YES

Problem:
 active(f(f(a()))) -> mark(c(f(g(f(a())))))
 active(f(X)) -> f(active(X))
 active(g(X)) -> g(active(X))
 f(mark(X)) -> mark(f(X))
 g(mark(X)) -> mark(g(X))
 proper(f(X)) -> f(proper(X))
 proper(a()) -> ok(a())
 proper(c(X)) -> c(proper(X))
 proper(g(X)) -> g(proper(X))
 f(ok(X)) -> ok(f(X))
 c(ok(X)) -> ok(c(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]     [1]
   [top](x0) = [0 0 0]x0 + [0]
               [0 0 1]     [0],
   
                
   [ok](x0) = x0
                ,
   
                    
   [proper](x0) = x0
                    ,
   
                  
   [mark](x0) = x0
                  ,
   
             [1 0 0]  
   [c](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 1 0]  
   [f](x0) = [0 0 1]x0
             [0 1 0]  ,
   
         [0]
   [a] = [0]
         [1]
  orientation:
                       [1]    [0]                        
   active(f(f(a()))) = [0] >= [0] = mark(c(f(g(f(a())))))
                       [0]    [0]                        
   
                  [1 1 0]     [1 0 0]                
   active(f(X)) = [0 0 0]X >= [0 0 0]X = f(active(X))
                  [0 0 0]     [0 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 1 0]              
   f(mark(X)) = [0 0 1]X >= [0 0 1]X = mark(f(X))
                [0 1 0]     [0 1 0]              
   
                [1 0 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 1 0]     [1 1 0]                
   proper(f(X)) = [0 0 1]X >= [0 0 1]X = f(proper(X))
                  [0 1 0]     [0 1 0]                
   
                 [0]    [0]          
   proper(a()) = [0] >= [0] = ok(a())
                 [1]    [1]          
   
                  [1 0 0]     [1 0 0]                
   proper(c(X)) = [0 0 0]X >= [0 0 0]X = c(proper(X))
                  [0 0 0]     [0 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 1 0]     [1 1 0]            
   f(ok(X)) = [0 0 1]X >= [0 0 1]X = ok(f(X))
              [0 1 0]     [0 1 0]            
   
              [1 0 0]     [1 0 0]            
   c(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(c(X))
              [0 0 0]     [0 0 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 0 0]    [1]    [1 0 0]    [1]                 
   top(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = top(proper(X))
                  [0 0 1]    [0]    [0 0 1]    [0]                 
   
                [1 0 0]    [1]    [1 0 0]    [1]                 
   top(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = top(active(X))
                [0 0 1]    [0]    [0 0 0]    [0]                 
  problem:
   active(f(X)) -> f(active(X))
   active(g(X)) -> g(active(X))
   f(mark(X)) -> mark(f(X))
   g(mark(X)) -> mark(g(X))
   proper(f(X)) -> f(proper(X))
   proper(a()) -> ok(a())
   proper(c(X)) -> c(proper(X))
   proper(g(X)) -> g(proper(X))
   f(ok(X)) -> ok(f(X))
   c(ok(X)) -> ok(c(X))
   g(ok(X)) -> ok(g(X))
   top(mark(X)) -> top(proper(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 0]  
    [ok](x0) = [0 0 0]x0
               [0 0 0]  ,
    
                   [1 0 0]  
    [proper](x0) = [0 1 0]x0
                   [0 0 0]  ,
    
                 [1 0 0]     [1]
    [mark](x0) = [0 0 0]x0 + [0]
                 [0 0 0]     [0],
    
              [1 0 0]  
    [c](x0) = [0 0 0]x0
              [0 0 0]  ,
    
              [1 0 0]  
    [g](x0) = [0 0 0]x0
              [0 0 0]  ,
    
                   [1 0 0]     [0]
    [active](x0) = [0 0 0]x0 + [1]
                   [0 0 0]     [0],
    
              [1 0 0]     [0]
    [f](x0) = [0 0 0]x0 + [1]
              [0 0 0]     [0],
    
          [1]
    [a] = [0]
          [0]
   orientation:
                   [1 0 0]    [0]    [1 0 0]    [0]               
    active(f(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = f(active(X))
                   [0 0 0]    [0]    [0 0 0]    [0]               
    
                   [1 0 0]    [0]    [1 0 0]                
    active(g(X)) = [0 0 0]X + [1] >= [0 0 0]X = g(active(X))
                   [0 0 0]    [0]    [0 0 0]                
    
                 [1 0 0]    [1]    [1 0 0]    [1]             
    f(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = mark(f(X))
                 [0 0 0]    [0]    [0 0 0]    [0]             
    
                 [1 0 0]    [1]    [1 0 0]    [1]             
    g(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(g(X))
                 [0 0 0]    [0]    [0 0 0]    [0]             
    
                   [1 0 0]    [0]    [1 0 0]    [0]               
    proper(f(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = f(proper(X))
                   [0 0 0]    [0]    [0 0 0]    [0]               
    
                  [1]    [1]          
    proper(a()) = [0] >= [0] = ok(a())
                  [0]    [0]          
    
                   [1 0 0]     [1 0 0]                
    proper(c(X)) = [0 0 0]X >= [0 0 0]X = c(proper(X))
                   [0 0 0]     [0 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 0]    [0]    [1 0 0]            
    f(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X = ok(f(X))
               [0 0 0]    [0]    [0 0 0]            
    
               [1 0 0]     [1 0 0]            
    c(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(c(X))
               [0 0 0]     [0 0 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 0 0]    [1]    [1 0 0]                  
    top(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = top(proper(X))
                   [0 0 0]    [0]    [0 0 0]                  
    
                 [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:
    active(f(X)) -> f(active(X))
    active(g(X)) -> g(active(X))
    f(mark(X)) -> mark(f(X))
    g(mark(X)) -> mark(g(X))
    proper(f(X)) -> f(proper(X))
    proper(a()) -> ok(a())
    proper(c(X)) -> c(proper(X))
    proper(g(X)) -> g(proper(X))
    f(ok(X)) -> ok(f(X))
    c(ok(X)) -> ok(c(X))
    g(ok(X)) -> ok(g(X))
    top(ok(X)) -> top(active(X))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                 [1 1 0]  
     [top](x0) = [0 0 0]x0
                 [0 0 0]  ,
     
                     [0]
     [ok](x0) = x0 + [1]
                     [1],
     
                         [0]
     [proper](x0) = x0 + [1]
                         [1],
     
                  [1 0 0]  
     [mark](x0) = [0 0 0]x0
                  [1 0 0]  ,
     
               [1 0 0]  
     [c](x0) = [0 1 0]x0
               [0 1 0]  ,
     
               [1 0 0]  
     [g](x0) = [0 0 1]x0
               [0 0 1]  ,
     
                    [1 0 0]  
     [active](x0) = [0 0 0]x0
                    [0 0 0]  ,
     
                 
     [f](x0) = x0
                 ,
     
           [0]
     [a] = [0]
           [0]
    orientation:
                    [1 0 0]     [1 0 0]                
     active(f(X)) = [0 0 0]X >= [0 0 0]X = f(active(X))
                    [0 0 0]     [0 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 0 0]     [1 0 0]              
     f(mark(X)) = [0 0 0]X >= [0 0 0]X = mark(f(X))
                  [1 0 0]     [1 0 0]              
     
                  [1 0 0]     [1 0 0]              
     g(mark(X)) = [1 0 0]X >= [0 0 0]X = mark(g(X))
                  [1 0 0]     [1 0 0]              
     
                        [0]        [0]               
     proper(f(X)) = X + [1] >= X + [1] = f(proper(X))
                        [1]        [1]               
     
                   [0]    [0]          
     proper(a()) = [1] >= [1] = ok(a())
                   [1]    [1]          
     
                    [1 0 0]    [0]    [1 0 0]    [0]               
     proper(c(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = c(proper(X))
                    [0 1 0]    [1]    [0 1 0]    [1]               
     
                    [1 0 0]    [0]    [1 0 0]    [0]               
     proper(g(X)) = [0 0 1]X + [1] >= [0 0 1]X + [1] = g(proper(X))
                    [0 0 1]    [1]    [0 0 1]    [1]               
     
                    [0]        [0]           
     f(ok(X)) = X + [1] >= X + [1] = ok(f(X))
                    [1]        [1]           
     
                [1 0 0]    [0]    [1 0 0]    [0]           
     c(ok(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = ok(c(X))
                [0 1 0]    [1]    [0 1 0]    [1]           
     
                [1 0 0]    [0]    [1 0 0]    [0]           
     g(ok(X)) = [0 0 1]X + [1] >= [0 0 1]X + [1] = ok(g(X))
                [0 0 1]    [1]    [0 0 1]    [1]           
     
                  [1 1 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:
     active(f(X)) -> f(active(X))
     active(g(X)) -> g(active(X))
     f(mark(X)) -> mark(f(X))
     g(mark(X)) -> mark(g(X))
     proper(f(X)) -> f(proper(X))
     proper(a()) -> ok(a())
     proper(c(X)) -> c(proper(X))
     proper(g(X)) -> g(proper(X))
     f(ok(X)) -> ok(f(X))
     c(ok(X)) -> ok(c(X))
     g(ok(X)) -> ok(g(X))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                 [1 0 0]     [1]
      [ok](x0) = [0 0 0]x0 + [0]
                 [0 0 0]     [0],
      
                     [1 1 1]  
      [proper](x0) = [0 1 0]x0
                     [0 0 1]  ,
      
                   [1 0 0]     [1]
      [mark](x0) = [0 0 0]x0 + [0]
                   [0 0 0]     [0],
      
                  
      [c](x0) = x0
                  ,
      
                [1 0 0]  
      [g](x0) = [0 0 1]x0
                [0 1 0]  ,
      
                     [1 1 1]  
      [active](x0) = [0 1 0]x0
                     [0 0 1]  ,
      
                [1 0 0]     [0]
      [f](x0) = [0 0 1]x0 + [1]
                [0 1 0]     [0],
      
            [0]
      [a] = [1]
            [0]
     orientation:
                     [1 1 1]    [1]    [1 1 1]    [0]               
      active(f(X)) = [0 0 1]X + [1] >= [0 0 1]X + [1] = f(active(X))
                     [0 1 0]    [0]    [0 1 0]    [0]               
      
                     [1 1 1]     [1 1 1]                
      active(g(X)) = [0 0 1]X >= [0 0 1]X = g(active(X))
                     [0 1 0]     [0 1 0]                
      
                   [1 0 0]    [1]    [1 0 0]    [1]             
      f(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = mark(f(X))
                   [0 0 0]    [0]    [0 0 0]    [0]             
      
                   [1 0 0]    [1]    [1 0 0]    [1]             
      g(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(g(X))
                   [0 0 0]    [0]    [0 0 0]    [0]             
      
                     [1 1 1]    [1]    [1 1 1]    [0]               
      proper(f(X)) = [0 0 1]X + [1] >= [0 0 1]X + [1] = f(proper(X))
                     [0 1 0]    [0]    [0 1 0]    [0]               
      
                    [1]    [1]          
      proper(a()) = [1] >= [0] = ok(a())
                    [0]    [0]          
      
                     [1 1 1]     [1 1 1]                
      proper(c(X)) = [0 1 0]X >= [0 1 0]X = c(proper(X))
                     [0 0 1]     [0 0 1]                
      
                     [1 1 1]     [1 1 1]                
      proper(g(X)) = [0 0 1]X >= [0 0 1]X = g(proper(X))
                     [0 1 0]     [0 1 0]                
      
                 [1 0 0]    [1]    [1 0 0]    [1]           
      f(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = ok(f(X))
                 [0 0 0]    [0]    [0 0 0]    [0]           
      
                 [1 0 0]    [1]    [1 0 0]    [1]           
      c(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(c(X))
                 [0 0 0]    [0]    [0 0 0]    [0]           
      
                 [1 0 0]    [1]    [1 0 0]    [1]           
      g(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(g(X))
                 [0 0 0]    [0]    [0 0 0]    [0]           
     problem:
      active(g(X)) -> g(active(X))
      f(mark(X)) -> mark(f(X))
      g(mark(X)) -> mark(g(X))
      proper(a()) -> ok(a())
      proper(c(X)) -> c(proper(X))
      proper(g(X)) -> g(proper(X))
      f(ok(X)) -> ok(f(X))
      c(ok(X)) -> ok(c(X))
      g(ok(X)) -> ok(g(X))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                  [1 0 0]  
       [ok](x0) = [0 1 0]x0
                  [0 1 0]  ,
       
                      [1 0 1]     [0]
       [proper](x0) = [0 0 0]x0 + [1]
                      [0 0 1]     [0],
       
                    [1 0 0]     [1]
       [mark](x0) = [0 1 0]x0 + [0]
                    [0 0 0]     [0],
       
                 [1 0 0]     [1]
       [c](x0) = [0 0 0]x0 + [0]
                 [0 0 1]     [0],
       
                 [1 1 0]     [0]
       [g](x0) = [0 0 0]x0 + [0]
                 [0 0 1]     [1],
       
                      [1 0 1]  
       [active](x0) = [0 0 0]x0
                      [0 0 1]  ,
       
                 [1 0 0]     [0]
       [f](x0) = [0 0 0]x0 + [1]
                 [0 0 0]     [1],
       
             [0]
       [a] = [0]
             [1]
      orientation:
                      [1 1 1]    [1]    [1 0 1]    [0]               
       active(g(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = g(active(X))
                      [0 0 1]    [1]    [0 0 1]    [1]               
       
                    [1 0 0]    [1]    [1 0 0]    [1]             
       f(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = mark(f(X))
                    [0 0 0]    [1]    [0 0 0]    [0]             
       
                    [1 1 0]    [1]    [1 1 0]    [1]             
       g(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(g(X))
                    [0 0 0]    [1]    [0 0 0]    [0]             
       
                     [1]    [0]          
       proper(a()) = [1] >= [0] = ok(a())
                     [1]    [0]          
       
                      [1 0 1]    [1]    [1 0 1]    [1]               
       proper(c(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = c(proper(X))
                      [0 0 1]    [0]    [0 0 1]    [0]               
       
                      [1 1 1]    [1]    [1 0 1]    [1]               
       proper(g(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = g(proper(X))
                      [0 0 1]    [1]    [0 0 1]    [1]               
       
                  [1 0 0]    [0]    [1 0 0]    [0]           
       f(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = ok(f(X))
                  [0 0 0]    [1]    [0 0 0]    [1]           
       
                  [1 0 0]    [1]    [1 0 0]    [1]           
       c(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(c(X))
                  [0 1 0]    [0]    [0 0 0]    [0]           
       
                  [1 1 0]    [0]    [1 1 0]            
       g(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X = ok(g(X))
                  [0 1 0]    [1]    [0 0 0]            
      problem:
       f(mark(X)) -> mark(f(X))
       g(mark(X)) -> mark(g(X))
       proper(c(X)) -> c(proper(X))
       proper(g(X)) -> g(proper(X))
       f(ok(X)) -> ok(f(X))
       c(ok(X)) -> ok(c(X))
       g(ok(X)) -> ok(g(X))
      Matrix Interpretation Processor: dim=3
       
       interpretation:
                   [1 1 0]     [1]
        [ok](x0) = [0 0 1]x0 + [0]
                   [0 0 1]     [0],
        
                       [1 0 0]  
        [proper](x0) = [0 0 0]x0
                       [0 0 0]  ,
        
                     [1 0 1]     [0]
        [mark](x0) = [0 1 0]x0 + [1]
                     [0 0 1]     [1],
        
                    
        [c](x0) = x0
                    ,
        
                  [1 1 0]  
        [g](x0) = [0 0 1]x0
                  [0 0 1]  ,
        
                  [1 1 0]  
        [f](x0) = [0 0 1]x0
                  [0 0 1]  
       orientation:
                     [1 1 1]    [1]    [1 1 1]    [0]             
        f(mark(X)) = [0 0 1]X + [1] >= [0 0 1]X + [1] = mark(f(X))
                     [0 0 1]    [1]    [0 0 1]    [1]             
        
                     [1 1 1]    [1]    [1 1 1]    [0]             
        g(mark(X)) = [0 0 1]X + [1] >= [0 0 1]X + [1] = mark(g(X))
                     [0 0 1]    [1]    [0 0 1]    [1]             
        
                       [1 0 0]     [1 0 0]                
        proper(c(X)) = [0 0 0]X >= [0 0 0]X = c(proper(X))
                       [0 0 0]     [0 0 0]                
        
                       [1 1 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 1 1]    [1]    [1 1 1]    [1]           
        f(ok(X)) = [0 0 1]X + [0] >= [0 0 1]X + [0] = ok(f(X))
                   [0 0 1]    [0]    [0 0 1]    [0]           
        
                   [1 1 0]    [1]    [1 1 0]    [1]           
        c(ok(X)) = [0 0 1]X + [0] >= [0 0 1]X + [0] = ok(c(X))
                   [0 0 1]    [0]    [0 0 1]    [0]           
        
                   [1 1 1]    [1]    [1 1 1]    [1]           
        g(ok(X)) = [0 0 1]X + [0] >= [0 0 1]X + [0] = ok(g(X))
                   [0 0 1]    [0]    [0 0 1]    [0]           
       problem:
        proper(c(X)) -> c(proper(X))
        proper(g(X)) -> g(proper(X))
        f(ok(X)) -> ok(f(X))
        c(ok(X)) -> ok(c(X))
        g(ok(X)) -> ok(g(X))
       Matrix Interpretation Processor: dim=3
        
        interpretation:
                    [1 0 0]     [0]
         [ok](x0) = [0 0 0]x0 + [0]
                    [0 0 1]     [1],
         
                        [1 0 0]     [0]
         [proper](x0) = [0 0 0]x0 + [1]
                        [0 0 0]     [1],
         
                   [1 0 0]     [1]
         [c](x0) = [0 0 0]x0 + [0]
                   [0 0 1]     [0],
         
                   [1 0 0]     [1]
         [g](x0) = [0 0 1]x0 + [0]
                   [0 0 1]     [0],
         
                   [1 0 1]  
         [f](x0) = [1 0 0]x0
                   [0 0 1]  
        orientation:
                        [1 0 0]    [1]    [1 0 0]    [1]               
         proper(c(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = c(proper(X))
                        [0 0 0]    [1]    [0 0 0]    [1]               
         
                        [1 0 0]    [1]    [1 0 0]    [1]               
         proper(g(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = g(proper(X))
                        [0 0 0]    [1]    [0 0 0]    [1]               
         
                    [1 0 1]    [1]    [1 0 1]    [0]           
         f(ok(X)) = [1 0 0]X + [0] >= [0 0 0]X + [0] = ok(f(X))
                    [0 0 1]    [1]    [0 0 1]    [1]           
         
                    [1 0 0]    [1]    [1 0 0]    [1]           
         c(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(c(X))
                    [0 0 1]    [1]    [0 0 1]    [1]           
         
                    [1 0 0]    [1]    [1 0 0]    [1]           
         g(ok(X)) = [0 0 1]X + [1] >= [0 0 0]X + [0] = ok(g(X))
                    [0 0 1]    [1]    [0 0 1]    [1]           
        problem:
         proper(c(X)) -> c(proper(X))
         proper(g(X)) -> g(proper(X))
         c(ok(X)) -> ok(c(X))
         g(ok(X)) -> ok(g(X))
        Matrix Interpretation Processor: dim=1
         
         interpretation:
          [ok](x0) = 3x0 + 1,
          
          [proper](x0) = 4x0 + 1,
          
          [c](x0) = x0,
          
          [g](x0) = 4x0 + 1
         orientation:
          proper(c(X)) = 4X + 1 >= 4X + 1 = c(proper(X))
          
          proper(g(X)) = 16X + 5 >= 16X + 5 = g(proper(X))
          
          c(ok(X)) = 3X + 1 >= 3X + 1 = ok(c(X))
          
          g(ok(X)) = 12X + 5 >= 12X + 4 = ok(g(X))
         problem:
          proper(c(X)) -> c(proper(X))
          proper(g(X)) -> g(proper(X))
          c(ok(X)) -> ok(c(X))
         Matrix Interpretation Processor: dim=3
          
          interpretation:
                           [0]
           [ok](x0) = x0 + [0]
                           [1],
           
                          [1 1 0]  
           [proper](x0) = [0 1 0]x0
                          [0 0 1]  ,
           
                     [1 0 1]     [0]
           [c](x0) = [0 1 0]x0 + [1]
                     [0 1 1]     [0],
           
                     [1 0 0]     [0]
           [g](x0) = [0 1 0]x0 + [1]
                     [0 0 0]     [1]
          orientation:
                          [1 1 1]    [1]    [1 1 1]    [0]               
           proper(c(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = c(proper(X))
                          [0 1 1]    [0]    [0 1 1]    [0]               
           
                          [1 1 0]    [1]    [1 1 0]    [0]               
           proper(g(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = g(proper(X))
                          [0 0 0]    [1]    [0 0 0]    [1]               
           
                      [1 0 1]    [1]    [1 0 1]    [0]           
           c(ok(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = ok(c(X))
                      [0 1 1]    [1]    [0 1 1]    [1]           
          problem:
           
          Qed