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

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