YES
Input TRS:
      1: g(0(),f(x,x)) -> x
      2: g(x,s(y)) -> g(f(x,y),0())
      3: g(s(x),y) -> g(f(x,y),0())
      4: g(f(x,y),0()) -> f(g(x,0()),g(y,0()))
Number of strict rules: 4
Direct POLO(bPol) ... removes: 1 3 2
      s 	w: 2 * x1 + 30614
      f 	w: x1 + x2 + 1
      0 	w: 0
      g 	w: x1 + x2
Number of strict rules: 1
Direct POLO(bPol) ... removes: 4
      s 	w: 2 * x1 + 15922
      f 	w: x1 + x2 + 15922
      0 	w: 0
      g 	w: 2 * x1 + 2 * x2
Number of strict rules: 0