YES
Input TRS:
      1: P(x1) -> Q(Q(p(x1)))
      2: p(p(x1)) -> q(q(x1))
      3: p(Q(Q(x1))) -> Q(Q(p(x1)))
      4: Q(p(q(x1))) -> q(p(Q(x1)))
      5: q(q(p(x1))) -> p(q(q(x1)))
      6: q(Q(x1)) -> x1
      7: Q(q(x1)) -> x1
      8: p(P(x1)) -> x1
      9: P(p(x1)) -> x1
Number of strict rules: 9
Direct POLO(bPol) ... removes: 8 1 7 9 6 2
      Q 	w: x1 + 1
      q 	w: x1 + 24338
      p 	w: x1 + 24339
      P 	w: x1 + 24342
Number of strict rules: 3
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #q(q(p(x1))) -> #p(q(q(x1)))
     #2: #q(q(p(x1))) -> #q(q(x1))
     #3: #q(q(p(x1))) -> #q(x1)
     #4: #p(Q(Q(x1))) -> #Q(Q(p(x1)))
     #5: #p(Q(Q(x1))) -> #Q(p(x1))
     #6: #p(Q(Q(x1))) -> #p(x1)
     #7: #Q(p(q(x1))) -> #q(p(Q(x1)))
     #8: #Q(p(q(x1))) -> #p(Q(x1))
     #9: #Q(p(q(x1))) -> #Q(x1)
Number of SCCs: 1, DPs: 9
  SCC { #1..9 }
POLO(Sum)... succeeded.
      Q 	w: x1 + 11798
      q 	w: x1 + 8366
      #Q 	w: x1 + 3432
      #p 	w: x1 + 490
      p 	w: x1 + 8856
      P 	w: 0
      #q 	w: x1
    USABLE RULES: { 3..5 }
    Removed DPs: #2 #3 #5 #6 #8 #9
Number of SCCs: 1, DPs: 3
  SCC { #1 #4 #7 }
POLO(Sum)... succeeded.
      Q 	w: x1 + 408
      q 	w: 21238
      #Q 	w: x1 + 3432
      #p 	w: x1 + 3025
      p 	w: x1
      P 	w: 0
      #q 	w: 24669
    USABLE RULES: { 3..5 }
    Removed DPs: #1 #4 #7
Number of SCCs: 0, DPs: 0