MAYBE
Input TRS:
      1: a(b(x1)) -> d(x1)
      2: b(a(x1)) -> a(b(x1))
      3: d(c(x1)) -> f(a(b(b(c(x1)))))
      4: d(f(x1)) -> f(a(b(x1)))
      5: a(f(x1)) -> a(x1)
Number of strict rules: 5
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #b(a(x1)) -> #a(b(x1))
     #2: #b(a(x1)) -> #b(x1)
     #3: #a(f(x1)) -> #a(x1)
     #4: #d(c(x1)) -> #a(b(b(c(x1))))
     #5: #d(c(x1)) -> #b(b(c(x1)))
     #6: #d(c(x1)) -> #b(c(x1))
     #7: #a(b(x1)) -> #d(x1)
     #8: #d(f(x1)) -> #a(b(x1))
     #9: #d(f(x1)) -> #b(x1)
Number of SCCs: 1, DPs: 7
  SCC { #1..4 #7..9 }
POLO(Sum)... succeeded.
      a 	w: x1 + 28102
      d 	w: x1 + 28102
      b 	w: x1
      c 	w: 1
      f 	w: x1
      #d 	w: x1 + 1
      #a 	w: x1 + 1
      #b 	w: x1
    USABLE RULES: { 1..5 }
    Removed DPs: #1 #2 #9
Number of SCCs: 1, DPs: 4
  SCC { #3 #4 #7 #8 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      a 	w: 0
      d 	w: 0
      b 	w: max(x1 - 1, 0)
      c 	w: 4
      f 	w: max(x1, 0)
      #d 	w: max(x1 - 2, 0)
      #a 	w: max(x1 - 1, 0)
      #b 	w: 0
    USABLE RULES: { 1..5 }
    Removed DPs: #4
Number of SCCs: 1, DPs: 3
  SCC { #3 #7 #8 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  failed.