MAYBE
Input TRS:
      1: a(b(b(x1))) -> P(a(b(x1)))
      2: a(P(x1)) -> P(a(x(x1)))
      3: a(x(x1)) -> x(a(x1))
      4: b(P(x1)) -> b(Q(x1))
      5: Q(x(x1)) -> a(Q(x1))
      6: Q(a(x1)) -> b(b(a(x1)))
Number of strict rules: 6
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #a(P(x1)) -> #a(x(x1))
     #2: #Q(a(x1)) -> #b(b(a(x1)))
     #3: #Q(a(x1)) -> #b(a(x1))
     #4: #Q(x(x1)) -> #a(Q(x1))
     #5: #Q(x(x1)) -> #Q(x1)
     #6: #a(x(x1)) -> #a(x1)
     #7: #a(b(b(x1))) -> #a(b(x1))
     #8: #b(P(x1)) -> #b(Q(x1))
     #9: #b(P(x1)) -> #Q(x1)
Number of SCCs: 3, DPs: 7
  SCC { #7 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  failed.