YES
Input TRS:
      1: a(b(x1)) -> b(r(x1))
      2: r(a(x1)) -> d(r(x1))
      3: r(x1) -> d(x1)
      4: d(a(x1)) -> a(a(d(x1)))
      5: d(x1) -> a(x1)
Number of strict rules: 5
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #r(a(x1)) -> #d(r(x1))
     #2: #r(a(x1)) -> #r(x1)
     #3: #d(x1) -> #a(x1)
     #4: #r(x1) -> #d(x1)
     #5: #a(b(x1)) -> #r(x1)
     #6: #d(a(x1)) -> #a(a(d(x1)))
     #7: #d(a(x1)) -> #a(d(x1))
     #8: #d(a(x1)) -> #d(x1)
Number of SCCs: 1, DPs: 8
  SCC { #1..8 }
POLO(Sum)... succeeded.
      a 	w: x1
      d 	w: x1
      b 	w: x1 + 3
      r 	w: x1
      #d 	w: x1 + 1
      #r 	w: x1 + 2
      #a 	w: x1
    USABLE RULES: { 1..5 }
    Removed DPs: #1 #3..7
Number of SCCs: 2, DPs: 2
  SCC { #8 }
POLO(Sum)... POLO(max)... succeeded.
      a 	w: x1 + 1
      d 	w: 0
      b 	w: 0
      r 	w: 0
      #d 	w: x1
      #r 	w: 0
      #a 	w: 0
    USABLE RULES: { }
    Removed DPs: #8
Number of SCCs: 1, DPs: 1
  SCC { #2 }
POLO(Sum)... succeeded.
      a 	w: x1 + 8367
      d 	w: 8366
      b 	w: x1 + 3
      r 	w: 0
      #d 	w: 1
      #r 	w: x1 + 2
      #a 	w: 0
    USABLE RULES: { }
    Removed DPs: #2
Number of SCCs: 0, DPs: 0