YES
Input TRS:
      1: a(d(x1)) -> d(b(x1))
      2: a(x1) -> b(b(b(x1)))
      3: b(d(b(x1))) -> a(c(x1))
      4: c(x1) -> d(x1)
Number of strict rules: 4
Direct POLO(bPol) ... removes: 1
      a 	w: x1 + 25098
      d 	w: 2 * x1 + 3
      b 	w: x1 + 8366
      c 	w: 2 * x1 + 3
Number of strict rules: 3
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #a(x1) -> #b(b(b(x1)))
     #2: #a(x1) -> #b(b(x1))
     #3: #a(x1) -> #b(x1)
     #4: #b(d(b(x1))) -> #a(c(x1))
     #5: #b(d(b(x1))) -> #c(x1)
Number of SCCs: 1, DPs: 2
  SCC { #3 #4 }
POLO(Sum)... succeeded.
      a 	w: 0
      d 	w: x1 + 1
      b 	w: x1 + 2
      c 	w: x1 + 1
      #c 	w: 0
      #a 	w: x1 + 1
      #b 	w: x1
    USABLE RULES: { 4 }
    Removed DPs: #3 #4
Number of SCCs: 0, DPs: 0