Problem:
 f(x,x) -> a()
 f(x,g(x)) -> b()

Proof:
 Church Rosser Transformation Processor (kb):
  f(x,x) -> a()
  f(x,g(x)) -> b()
  critical peaks: joinable
  Matrix Interpretation Processor: dim=3
   
   interpretation:
          [0]
    [b] = [0]
          [0],
    
              [1 0 0]     [0]
    [g](x0) = [0 0 0]x0 + [0]
              [0 0 0]     [1],
    
          [0]
    [a] = [0]
          [0],
    
                  [1 0 0]     [1 0 1]  
    [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                  [0 0 0]     [0 0 0]  
   orientation:
             [2 0 1]     [0]      
    f(x,x) = [0 0 0]x >= [0] = a()
             [0 0 0]     [0]      
    
                [2 0 0]    [1]    [0]      
    f(x,g(x)) = [0 0 0]x + [0] >= [0] = b()
                [0 0 0]    [0]    [0]      
   problem:
    f(x,x) -> a()
   Matrix Interpretation Processor: dim=3
    
    interpretation:
           [0]
     [a] = [0]
           [0],
     
                   [1 0 0]     [1 0 0]     [1]
     [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                   [0 0 0]     [0 0 0]     [0]
    orientation:
              [2 0 0]    [1]    [0]      
     f(x,x) = [0 0 0]x + [0] >= [0] = a()
              [0 0 0]    [0]    [0]      
    problem:
     
    Qed