YES
Input TRS:
      1: a(a(x1)) -> b(b(b(x1)))
      2: a(x1) -> d(c(d(x1)))
      3: b(b(x1)) -> c(c(c(x1)))
      4: c(c(x1)) -> d(d(d(x1)))
      5: c(d(d(x1))) -> a(x1)
Number of strict rules: 5
Direct POLO(bPol) ... removes: 1 3
      a 	w: x1 + 81977
      d 	w: x1 + 23422
      b 	w: x1 + 52700
      c 	w: x1 + 35133
Number of strict rules: 3
Direct POLO(bPol) ... removes: 4
      a 	w: x1 + 18
      d 	w: x1 + 5
      b 	w: x1 + 12
      c 	w: x1 + 8
Number of strict rules: 2
Direct POLO(bPol) ... failed.
Uncurrying c
      2: a(x1) -> d(c^1_d(x1))
      5: c^1_d(d(x1)) -> a(x1)
      6: c(d(_1)) ->= c^1_d(_1)
Number of strict rules: 2
Direct POLO(bPol) ... removes: 6
      a 	w: x1 + 4
      d 	w: x1 + 3
      b 	w: x1
      c 	w: x1
      c^1_d	w: x1 + 1
Number of strict rules: 2
Direct POLO(bPol) ... removes: 5 2
      a 	w: 2 * x1 + 4
      d 	w: x1 + 2
      b 	w: x1
      c 	w: 2 * x1
      c^1_d	w: 2 * x1 + 1
Number of strict rules: 0