YES
Input TRS:
      1: a(a(x1)) -> b(b(b(x1)))
      2: a(x1) -> d(c(d(x1)))
      3: b(b(b(x1))) -> a(f(x1))
      4: b(b(x1)) -> c(c(c(x1)))
      5: c(c(x1)) -> d(d(d(x1)))
      6: c(d(d(x1))) -> f(x1)
      7: f(f(x1)) -> f(a(x1))
Number of strict rules: 7
Direct POLO(bPol) ... removes: 4 5
      a 	w: x1 + 39
      d 	w: x1 + 11
      b 	w: x1 + 26
      c 	w: x1 + 17
      f 	w: x1 + 39
Number of strict rules: 5
Direct POLO(bPol) ... failed.
Uncurrying c
      1: a(a(x1)) -> b(b(b(x1)))
      2: a(x1) -> d(c^1_d(x1))
      3: b(b(b(x1))) -> a(f(x1))
      6: c^1_d(d(x1)) -> f(x1)
      7: f(f(x1)) -> f(a(x1))
      8: c(d(_1)) ->= c^1_d(_1)
Number of strict rules: 5
Direct POLO(bPol) ... removes: 8
      a 	w: x1 + 9
      d 	w: x1 + 3
      b 	w: x1 + 6
      c 	w: 2 * x1 + 6
      c^1_d	w: x1 + 6
      f 	w: x1 + 9
Number of strict rules: 5
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #a(x1) -> #c^1_d(x1)
     #2: #c^1_d(d(x1)) -> #f(x1)
     #3: #f(f(x1)) -> #f(a(x1))
     #4: #f(f(x1)) -> #a(x1)
     #5: #b(b(b(x1))) -> #a(f(x1))
     #6: #b(b(b(x1))) -> #f(x1)
     #7: #a(a(x1)) -> #b(b(b(x1)))
     #8: #a(a(x1)) -> #b(b(x1))
     #9: #a(a(x1)) -> #b(x1)
Number of SCCs: 1, DPs: 8
  SCC { #1 #2 #4..9 }
POLO(Sum)... succeeded.
      a 	w: x1 + 78861
      d 	w: x1 + 3
      b 	w: x1 + 52574
      #c^1_d	w: x1
      c 	w: 0
      c^1_d	w: x1 + 78858
      f 	w: x1 + 78861
      #f 	w: x1
      #a 	w: x1 + 78858
      #b 	w: x1 + 52571
    USABLE RULES: { 1..3 6 7 }
    Removed DPs: #1 #2 #4 #6 #8 #9
Number of SCCs: 0, DPs: 0