/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(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]     [0]
   [mark](x0) = [0 0 0]x0 + [0]
                [0 1 1]     [1],
   
             [1 0 1]  
   [c](x0) = [0 0 0]x0
             [0 0 0]  ,
   
             [1 0 0]     [0]
   [g](x0) = [0 0 1]x0 + [1]
             [0 0 0]     [1],
   
                  [1 0 0]     [0]
   [active](x0) = [0 0 0]x0 + [0]
                  [0 0 1]     [1],
   
             [1 0 0]  
   [f](x0) = [0 0 1]x0
             [0 0 0]  ,
   
         [0]
   [a] = [0]
         [0]
  orientation:
                       [0]    [0]                        
   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 1]    [1]    [0 0 0]    [1]                     
   
               [0]    [0]              
   mark(a()) = [0] >= [0] = active(a())
               [1]    [1]              
   
                [1 0 1]    [0]    [1 0 1]    [0]               
   mark(c(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(c(X))
                [0 0 0]    [1]    [0 0 0]    [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 1]    [3]    [0 0 0]    [2]                     
   
                [1 0 0]    [0]    [1 0 0]        
   f(mark(X)) = [0 1 1]X + [1] >= [0 0 1]X = f(X)
                [0 0 0]    [0]    [0 0 0]        
   
                  [1 0 0]    [0]    [1 0 0]        
   f(active(X)) = [0 0 1]X + [1] >= [0 0 1]X = f(X)
                  [0 0 0]    [0]    [0 0 0]        
   
                [1 1 1]    [1]    [1 0 1]        
   c(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = c(X)
                [0 0 0]    [0]    [0 0 0]        
   
                  [1 0 1]    [1]    [1 0 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]    [0]    [1 0 0]    [0]       
   g(mark(X)) = [0 1 1]X + [2] >= [0 0 1]X + [1] = g(X)
                [0 0 0]    [1]    [0 0 0]    [1]       
   
                  [1 0 0]    [0]    [1 0 0]    [0]       
   g(active(X)) = [0 0 1]X + [2] >= [0 0 1]X + [1] = g(X)
                  [0 0 0]    [1]    [0 0 0]    [1]       
  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)
   g(mark(X)) -> g(X)
   g(active(X)) -> g(X)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                 [1 0 1]  
    [mark](x0) = [0 1 0]x0
                 [0 0 0]  ,
    
              [1 0 0]  
    [c](x0) = [1 0 0]x0
              [0 0 0]  ,
    
              [1 0 1]  
    [g](x0) = [1 0 1]x0
              [0 0 0]  ,
    
                   [1 0 1]  
    [active](x0) = [0 1 0]x0
                   [0 0 0]  ,
    
              [1 1 1]     [0]
    [f](x0) = [0 0 0]x0 + [1]
              [0 0 0]     [0],
    
          [0]
    [a] = [0]
          [0]
   orientation:
                        [1]    [0]                        
    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 0]    [0]    [0 0 0]    [0]                     
    
                [0]    [0]              
    mark(a()) = [0] >= [0] = active(a())
                [0]    [0]              
    
                 [1 0 0]     [1 0 0]                
    mark(c(X)) = [1 0 0]X >= [1 0 0]X = active(c(X))
                 [0 0 0]     [0 0 0]                
    
                 [1 0 1]     [1 0 1]                      
    mark(g(X)) = [1 0 1]X >= [1 0 1]X = active(g(mark(X)))
                 [0 0 0]     [0 0 0]                      
    
                 [1 1 1]    [0]    [1 1 1]    [0]       
    f(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = f(X)
                 [0 0 0]    [0]    [0 0 0]    [0]       
    
                   [1 1 1]    [0]    [1 1 1]    [0]       
    f(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = f(X)
                   [0 0 0]    [0]    [0 0 0]    [0]       
    
                 [1 0 1]     [1 0 1]        
    g(mark(X)) = [1 0 1]X >= [1 0 1]X = g(X)
                 [0 0 0]     [0 0 0]        
    
                   [1 0 1]     [1 0 1]        
    g(active(X)) = [1 0 1]X >= [1 0 1]X = g(X)
                   [0 0 0]     [0 0 0]        
   problem:
    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)
    g(mark(X)) -> g(X)
    g(active(X)) -> g(X)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                  [1 1 1]  
     [mark](x0) = [0 0 1]x0
                  [0 1 0]  ,
     
               [1 0 0]     [0]
     [c](x0) = [0 0 0]x0 + [1]
               [0 0 0]     [0],
     
               [1 0 0]     [0]
     [g](x0) = [0 0 0]x0 + [0]
               [0 1 1]     [1],
     
                    [1 0 0]  
     [active](x0) = [0 0 1]x0
                    [0 1 0]  ,
     
               [1 0 0]     [0]
     [f](x0) = [0 1 1]x0 + [0]
               [0 0 0]     [1],
     
           [0]
     [a] = [0]
           [1]
    orientation:
                  [1 1 1]    [1]    [1 1 1]    [0]                     
     mark(f(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = active(f(mark(X)))
                  [0 1 1]    [0]    [0 1 1]    [0]                     
     
                 [1]    [0]              
     mark(a()) = [1] >= [1] = active(a())
                 [0]    [0]              
     
                  [1 0 0]    [1]    [1 0 0]    [0]               
     mark(c(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(c(X))
                  [0 0 0]    [1]    [0 0 0]    [1]               
     
                  [1 1 1]    [1]    [1 1 1]    [0]                     
     mark(g(X)) = [0 1 1]X + [1] >= [0 1 1]X + [1] = active(g(mark(X)))
                  [0 0 0]    [0]    [0 0 0]    [0]                     
     
                  [1 1 1]    [0]    [1 0 0]    [0]       
     f(mark(X)) = [0 1 1]X + [0] >= [0 1 1]X + [0] = f(X)
                  [0 0 0]    [1]    [0 0 0]    [1]       
     
                    [1 0 0]    [0]    [1 0 0]    [0]       
     f(active(X)) = [0 1 1]X + [0] >= [0 1 1]X + [0] = f(X)
                    [0 0 0]    [1]    [0 0 0]    [1]       
     
                  [1 1 1]    [0]    [1 0 0]    [0]       
     g(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = g(X)
                  [0 1 1]    [1]    [0 1 1]    [1]       
     
                    [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 1]    [1]       
    problem:
     f(mark(X)) -> f(X)
     f(active(X)) -> f(X)
     g(mark(X)) -> g(X)
     g(active(X)) -> g(X)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [mark](x0) = x0 + 4,
      
      [g](x0) = 2x0 + 2,
      
      [active](x0) = 3x0 + 1,
      
      [f](x0) = 2x0
     orientation:
      f(mark(X)) = 2X + 8 >= 2X = f(X)
      
      f(active(X)) = 6X + 2 >= 2X = f(X)
      
      g(mark(X)) = 2X + 10 >= 2X + 2 = g(X)
      
      g(active(X)) = 6X + 4 >= 2X + 2 = g(X)
     problem:
      
     Qed