YES
Input TRS:
      1: a(a(x1)) -> b(c(x1))
      2: b(b(x1)) -> c(d(x1))
      3: b(x1) -> a(x1)
      4: c(c(x1)) -> d(f(x1))
      5: d(d(x1)) -> f(f(f(x1)))
      6: d(x1) -> b(x1)
      7: f(f(x1)) -> g(a(x1))
      8: g(g(x1)) -> a(x1)
Number of strict rules: 8
Direct POLO(bPol) ... removes: 4 8 1 3 5 7 6 2
      a 	w: x1 + 155
      d 	w: x1 + 176
      b 	w: x1 + 162
      c 	w: x1 + 147
      f 	w: x1 + 117
      g 	w: x1 + 78
Number of strict rules: 0