YES
Input TRS:
      1: f(g(x,y),f(y,y)) -> f(g(y,x),y)
Number of strict rules: 1
Direct POLO(bPol) ... removes: 1
      f 	w: 2 * x1 + 2 * x2 + 8366
      g 	w: 2 * x1 + 2 * x2 + 1
Number of strict rules: 0