YES
Input TRS:
      1: f(f(x1)) -> b(b(b(x1)))
      2: a(f(x1)) -> f(a(a(x1)))
      3: b(b(x1)) -> c(c(a(c(x1))))
      4: d(b(x1)) -> d(a(b(x1)))
      5: c(c(x1)) -> d(d(d(x1)))
      6: b(d(x1)) -> d(b(x1))
      7: c(d(d(x1))) -> f(x1)
Number of strict rules: 7
Direct POLO(bPol) ... removes: 1 3 5 7
      a 	w: x1
      d 	w: x1 + 2271
      b 	w: x1 + 5111
      c 	w: x1 + 3407
      f 	w: x1 + 7667
Number of strict rules: 3
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #a(f(x1)) -> #a(a(x1))
     #2: #a(f(x1)) -> #a(x1)
     #3: #b(d(x1)) -> #d(b(x1))
     #4: #b(d(x1)) -> #b(x1)
     #5: #d(b(x1)) -> #d(a(b(x1)))
     #6: #d(b(x1)) -> #a(b(x1))
Number of SCCs: 2, DPs: 3
  SCC { #4 }
POLO(Sum)... succeeded.
      a 	w: 0
      d 	w: x1 + 1
      b 	w: 0
      c 	w: 0
      f 	w: 0
      #d 	w: 0
      #a 	w: 0
      #b 	w: x1
    USABLE RULES: { }
    Removed DPs: #4
Number of SCCs: 1, DPs: 2
  SCC { #1 #2 }
POLO(Sum)... succeeded.
      a 	w: x1
      d 	w: 1
      b 	w: 0
      c 	w: 0
      f 	w: x1 + 1
      #d 	w: 0
      #a 	w: x1
      #b 	w: 0
    USABLE RULES: { 2 }
    Removed DPs: #1 #2
Number of SCCs: 0, DPs: 0