/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:
  top(left(car(x,y),car(old(),z))) -> top(right(y,car(old(),z)))
  top(left(car(x,car(old(),y)),z)) -> top(right(car(old(),y),z))
  top(right(x,car(y,car(old(),z)))) -> top(left(x,car(old(),z)))
  top(right(car(old(),x),car(y,z))) -> top(left(car(old(),x),z))
  top(left(bot(),car(old(),x))) -> top(right(bot(),car(old(),x)))
  top(right(car(old(),x),bot())) -> top(left(car(old(),x),bot()))
 weak:
  top(left(car(x,y),z)) -> top(left(y,z))
  top(right(x,car(y,z))) -> top(right(x,z))
  bot() -> car(new(),bot())

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
           [0]
   [new] = [0],
   
           [0]
   [bot] = [0],
   
                     [1 0]     [1 0]  
   [right](x0, x1) = [0 0]x0 + [0 0]x1,
   
               [1 0]  
   [top](x0) = [1 0]x0,
   
                    [1 0]     [1 0]  
   [left](x0, x1) = [0 0]x0 + [0 0]x1,
   
           [0]
   [old] = [1],
   
                   [1 0]     [1 1]  
   [car](x0, x1) = [0 2]x0 + [0 0]x1
  orientation:
                                      [1 0]    [1 1]    [1 1]     [1 0]    [1 1]                              
   top(left(car(x,y),car(old(),z))) = [1 0]x + [1 1]y + [1 1]z >= [1 0]y + [1 1]z = top(right(y,car(old(),z)))
   
                                      [1 0]    [1 1]    [1 0]    [2]    [1 1]    [1 0]                              
   top(left(car(x,car(old(),y)),z)) = [1 0]x + [1 1]y + [1 0]z + [2] >= [1 1]y + [1 0]z = top(right(car(old(),y),z))
   
                                       [1 0]    [1 0]    [1 1]    [2]    [1 0]    [1 1]                             
   top(right(x,car(y,car(old(),z)))) = [1 0]x + [1 0]y + [1 1]z + [2] >= [1 0]x + [1 1]z = top(left(x,car(old(),z)))
   
                                       [1 1]    [1 0]    [1 1]     [1 1]    [1 0]                             
   top(right(car(old(),x),car(y,z))) = [1 1]x + [1 0]y + [1 1]z >= [1 1]x + [1 0]z = top(left(car(old(),x),z))
   
                                   [1 1]     [1 1]                                  
   top(left(bot(),car(old(),x))) = [1 1]x >= [1 1]x = top(right(bot(),car(old(),x)))
   
                                    [1 1]     [1 1]                                 
   top(right(car(old(),x),bot())) = [1 1]x >= [1 1]x = top(left(car(old(),x),bot()))
   
                           [1 0]    [1 1]    [1 0]     [1 0]    [1 0]                  
   top(left(car(x,y),z)) = [1 0]x + [1 1]y + [1 0]z >= [1 0]y + [1 0]z = top(left(y,z))
   
                            [1 0]    [1 0]    [1 1]     [1 0]    [1 0]                   
   top(right(x,car(y,z))) = [1 0]x + [1 0]y + [1 1]z >= [1 0]x + [1 0]z = top(right(x,z))
   
           [0]    [0]                   
   bot() = [0] >= [0] = car(new(),bot())
  problem:
   strict:
    top(left(car(x,y),car(old(),z))) -> top(right(y,car(old(),z)))
    top(right(car(old(),x),car(y,z))) -> top(left(car(old(),x),z))
    top(left(bot(),car(old(),x))) -> top(right(bot(),car(old(),x)))
    top(right(car(old(),x),bot())) -> top(left(car(old(),x),bot()))
   weak:
    top(left(car(x,y),z)) -> top(left(y,z))
    top(right(x,car(y,z))) -> top(right(x,z))
    bot() -> car(new(),bot())
  Matrix Interpretation Processor: dim=2
   
   interpretation:
            [0]
    [new] = [0],
    
            [0]
    [bot] = [0],
    
                      [1 0]     [3 0]  
    [right](x0, x1) = [1 0]x0 + [0 0]x1,
    
                [1 2]  
    [top](x0) = [0 3]x0,
    
                          [2 1]     [1]
    [left](x0, x1) = x0 + [0 0]x1 + [0],
    
            [1]
    [old] = [0],
    
                    [1 0]     [1 1]  
    [car](x0, x1) = [0 0]x0 + [1 1]x1
   orientation:
                                       [1 0]    [3 3]    [3 3]    [3]    [3 0]    [3 3]    [3]                             
    top(left(car(x,y),car(old(),z))) = [0 0]x + [3 3]y + [0 0]z + [0] >= [3 0]y + [0 0]z + [0] = top(right(y,car(old(),z)))
    
                                        [3 3]    [3 0]    [3 3]    [3]    [3 3]    [2 1]    [2]                            
    top(right(car(old(),x),car(y,z))) = [3 3]x + [0 0]y + [0 0]z + [3] >= [3 3]x + [0 0]z + [0] = top(left(car(old(),x),z))
    
                                    [3 3]    [3]    [3 3]    [3]                                 
    top(left(bot(),car(old(),x))) = [0 0]x + [0] >= [0 0]x + [0] = top(right(bot(),car(old(),x)))
    
                                     [3 3]    [3]    [3 3]    [2]                                
    top(right(car(old(),x),bot())) = [3 3]x + [3] >= [3 3]x + [0] = top(left(car(old(),x),bot()))
    
                            [1 0]    [3 3]    [2 1]    [1]    [1 2]    [2 1]    [1]                 
    top(left(car(x,y),z)) = [0 0]x + [3 3]y + [0 0]z + [0] >= [0 3]y + [0 0]z + [0] = top(left(y,z))
    
                             [3 0]    [3 0]    [3 3]     [3 0]    [3 0]                   
    top(right(x,car(y,z))) = [3 0]x + [0 0]y + [0 0]z >= [3 0]x + [0 0]z = top(right(x,z))
    
            [0]    [0]                   
    bot() = [0] >= [0] = car(new(),bot())
   problem:
    strict:
     top(left(car(x,y),car(old(),z))) -> top(right(y,car(old(),z)))
     top(left(bot(),car(old(),x))) -> top(right(bot(),car(old(),x)))
    weak:
     top(left(car(x,y),z)) -> top(left(y,z))
     top(right(x,car(y,z))) -> top(right(x,z))
     bot() -> car(new(),bot())
   Matrix Interpretation Processor: dim=2
    
    interpretation:
             [0]
     [new] = [0],
     
             [1]
     [bot] = [0],
     
                       [1 0]       
     [right](x0, x1) = [0 0]x0 + x1,
     
                 [1 0]  
     [top](x0) = [0 0]x0,
     
                      [2 0]     [1 0]  
     [left](x0, x1) = [0 0]x0 + [0 0]x1,
     
             [0]
     [old] = [1],
     
                          [1 0]  
     [car](x0, x1) = x0 + [0 0]x1
    orientation:
                                        [2 0]    [2 0]    [1 0]     [1 0]    [1 0]                              
     top(left(car(x,y),car(old(),z))) = [0 0]x + [0 0]y + [0 0]z >= [0 0]y + [0 0]z = top(right(y,car(old(),z)))
     
                                     [1 0]    [2]    [1 0]    [1]                                 
     top(left(bot(),car(old(),x))) = [0 0]x + [0] >= [0 0]x + [0] = top(right(bot(),car(old(),x)))
     
                             [2 0]    [2 0]    [1 0]     [2 0]    [1 0]                  
     top(left(car(x,y),z)) = [0 0]x + [0 0]y + [0 0]z >= [0 0]y + [0 0]z = top(left(y,z))
     
                              [1 0]    [1 0]    [1 0]     [1 0]    [1 0]                   
     top(right(x,car(y,z))) = [0 0]x + [0 0]y + [0 0]z >= [0 0]x + [0 0]z = top(right(x,z))
     
             [1]    [1]                   
     bot() = [0] >= [0] = car(new(),bot())
    problem:
     strict:
      top(left(car(x,y),car(old(),z))) -> top(right(y,car(old(),z)))
     weak:
      top(left(car(x,y),z)) -> top(left(y,z))
      top(right(x,car(y,z))) -> top(right(x,z))
      bot() -> car(new(),bot())
    Matrix Interpretation Processor: dim=2
     
     interpretation:
              [0]
      [new] = [0],
      
              [1]
      [bot] = [0],
      
                        [1 1]     [1 0]     [0]
      [right](x0, x1) = [0 0]x0 + [0 0]x1 + [1],
      
                  [2 1]     [0]
      [top](x0) = [0 1]x0 + [1],
      
                       [1 0]          [0]
      [left](x0, x1) = [1 2]x0 + x1 + [1],
      
              [0]
      [old] = [1],
      
                             
      [car](x0, x1) = x0 + x1
     orientation:
                                         [3 2]    [3 2]    [2 1]    [2]    [2 2]    [2 0]    [1]                             
      top(left(car(x,y),car(old(),z))) = [1 2]x + [1 2]y + [0 1]z + [3] >= [0 0]y + [0 0]z + [2] = top(right(y,car(old(),z)))
      
                              [3 2]    [3 2]    [2 1]    [1]    [3 2]    [2 1]    [1]                 
      top(left(car(x,y),z)) = [1 2]x + [1 2]y + [0 1]z + [2] >= [1 2]y + [0 1]z + [2] = top(left(y,z))
      
                               [2 2]    [2 0]    [2 0]    [1]    [2 2]    [2 0]    [1]                  
      top(right(x,car(y,z))) = [0 0]x + [0 0]y + [0 0]z + [2] >= [0 0]x + [0 0]z + [2] = top(right(x,z))
      
              [1]    [1]                   
      bot() = [0] >= [0] = car(new(),bot())
     problem:
      strict:
       
      weak:
       top(left(car(x,y),z)) -> top(left(y,z))
       top(right(x,car(y,z))) -> top(right(x,z))
       bot() -> car(new(),bot())
     Qed