YES
Input TRS:
AC symbols: f
      1: f(g(f(h(x),x)),x) -> f(h(x),f(x,x))
      2: f(h(x),g(x)) -> f(g(h(x)),x)
      3: f(g(h(x)),f(x,f(x,y))) -> f(g(f(h(x),y)),x)
      4: f(g(g(x)),x) -> f(g(x),g(x))
Number of strict rules: 4
Direct POLO(bPol) ... removes: 1 3
      h 	w: x1
      f 	w: x1 + x2 + 1
      g 	w: x1 + 1
Number of strict rules: 2
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #f(h(x),g(x)) -> #f(g(h(x)),x)
     #2: #f(x,f(y,z)) ->= #f(f(x,y),z)
     #3: #f(x,f(y,z)) ->= #f(x,y)
     #4: #f(g(g(x)),x) -> #f(g(x),g(x))
Number of SCCs: 1, DPs: 4
  SCC { #1..4 }
POLO(Sum)... succeeded.
      h 	w: x1 + 1
      f 	w: x1 + x2 + 1
      #f 	w: x1 + x2
      g 	w: x1 + 20653
    USABLE RULES: { 2 4 5 }
    Removed DPs: #3
Number of SCCs: 1, DPs: 3
  SCC { #1 #2 #4 }
POLO(Sum)... succeeded.
      h 	w: x1 + 20654
      f 	w: x1 + x2 + 1
      #f 	w: x1 + x2
      g 	w: 0
    USABLE RULES: { 2 4 5 }
    Removed DPs: #1
Number of SCCs: 1, DPs: 2
  SCC { #2 #4 }
POLO(Sum)... POLO(max)... succeeded.
      h 	w: 0
      f 	w: max(x1, x2)
      #f 	w: max(x1, x2)
      g 	w: x1 + 1
    USABLE RULES: { 2 4 5 }
    Removed DPs: #4
Number of SCCs: 1, DPs: 1
  SCC { #2 }
only weak rules.
Number of SCCs: 0, DPs: 0
Next Dependency Pairs:
     #5: #f(f(h(x),g(x)),_1) -> #f(f(g(h(x)),x),_1)
     #6: #f(x,f(y,z)) ->= #f(f(x,y),z)
     #7: #f(x,f(y,z)) ->= #f(x,y)
     #8: #f(f(g(g(x)),x),_1) -> #f(f(g(x),g(x)),_1)
Number of SCCs: 1, DPs: 4
  SCC { #5..8 }
POLO(Sum)... succeeded.
      h 	w: x1 + 1
      f 	w: x1 + x2 + 1
      #f 	w: x1 + x2
      g 	w: x1 + 1424
    USABLE RULES: { 2 4 5 }
    Removed DPs: #7
Number of SCCs: 1, DPs: 3
  SCC { #5 #6 #8 }
POLO(Sum)... succeeded.
      h 	w: x1 + 1
      f 	w: x1 + x2 + 29283
      #f 	w: x1 + x2
      g 	w: 0
    USABLE RULES: { 2 4 5 }
    Removed DPs: #5
Number of SCCs: 1, DPs: 2
  SCC { #6 #8 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      h 	s: []	p: 1
      f 	s: {1,2}	p: 2
      #f 	s: {1,2}	p: 2
      g 	s: 1
    USABLE RULES: { 2 4 5 }
    Removed DPs: #8
Number of SCCs: 1, DPs: 1
  SCC { #6 }
only weak rules.
Number of SCCs: 0, DPs: 0