YES
Input TRS:
      1: b(a(a(x1))) -> a(b(c(x1)))
      2: c(a(x1)) -> a(c(x1))
      3: b(c(a(x1))) -> a(b(c(x1)))
      4: c(b(x1)) -> d(x1)
      5: a(d(x1)) -> d(a(x1))
      6: d(x1) -> b(a(x1))
      7: L(a(a(x1))) -> L(a(b(c(x1))))
      8: c(R(x1)) -> c(b(R(x1)))
Number of strict rules: 8
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #c(a(x1)) -> #a(c(x1))
     #2: #c(a(x1)) -> #c(x1)
     #3: #d(x1) -> #b(a(x1))
     #4: #d(x1) -> #a(x1)
     #5: #L(a(a(x1))) -> #L(a(b(c(x1))))
     #6: #L(a(a(x1))) -> #a(b(c(x1)))
     #7: #L(a(a(x1))) -> #b(c(x1))
     #8: #L(a(a(x1))) -> #c(x1)
     #9: #a(d(x1)) -> #d(a(x1))
     #10: #a(d(x1)) -> #a(x1)
     #11: #b(c(a(x1))) -> #a(b(c(x1)))
     #12: #b(c(a(x1))) -> #b(c(x1))
     #13: #b(c(a(x1))) -> #c(x1)
     #14: #b(a(a(x1))) -> #a(b(c(x1)))
     #15: #b(a(a(x1))) -> #b(c(x1))
     #16: #b(a(a(x1))) -> #c(x1)
     #17: #c(R(x1)) -> #c(b(R(x1)))
     #18: #c(R(x1)) -> #b(R(x1))
     #19: #c(b(x1)) -> #d(x1)
Number of SCCs: 2, DPs: 15
  SCC { #5 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      a 	w: max(x1 + 8858, 0)
      d 	w: max(x1 + 8856, 0)
      b 	w: max(x1 - 2, 0)
      #L 	w: max(x1 - 17715, 0)
      c 	w: max(x1 + 8858, 0)
      #d 	w: 0
      R 	w: max(x1 + 20165, 0)
      L 	w: 0
      #c 	w: max(x1 - 1, 0)
      #a 	w: 0
      #b 	w: 0
    USABLE RULES: { 1..6 8 }
    Removed DPs: #5
Number of SCCs: 1, DPs: 14
  SCC { #1..4 #9..17 #19 }
POLO(Sum)... succeeded.
      a 	w: x1 + 5855
      d 	w: x1 + 5855
      b 	w: x1
      #L 	w: 0
      c 	w: x1 + 5855
      #d 	w: x1 + 5855
      R 	w: 29243
      L 	w: 0
      #c 	w: x1 + 11709
      #a 	w: x1 + 5855
      #b 	w: x1
    USABLE RULES: { 1..6 8 }
    Removed DPs: #1 #2 #10 #12 #13 #15 #16 #19
Number of SCCs: 1, DPs: 4
  SCC { #3 #4 #9 #14 }
POLO(Sum)... POLO(max)... succeeded.
      a 	w: x1
      d 	w: x1 + 5857
      b 	w: 5854
      #L 	w: 0
      c 	w: 1
      #d 	w: x1 + 5856
      R 	w: 1
      L 	w: 0
      #c 	w: 0
      #a 	w: x1
      #b 	w: 5855
    USABLE RULES: { 1 3 5 6 }
    Removed DPs: #3 #4 #9 #14
Number of SCCs: 0, DPs: 0