YES
Input TRS:
      1: f(f(x)) -> f(g(f(x),x))
      2: f(f(x)) -> f(h(f(x),f(x)))
      3: g(x,y) -> y
      4: h(x,x) -> g(x,0())
Number of strict rules: 4
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #f(f(x)) -> #f(h(f(x),f(x)))
     #2: #f(f(x)) -> #h(f(x),f(x))
     #3: #f(f(x)) -> #f(g(f(x),x))
     #4: #f(f(x)) -> #g(f(x),x)
     #5: #h(x,x) -> #g(x,0())
Number of SCCs: 1, DPs: 2
  SCC { #1 #3 }
POLO(Sum)... succeeded.
      h 	w: 23677
      f 	w: x1 + 23678
      0 	w: 1
      #h 	w: 0
      #f 	w: x1
      #g 	w: 0
      g 	w: x2 + 23676
    USABLE RULES: { 1..4 }
    Removed DPs: #1 #3
Number of SCCs: 0, DPs: 0