MAYBE

Problem:
 h(f(f(x))) -> h(f(g(f(x))))
 f(g(f(x))) -> f(f(x))

Proof:
 DP Processor:
  DPs:
   h#(f(f(x))) -> f#(g(f(x)))
   h#(f(f(x))) -> h#(f(g(f(x))))
   f#(g(f(x))) -> f#(f(x))
  TRS:
   h(f(f(x))) -> h(f(g(f(x))))
   f(g(f(x))) -> f(f(x))
  TDG Processor:
   DPs:
    h#(f(f(x))) -> f#(g(f(x)))
    h#(f(f(x))) -> h#(f(g(f(x))))
    f#(g(f(x))) -> f#(f(x))
   TRS:
    h(f(f(x))) -> h(f(g(f(x))))
    f(g(f(x))) -> f(f(x))
   graph:
    f#(g(f(x))) -> f#(f(x)) -> f#(g(f(x))) -> f#(f(x))
    h#(f(f(x))) -> f#(g(f(x))) -> f#(g(f(x))) -> f#(f(x))
    h#(f(f(x))) -> h#(f(g(f(x)))) -> h#(f(f(x))) -> h#(f(g(f(x))))
    h#(f(f(x))) -> h#(f(g(f(x)))) -> h#(f(f(x))) -> f#(g(f(x)))
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 4/9
    DPs:
     h#(f(f(x))) -> h#(f(g(f(x))))
    TRS:
     h(f(f(x))) -> h(f(g(f(x))))
     f(g(f(x))) -> f(f(x))
    Open
    
    DPs:
     f#(g(f(x))) -> f#(f(x))
    TRS:
     h(f(f(x))) -> h(f(g(f(x))))
     f(g(f(x))) -> f(f(x))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [f#](x0) = x0,
      
      [g](x0) = 1,
      
      [h](x0) = 0,
      
      [f](x0) = 0
     orientation:
      f#(g(f(x))) = 1 >= 0 = f#(f(x))
      
      h(f(f(x))) = 0 >= 0 = h(f(g(f(x))))
      
      f(g(f(x))) = 0 >= 0 = f(f(x))
     problem:
      DPs:
       
      TRS:
       h(f(f(x))) -> h(f(g(f(x))))
       f(g(f(x))) -> f(f(x))
     Qed