/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:
 active(g(X)) -> mark(h(X))
 active(c()) -> mark(d())
 active(h(d())) -> mark(g(c()))
 mark(g(X)) -> active(g(X))
 mark(h(X)) -> active(h(X))
 mark(c()) -> active(c())
 mark(d()) -> active(d())
 g(mark(X)) -> g(X)
 g(active(X)) -> g(X)
 h(mark(X)) -> h(X)
 h(active(X)) -> h(X)

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
         [0]
   [d] = [0]
         [1],
   
         [0]
   [c] = [1]
         [0],
   
                [1 1 0]     [0]
   [mark](x0) = [0 0 0]x0 + [1]
                [0 1 1]     [0],
   
             [1 0 0]  
   [h](x0) = [0 0 1]x0
             [0 0 0]  ,
   
                  [1 1 0]     [0]
   [active](x0) = [0 0 0]x0 + [1]
                  [0 1 1]     [0],
   
             [1 0 0]     [1]
   [g](x0) = [0 0 1]x0 + [0]
             [0 0 0]     [0]
  orientation:
                  [1 0 1]    [1]    [1 0 1]    [0]             
   active(g(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = mark(h(X))
                  [0 0 1]    [0]    [0 0 1]    [0]             
   
                 [1]    [0]            
   active(c()) = [1] >= [1] = mark(d())
                 [1]    [1]            
   
                    [1]    [1]               
   active(h(d())) = [1] >= [1] = mark(g(c()))
                    [1]    [0]               
   
                [1 0 1]    [1]    [1 0 1]    [1]               
   mark(g(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = active(g(X))
                [0 0 1]    [0]    [0 0 1]    [0]               
   
                [1 0 1]    [0]    [1 0 1]    [0]               
   mark(h(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = active(h(X))
                [0 0 1]    [0]    [0 0 1]    [0]               
   
               [1]    [1]              
   mark(c()) = [1] >= [1] = active(c())
               [1]    [1]              
   
               [0]    [0]              
   mark(d()) = [1] >= [1] = active(d())
               [1]    [1]              
   
                [1 1 0]    [1]    [1 0 0]    [1]       
   g(mark(X)) = [0 1 1]X + [0] >= [0 0 1]X + [0] = g(X)
                [0 0 0]    [0]    [0 0 0]    [0]       
   
                  [1 1 0]    [1]    [1 0 0]    [1]       
   g(active(X)) = [0 1 1]X + [0] >= [0 0 1]X + [0] = g(X)
                  [0 0 0]    [0]    [0 0 0]    [0]       
   
                [1 1 0]     [1 0 0]        
   h(mark(X)) = [0 1 1]X >= [0 0 1]X = h(X)
                [0 0 0]     [0 0 0]        
   
                  [1 1 0]     [1 0 0]        
   h(active(X)) = [0 1 1]X >= [0 0 1]X = h(X)
                  [0 0 0]     [0 0 0]        
  problem:
   active(h(d())) -> mark(g(c()))
   mark(g(X)) -> active(g(X))
   mark(h(X)) -> active(h(X))
   mark(c()) -> active(c())
   mark(d()) -> active(d())
   g(mark(X)) -> g(X)
   g(active(X)) -> g(X)
   h(mark(X)) -> h(X)
   h(active(X)) -> h(X)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
          [0]
    [d] = [0]
          [0],
    
          [0]
    [c] = [0]
          [0],
    
                 [1 1 1]     [0]
    [mark](x0) = [0 1 0]x0 + [0]
                 [0 0 0]     [1],
    
              [1 0 0]     [0]
    [h](x0) = [0 1 0]x0 + [0]
              [0 0 0]     [1],
    
                     
    [active](x0) = x0
                     ,
    
              [1 0 0]  
    [g](x0) = [0 1 0]x0
              [0 0 0]  
   orientation:
                     [0]    [0]               
    active(h(d())) = [0] >= [0] = mark(g(c()))
                     [1]    [1]               
    
                 [1 1 0]    [0]    [1 0 0]                
    mark(g(X)) = [0 1 0]X + [0] >= [0 1 0]X = active(g(X))
                 [0 0 0]    [1]    [0 0 0]                
    
                 [1 1 0]    [1]    [1 0 0]    [0]               
    mark(h(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = active(h(X))
                 [0 0 0]    [1]    [0 0 0]    [1]               
    
                [0]    [0]              
    mark(c()) = [0] >= [0] = active(c())
                [1]    [0]              
    
                [0]    [0]              
    mark(d()) = [0] >= [0] = active(d())
                [1]    [0]              
    
                 [1 1 1]     [1 0 0]        
    g(mark(X)) = [0 1 0]X >= [0 1 0]X = g(X)
                 [0 0 0]     [0 0 0]        
    
                   [1 0 0]     [1 0 0]        
    g(active(X)) = [0 1 0]X >= [0 1 0]X = g(X)
                   [0 0 0]     [0 0 0]        
    
                 [1 1 1]    [0]    [1 0 0]    [0]       
    h(mark(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = h(X)
                 [0 0 0]    [1]    [0 0 0]    [1]       
    
                   [1 0 0]    [0]    [1 0 0]    [0]       
    h(active(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = h(X)
                   [0 0 0]    [1]    [0 0 0]    [1]       
   problem:
    active(h(d())) -> mark(g(c()))
    mark(g(X)) -> active(g(X))
    mark(c()) -> active(c())
    mark(d()) -> active(d())
    g(mark(X)) -> g(X)
    g(active(X)) -> g(X)
    h(mark(X)) -> h(X)
    h(active(X)) -> h(X)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
           [0]
     [d] = [0]
           [0],
     
           [0]
     [c] = [0]
           [0],
     
                  [1 0 0]     [0]
     [mark](x0) = [1 0 0]x0 + [1]
                  [0 1 1]     [1],
     
               [1 0 0]     [1]
     [h](x0) = [1 0 0]x0 + [0]
               [0 0 0]     [0],
     
                    [1 0 0]     [0]
     [active](x0) = [1 0 0]x0 + [0]
                    [0 1 1]     [1],
     
               [1 0 1]  
     [g](x0) = [0 0 1]x0
               [0 0 0]  
    orientation:
                      [1]    [0]               
     active(h(d())) = [1] >= [1] = mark(g(c()))
                      [1]    [1]               
     
                  [1 0 1]    [0]    [1 0 1]    [0]               
     mark(g(X)) = [1 0 1]X + [1] >= [1 0 1]X + [0] = active(g(X))
                  [0 0 1]    [1]    [0 0 1]    [1]               
     
                 [0]    [0]              
     mark(c()) = [1] >= [0] = active(c())
                 [1]    [1]              
     
                 [0]    [0]              
     mark(d()) = [1] >= [0] = active(d())
                 [1]    [1]              
     
                  [1 1 1]    [1]    [1 0 1]        
     g(mark(X)) = [0 1 1]X + [1] >= [0 0 1]X = g(X)
                  [0 0 0]    [0]    [0 0 0]        
     
                    [1 1 1]    [1]    [1 0 1]        
     g(active(X)) = [0 1 1]X + [1] >= [0 0 1]X = g(X)
                    [0 0 0]    [0]    [0 0 0]        
     
                  [1 0 0]    [1]    [1 0 0]    [1]       
     h(mark(X)) = [1 0 0]X + [0] >= [1 0 0]X + [0] = h(X)
                  [0 0 0]    [0]    [0 0 0]    [0]       
     
                    [1 0 0]    [1]    [1 0 0]    [1]       
     h(active(X)) = [1 0 0]X + [0] >= [1 0 0]X + [0] = h(X)
                    [0 0 0]    [0]    [0 0 0]    [0]       
    problem:
     mark(g(X)) -> active(g(X))
     mark(c()) -> active(c())
     mark(d()) -> active(d())
     h(mark(X)) -> h(X)
     h(active(X)) -> h(X)
    Matrix Interpretation Processor: dim=3
     
     interpretation:
            [0]
      [d] = [0]
            [1],
      
            [0]
      [c] = [0]
            [0],
      
                   [1 0 0]     [1]
      [mark](x0) = [0 1 1]x0 + [0]
                   [0 0 0]     [0],
      
                [1 0 0]  
      [h](x0) = [0 0 0]x0
                [0 1 1]  ,
      
                     [1 0 0]  
      [active](x0) = [0 0 1]x0
                     [0 1 0]  ,
      
                [1 0 0]  
      [g](x0) = [0 0 0]x0
                [0 0 0]  
     orientation:
                   [1 0 0]    [1]    [1 0 0]                
      mark(g(X)) = [0 0 0]X + [0] >= [0 0 0]X = active(g(X))
                   [0 0 0]    [0]    [0 0 0]                
      
                  [1]    [0]              
      mark(c()) = [0] >= [0] = active(c())
                  [0]    [0]              
      
                  [1]    [0]              
      mark(d()) = [1] >= [1] = active(d())
                  [0]    [0]              
      
                   [1 0 0]    [1]    [1 0 0]        
      h(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = h(X)
                   [0 1 1]    [0]    [0 1 1]        
      
                     [1 0 0]     [1 0 0]        
      h(active(X)) = [0 0 0]X >= [0 0 0]X = h(X)
                     [0 1 1]     [0 1 1]        
     problem:
      h(active(X)) -> h(X)
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                 [1 0 0]  
       [h](x0) = [0 0 0]x0
                 [0 0 0]  ,
       
                      [1 0 0]     [1]
       [active](x0) = [0 0 0]x0 + [0]
                      [0 0 0]     [0]
      orientation:
                      [1 0 0]    [1]    [1 0 0]        
       h(active(X)) = [0 0 0]X + [0] >= [0 0 0]X = h(X)
                      [0 0 0]    [0]    [0 0 0]        
      problem:
       
      Qed