YES
Time: 0.008288
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)}
   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:
       
     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:
      
    Qed