YES
Input TRS:
      1: a(a(x1)) -> b(c(c(c(x1))))
      2: b(c(x1)) -> d(d(d(d(x1))))
      3: a(x1) -> d(c(d(x1)))
      4: b(b(x1)) -> c(c(c(x1)))
      5: c(c(x1)) -> d(d(d(x1)))
      6: c(d(d(x1))) -> a(x1)
Number of strict rules: 6
Direct POLO(bPol) ... removes: 4 5
      a 	w: x1 + 20581
      d 	w: x1 + 5717
      b 	w: x1 + 13721
      c 	w: x1 + 9147
Number of strict rules: 4
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #c(d(d(x1))) -> #a(x1)
     #2: #a(x1) -> #c(d(x1))
     #3: #a(a(x1)) -> #b(c(c(c(x1))))
     #4: #a(a(x1)) -> #c(c(c(x1)))
     #5: #a(a(x1)) -> #c(c(x1))
     #6: #a(a(x1)) -> #c(x1)
Number of SCCs: 1, DPs: 5
  SCC { #1 #2 #4..6 }
POLO(Sum)... succeeded.
      a 	w: x1 + 9
      d 	w: x1 + 2
      b 	w: x1 + 3
      c 	w: x1 + 5
      #c 	w: x1
      #a 	w: x1 + 3
      #b 	w: 0
    USABLE RULES: { 1..3 6 }
    Removed DPs: #1 #2 #4..6
Number of SCCs: 0, DPs: 0