/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(f(X)) -> f(active(X))
 f(mark(X)) -> mark(f(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 1 0]     [0]
   [top](x0) = [1 1 0]x0 + [1]
               [0 0 1]     [0],
   
              [1 1 0]  
   [ok](x0) = [0 0 0]x0
              [0 0 1]  ,
   
                  [1 1 0]  
   [proper](x0) = [0 0 0]x0
                  [0 0 1]  ,
   
                  
   [mark](x0) = x0
                  ,
   
             [1 0 0]  
   [g](x0) = [0 1 0]x0
             [0 0 0]  ,
   
                    
   [active](x0) = x0
                    ,
   
             [1 0 1]  
   [f](x0) = [0 1 0]x0
             [1 1 0]  ,
   
         [0]
   [a] = [1]
         [0]
  orientation:
                       [1]    [0]                     
   active(f(f(a()))) = [1] >= [1] = mark(f(g(f(a()))))
                       [1]    [1]                     
   
                  [1 0 1]     [1 0 1]                
   active(f(X)) = [0 1 0]X >= [0 1 0]X = f(active(X))
                  [1 1 0]     [1 1 0]                
   
                [1 0 1]     [1 0 1]              
   f(mark(X)) = [0 1 0]X >= [0 1 0]X = mark(f(X))
                [1 1 0]     [1 1 0]              
   
                  [1 1 1]     [1 1 1]                
   proper(f(X)) = [0 0 0]X >= [0 0 0]X = f(proper(X))
                  [1 1 0]     [1 1 0]                
   
                 [1]    [1]          
   proper(a()) = [0] >= [0] = ok(a())
                 [0]    [0]          
   
                  [1 1 0]     [1 1 0]                
   proper(g(X)) = [0 0 0]X >= [0 0 0]X = g(proper(X))
                  [0 0 0]     [0 0 0]                
   
              [1 1 1]     [1 1 1]            
   f(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(f(X))
              [1 1 0]     [1 1 0]            
   
              [1 1 0]     [1 1 0]            
   g(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(g(X))
              [0 0 0]     [0 0 0]            
   
                  [1 1 0]    [0]    [1 1 0]    [0]                 
   top(mark(X)) = [1 1 0]X + [1] >= [1 1 0]X + [1] = top(proper(X))
                  [0 0 1]    [0]    [0 0 1]    [0]                 
   
                [1 1 0]    [0]    [1 1 0]    [0]                 
   top(ok(X)) = [1 1 0]X + [1] >= [1 1 0]X + [1] = top(active(X))
                [0 0 1]    [0]    [0 0 1]    [0]                 
  problem:
   active(f(X)) -> f(active(X))
   f(mark(X)) -> mark(f(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) = 4x0,
    
    [ok](x0) = 2x0,
    
    [proper](x0) = x0 + 1,
    
    [mark](x0) = 2x0 + 5,
    
    [g](x0) = x0,
    
    [active](x0) = 2x0,
    
    [f](x0) = x0,
    
    [a] = 0
   orientation:
    active(f(X)) = 2X >= 2X = f(active(X))
    
    f(mark(X)) = 2X + 5 >= 2X + 5 = mark(f(X))
    
    proper(f(X)) = X + 1 >= X + 1 = f(proper(X))
    
    proper(a()) = 1 >= 0 = ok(a())
    
    proper(g(X)) = X + 1 >= X + 1 = g(proper(X))
    
    f(ok(X)) = 2X >= 2X = ok(f(X))
    
    g(ok(X)) = 2X >= 2X = ok(g(X))
    
    top(mark(X)) = 8X + 20 >= 4X + 4 = top(proper(X))
    
    top(ok(X)) = 8X >= 8X = top(active(X))
   problem:
    active(f(X)) -> f(active(X))
    f(mark(X)) -> mark(f(X))
    proper(f(X)) -> f(proper(X))
    proper(g(X)) -> g(proper(X))
    f(ok(X)) -> ok(f(X))
    g(ok(X)) -> ok(g(X))
    top(ok(X)) -> top(active(X))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                 [1 0 0]  
     [top](x0) = [0 0 0]x0
                 [0 0 0]  ,
     
                [1 0 1]     [0]
     [ok](x0) = [0 1 0]x0 + [1]
                [0 0 0]     [0],
     
                    [1 0 0]     [1]
     [proper](x0) = [0 0 0]x0 + [0]
                    [0 0 1]     [0],
     
                  [1 0 1]     [0]
     [mark](x0) = [0 1 0]x0 + [1]
                  [0 0 0]     [0],
     
               [1 0 1]  
     [g](x0) = [0 1 0]x0
               [0 0 0]  ,
     
                    [1 0 1]  
     [active](x0) = [0 0 0]x0
                    [0 0 1]  ,
     
               [1 1 0]     [0]
     [f](x0) = [0 1 0]x0 + [0]
               [0 0 1]     [1]
    orientation:
                    [1 1 1]    [1]    [1 0 1]    [0]               
     active(f(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = f(active(X))
                    [0 0 1]    [1]    [0 0 1]    [1]               
     
                  [1 1 1]    [1]    [1 1 1]    [1]             
     f(mark(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = mark(f(X))
                  [0 0 0]    [1]    [0 0 0]    [0]             
     
                    [1 1 0]    [1]    [1 0 0]    [1]               
     proper(f(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = f(proper(X))
                    [0 0 1]    [1]    [0 0 1]    [1]               
     
                    [1 0 1]    [1]    [1 0 1]    [1]               
     proper(g(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = g(proper(X))
                    [0 0 0]    [0]    [0 0 0]    [0]               
     
                [1 1 1]    [1]    [1 1 1]    [1]           
     f(ok(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = ok(f(X))
                [0 0 0]    [1]    [0 0 0]    [0]           
     
                [1 0 1]    [0]    [1 0 1]    [0]           
     g(ok(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = ok(g(X))
                [0 0 0]    [0]    [0 0 0]    [0]           
     
                  [1 0 1]     [1 0 1]                  
     top(ok(X)) = [0 0 0]X >= [0 0 0]X = top(active(X))
                  [0 0 0]     [0 0 0]                  
    problem:
     f(mark(X)) -> mark(f(X))
     proper(f(X)) -> f(proper(X))
     proper(g(X)) -> g(proper(X))
     f(ok(X)) -> ok(f(X))
     g(ok(X)) -> ok(g(X))
     top(ok(X)) -> top(active(X))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                  [1 0 0]  
      [top](x0) = [0 0 0]x0
                  [0 0 0]  ,
      
                      [0]
      [ok](x0) = x0 + [0]
                      [1],
      
                     [1 1 0]  
      [proper](x0) = [0 1 0]x0
                     [0 0 1]  ,
      
                        [0]
      [mark](x0) = x0 + [0]
                        [1],
      
                [1 0 1]     [0]
      [g](x0) = [0 1 0]x0 + [1]
                [0 0 1]     [0],
      
                     [1 0 0]  
      [active](x0) = [0 0 0]x0
                     [0 0 0]  ,
      
                [1 0 1]     [0]
      [f](x0) = [0 1 0]x0 + [1]
                [0 0 1]     [0]
     orientation:
                   [1 0 1]    [1]    [1 0 1]    [0]             
      f(mark(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = mark(f(X))
                   [0 0 1]    [1]    [0 0 1]    [1]             
      
                     [1 1 1]    [1]    [1 1 1]    [0]               
      proper(f(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = f(proper(X))
                     [0 0 1]    [0]    [0 0 1]    [0]               
      
                     [1 1 1]    [1]    [1 1 1]    [0]               
      proper(g(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = g(proper(X))
                     [0 0 1]    [0]    [0 0 1]    [0]               
      
                 [1 0 1]    [1]    [1 0 1]    [0]           
      f(ok(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = ok(f(X))
                 [0 0 1]    [1]    [0 0 1]    [1]           
      
                 [1 0 1]    [1]    [1 0 1]    [0]           
      g(ok(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = ok(g(X))
                 [0 0 1]    [1]    [0 0 1]    [1]           
      
                   [1 0 0]     [1 0 0]                  
      top(ok(X)) = [0 0 0]X >= [0 0 0]X = top(active(X))
                   [0 0 0]     [0 0 0]                  
     problem:
      top(ok(X)) -> top(active(X))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                   [1 0 0]  
       [top](x0) = [0 0 0]x0
                   [0 0 0]  ,
       
                  [1 0 0]     [1]
       [ok](x0) = [0 0 0]x0 + [0]
                  [0 0 0]     [0],
       
                      [1 0 0]  
       [active](x0) = [0 0 0]x0
                      [0 0 0]  
      orientation:
                    [1 0 0]    [1]    [1 0 0]                  
       top(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X = top(active(X))
                    [0 0 0]    [0]    [0 0 0]                  
      problem:
       
      Qed