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 1]     [1]
    [g](x0) = [0 0]x0 + [0],
    
              [1 2]     [1]
    [f](x0) = [0 0]x0 + [2]
   orientation:
                  [1 1]     [7]    [1 1]     [6]                 
    f(f(g(x5))) = [0 0]x5 + [2] >= [0 0]x5 + [2] = f(g(f(g(x5))))
    
               [1 2]     [6]    [1 2]     [5]              
    f(f(x6)) = [0 0]x6 + [2] >= [0 0]x6 + [2] = f(g(f(x6)))
   problem:
    
   Qed