/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 strict:
  f(a(),g(y),z) -> f(a(),y,g(y))
  f(b(),g(y),z) -> f(a(),y,z)
  a() -> b()
 weak:
  f(x,y,z) -> f(x,y,g(z))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
         [0]
   [b] = [0]
         [2],
   
                     [2 0 3]     [1 1 1]     [1 0 0]  
   [f](x0, x1, x2) = [0 0 3]x0 + [2 0 0]x1 + [0 0 0]x2
                     [0 0 0]     [0 0 0]     [0 0 0]  ,
   
             [1 0 0]     [0]
   [g](x0) = [0 1 2]x0 + [1]
             [2 0 0]     [0],
   
         [0]
   [a] = [0]
         [2]
  orientation:
                   [3 1 2]    [1 0 0]    [7]    [2 1 1]    [6]                
   f(a(),g(y),z) = [2 0 0]y + [0 0 0]z + [6] >= [2 0 0]y + [6] = f(a(),y,g(y))
                   [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0]                
   
                   [3 1 2]    [1 0 0]    [7]    [1 1 1]    [1 0 0]    [6]             
   f(b(),g(y),z) = [2 0 0]y + [0 0 0]z + [6] >= [2 0 0]y + [0 0 0]z + [6] = f(a(),y,z)
                   [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0]             
   
         [0]    [0]      
   a() = [0] >= [0] = b()
         [2]    [2]      
   
              [2 0 3]    [1 1 1]    [1 0 0]     [2 0 3]    [1 1 1]    [1 0 0]               
   f(x,y,z) = [0 0 3]x + [2 0 0]y + [0 0 0]z >= [0 0 3]x + [2 0 0]y + [0 0 0]z = f(x,y,g(z))
              [0 0 0]    [0 0 0]    [0 0 0]     [0 0 0]    [0 0 0]    [0 0 0]               
  problem:
   strict:
    a() -> b()
   weak:
    f(x,y,z) -> f(x,y,g(z))
  Matrix Interpretation Processor: dim=5
   
   interpretation:
          [0]
          [0]
    [b] = [0]
          [0]
          [0],
    
                      [1 0 0 0 0]     [1 0 0 0 0]     [1 0 0 0 0]  
                      [0 0 0 0 0]     [0 0 0 0 0]     [0 0 0 0 0]  
    [f](x0, x1, x2) = [0 0 0 0 0]x0 + [0 0 0 0 0]x1 + [0 0 0 0 0]x2
                      [0 0 0 0 0]     [0 0 0 0 0]     [0 1 0 0 0]  
                      [0 0 0 0 0]     [0 0 0 0 0]     [1 0 0 0 0]  ,
    
              [1 0 0 0 0]  
              [0 0 0 0 0]  
    [g](x0) = [0 0 0 0 0]x0
              [0 0 0 0 0]  
              [0 0 0 0 0]  ,
    
          [1]
          [1]
    [a] = [0]
          [0]
          [0]
   orientation:
          [1]    [0]      
          [1]    [0]      
    a() = [0] >= [0] = b()
          [0]    [0]      
          [0]    [0]      
    
               [1 0 0 0 0]    [1 0 0 0 0]    [1 0 0 0 0]     [1 0 0 0 0]    [1 0 0 0 0]    [1 0 0 0 0]               
               [0 0 0 0 0]    [0 0 0 0 0]    [0 0 0 0 0]     [0 0 0 0 0]    [0 0 0 0 0]    [0 0 0 0 0]               
    f(x,y,z) = [0 0 0 0 0]x + [0 0 0 0 0]y + [0 0 0 0 0]z >= [0 0 0 0 0]x + [0 0 0 0 0]y + [0 0 0 0 0]z = f(x,y,g(z))
               [0 0 0 0 0]    [0 0 0 0 0]    [0 1 0 0 0]     [0 0 0 0 0]    [0 0 0 0 0]    [0 0 0 0 0]               
               [0 0 0 0 0]    [0 0 0 0 0]    [1 0 0 0 0]     [0 0 0 0 0]    [0 0 0 0 0]    [1 0 0 0 0]               
   problem:
    strict:
     
    weak:
     f(x,y,z) -> f(x,y,g(z))
   Qed