/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 active(f(f(a()))) -> mark(c(f(g(f(a())))))
 mark(f(X)) -> active(f(mark(X)))
 mark(a()) -> active(a())
 mark(c(X)) -> active(c(X))
 mark(g(X)) -> active(g(mark(X)))
 f(mark(X)) -> f(X)
 f(active(X)) -> f(X)
 c(mark(X)) -> c(X)
 c(active(X)) -> c(X)
 g(mark(X)) -> g(X)
 g(active(X)) -> g(X)

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