YES
Input TRS:
      1: a(a(x1)) -> b(b(b(x1)))
      2: b(b(x1)) -> c(c(c(x1)))
      3: c(c(x1)) -> d(d(d(x1)))
      4: b(x1) -> d(d(x1))
      5: c(d(d(x1))) -> a(x1)
Number of strict rules: 5
Direct POLO(bPol) ... removes: 4 1 3 5 2
      a 	w: x1 + 80
      d 	w: x1 + 23
      b 	w: x1 + 53
      c 	w: x1 + 35
Number of strict rules: 0