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CSI-0.1


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

Proof:
 Church Rosser Transformation Processor (kb):
  f(i(x),g(a())) -> f(j(x,x),g(b()))
  b() -> a()
  i(x) -> j(x,x)
  critical peaks: joinable
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [b] = 0,
    
    [j](x0, x1) = 4x0 + x1 + 6,
    
    [f](x0, x1) = 3x0 + x1 + 5,
    
    [g](x0) = 4x0 + 2,
    
    [a] = 0,
    
    [i](x0) = 5x0 + 7
   orientation:
    f(i(x),g(a())) = 15x + 28 >= 15x + 25 = f(j(x,x),g(b()))
    
    b() = 0 >= 0 = a()
    
    i(x) = 5x + 7 >= 5x + 6 = j(x,x)
   problem:
    b() -> a()
   Matrix Interpretation Processor: dim=3
    
    interpretation:
           [1]
     [b] = [0]
           [0],
     
           [0]
     [a] = [0]
           [0]
    orientation:
           [1]    [0]      
     b() = [0] >= [0] = a()
           [0]    [0]      
    problem:
     
    Qed
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