YES
Input TRS:
      1: b(c(a(x1))) -> a(b(x1))
      2: b(b(b(x1))) -> c(a(c(x1)))
      3: c(d(x1)) -> d(c(x1))
      4: c(d(b(x1))) -> d(c(c(x1)))
      5: d(c(x1)) -> b(b(b(x1)))
      6: c(b(x1)) -> d(a(x1))
      7: d(b(c(x1))) -> a(a(x1))
      8: d(a(x1)) -> b(x1)
Number of strict rules: 8
Direct POLO(bPol) ... removes: 8 1 7 2
      a 	w: x1
      d 	w: x1 + 41954
      b 	w: x1 + 20977
      c 	w: x1 + 20977
Number of strict rules: 4
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #c(b(x1)) -> #d(a(x1))
     #2: #c(d(x1)) -> #d(c(x1))
     #3: #c(d(x1)) -> #c(x1)
     #4: #c(d(b(x1))) -> #d(c(c(x1)))
     #5: #c(d(b(x1))) -> #c(c(x1))
     #6: #c(d(b(x1))) -> #c(x1)
Number of SCCs: 1, DPs: 3
  SCC { #3 #5 #6 }
POLO(Sum)... succeeded.
      a 	w: 0
      d 	w: x1 + 42478
      b 	w: x1 + 21239
      c 	w: x1 + 21239
      #d 	w: 0
      #c 	w: x1
    USABLE RULES: { 3..6 }
    Removed DPs: #3 #5 #6
Number of SCCs: 0, DPs: 0