/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:
 active(f(f(a()))) -> mark(f(g(f(a()))))
 active(g(X)) -> g(active(X))
 g(mark(X)) -> mark(g(X))
 proper(f(X)) -> f(proper(X))
 proper(a()) -> ok(a())
 proper(g(X)) -> g(proper(X))
 f(ok(X)) -> ok(f(X))
 g(ok(X)) -> ok(g(X))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
               [1 0 0]  
   [top](x0) = [1 1 0]x0
               [0 0 0]  ,
   
                
   [ok](x0) = x0
                ,
   
                    
   [proper](x0) = x0
                    ,
   
                [1 1 0]  
   [mark](x0) = [0 0 0]x0
                [0 0 0]  ,
   
             [1 0 0]  
   [g](x0) = [0 0 0]x0
             [0 0 0]  ,
   
                  [1 0 0]  
   [active](x0) = [0 0 0]x0
                  [0 0 0]  ,
   
             [1 0 1]  
   [f](x0) = [0 0 0]x0
             [0 1 0]  ,
   
         [0]
   [a] = [1]
         [0]
  orientation:
                       [1]    [0]                     
   active(f(f(a()))) = [0] >= [0] = mark(f(g(f(a()))))
                       [0]    [0]                     
   
                  [1 0 0]     [1 0 0]                
   active(g(X)) = [0 0 0]X >= [0 0 0]X = g(active(X))
                  [0 0 0]     [0 0 0]                
   
                [1 1 0]     [1 0 0]              
   g(mark(X)) = [0 0 0]X >= [0 0 0]X = mark(g(X))
                [0 0 0]     [0 0 0]              
   
                  [1 0 1]     [1 0 1]                
   proper(f(X)) = [0 0 0]X >= [0 0 0]X = f(proper(X))
                  [0 1 0]     [0 1 0]                
   
                 [0]    [0]          
   proper(a()) = [1] >= [1] = ok(a())
                 [0]    [0]          
   
                  [1 0 0]     [1 0 0]                
   proper(g(X)) = [0 0 0]X >= [0 0 0]X = g(proper(X))
                  [0 0 0]     [0 0 0]                
   
              [1 0 1]     [1 0 1]            
   f(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(f(X))
              [0 1 0]     [0 1 0]            
   
              [1 0 0]     [1 0 0]            
   g(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(g(X))
              [0 0 0]     [0 0 0]            
   
                  [1 1 0]     [1 0 0]                  
   top(mark(X)) = [1 1 0]X >= [1 1 0]X = top(proper(X))
                  [0 0 0]     [0 0 0]                  
   
                [1 0 0]     [1 0 0]                  
   top(ok(X)) = [1 1 0]X >= [1 0 0]X = top(active(X))
                [0 0 0]     [0 0 0]                  
  problem:
   active(g(X)) -> g(active(X))
   g(mark(X)) -> mark(g(X))
   proper(f(X)) -> f(proper(X))
   proper(a()) -> ok(a())
   proper(g(X)) -> g(proper(X))
   f(ok(X)) -> ok(f(X))
   g(ok(X)) -> ok(g(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [top](x0) = 3x0 + 4,
    
    [ok](x0) = 2x0 + 5,
    
    [proper](x0) = 3x0 + 4,
    
    [mark](x0) = 3x0 + 4,
    
    [g](x0) = x0,
    
    [active](x0) = 2x0 + 4,
    
    [f](x0) = x0,
    
    [a] = 1
   orientation:
    active(g(X)) = 2X + 4 >= 2X + 4 = g(active(X))
    
    g(mark(X)) = 3X + 4 >= 3X + 4 = mark(g(X))
    
    proper(f(X)) = 3X + 4 >= 3X + 4 = f(proper(X))
    
    proper(a()) = 7 >= 7 = ok(a())
    
    proper(g(X)) = 3X + 4 >= 3X + 4 = g(proper(X))
    
    f(ok(X)) = 2X + 5 >= 2X + 5 = ok(f(X))
    
    g(ok(X)) = 2X + 5 >= 2X + 5 = ok(g(X))
    
    top(mark(X)) = 9X + 16 >= 9X + 16 = top(proper(X))
    
    top(ok(X)) = 6X + 19 >= 6X + 16 = top(active(X))
   problem:
    active(g(X)) -> g(active(X))
    g(mark(X)) -> mark(g(X))
    proper(f(X)) -> f(proper(X))
    proper(a()) -> ok(a())
    proper(g(X)) -> g(proper(X))
    f(ok(X)) -> ok(f(X))
    g(ok(X)) -> ok(g(X))
    top(mark(X)) -> top(proper(X))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [top](x0) = x0 + 3,
     
     [ok](x0) = x0 + 1,
     
     [proper](x0) = x0 + 1,
     
     [mark](x0) = x0 + 4,
     
     [g](x0) = x0 + 6,
     
     [active](x0) = x0 + 6,
     
     [f](x0) = x0 + 7,
     
     [a] = 2
    orientation:
     active(g(X)) = X + 12 >= X + 12 = g(active(X))
     
     g(mark(X)) = X + 10 >= X + 10 = mark(g(X))
     
     proper(f(X)) = X + 8 >= X + 8 = f(proper(X))
     
     proper(a()) = 3 >= 3 = ok(a())
     
     proper(g(X)) = X + 7 >= X + 7 = g(proper(X))
     
     f(ok(X)) = X + 8 >= X + 8 = ok(f(X))
     
     g(ok(X)) = X + 7 >= X + 7 = ok(g(X))
     
     top(mark(X)) = X + 7 >= X + 4 = top(proper(X))
    problem:
     active(g(X)) -> g(active(X))
     g(mark(X)) -> mark(g(X))
     proper(f(X)) -> f(proper(X))
     proper(a()) -> ok(a())
     proper(g(X)) -> g(proper(X))
     f(ok(X)) -> ok(f(X))
     g(ok(X)) -> ok(g(X))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [ok](x0) = 4x0 + 3,
      
      [proper](x0) = 4x0 + 3,
      
      [mark](x0) = 6x0 + 5,
      
      [g](x0) = 4x0 + 3,
      
      [active](x0) = 5x0 + 1,
      
      [f](x0) = x0,
      
      [a] = 1
     orientation:
      active(g(X)) = 20X + 16 >= 20X + 7 = g(active(X))
      
      g(mark(X)) = 24X + 23 >= 24X + 23 = mark(g(X))
      
      proper(f(X)) = 4X + 3 >= 4X + 3 = f(proper(X))
      
      proper(a()) = 7 >= 7 = ok(a())
      
      proper(g(X)) = 16X + 15 >= 16X + 15 = g(proper(X))
      
      f(ok(X)) = 4X + 3 >= 4X + 3 = ok(f(X))
      
      g(ok(X)) = 16X + 15 >= 16X + 15 = ok(g(X))
     problem:
      g(mark(X)) -> mark(g(X))
      proper(f(X)) -> f(proper(X))
      proper(a()) -> ok(a())
      proper(g(X)) -> g(proper(X))
      f(ok(X)) -> ok(f(X))
      g(ok(X)) -> ok(g(X))
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [ok](x0) = 4x0 + 2,
       
       [proper](x0) = 5x0 + 2,
       
       [mark](x0) = 3x0 + 1,
       
       [g](x0) = 3x0 + 1,
       
       [f](x0) = x0,
       
       [a] = 0
      orientation:
       g(mark(X)) = 9X + 4 >= 9X + 4 = mark(g(X))
       
       proper(f(X)) = 5X + 2 >= 5X + 2 = f(proper(X))
       
       proper(a()) = 2 >= 2 = ok(a())
       
       proper(g(X)) = 15X + 7 >= 15X + 7 = g(proper(X))
       
       f(ok(X)) = 4X + 2 >= 4X + 2 = ok(f(X))
       
       g(ok(X)) = 12X + 7 >= 12X + 6 = ok(g(X))
      problem:
       g(mark(X)) -> mark(g(X))
       proper(f(X)) -> f(proper(X))
       proper(a()) -> ok(a())
       proper(g(X)) -> g(proper(X))
       f(ok(X)) -> ok(f(X))
      Matrix Interpretation Processor: dim=1
       
       interpretation:
        [ok](x0) = 4x0 + 6,
        
        [proper](x0) = 5x0 + 4,
        
        [mark](x0) = 2x0 + 1,
        
        [g](x0) = 4x0 + 3,
        
        [f](x0) = 4x0 + 3,
        
        [a] = 2
       orientation:
        g(mark(X)) = 8X + 7 >= 8X + 7 = mark(g(X))
        
        proper(f(X)) = 20X + 19 >= 20X + 19 = f(proper(X))
        
        proper(a()) = 14 >= 14 = ok(a())
        
        proper(g(X)) = 20X + 19 >= 20X + 19 = g(proper(X))
        
        f(ok(X)) = 16X + 27 >= 16X + 18 = ok(f(X))
       problem:
        g(mark(X)) -> mark(g(X))
        proper(f(X)) -> f(proper(X))
        proper(a()) -> ok(a())
        proper(g(X)) -> g(proper(X))
       Matrix Interpretation Processor: dim=3
        
        interpretation:
                    [1 0 0]  
         [ok](x0) = [0 0 0]x0
                    [0 0 0]  ,
         
                        [1 1 0]  
         [proper](x0) = [0 0 0]x0
                        [0 0 0]  ,
         
                      [1 1 1]  
         [mark](x0) = [0 0 0]x0
                      [0 0 0]  ,
         
                   [1 0 0]  
         [g](x0) = [0 1 1]x0
                   [0 0 0]  ,
         
                   [1 0 0]     [1]
         [f](x0) = [0 1 0]x0 + [0]
                   [0 0 0]     [0],
         
               [0]
         [a] = [1]
               [0]
        orientation:
                      [1 1 1]     [1 1 1]              
         g(mark(X)) = [0 0 0]X >= [0 0 0]X = mark(g(X))
                      [0 0 0]     [0 0 0]              
         
                        [1 1 0]    [1]    [1 1 0]    [1]               
         proper(f(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = f(proper(X))
                        [0 0 0]    [0]    [0 0 0]    [0]               
         
                       [1]    [0]          
         proper(a()) = [0] >= [0] = ok(a())
                       [0]    [0]          
         
                        [1 1 1]     [1 1 0]                
         proper(g(X)) = [0 0 0]X >= [0 0 0]X = g(proper(X))
                        [0 0 0]     [0 0 0]                
        problem:
         g(mark(X)) -> mark(g(X))
         proper(f(X)) -> f(proper(X))
         proper(g(X)) -> g(proper(X))
        Matrix Interpretation Processor: dim=1
         
         interpretation:
          [proper](x0) = 2x0 + 1,
          
          [mark](x0) = x0 + 3,
          
          [g](x0) = x0 + 3,
          
          [f](x0) = 3x0 + 2
         orientation:
          g(mark(X)) = X + 6 >= X + 6 = mark(g(X))
          
          proper(f(X)) = 6X + 5 >= 6X + 5 = f(proper(X))
          
          proper(g(X)) = 2X + 7 >= 2X + 4 = g(proper(X))
         problem:
          g(mark(X)) -> mark(g(X))
          proper(f(X)) -> f(proper(X))
         Matrix Interpretation Processor: dim=3
          
          interpretation:
                          [1 0 0]     [0]
           [proper](x0) = [0 0 0]x0 + [1]
                          [0 0 0]     [0],
           
                        [1 0 0]     [0]
           [mark](x0) = [0 1 1]x0 + [1]
                        [0 1 0]     [0],
           
                     [1 1 0]  
           [g](x0) = [0 1 0]x0
                     [0 0 1]  ,
           
                     [1 0 0]     [1]
           [f](x0) = [0 0 0]x0 + [1]
                     [0 0 0]     [0]
          orientation:
                        [1 1 1]    [1]    [1 1 0]    [0]             
           g(mark(X)) = [0 1 1]X + [1] >= [0 1 1]X + [1] = mark(g(X))
                        [0 1 0]    [0]    [0 1 0]    [0]             
           
                          [1 0 0]    [1]    [1 0 0]    [1]               
           proper(f(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = f(proper(X))
                          [0 0 0]    [0]    [0 0 0]    [0]               
          problem:
           proper(f(X)) -> f(proper(X))
          Matrix Interpretation Processor: dim=1
           
           interpretation:
            [proper](x0) = 2x0 + 1,
            
            [f](x0) = x0 + 1
           orientation:
            proper(f(X)) = 2X + 3 >= 2X + 2 = f(proper(X))
           problem:
            
           Qed