/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /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=1
  
  interpretation:
   [c] = 0,
   
   [active](x0) = x0 + 1,
   
   [mark](x0) = 4x0 + 1,
   
   [d] = 0,
   
   [g](x0) = 4x0,
   
   [h](x0) = x0
  orientation:
   active(g(X)) = 4X + 1 >= 4X + 1 = mark(h(X))
   
   active(c()) = 1 >= 1 = mark(d())
   
   active(h(d())) = 1 >= 1 = mark(g(c()))
   
   mark(g(X)) = 16X + 1 >= 4X + 1 = active(g(X))
   
   mark(h(X)) = 4X + 1 >= X + 1 = active(h(X))
   
   mark(c()) = 1 >= 1 = active(c())
   
   mark(d()) = 1 >= 1 = active(d())
   
   g(mark(X)) = 16X + 4 >= 4X = g(X)
   
   g(active(X)) = 4X + 4 >= 4X = g(X)
   
   h(mark(X)) = 4X + 1 >= X = h(X)
   
   h(active(X)) = X + 1 >= X = h(X)
  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())
  Matrix Interpretation Processor: dim=3
   
   interpretation:
          [0]
    [c] = [0]
          [0],
    
                   [1 1 0]  
    [active](x0) = [1 0 0]x0
                   [1 0 0]  ,
    
                 [1 1 0]  
    [mark](x0) = [1 0 0]x0
                 [1 0 0]  ,
    
          [0]
    [d] = [0]
          [1],
    
              [1 1 0]     [0]
    [g](x0) = [0 0 1]x0 + [1]
              [0 0 0]     [0],
    
              [1 1 0]  
    [h](x0) = [0 0 1]x0
              [0 0 0]  
   orientation:
                   [1 1 1]    [1]    [1 1 1]              
    active(g(X)) = [1 1 0]X + [0] >= [1 1 0]X = mark(h(X))
                   [1 1 0]    [0]    [1 1 0]              
    
                  [0]    [0]            
    active(c()) = [0] >= [0] = mark(d())
                  [0]    [0]            
    
                     [1]    [1]               
    active(h(d())) = [0] >= [0] = mark(g(c()))
                     [0]    [0]               
    
                 [1 1 1]    [1]    [1 1 1]    [1]               
    mark(g(X)) = [1 1 0]X + [0] >= [1 1 0]X + [0] = active(g(X))
                 [1 1 0]    [0]    [1 1 0]    [0]               
    
                 [1 1 1]     [1 1 1]                
    mark(h(X)) = [1 1 0]X >= [1 1 0]X = active(h(X))
                 [1 1 0]     [1 1 0]                
    
                [0]    [0]              
    mark(c()) = [0] >= [0] = active(c())
                [0]    [0]              
    
                [0]    [0]              
    mark(d()) = [0] >= [0] = active(d())
                [0]    [0]              
   problem:
    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())
   Matrix Interpretation Processor: dim=3
    
    interpretation:
           [0]
     [c] = [1]
           [1],
     
                    [1 1 0]     [0]
     [active](x0) = [0 0 0]x0 + [0]
                    [0 0 0]     [1],
     
                  [1 1 0]  
     [mark](x0) = [0 0 0]x0
                  [0 0 1]  ,
     
           [0]
     [d] = [0]
           [1],
     
               [1 0 0]     [0]
     [g](x0) = [0 0 0]x0 + [0]
               [0 0 0]     [1],
     
               [1 0 1]     [0]
     [h](x0) = [0 0 0]x0 + [0]
               [0 0 0]     [1]
    orientation:
                   [1]    [0]            
     active(c()) = [0] >= [0] = mark(d())
                   [1]    [1]            
     
                      [1]    [0]               
     active(h(d())) = [0] >= [0] = mark(g(c()))
                      [1]    [1]               
     
                  [1 0 0]    [0]    [1 0 0]    [0]               
     mark(g(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(g(X))
                  [0 0 0]    [1]    [0 0 0]    [1]               
     
                  [1 0 1]    [0]    [1 0 1]    [0]               
     mark(h(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(h(X))
                  [0 0 0]    [1]    [0 0 0]    [1]               
     
                 [1]    [1]              
     mark(c()) = [0] >= [0] = active(c())
                 [1]    [1]              
     
                 [0]    [0]              
     mark(d()) = [0] >= [0] = active(d())
                 [1]    [1]              
    problem:
     mark(g(X)) -> active(g(X))
     mark(h(X)) -> active(h(X))
     mark(c()) -> active(c())
     mark(d()) -> active(d())
    Matrix Interpretation Processor: dim=3
     
     interpretation:
            [0]
      [c] = [0]
            [0],
      
                     [1 0 0]  
      [active](x0) = [0 0 0]x0
                     [0 0 0]  ,
      
                   [1 0 0]     [1]
      [mark](x0) = [0 0 0]x0 + [0]
                   [0 0 0]     [0],
      
            [0]
      [d] = [0]
            [0],
      
                [1 0 0]  
      [g](x0) = [0 0 0]x0
                [0 0 0]  ,
      
                [1 0 0]  
      [h](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 0]    [1]    [1 0 0]                
      mark(h(X)) = [0 0 0]X + [0] >= [0 0 0]X = active(h(X))
                   [0 0 0]    [0]    [0 0 0]                
      
                  [1]    [0]              
      mark(c()) = [0] >= [0] = active(c())
                  [0]    [0]              
      
                  [1]    [0]              
      mark(d()) = [0] >= [0] = active(d())
                  [0]    [0]              
     problem:
      
     Qed