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CSI-0.1


Problem:
 f(g(g(x))) -> a()
 f(g(h(x))) -> b()
 f(h(g(x))) -> b()
 f(h(h(x))) -> c()
 g(x) -> h(x)
 a() -> b()
 b() -> c()

Proof:
 Church Rosser Transformation Processor (kb):
  f(g(g(x))) -> a()
  f(g(h(x))) -> b()
  f(h(g(x))) -> b()
  f(h(h(x))) -> c()
  g(x) -> h(x)
  a() -> b()
  b() -> c()
  critical peaks: joinable
  Matrix Interpretation Processor: dim=3

   interpretation:
          [0]
    [c] = [0]
          [0],

          [0]
    [b] = [0]
          [0],

              [1 0 0]  
    [h](x0) = [0 0 0]x0
              [0 1 0]  ,

          [0]
    [a] = [0]
          [0],

              [1 0 0]     [1]
    [f](x0) = [0 0 1]x0 + [0]
              [0 0 0]     [0],

              [1 0 0]     [0]
    [g](x0) = [0 0 0]x0 + [1]
              [0 1 0]     [0]
   orientation:
                 [1 0 0]    [1]    [0]      
    f(g(g(x))) = [0 0 0]x + [1] >= [0] = a()
                 [0 0 0]    [0]    [0]      

                 [1 0 0]    [1]    [0]      
    f(g(h(x))) = [0 0 0]x + [0] >= [0] = b()
                 [0 0 0]    [0]    [0]      

                 [1 0 0]    [1]    [0]      
    f(h(g(x))) = [0 0 0]x + [1] >= [0] = b()
                 [0 0 0]    [0]    [0]      

                 [1 0 0]    [1]    [0]      
    f(h(h(x))) = [0 0 0]x + [0] >= [0] = c()
                 [0 0 0]    [0]    [0]      

           [1 0 0]    [0]    [1 0 0]        
    g(x) = [0 0 0]x + [1] >= [0 0 0]x = h(x)
           [0 1 0]    [0]    [0 1 0]        

          [0]    [0]      
    a() = [0] >= [0] = b()
          [0]    [0]      

          [0]    [0]      
    b() = [0] >= [0] = c()
          [0]    [0]      
   problem:
    g(x) -> h(x)
    a() -> b()
    b() -> c()
   Matrix Interpretation Processor: dim=3

    interpretation:
           [0]
     [c] = [0]
           [0],

           [0]
     [b] = [0]
           [0],

               [1 0 0]  
     [h](x0) = [0 0 0]x0
               [0 0 0]  ,

           [1]
     [a] = [0]
           [0],

               [1 0 0]     [1]
     [g](x0) = [0 0 0]x0 + [0]
               [0 0 0]     [0]
    orientation:
            [1 0 0]    [1]    [1 0 0]        
     g(x) = [0 0 0]x + [0] >= [0 0 0]x = h(x)
            [0 0 0]    [0]    [0 0 0]        

           [1]    [0]      
     a() = [0] >= [0] = b()
           [0]    [0]      

           [0]    [0]      
     b() = [0] >= [0] = c()
           [0]    [0]      
    problem:
     b() -> c()
    Matrix Interpretation Processor: dim=3

     interpretation:
            [0]
      [c] = [0]
            [0],

            [1]
      [b] = [0]
            [0]
     orientation:
            [1]    [0]      
      b() = [0] >= [0] = c()
            [0]    [0]      
     problem:

     Qed
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