MAYBE
Input TRS:
      1: a(b(x1)) -> b(d(x1))
      2: a(c(x1)) -> d(d(d(x1)))
      3: b(d(x1)) -> a(c(b(x1)))
      4: c(f(x1)) -> d(d(c(x1)))
      5: d(d(x1)) -> f(x1)
      6: f(f(x1)) -> a(x1)
Number of strict rules: 6
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #a(c(x1)) -> #d(d(d(x1)))
     #2: #a(c(x1)) -> #d(d(x1))
     #3: #a(c(x1)) -> #d(x1)
     #4: #f(f(x1)) -> #a(x1)
     #5: #d(d(x1)) -> #f(x1)
     #6: #b(d(x1)) -> #a(c(b(x1)))
     #7: #b(d(x1)) -> #c(b(x1))
     #8: #b(d(x1)) -> #b(x1)
     #9: #a(b(x1)) -> #b(d(x1))
     #10: #a(b(x1)) -> #d(x1)
     #11: #c(f(x1)) -> #d(d(c(x1)))
     #12: #c(f(x1)) -> #d(c(x1))
     #13: #c(f(x1)) -> #c(x1)
Number of SCCs: 1, DPs: 13
  SCC { #1..13 }
POLO(Sum)... succeeded.
      a 	w: x1
      d 	w: x1
      b 	w: x1 + 20538
      c 	w: x1
      f 	w: x1
      #d 	w: x1
      #f 	w: x1
      #c 	w: x1
      #a 	w: x1
      #b 	w: x1 + 20538
    USABLE RULES: { 1..6 }
    Removed DPs: #10
Number of SCCs: 1, DPs: 12
  SCC { #1..9 #11..13 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  failed.