YES
Time: 0.003511
TRS:
 {g(h x, y) -> h g(x, y),
  g(h x, y) -> h f(x, y),
    f(x, y) -> g(x, y)}
 DP:
  DP:
   {g#(h x, y) -> g#(x, y),
    g#(h x, y) -> f#(x, y),
      f#(x, y) -> g#(x, y)}
  TRS:
  {g(h x, y) -> h g(x, y),
   g(h x, y) -> h f(x, y),
     f(x, y) -> g(x, y)}
  EDG:
   {(g#(h x, y) -> f#(x, y), f#(x, y) -> g#(x, y))
    (f#(x, y) -> g#(x, y), g#(h x, y) -> g#(x, y))
    (f#(x, y) -> g#(x, y), g#(h x, y) -> f#(x, y))
    (g#(h x, y) -> g#(x, y), g#(h x, y) -> g#(x, y))
    (g#(h x, y) -> g#(x, y), g#(h x, y) -> f#(x, y))}
   STATUS:
    arrows: 0.444444
    SCCS (1):
     Scc:
      {g#(h x, y) -> g#(x, y),
       g#(h x, y) -> f#(x, y),
         f#(x, y) -> g#(x, y)}
     
     SCC (3):
      Strict:
       {g#(h x, y) -> g#(x, y),
        g#(h x, y) -> f#(x, y),
          f#(x, y) -> g#(x, y)}
      Weak:
      {g(h x, y) -> h g(x, y),
       g(h x, y) -> h f(x, y),
         f(x, y) -> g(x, y)}
      POLY:
       Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
       Interpretation:
        [g](x0, x1) = 0,
        
        [f](x0, x1) = 0,
        
        [h](x0) = x0 + 1,
        
        [g#](x0, x1) = x0 + 1,
        
        [f#](x0, x1) = x0 + 1
       Strict:
        f#(x, y) -> g#(x, y)
        1 + 1x + 0y >= 1 + 1x + 0y
        g#(h x, y) -> f#(x, y)
        2 + 1x + 0y >= 1 + 1x + 0y
        g#(h x, y) -> g#(x, y)
        2 + 1x + 0y >= 1 + 1x + 0y
       Weak:
        f(x, y) -> g(x, y)
        0 + 0x + 0y >= 0 + 0x + 0y
        g(h x, y) -> h f(x, y)
        0 + 0x + 0y >= 1 + 0x + 0y
        g(h x, y) -> h g(x, y)
        0 + 0x + 0y >= 1 + 0x + 0y
      SCCS (0):