MAYBE

Problem:
 f(f(X)) -> f(g(f(g(f(X)))))
 f(g(f(X))) -> f(g(X))

Proof:
 DP Processor:
  DPs:
   f#(f(X)) -> f#(g(f(X)))
   f#(f(X)) -> f#(g(f(g(f(X)))))
   f#(g(f(X))) -> f#(g(X))
  TRS:
   f(f(X)) -> f(g(f(g(f(X)))))
   f(g(f(X))) -> f(g(X))
  Restore Modifier:
   DPs:
    f#(f(X)) -> f#(g(f(X)))
    f#(f(X)) -> f#(g(f(g(f(X)))))
    f#(g(f(X))) -> f#(g(X))
   TRS:
    f(f(X)) -> f(g(f(g(f(X)))))
    f(g(f(X))) -> f(g(X))
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 9/9
    DPs:
     f#(f(X)) -> f#(g(f(X)))
     f#(f(X)) -> f#(g(f(g(f(X)))))
     f#(g(f(X))) -> f#(g(X))
    TRS:
     f(f(X)) -> f(g(f(g(f(X)))))
     f(g(f(X))) -> f(g(X))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [f#](x0) = x0,
      
      [g](x0) = 0,
      
      [f](x0) = 1
     orientation:
      f#(f(X)) = 1 >= 0 = f#(g(f(X)))
      
      f#(f(X)) = 1 >= 0 = f#(g(f(g(f(X)))))
      
      f#(g(f(X))) = 0 >= 0 = f#(g(X))
      
      f(f(X)) = 1 >= 1 = f(g(f(g(f(X)))))
      
      f(g(f(X))) = 1 >= 1 = f(g(X))
     problem:
      DPs:
       f#(g(f(X))) -> f#(g(X))
      TRS:
       f(f(X)) -> f(g(f(g(f(X)))))
       f(g(f(X))) -> f(g(X))
     Open