YES
Input TRS:
      1: a(a(x1)) -> b(c(x1))
      2: b(b(x1)) -> c(d(x1))
      3: c(c(x1)) -> d(d(d(x1)))
      4: d(d(d(x1))) -> a(c(x1))
Number of strict rules: 4
Direct POLO(bPol) ... removes: 4 1 3 2
      a 	w: x1 + 30
      d 	w: x1 + 21
      b 	w: x1 + 27
      c 	w: x1 + 32
Number of strict rules: 0