/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(a(),X,X)) -> mark(f(X,b(),b()))
 active(b()) -> mark(a())
 active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
 f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
 proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
 proper(a()) -> ok(a())
 proper(b()) -> ok(b())
 f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
 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 0 0]x0
               [0 0 0]  ,
   
                
   [ok](x0) = x0
                ,
   
                    
   [proper](x0) = x0
                    ,
   
                [1 0 0]  
   [mark](x0) = [0 0 0]x0
                [0 0 1]  ,
   
         [0]
   [b] = [0]
         [0],
   
                  [1 0 0]  
   [active](x0) = [0 0 0]x0
                  [0 0 0]  ,
   
                     [1 1 0]     [1 0 1]     [1 1 0]  
   [f](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2
                     [0 0 0]     [0 0 0]     [0 0 0]  ,
   
         [0]
   [a] = [1]
         [0]
  orientation:
                        [2 1 1]    [1]    [1 1 0]                      
   active(f(a(),X,X)) = [0 0 0]X + [0] >= [0 0 0]X = mark(f(X,b(),b()))
                        [0 0 0]    [0]    [0 0 0]                      
   
                 [0]    [0]            
   active(b()) = [0] >= [0] = mark(a())
                 [0]    [0]            
   
                         [1 1 0]     [1 0 1]     [1 1 0]      [1 1 0]     [1 0 0]     [1 1 0]                        
   active(f(X1,X2,X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = f(X1,active(X2),X3)
                         [0 0 0]     [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]     [0 0 0]                        
   
                       [1 1 0]     [1 0 1]     [1 1 0]      [1 1 0]     [1 0 1]     [1 1 0]                      
   f(X1,mark(X2),X3) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = mark(f(X1,X2,X3))
                       [0 0 0]     [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]     [0 0 0]                      
   
                         [1 1 0]     [1 0 1]     [1 1 0]      [1 1 0]     [1 0 1]     [1 1 0]                                        
   proper(f(X1,X2,X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = f(proper(X1),proper(X2),proper(X3))
                         [0 0 0]     [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]     [0 0 0]                                        
   
                 [0]    [0]          
   proper(a()) = [1] >= [1] = ok(a())
                 [0]    [0]          
   
                 [0]    [0]          
   proper(b()) = [0] >= [0] = ok(b())
                 [0]    [0]          
   
                             [1 1 0]     [1 0 1]     [1 1 0]      [1 1 0]     [1 0 1]     [1 1 0]                    
   f(ok(X1),ok(X2),ok(X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = ok(f(X1,X2,X3))
                             [0 0 0]     [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]     [0 0 0]                    
   
                  [1 0 0]     [1 0 0]                  
   top(mark(X)) = [1 0 0]X >= [1 0 0]X = top(proper(X))
                  [0 0 0]     [0 0 0]                  
   
                [1 0 0]     [1 0 0]                  
   top(ok(X)) = [1 0 0]X >= [1 0 0]X = top(active(X))
                [0 0 0]     [0 0 0]                  
  problem:
   active(b()) -> mark(a())
   active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
   f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
   proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
   proper(a()) -> ok(a())
   proper(b()) -> ok(b())
   f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [top](x0) = x0 + 2,
    
    [ok](x0) = x0,
    
    [proper](x0) = x0,
    
    [mark](x0) = x0 + 1,
    
    [b] = 3,
    
    [active](x0) = x0,
    
    [f](x0, x1, x2) = x0 + x1 + x2,
    
    [a] = 2
   orientation:
    active(b()) = 3 >= 3 = mark(a())
    
    active(f(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = f(X1,active(X2),X3)
    
    f(X1,mark(X2),X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = mark(f(X1,X2,X3))
    
    proper(f(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = f(proper(X1),proper(X2),proper(X3))
    
    proper(a()) = 2 >= 2 = ok(a())
    
    proper(b()) = 3 >= 3 = ok(b())
    
    f(ok(X1),ok(X2),ok(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = ok(f(X1,X2,X3))
    
    top(mark(X)) = X + 3 >= X + 2 = top(proper(X))
    
    top(ok(X)) = X + 2 >= X + 2 = top(active(X))
   problem:
    active(b()) -> mark(a())
    active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
    f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
    proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
    proper(a()) -> ok(a())
    proper(b()) -> ok(b())
    f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
    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 1 1]  
     [ok](x0) = [0 0 0]x0
                [0 0 0]  ,
     
                    [1 0 0]  
     [proper](x0) = [0 0 0]x0
                    [0 0 0]  ,
     
                  [1 0 0]  
     [mark](x0) = [0 0 0]x0
                  [0 0 0]  ,
     
           [1]
     [b] = [0]
           [0],
     
                    [1 1 1]  
     [active](x0) = [0 1 1]x0
                    [0 1 1]  ,
     
                       [1 0 0]     [1 0 0]     [1 0 0]  
     [f](x0, x1, x2) = [0 0 0]x0 + [0 0 1]x1 + [0 0 0]x2
                       [0 0 1]     [0 1 0]     [0 0 0]  ,
     
           [0]
     [a] = [0]
           [0]
    orientation:
                   [1]    [0]            
     active(b()) = [0] >= [0] = mark(a())
                   [0]    [0]            
     
                           [1 0 1]     [1 1 1]     [1 0 0]      [1 0 0]     [1 1 1]     [1 0 0]                        
     active(f(X1,X2,X3)) = [0 0 1]X1 + [0 1 1]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 1 1]X2 + [0 0 0]X3 = f(X1,active(X2),X3)
                           [0 0 1]     [0 1 1]     [0 0 0]      [0 0 1]     [0 1 1]     [0 0 0]                        
     
                         [1 0 0]     [1 0 0]     [1 0 0]      [1 0 0]     [1 0 0]     [1 0 0]                      
     f(X1,mark(X2),X3) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = mark(f(X1,X2,X3))
                         [0 0 1]     [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]     [0 0 0]                      
     
                           [1 0 0]     [1 0 0]     [1 0 0]      [1 0 0]     [1 0 0]     [1 0 0]                                        
     proper(f(X1,X2,X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = f(proper(X1),proper(X2),proper(X3))
                           [0 0 0]     [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]     [0 0 0]                                        
     
                   [0]    [0]          
     proper(a()) = [0] >= [0] = ok(a())
                   [0]    [0]          
     
                   [1]    [1]          
     proper(b()) = [0] >= [0] = ok(b())
                   [0]    [0]          
     
                               [1 1 1]     [1 1 1]     [1 1 1]      [1 0 1]     [1 1 1]     [1 0 0]                    
     f(ok(X1),ok(X2),ok(X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = ok(f(X1,X2,X3))
                               [0 0 0]     [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]     [0 0 0]                    
     
                  [1 1 1]     [1 1 1]                  
     top(ok(X)) = [0 0 0]X >= [0 0 0]X = top(active(X))
                  [0 0 0]     [0 0 0]                  
    problem:
     active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
     f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
     proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
     proper(a()) -> ok(a())
     proper(b()) -> ok(b())
     f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
     top(ok(X)) -> top(active(X))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                  [1 0 0]     [1]
      [top](x0) = [0 0 0]x0 + [0]
                  [0 1 0]     [0],
      
                 [1 1 0]     [0]
      [ok](x0) = [0 1 0]x0 + [0]
                 [0 0 1]     [1],
      
                     [1 1 0]     [0]
      [proper](x0) = [1 1 0]x0 + [0]
                     [0 0 0]     [1],
      
                   [1 0 0]  
      [mark](x0) = [0 0 0]x0
                   [0 0 1]  ,
      
            [0]
      [b] = [0]
            [0],
      
                     [1 1 0]     [0]
      [active](x0) = [0 1 0]x0 + [0]
                     [1 0 0]     [1],
      
                        [1 0 1]     [1 0 0]     [1 0 0]     [0]
      [f](x0, x1, x2) = [0 1 0]x0 + [0 1 0]x1 + [0 1 0]x2 + [1]
                        [0 0 1]     [0 0 0]     [0 0 0]     [0],
      
            [1]
      [a] = [0]
            [0]
     orientation:
                            [1 1 1]     [1 1 0]     [1 1 0]     [1]    [1 0 1]     [1 1 0]     [1 0 0]     [0]                      
      active(f(X1,X2,X3)) = [0 1 0]X1 + [0 1 0]X2 + [0 1 0]X3 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [0 1 0]X3 + [1] = f(X1,active(X2),X3)
                            [1 0 1]     [1 0 0]     [1 0 0]     [1]    [0 0 1]     [0 0 0]     [0 0 0]     [0]                      
      
                          [1 0 1]     [1 0 0]     [1 0 0]     [0]    [1 0 1]     [1 0 0]     [1 0 0]                      
      f(X1,mark(X2),X3) = [0 1 0]X1 + [0 0 0]X2 + [0 1 0]X3 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = mark(f(X1,X2,X3))
                          [0 0 1]     [0 0 0]     [0 0 0]     [0]    [0 0 1]     [0 0 0]     [0 0 0]                      
      
                            [1 1 1]     [1 1 0]     [1 1 0]     [1]    [1 1 0]     [1 1 0]     [1 1 0]     [1]                                      
      proper(f(X1,X2,X3)) = [1 1 1]X1 + [1 1 0]X2 + [1 1 0]X3 + [1] >= [1 1 0]X1 + [1 1 0]X2 + [1 1 0]X3 + [1] = f(proper(X1),proper(X2),proper(X3))
                            [0 0 0]     [0 0 0]     [0 0 0]     [1]    [0 0 0]     [0 0 0]     [0 0 0]     [1]                                      
      
                    [1]    [1]          
      proper(a()) = [1] >= [0] = ok(a())
                    [1]    [1]          
      
                    [0]    [0]          
      proper(b()) = [0] >= [0] = ok(b())
                    [1]    [1]          
      
                                [1 1 1]     [1 1 0]     [1 1 0]     [1]    [1 1 1]     [1 1 0]     [1 1 0]     [1]                  
      f(ok(X1),ok(X2),ok(X3)) = [0 1 0]X1 + [0 1 0]X2 + [0 1 0]X3 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [0 1 0]X3 + [1] = ok(f(X1,X2,X3))
                                [0 0 1]     [0 0 0]     [0 0 0]     [1]    [0 0 1]     [0 0 0]     [0 0 0]     [1]                  
      
                   [1 1 0]    [1]    [1 1 0]    [1]                 
      top(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = top(active(X))
                   [0 1 0]    [0]    [0 1 0]    [0]                 
     problem:
      f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
      proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
      proper(a()) -> ok(a())
      proper(b()) -> ok(b())
      f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
      top(ok(X)) -> top(active(X))
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [top](x0) = 2x0 + 4,
       
       [ok](x0) = x0,
       
       [proper](x0) = 4x0,
       
       [mark](x0) = x0 + 4,
       
       [b] = 0,
       
       [active](x0) = x0,
       
       [f](x0, x1, x2) = 4x0 + 2x1 + x2,
       
       [a] = 0
      orientation:
       f(X1,mark(X2),X3) = 4X1 + 2X2 + X3 + 8 >= 4X1 + 2X2 + X3 + 4 = mark(f(X1,X2,X3))
       
       proper(f(X1,X2,X3)) = 16X1 + 8X2 + 4X3 >= 16X1 + 8X2 + 4X3 = f(proper(X1),proper(X2),proper(X3))
       
       proper(a()) = 0 >= 0 = ok(a())
       
       proper(b()) = 0 >= 0 = ok(b())
       
       f(ok(X1),ok(X2),ok(X3)) = 4X1 + 2X2 + X3 >= 4X1 + 2X2 + X3 = ok(f(X1,X2,X3))
       
       top(ok(X)) = 2X + 4 >= 2X + 4 = top(active(X))
      problem:
       proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
       proper(a()) -> ok(a())
       proper(b()) -> ok(b())
       f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
       top(ok(X)) -> top(active(X))
      Matrix Interpretation Processor: dim=1
       
       interpretation:
        [top](x0) = x0,
        
        [ok](x0) = 6x0 + 1,
        
        [proper](x0) = 6x0 + 1,
        
        [b] = 4,
        
        [active](x0) = 6x0,
        
        [f](x0, x1, x2) = 4x0 + x1 + x2 + 1,
        
        [a] = 4
       orientation:
        proper(f(X1,X2,X3)) = 24X1 + 6X2 + 6X3 + 7 >= 24X1 + 6X2 + 6X3 + 7 = f(proper(X1),proper(X2),proper(X3))
        
        proper(a()) = 25 >= 25 = ok(a())
        
        proper(b()) = 25 >= 25 = ok(b())
        
        f(ok(X1),ok(X2),ok(X3)) = 24X1 + 6X2 + 6X3 + 7 >= 24X1 + 6X2 + 6X3 + 7 = ok(f(X1,X2,X3))
        
        top(ok(X)) = 6X + 1 >= 6X = top(active(X))
       problem:
        proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
        proper(a()) -> ok(a())
        proper(b()) -> ok(b())
        f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
       Matrix Interpretation Processor: dim=1
        
        interpretation:
         [ok](x0) = x0 + 1,
         
         [proper](x0) = 6x0 + 1,
         
         [b] = 0,
         
         [f](x0, x1, x2) = 4x0 + x1 + x2 + 1,
         
         [a] = 0
        orientation:
         proper(f(X1,X2,X3)) = 24X1 + 6X2 + 6X3 + 7 >= 24X1 + 6X2 + 6X3 + 7 = f(proper(X1),proper(X2),proper(X3))
         
         proper(a()) = 1 >= 1 = ok(a())
         
         proper(b()) = 1 >= 1 = ok(b())
         
         f(ok(X1),ok(X2),ok(X3)) = 4X1 + X2 + X3 + 7 >= 4X1 + X2 + X3 + 2 = ok(f(X1,X2,X3))
        problem:
         proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
         proper(a()) -> ok(a())
         proper(b()) -> ok(b())
        Matrix Interpretation Processor: dim=3
         
         interpretation:
                     [1 0 1]  
          [ok](x0) = [0 0 0]x0
                     [0 0 0]  ,
          
                         [1 1 0]  
          [proper](x0) = [0 1 0]x0
                         [0 0 0]  ,
          
                [0]
          [b] = [1]
                [0],
          
                            [1 0 0]     [1 0 0]     [1 0 0]     [0]
          [f](x0, x1, x2) = [0 1 1]x0 + [0 1 0]x1 + [0 1 1]x2 + [1]
                            [0 0 0]     [0 0 0]     [0 0 0]     [0],
          
                [0]
          [a] = [1]
                [1]
         orientation:
                                [1 1 1]     [1 1 0]     [1 1 1]     [1]    [1 1 0]     [1 1 0]     [1 1 0]     [0]                                      
          proper(f(X1,X2,X3)) = [0 1 1]X1 + [0 1 0]X2 + [0 1 1]X3 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [0 1 0]X3 + [1] = f(proper(X1),proper(X2),proper(X3))
                                [0 0 0]     [0 0 0]     [0 0 0]     [0]    [0 0 0]     [0 0 0]     [0 0 0]     [0]                                      
          
                        [1]    [1]          
          proper(a()) = [1] >= [0] = ok(a())
                        [0]    [0]          
          
                        [1]    [0]          
          proper(b()) = [1] >= [0] = ok(b())
                        [0]    [0]          
         problem:
          proper(a()) -> ok(a())
         Matrix Interpretation Processor: dim=3
          
          interpretation:
                      [1 0 0]     [0]
           [ok](x0) = [0 0 0]x0 + [0]
                      [0 0 0]     [1],
           
                          [1 0 0]     [1]
           [proper](x0) = [0 1 0]x0 + [0]
                          [0 1 0]     [0],
           
                 [0]
           [a] = [1]
                 [0]
          orientation:
                         [1]    [0]          
           proper(a()) = [1] >= [0] = ok(a())
                         [1]    [1]          
          problem:
           
          Qed