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


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YES

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

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