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

Proof:
 Church Rosser Transformation Processor (critical pair closing system, Thm 2.11):
  f(f(g(x5))) -> f(g(f(g(x5))))
  f(f(x6)) -> f(g(f(x6)))
  critical peaks: joinable
  Matrix Interpretation Processor: dim=2
   
   interpretation:
              [1 0]     [0]
    [g](x0) = [0 0]x0 + [1],
    
              [1 1]     [0]
    [f](x0) = [0 2]x0 + [1]
   orientation:
                  [1 0]     [4]    [1 0]     [2]                 
    f(f(g(x5))) = [0 0]x5 + [7] >= [0 0]x5 + [3] = f(g(f(g(x5))))
    
               [1 3]     [1]    [1 1]     [1]              
    f(f(x6)) = [0 4]x6 + [3] >= [0 0]x6 + [3] = f(g(f(x6)))
   problem:
    f(f(x6)) -> f(g(f(x6)))
   Matrix Interpretation Processor: dim=2
    
    interpretation:
               [2 0]     [2]
     [g](x0) = [0 0]x0 + [0],
     
               [1 1]     [0]
     [f](x0) = [1 1]x0 + [3]
    orientation:
                [2 2]     [3]    [2 2]     [2]              
     f(f(x6)) = [2 2]x6 + [6] >= [2 2]x6 + [5] = f(g(f(x6)))
    problem:
     
    Qed