MAYBE
Input TRS:
      1: a(a(a(b(b(x1))))) -> b(b(b(x1)))
      2: b(a(a(a(b(x1))))) -> a(a(a(b(a(a(a(x1)))))))
      3: a(a(a(x1))) -> a(a(x1))
      4: b(b(x1)) -> a(b(a(x1)))
Number of strict rules: 4
Direct POLO(bPol) ... removes: 4 3
      a 	w: x1 + 8366
      b 	w: x1 + 25098
Number of strict rules: 2
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #b(a(a(a(b(x1))))) -> #a(a(a(b(a(a(a(x1)))))))
     #2: #b(a(a(a(b(x1))))) -> #a(a(b(a(a(a(x1))))))
     #3: #b(a(a(a(b(x1))))) -> #a(b(a(a(a(x1)))))
     #4: #b(a(a(a(b(x1))))) -> #b(a(a(a(x1))))
     #5: #b(a(a(a(b(x1))))) -> #a(a(a(x1)))
     #6: #b(a(a(a(b(x1))))) -> #a(a(x1))
     #7: #b(a(a(a(b(x1))))) -> #a(x1)
     #8: #a(a(a(b(b(x1))))) -> #b(b(b(x1)))
Number of SCCs: 1, DPs: 8
  SCC { #1..8 }
POLO(Sum)... succeeded.
      a 	w: x1 + 11798
      b 	w: x1 + 35394
      #a 	w: x1 + 2
      #b 	w: x1 + 23598
    USABLE RULES: { 1 2 }
    Removed DPs: #2..7
Number of SCCs: 1, DPs: 2
  SCC { #1 #8 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  failed.