YES

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

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                [1 0 1]     [0]
   [mark](x0) = [0 0 0]x0 + [1]
                [0 0 0]     [1],
   
             [1 0 1]     [0]
   [f](x0) = [0 0 0]x0 + [1]
             [0 0 0]     [0],
   
             [1 0 0]  
   [g](x0) = [0 0 0]x0
             [0 0 0]  ,
   
                  [1 0 1]     [0]
   [active](x0) = [0 1 1]x0 + [0]
                  [0 0 0]     [1],
   
         [0]
   [c] = [0]
         [1]
  orientation:
                 [1]    [0]                  
   active(c()) = [1] >= [1] = mark(f(g(c())))
                 [1]    [1]                  
   
                     [1 0 0]    [0]    [1 0 0]    [0]             
   active(f(g(X))) = [0 0 0]X + [1] >= [0 0 0]X + [1] = mark(g(X))
                     [0 0 0]    [1]    [0 0 0]    [1]             
   
               [1]    [1]              
   mark(c()) = [1] >= [1] = active(c())
               [1]    [1]              
   
                [1 0 1]    [0]    [1 0 1]    [0]               
   mark(f(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = active(f(X))
                [0 0 0]    [1]    [0 0 0]    [1]               
   
                [1 0 0]    [0]    [1 0 0]    [0]               
   mark(g(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = active(g(X))
                [0 0 0]    [1]    [0 0 0]    [1]               
   
                [1 0 1]    [1]    [1 0 1]    [0]       
   f(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = f(X)
                [0 0 0]    [0]    [0 0 0]    [0]       
   
                  [1 0 1]    [1]    [1 0 1]    [0]       
   f(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = f(X)
                  [0 0 0]    [0]    [0 0 0]    [0]       
   
                [1 0 1]     [1 0 0]        
   g(mark(X)) = [0 0 0]X >= [0 0 0]X = g(X)
                [0 0 0]     [0 0 0]        
   
                  [1 0 1]     [1 0 0]        
   g(active(X)) = [0 0 0]X >= [0 0 0]X = g(X)
                  [0 0 0]     [0 0 0]        
  problem:
   active(f(g(X))) -> mark(g(X))
   mark(c()) -> active(c())
   mark(f(X)) -> active(f(X))
   mark(g(X)) -> active(g(X))
   g(mark(X)) -> g(X)
   g(active(X)) -> g(X)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [mark](x0) = 2x0 + 6,
    
    [f](x0) = x0 + 5,
    
    [g](x0) = x0 + 2,
    
    [active](x0) = 2x0 + 4,
    
    [c] = 1
   orientation:
    active(f(g(X))) = 2X + 18 >= 2X + 10 = mark(g(X))
    
    mark(c()) = 8 >= 6 = active(c())
    
    mark(f(X)) = 2X + 16 >= 2X + 14 = active(f(X))
    
    mark(g(X)) = 2X + 10 >= 2X + 8 = active(g(X))
    
    g(mark(X)) = 2X + 8 >= X + 2 = g(X)
    
    g(active(X)) = 2X + 6 >= X + 2 = g(X)
   problem:
    
   Qed