YES

Problem:
 active(c()) -> mark(f(g(c())))
 active(f(g(X))) -> mark(g(X))
 proper(c()) -> ok(c())
 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(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                [1 1 1]  
   [mark](x0) = [0 0 0]x0
                [0 0 0]  ,
   
                  [1 1 0]  
   [active](x0) = [0 0 0]x0
                  [0 0 0]  ,
   
             [1 0 0]  
   [f](x0) = [0 0 0]x0
             [0 0 0]  ,
   
                  [1 0 0]  
   [proper](x0) = [0 0 0]x0
                  [0 1 0]  ,
   
         [0]
   [c] = [1]
         [0],
   
               [1 0 1]  
   [top](x0) = [0 0 0]x0
               [1 0 1]  ,
   
              [1 0 0]  
   [ok](x0) = [0 0 0]x0
              [0 1 0]  ,
   
             [1 0 0]  
   [g](x0) = [0 0 0]x0
             [0 0 0]  
  orientation:
                 [1]    [0]                  
   active(c()) = [0] >= [0] = mark(f(g(c())))
                 [0]    [0]                  
   
                     [1 0 0]     [1 0 0]              
   active(f(g(X))) = [0 0 0]X >= [0 0 0]X = mark(g(X))
                     [0 0 0]     [0 0 0]              
   
                 [0]    [0]          
   proper(c()) = [0] >= [0] = ok(c())
                 [1]    [1]          
   
                  [1 0 0]     [1 0 0]                
   proper(f(X)) = [0 0 0]X >= [0 0 0]X = f(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]     [1 0 0]            
   f(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(f(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 1 1]     [1 1 0]                  
   top(mark(X)) = [0 0 0]X >= [0 0 0]X = top(proper(X))
                  [1 1 1]     [1 1 0]                  
   
                [1 1 0]     [1 1 0]                  
   top(ok(X)) = [0 0 0]X >= [0 0 0]X = top(active(X))
                [1 1 0]     [1 1 0]                  
  problem:
   active(f(g(X))) -> mark(g(X))
   proper(c()) -> ok(c())
   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(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [mark](x0) = 4x0,
    
    [active](x0) = x0,
    
    [f](x0) = 6x0 + 6,
    
    [proper](x0) = 4x0,
    
    [c] = 4,
    
    [top](x0) = x0,
    
    [ok](x0) = 2x0 + 4,
    
    [g](x0) = 4x0 + 4
   orientation:
    active(f(g(X))) = 24X + 30 >= 16X + 16 = mark(g(X))
    
    proper(c()) = 16 >= 12 = ok(c())
    
    proper(f(X)) = 24X + 24 >= 24X + 6 = f(proper(X))
    
    proper(g(X)) = 16X + 16 >= 16X + 4 = g(proper(X))
    
    f(ok(X)) = 12X + 30 >= 12X + 16 = ok(f(X))
    
    g(ok(X)) = 8X + 20 >= 8X + 12 = ok(g(X))
    
    top(mark(X)) = 4X >= 4X = top(proper(X))
    
    top(ok(X)) = 2X + 4 >= X = top(active(X))
   problem:
    top(mark(X)) -> top(proper(X))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                  [1 0 0]     [0]
     [mark](x0) = [0 0 0]x0 + [0]
                  [0 0 0]     [1],
     
                    [1 0 0]  
     [proper](x0) = [0 0 0]x0
                    [0 0 0]  ,
     
                 [1 0 1]  
     [top](x0) = [0 0 0]x0
                 [0 0 0]  
    orientation:
                    [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]                  
    problem:
     
    Qed