YES
Input TRS:
      1: 1(1(x1)) -> 4(3(x1))
      2: 1(2(x1)) -> 2(1(x1))
      3: 2(2(x1)) -> 1(1(1(x1)))
      4: 3(3(x1)) -> 5(6(x1))
      5: 3(4(x1)) -> 1(1(x1))
      6: 4(4(x1)) -> 3(x1)
      7: 5(5(x1)) -> 6(2(x1))
      8: 5(6(x1)) -> 1(2(x1))
      9: 6(6(x1)) -> 2(1(x1))
Number of strict rules: 9
Direct POLO(bPol) ... removes: 4 8 3 7 9 6
      1 	w: x1 + 414581
      4 	w: x1 + 285023
      5 	w: x1 + 570050
      3 	w: x1 + 544139
      2 	w: x1 + 621872
      6 	w: x1 + 518227
Number of strict rules: 3
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #1(2(x1)) -> #1(x1)
     #2: #3(4(x1)) -> #1(1(x1))
     #3: #3(4(x1)) -> #1(x1)
     #4: #1(1(x1)) -> #3(x1)
Number of SCCs: 1, DPs: 4
  SCC { #1..4 }
POLO(Sum)... succeeded.
      1 	w: x1 + 3
      4 	w: x1 + 4
      5 	w: 0
      3 	w: x1 + 2
      #3 	w: x1 + 1
      2 	w: x1 + 1
      6 	w: 0
      #1 	w: x1
    USABLE RULES: { 1 2 5 }
    Removed DPs: #1..4
Number of SCCs: 0, DPs: 0