YES

Problem:
 active(f(g(X),Y)) -> mark(f(X,f(g(X),Y)))
 active(f(X1,X2)) -> f(active(X1),X2)
 active(g(X)) -> g(active(X))
 f(mark(X1),X2) -> mark(f(X1,X2))
 g(mark(X)) -> mark(g(X))
 proper(f(X1,X2)) -> f(proper(X1),proper(X2))
 proper(g(X)) -> g(proper(X))
 f(ok(X1),ok(X2)) -> ok(f(X1,X2))
 g(ok(X)) -> ok(g(X))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [top](x0) = 2x0 + 2,
   
   [ok](x0) = 6x0 + 4,
   
   [proper](x0) = x0,
   
   [mark](x0) = x0,
   
   [active](x0) = 6x0 + 4,
   
   [f](x0, x1) = 2x0 + 4x1 + 4,
   
   [g](x0) = x0
  orientation:
   active(f(g(X),Y)) = 12X + 24Y + 28 >= 10X + 16Y + 20 = mark(f(X,f(g(X),Y)))
   
   active(f(X1,X2)) = 12X1 + 24X2 + 28 >= 12X1 + 4X2 + 12 = f(active(X1),X2)
   
   active(g(X)) = 6X + 4 >= 6X + 4 = g(active(X))
   
   f(mark(X1),X2) = 2X1 + 4X2 + 4 >= 2X1 + 4X2 + 4 = mark(f(X1,X2))
   
   g(mark(X)) = X >= X = mark(g(X))
   
   proper(f(X1,X2)) = 2X1 + 4X2 + 4 >= 2X1 + 4X2 + 4 = f(proper(X1),proper(X2))
   
   proper(g(X)) = X >= X = g(proper(X))
   
   f(ok(X1),ok(X2)) = 12X1 + 24X2 + 28 >= 12X1 + 24X2 + 28 = ok(f(X1,X2))
   
   g(ok(X)) = 6X + 4 >= 6X + 4 = ok(g(X))
   
   top(mark(X)) = 2X + 2 >= 2X + 2 = top(proper(X))
   
   top(ok(X)) = 12X + 10 >= 12X + 10 = top(active(X))
  problem:
   active(g(X)) -> g(active(X))
   f(mark(X1),X2) -> mark(f(X1,X2))
   g(mark(X)) -> mark(g(X))
   proper(f(X1,X2)) -> f(proper(X1),proper(X2))
   proper(g(X)) -> g(proper(X))
   f(ok(X1),ok(X2)) -> ok(f(X1,X2))
   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]     [0]
    [top](x0) = [1 0 0]x0 + [1]
                [1 0 0]     [0],
    
                 
    [ok](x0) = x0
                 ,
    
                   [1 1 0]  
    [proper](x0) = [0 0 1]x0
                   [0 0 0]  ,
    
                 [1 1 0]     [0]
    [mark](x0) = [0 0 1]x0 + [1]
                 [0 0 1]     [1],
    
                   [1 0 0]     [0]
    [active](x0) = [0 0 0]x0 + [0]
                   [0 0 1]     [1],
    
                  [1 1 0]     [1 1 1]  
    [f](x0, x1) = [0 0 1]x0 + [0 0 0]x1
                  [0 0 1]     [0 0 0]  ,
    
                
    [g](x0) = x0
                
   orientation:
                   [1 0 0]    [0]    [1 0 0]    [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 1 1]     [1 1 1]     [1]    [1 1 1]     [1 1 1]     [0]                 
    f(mark(X1),X2) = [0 0 1]X1 + [0 0 0]X2 + [1] >= [0 0 1]X1 + [0 0 0]X2 + [1] = mark(f(X1,X2))
                     [0 0 1]     [0 0 0]     [1]    [0 0 1]     [0 0 0]     [1]                 
    
                 [1 1 0]    [0]    [1 1 0]    [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 1 1]     [1 1 1]      [1 1 1]     [1 1 1]                             
    proper(f(X1,X2)) = [0 0 1]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = f(proper(X1),proper(X2))
                       [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]                             
    
                   [1 1 0]     [1 1 0]                
    proper(g(X)) = [0 0 1]X >= [0 0 1]X = g(proper(X))
                   [0 0 0]     [0 0 0]                
    
                       [1 1 0]     [1 1 1]      [1 1 0]     [1 1 1]                 
    f(ok(X1),ok(X2)) = [0 0 1]X1 + [0 0 0]X2 >= [0 0 1]X1 + [0 0 0]X2 = ok(f(X1,X2))
                       [0 0 1]     [0 0 0]      [0 0 1]     [0 0 0]                 
    
                                
    g(ok(X)) = X >= X = ok(g(X))
                                
    
                   [1 1 0]    [0]    [1 1 0]    [0]                 
    top(mark(X)) = [1 1 0]X + [1] >= [1 1 0]X + [1] = top(proper(X))
                   [1 1 0]    [0]    [1 1 0]    [0]                 
    
                 [1 0 0]    [0]    [1 0 0]    [0]                 
    top(ok(X)) = [1 0 0]X + [1] >= [1 0 0]X + [1] = top(active(X))
                 [1 0 0]    [0]    [1 0 0]    [0]                 
   problem:
    active(g(X)) -> g(active(X))
    g(mark(X)) -> mark(g(X))
    proper(f(X1,X2)) -> f(proper(X1),proper(X2))
    proper(g(X)) -> g(proper(X))
    f(ok(X1),ok(X2)) -> ok(f(X1,X2))
    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]     [1]
     [top](x0) = [0 0 0]x0 + [0]
                 [0 0 0]     [0],
     
                [1 1 0]     [0]
     [ok](x0) = [0 0 0]x0 + [0]
                [0 0 1]     [1],
     
                    [1 0 0]  
     [proper](x0) = [1 1 0]x0
                    [0 0 0]  ,
     
                       [0]
     [mark](x0) = x0 + [0]
                       [1],
     
                    [1 1 0]  
     [active](x0) = [0 1 0]x0
                    [0 0 0]  ,
     
                   [1 0 0]     [1 0 1]  
     [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                   [0 0 1]     [0 0 0]  ,
     
               [1 0 1]     [0]
     [g](x0) = [0 1 0]x0 + [1]
               [0 0 1]     [0]
    orientation:
                    [1 1 1]    [1]    [1 1 0]    [0]               
     active(g(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = g(active(X))
                    [0 0 0]    [0]    [0 0 0]    [0]               
     
                  [1 0 1]    [1]    [1 0 1]    [0]             
     g(mark(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = mark(g(X))
                  [0 0 1]    [1]    [0 0 1]    [1]             
     
                        [1 0 0]     [1 0 1]      [1 0 0]     [1 0 0]                             
     proper(f(X1,X2)) = [1 0 0]X1 + [1 0 1]X2 >= [0 0 0]X1 + [0 0 0]X2 = f(proper(X1),proper(X2))
                        [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]                             
     
                    [1 0 1]    [0]    [1 0 0]    [0]               
     proper(g(X)) = [1 1 1]X + [1] >= [1 1 0]X + [1] = g(proper(X))
                    [0 0 0]    [0]    [0 0 0]    [0]               
     
                        [1 1 0]     [1 1 1]     [1]    [1 0 0]     [1 0 1]     [0]               
     f(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = ok(f(X1,X2))
                        [0 0 1]     [0 0 0]     [1]    [0 0 1]     [0 0 0]     [1]               
     
                [1 1 1]    [1]    [1 1 1]    [1]           
     g(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = ok(g(X))
                [0 0 1]    [1]    [0 0 1]    [1]           
     
                    [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 0]    [0]    [0 0 0]    [0]                 
     
                  [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 0 0]    [0]    [0 0 0]    [0]                 
    problem:
     proper(f(X1,X2)) -> f(proper(X1),proper(X2))
     proper(g(X)) -> g(proper(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) = [1 0 0]x0
                  [0 1 0]  ,
      
                   
      [ok](x0) = x0
                   ,
      
                     [1 0 1]  
      [proper](x0) = [0 0 1]x0
                     [0 1 0]  ,
      
                   [1 0 1]  
      [mark](x0) = [1 1 1]x0
                   [0 0 0]  ,
      
                     [1 0 0]  
      [active](x0) = [0 0 0]x0
                     [0 0 0]  ,
      
                    [1 0 1]          [0]
      [f](x0, x1) = [0 0 1]x0 + x1 + [1]
                    [0 1 0]          [1],
      
                [1 0 1]     [0]
      [g](x0) = [0 0 1]x0 + [1]
                [0 1 0]     [1]
     orientation:
                         [1 1 1]     [1 0 1]     [1]    [1 1 1]     [1 0 1]     [0]                           
      proper(f(X1,X2)) = [0 1 0]X1 + [0 0 1]X2 + [1] >= [0 1 0]X1 + [0 0 1]X2 + [1] = f(proper(X1),proper(X2))
                         [0 0 1]     [0 1 0]     [1]    [0 0 1]     [0 1 0]     [1]                           
      
                     [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]    [1]    [0 0 1]    [1]               
      
                 [1 0 1]    [0]    [1 0 1]    [0]           
      g(ok(X)) = [0 0 1]X + [1] >= [0 0 1]X + [1] = ok(g(X))
                 [0 1 0]    [1]    [0 1 0]    [1]           
      
                     [1 0 1]     [1 0 1]                  
      top(mark(X)) = [1 0 1]X >= [1 0 1]X = top(proper(X))
                     [1 1 1]     [0 0 1]                  
      
                   [1 0 0]     [1 0 0]                  
      top(ok(X)) = [1 0 0]X >= [1 0 0]X = top(active(X))
                   [0 1 0]     [0 0 0]                  
     problem:
      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 1 1]  
       [top](x0) = [0 0 0]x0
                   [0 0 0]  ,
       
                  [1 0 0]     [0]
       [ok](x0) = [0 0 0]x0 + [0]
                  [0 0 1]     [1],
       
                      [1 0 0]  
       [proper](x0) = [0 0 0]x0
                      [0 0 0]  ,
       
                    [1 0 0]     [0]
       [mark](x0) = [0 0 0]x0 + [1]
                    [0 0 0]     [0],
       
                      [1 0 0]  
       [active](x0) = [0 0 0]x0
                      [0 0 1]  ,
       
                 [1 0 1]  
       [g](x0) = [0 0 0]x0
                 [0 0 1]  
      orientation:
                  [1 0 1]    [1]    [1 0 1]    [0]           
       g(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(g(X))
                  [0 0 1]    [1]    [0 0 1]    [1]           
       
                      [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 1]    [1]    [1 0 1]                  
       top(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X = top(active(X))
                    [0 0 0]    [0]    [0 0 0]                  
      problem:
       
      Qed