YES
Input TRS:
      1: a(a(x1)) -> b(b(b(x1)))
      2: a(x1) -> c(d(x1))
      3: b(b(x1)) -> c(c(c(x1)))
      4: c(c(x1)) -> d(d(d(x1)))
      5: e(d(x1)) -> a(b(c(d(e(x1)))))
      6: b(x1) -> d(d(x1))
      7: e(c(x1)) -> b(a(a(e(x1))))
      8: c(d(d(x1))) -> a(x1)
Number of strict rules: 8
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #a(x1) -> #c(d(x1))
     #2: #e(c(x1)) -> #b(a(a(e(x1))))
     #3: #e(c(x1)) -> #a(a(e(x1)))
     #4: #e(c(x1)) -> #a(e(x1))
     #5: #e(c(x1)) -> #e(x1)
     #6: #e(d(x1)) -> #a(b(c(d(e(x1)))))
     #7: #e(d(x1)) -> #b(c(d(e(x1))))
     #8: #e(d(x1)) -> #c(d(e(x1)))
     #9: #e(d(x1)) -> #e(x1)
     #10: #b(b(x1)) -> #c(c(c(x1)))
     #11: #b(b(x1)) -> #c(c(x1))
     #12: #b(b(x1)) -> #c(x1)
     #13: #a(a(x1)) -> #b(b(b(x1)))
     #14: #a(a(x1)) -> #b(b(x1))
     #15: #a(a(x1)) -> #b(x1)
     #16: #c(d(d(x1))) -> #a(x1)
Number of SCCs: 2, DPs: 10
  SCC { #5 #9 }
POLO(Sum)... succeeded.
      a 	w: 0
      d 	w: x1 + 1
      b 	w: 0
      #e 	w: x1
      c 	w: x1 + 1
      #c 	w: 0
      e 	w: 0
      #a 	w: 0
      #b 	w: 0
    USABLE RULES: { }
    Removed DPs: #5 #9
Number of SCCs: 1, DPs: 8
  SCC { #1 #10..16 }
POLO(Sum)... succeeded.
      a 	w: x1 + 42
      d 	w: x1 + 12
      b 	w: x1 + 27
      #e 	w: 0
      c 	w: x1 + 18
      #c 	w: x1
      e 	w: 0
      #a 	w: x1 + 23
      #b 	w: x1 + 10
    USABLE RULES: { 1..4 6 8 }
    Removed DPs: #1 #10..16
Number of SCCs: 0, DPs: 0