YES

Problem:
 f(f(x)) -> f(g(f(x),x))
 f(f(x)) -> f(h(f(x),f(x)))
 g(x,y) -> y
 h(x,x) -> g(x,0())

Proof:
 DP Processor:
  DPs:
   f#(f(x)) -> g#(f(x),x)
   f#(f(x)) -> f#(g(f(x),x))
   f#(f(x)) -> h#(f(x),f(x))
   f#(f(x)) -> f#(h(f(x),f(x)))
   h#(x,x) -> g#(x,0())
  TRS:
   f(f(x)) -> f(g(f(x),x))
   f(f(x)) -> f(h(f(x),f(x)))
   g(x,y) -> y
   h(x,x) -> g(x,0())
  TDG Processor:
   DPs:
    f#(f(x)) -> g#(f(x),x)
    f#(f(x)) -> f#(g(f(x),x))
    f#(f(x)) -> h#(f(x),f(x))
    f#(f(x)) -> f#(h(f(x),f(x)))
    h#(x,x) -> g#(x,0())
   TRS:
    f(f(x)) -> f(g(f(x),x))
    f(f(x)) -> f(h(f(x),f(x)))
    g(x,y) -> y
    h(x,x) -> g(x,0())
   graph:
    f#(f(x)) -> h#(f(x),f(x)) -> h#(x,x) -> g#(x,0())
    f#(f(x)) -> f#(h(f(x),f(x))) -> f#(f(x)) -> f#(h(f(x),f(x)))
    f#(f(x)) -> f#(h(f(x),f(x))) -> f#(f(x)) -> h#(f(x),f(x))
    f#(f(x)) -> f#(h(f(x),f(x))) -> f#(f(x)) -> f#(g(f(x),x))
    f#(f(x)) -> f#(h(f(x),f(x))) -> f#(f(x)) -> g#(f(x),x)
    f#(f(x)) -> f#(g(f(x),x)) -> f#(f(x)) -> f#(h(f(x),f(x)))
    f#(f(x)) -> f#(g(f(x),x)) -> f#(f(x)) -> h#(f(x),f(x))
    f#(f(x)) -> f#(g(f(x),x)) -> f#(f(x)) -> f#(g(f(x),x))
    f#(f(x)) -> f#(g(f(x),x)) -> f#(f(x)) -> g#(f(x),x)
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 9/25
    DPs:
     f#(f(x)) -> f#(h(f(x),f(x)))
     f#(f(x)) -> f#(g(f(x),x))
    TRS:
     f(f(x)) -> f(g(f(x),x))
     f(f(x)) -> f(h(f(x),f(x)))
     g(x,y) -> y
     h(x,x) -> g(x,0())
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [f#](x0) = x0 + -16,
      
      [0] = 0,
      
      [h](x0, x1) = -7x0 + -2x1 + 0,
      
      [g](x0, x1) = -2x0 + x1 + -16,
      
      [f](x0) = x0 + 1
     orientation:
      f#(f(x)) = x + 1 >= -2x + 0 = f#(h(f(x),f(x)))
      
      f#(f(x)) = x + 1 >= x + -1 = f#(g(f(x),x))
      
      f(f(x)) = x + 1 >= x + 1 = f(g(f(x),x))
      
      f(f(x)) = x + 1 >= -2x + 1 = f(h(f(x),f(x)))
      
      g(x,y) = -2x + y + -16 >= y = y
      
      h(x,x) = -2x + 0 >= -2x + 0 = g(x,0())
     problem:
      DPs:
       f#(f(x)) -> f#(g(f(x),x))
      TRS:
       f(f(x)) -> f(g(f(x),x))
       f(f(x)) -> f(h(f(x),f(x)))
       g(x,y) -> y
       h(x,x) -> g(x,0())
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [f#](x0) = 1x0 + -6,
       
       [0] = 0,
       
       [h](x0, x1) = x0 + -1x1 + 1,
       
       [g](x0, x1) = -9x0 + 1x1,
       
       [f](x0) = 2x0 + 1
      orientation:
       f#(f(x)) = 3x + 2 >= 2x + -6 = f#(g(f(x),x))
       
       f(f(x)) = 4x + 3 >= 3x + 1 = f(g(f(x),x))
       
       f(f(x)) = 4x + 3 >= 4x + 3 = f(h(f(x),f(x)))
       
       g(x,y) = -9x + 1y >= y = y
       
       h(x,x) = x + 1 >= -9x + 1 = g(x,0())
      problem:
       DPs:
        
       TRS:
        f(f(x)) -> f(g(f(x),x))
        f(f(x)) -> f(h(f(x),f(x)))
        g(x,y) -> y
        h(x,x) -> g(x,0())
      Qed