/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:
 minus(minus(x)) -> x
 minus(+(x,y)) -> *(minus(minus(minus(x))),minus(minus(minus(y))))
 minus(*(x,y)) -> +(minus(minus(minus(x))),minus(minus(minus(y))))
 f(minus(x)) -> minus(minus(minus(f(x))))

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
             [1 2]     [2]
   [f](x0) = [0 3]x0 + [0],
   
                 [2 0]     [1 0]     [1]
   [*](x0, x1) = [0 0]x0 + [0 0]x1 + [0],
   
                 [2 0]     [1 0]     [1]
   [+](x0, x1) = [0 0]x0 + [0 0]x1 + [0],
   
                      [0]
   [minus](x0) = x0 + [1]
  orientation:
                         [0]         
   minus(minus(x)) = x + [2] >= x = x
   
                   [2 0]    [1 0]    [1]    [2 0]    [1 0]    [1]                                                   
   minus(+(x,y)) = [0 0]x + [0 0]y + [1] >= [0 0]x + [0 0]y + [0] = *(minus(minus(minus(x))),minus(minus(minus(y))))
   
                   [2 0]    [1 0]    [1]    [2 0]    [1 0]    [1]                                                   
   minus(*(x,y)) = [0 0]x + [0 0]y + [1] >= [0 0]x + [0 0]y + [0] = +(minus(minus(minus(x))),minus(minus(minus(y))))
   
                 [1 2]    [4]    [1 2]    [2]                            
   f(minus(x)) = [0 3]x + [3] >= [0 3]x + [3] = minus(minus(minus(f(x))))
  problem:
   minus(minus(x)) -> x
   minus(+(x,y)) -> *(minus(minus(minus(x))),minus(minus(minus(y))))
   minus(*(x,y)) -> +(minus(minus(minus(x))),minus(minus(minus(y))))
  Matrix Interpretation Processor: dim=2
   
   interpretation:
                  [1 0]     [1 2]     [0]
    [*](x0, x1) = [0 3]x0 + [0 3]x1 + [1],
    
                  [1 0]     [1 2]     [0]
    [+](x0, x1) = [0 3]x0 + [0 3]x1 + [1],
    
                  [1 1]  
    [minus](x0) = [0 1]x0
   orientation:
                      [1 2]          
    minus(minus(x)) = [0 1]x >= x = x
    
                    [1 3]    [1 5]    [1]    [1 3]    [1 5]    [0]                                                   
    minus(+(x,y)) = [0 3]x + [0 3]y + [1] >= [0 3]x + [0 3]y + [1] = *(minus(minus(minus(x))),minus(minus(minus(y))))
    
                    [1 3]    [1 5]    [1]    [1 3]    [1 5]    [0]                                                   
    minus(*(x,y)) = [0 3]x + [0 3]y + [1] >= [0 3]x + [0 3]y + [1] = +(minus(minus(minus(x))),minus(minus(minus(y))))
   problem:
    minus(minus(x)) -> x
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                   [1 0 1]     [0]
     [minus](x0) = [0 0 1]x0 + [0]
                   [0 1 0]     [1]
    orientation:
                       [1 1 1]    [1]         
     minus(minus(x)) = [0 1 0]x + [1] >= x = x
                       [0 0 1]    [1]         
    problem:
     
    Qed