + 1,
        
        [f'#](x0, x1, x2) = x0 + x1
       Strict:
        f'#(s x, y, y) -> f'#(y, x, s x)
        1 + 1x + 1y >= 0 + 1x + 1y
       Weak:
        f'(s x, y, y) -> f'(y, x, s x)
        0 + 0x + 1y >= 1 + 1x + 0y
        f h x -> h g x
        2 + 1x >= 2 + 1x
        f g x -> g f f x
        2 + 1x >= 3 + 1x
      Qed
    SCC (2):
     Strict:
      {f# g x -> f# x,
       f# g x -> f# f x}
     Weak:
     {        f g x -> g f f x,
              f h x -> h g x,
      f'(s x, y, y) -> f'(y, x, s x)}
     POLY:
      Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
      Interpretation:
       [f'](x0, x1, x2) = x0 + x1 + 1,
       
       [g](x0) = x0 + 1,
       
       [f](x0) = x0,
       
       [h](x0) = 0,
       
       [s](x0) = 1,
       
       [f#](x0) = x0
      Strict:
       f# g x -> f# f x
       1 + 1x >= 0 + 1x
       f# g x -> f# x
       1 + 1x >= 0 + 1x
      Weak:
       f'(s x, y, y) -> f'(y, x, s x)
       2 + 0x + 1y >= 2 + 0x + 1y
       f h x -> h g x
       0 + 0x >= 0 + 0x
       f g x -> g f f x
       1 + 1x >= 1 + 1x
     Qed