YES
Time: 0.003801
TRS:
 {f(g(x, y), f(y, y)) -> f(g(y, x), y)}
 DP:
  DP:
   {f#(g(x, y), f(y, y)) -> f#(g(y, x), y)}
  TRS:
  {f(g(x, y), f(y, y)) -> f(g(y, x), y)}
  UR:
   {}
   EDG:
    {(f#(g(x, y), f(y, y)) -> f#(g(y, x), y), f#(g(x, y), f(y, y)) -> f#(g(y, x), y))}
    STATUS:
     arrows: 0.000000
     SCCS (1):
      Scc:
       {f#(g(x, y), f(y, y)) -> f#(g(y, x), y)}
      
      SCC (1):
       Strict:
        {f#(g(x, y), f(y, y)) -> f#(g(y, x), y)}
       Weak:
       {f(g(x, y), f(y, y)) -> f(g(y, x), y)}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [f](x0, x1) = x0 + x1 + 1,
         
         [g](x0, x1) = 1,
         
         [f#](x0, x1) = x0 + x1
        Strict:
         f#(g(x, y), f(y, y)) -> f#(g(y, x), y)
         2 + 2y + 0x >= 1 + 1y + 0x
        Weak:
         f(g(x, y), f(y, y)) -> f(g(y, x), y)
         3 + 2y + 0x >= 2 + 1y + 0x
       Qed