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