/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


YES

Problem:
 max(L(x)) -> x
 max(N(L(0()),L(y))) -> y
 max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y))))
 max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z)))))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
             [1 0 0]  
   [s](x0) = [0 0 0]x0
             [0 0 0]  ,
   
                 
   [max](x0) = x0
                 ,
   
                 [1 0 0]       
   [N](x0, x1) = [0 0 0]x0 + x1
                 [0 1 0]       ,
   
               
   [L](x0) = x0
               ,
   
         [1]
   [0] = [1]
         [0]
  orientation:
                         
   max(L(x)) = x >= x = x
                         
   
                             [1]         
   max(N(L(0()),L(y))) = y + [0] >= y = y
                             [1]         
   
                             [1 0 0]    [1 0 0]     [1 0 0]    [1 0 0]                        
   max(N(L(s(x)),L(s(y)))) = [0 0 0]x + [0 0 0]y >= [0 0 0]x + [0 0 0]y = s(max(N(L(x),L(y))))
                             [0 0 0]    [0 0 0]     [0 0 0]    [0 0 0]                        
   
                         [1 0 0]    [1 0 0]         [1 0 0]    [1 0 0]                                   
   max(N(L(x),N(y,z))) = [0 0 0]x + [0 0 0]y + z >= [0 0 0]x + [0 0 0]y + z = max(N(L(x),L(max(N(y,z)))))
                         [0 1 0]    [0 1 0]         [0 1 0]    [0 1 0]                                   
  problem:
   max(L(x)) -> x
   max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y))))
   max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z)))))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [s](x0) = 2x0 + 4,
    
    [max](x0) = x0,
    
    [N](x0, x1) = 2x0 + 4x1,
    
    [L](x0) = x0
   orientation:
    max(L(x)) = x >= x = x
    
    max(N(L(s(x)),L(s(y)))) = 4x + 8y + 24 >= 4x + 8y + 4 = s(max(N(L(x),L(y))))
    
    max(N(L(x),N(y,z))) = 2x + 8y + 16z >= 2x + 8y + 16z = max(N(L(x),L(max(N(y,z)))))
   problem:
    max(L(x)) -> x
    max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z)))))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                 [1 0 1]  
     [max](x0) = [0 0 1]x0
                 [0 0 1]  ,
     
                   [1 0 0]     [1 0 0]  
     [N](x0, x1) = [0 0 0]x0 + [0 1 0]x1
                   [0 0 0]     [0 0 0]  ,
     
               [1 0 0]     [0]
     [L](x0) = [0 0 0]x0 + [1]
               [0 1 1]     [1]
    orientation:
                 [1 1 1]    [1]         
     max(L(x)) = [0 1 1]x + [1] >= x = x
                 [0 1 1]    [1]         
     
                           [1 0 0]    [1 0 0]    [1 0 0]     [1 0 0]    [1 0 0]    [1 0 0]                               
     max(N(L(x),N(y,z))) = [0 0 0]x + [0 0 0]y + [0 0 0]z >= [0 0 0]x + [0 0 0]y + [0 0 0]z = max(N(L(x),L(max(N(y,z)))))
                           [0 0 0]    [0 0 0]    [0 0 0]     [0 0 0]    [0 0 0]    [0 0 0]                               
    problem:
     max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z)))))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                  [1 0 0]  
      [max](x0) = [0 0 0]x0
                  [0 1 0]  ,
      
                    [1 1 0]     [1 0 1]     [0]
      [N](x0, x1) = [0 0 0]x0 + [1 0 0]x1 + [1]
                    [0 0 0]     [0 0 0]     [1],
      
                [1 0 0]  
      [L](x0) = [0 0 0]x0
                [0 0 0]  
     orientation:
                            [1 0 0]    [1 1 0]    [1 0 1]    [1]    [1 0 0]    [1 1 0]    [1 0 1]    [0]                              
      max(N(L(x),N(y,z))) = [0 0 0]x + [0 0 0]y + [0 0 0]z + [0] >= [0 0 0]x + [0 0 0]y + [0 0 0]z + [0] = max(N(L(x),L(max(N(y,z)))))
                            [0 0 0]    [1 1 0]    [1 0 1]    [1]    [0 0 0]    [1 1 0]    [1 0 1]    [1]                              
     problem:
      
     Qed