MAYBE
Input TRS:
      1: g(h(x1)) -> g(f(s(x1)))
      2: f(s(s(s(x1)))) -> h(f(s(h(x1))))
      3: f(h(x1)) -> h(f(s(h(x1))))
      4: h(x1) -> x1
      5: f(f(s(s(x1)))) -> s(s(s(f(f(x1)))))
      6: b(a(x1)) -> a(b(x1))
      7: a(a(a(x1))) -> b(a(a(b(x1))))
      8: b(b(b(b(x1)))) -> a(x1)
Number of strict rules: 8
Direct POLO(bPol) ... removes: 8 7
      h 	w: x1
      a 	w: x1 + 4483
      s 	w: x1
      b 	w: x1 + 2241
      f 	w: x1
      g 	w: x1 + 28881
Number of strict rules: 6
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #f(s(s(s(x1)))) -> #h(f(s(h(x1))))
     #2: #f(s(s(s(x1)))) -> #f(s(h(x1)))
     #3: #f(s(s(s(x1)))) -> #h(x1)
     #4: #b(a(x1)) -> #b(x1)
     #5: #f(f(s(s(x1)))) -> #f(f(x1))
     #6: #f(f(s(s(x1)))) -> #f(x1)
     #7: #f(h(x1)) -> #h(f(s(h(x1))))
     #8: #f(h(x1)) -> #f(s(h(x1)))
     #9: #g(h(x1)) -> #g(f(s(x1)))
     #10: #g(h(x1)) -> #f(s(x1))
Number of SCCs: 4, DPs: 5
  SCC { #4 }
POLO(Sum)... succeeded.
      h 	w: 0
      a 	w: x1 + 1
      s 	w: 0
      b 	w: 0
      f 	w: 0
      #h 	w: 0
      #f 	w: 0
      #g 	w: 0
      g 	w: 0
      #b 	w: x1
    USABLE RULES: { }
    Removed DPs: #4
Number of SCCs: 3, DPs: 4
  SCC { #9 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      h 	w: max(x1 + 2, 0)
      a 	w: 0
      s 	w: max(x1 + 2, 0)
      b 	w: 0
      f 	w: max(x1 - 3, 0)
      #h 	w: max(x1 - 1, 0)
      #f 	w: 0
      #g 	w: max(x1 - 1, 0)
      g 	w: max(x1 - 1, 0)
      #b 	w: max(x1 - 1, 0)
    USABLE RULES: { 2 4 }
    Removed DPs: #9
Number of SCCs: 2, DPs: 3
  SCC { #2 }
POLO(Sum)... succeeded.
      h 	w: x1 + 1
      a 	w: 1
      s 	w: x1 + 11798
      b 	w: 0
      f 	w: 0
      #h 	w: 0
      #f 	w: x1
      #g 	w: 0
      g 	w: 0
      #b 	w: 0
    USABLE RULES: { 4 }
    Removed DPs: #2
Number of SCCs: 1, DPs: 2
  SCC { #5 #6 }
POLO(Sum)... succeeded.
      h 	w: x1
      a 	w: 1
      s 	w: x1
      b 	w: 0
      f 	w: x1 + 1424
      #h 	w: 0
      #f 	w: x1
      #g 	w: 0
      g 	w: 0
      #b 	w: 0
    USABLE RULES: { 2..5 }
    Removed DPs: #6
Number of SCCs: 1, DPs: 1
  SCC { #5 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  failed.