MAYBE
Input TRS:
      1: g(x) -> h(x,x)
      2: s(x) -> h(x,0())
      3: s(x) -> h(0(),x)
      4: f(g(x)) -> g(g(f(x)))
      5: g(s(x)) -> s(s(g(x)))
      6: h(f(x),g(x)) -> f(s(x))
      7: s(0()) -> f(0())
      8: s(s(0())) -> f(s(0()))
      9: f(s(0())) -> 0()
      10: s(s(s(s(s(s(s(0()))))))) -> f(s(s(0())))
      11: f(s(s(0()))) -> s(s(s(s(s(0())))))
      12: f(s(s(x))) -> h(f(x),g(h(x,x)))
Number of strict rules: 12
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #s(x) -> #h(x,0())
     #2: #h(f(x),g(x)) -> #f(s(x))
     #3: #h(f(x),g(x)) -> #s(x)
     #4: #f(s(s(0()))) -> #s(s(s(s(s(0())))))
     #5: #f(s(s(0()))) -> #s(s(s(s(0()))))
     #6: #f(s(s(0()))) -> #s(s(s(0())))
     #7: #f(s(s(x))) -> #h(f(x),g(h(x,x)))
     #8: #f(s(s(x))) -> #f(x)
     #9: #f(s(s(x))) -> #g(h(x,x))
     #10: #f(s(s(x))) -> #h(x,x)
     #11: #s(0()) -> #f(0())
     #12: #s(s(s(s(s(s(s(0()))))))) -> #f(s(s(0())))
     #13: #g(s(x)) -> #s(s(g(x)))
     #14: #g(s(x)) -> #s(g(x))
     #15: #g(s(x)) -> #g(x)
     #16: #s(x) -> #h(0(),x)
     #17: #g(x) -> #h(x,x)
     #18: #s(s(0())) -> #f(s(0()))
     #19: #f(g(x)) -> #g(g(f(x)))
     #20: #f(g(x)) -> #g(f(x))
     #21: #f(g(x)) -> #f(x)
Number of SCCs: 1, DPs: 14
  SCC { #2 #3 #7..10 #12..15 #17 #19..21 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded.
      h 	w: x1
      s 	w: x1
      f 	w: [1,1;1,1] * x1
      0 	w: [0;0]
      #h 	w: [0,1;1,0] * x1
      #s 	w: [0;0]
      #f 	w: [1,1;1,1] * x1
      #g 	w: [0,1;1,0] * x1
      g 	w: x1 + [1;1]
    USABLE RULES: { 1..12 }
    Removed DPs: #19..21
Number of SCCs: 1, DPs: 11
  SCC { #2 #3 #7..10 #12..15 #17 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded.
      h 	w: x1
      s 	w: x1
      f 	w: [1,1;1,1] * x1
      0 	w: [0;0]
      #h 	w: [0,1;0,0] * x2
      #s 	w: [1;0]
      #f 	w: [0,1;0,0] * x1 + [1;0]
      #g 	w: [0,1;0,0] * x1 + [1;0]
      g 	w: x1 + [1;1]
    USABLE RULES: { 1..12 }
    Removed DPs: #10 #17
Number of SCCs: 1, DPs: 9
  SCC { #2 #3 #7..9 #12..15 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  failed.