YES

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

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                 [1 1 0]     [1 0 0]  
   [f](x0, x1) = [0 0 1]x0 + [0 0 0]x1
                 [0 0 0]     [0 0 0]  ,
   
                [1 1 0]  
   [mark](x0) = [0 0 0]x0
                [0 0 1]  ,
   
             [1 1 0]     [0]
   [g](x0) = [1 1 0]x0 + [0]
             [1 1 1]     [1],
   
                  [1 1 0]  
   [active](x0) = [0 0 0]x0
                  [0 0 1]  
  orientation:
                       [3 3 1]    [1 0 0]    [1]    [3 3 1]    [1 0 0]                        
   active(f(g(X),Y)) = [0 0 0]X + [0 0 0]Y + [0] >= [0 0 0]X + [0 0 0]Y = mark(f(X,f(g(X),Y)))
                       [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]                        
   
                    [1 1 1]     [1 0 0]      [1 1 1]     [1 0 0]                           
   mark(f(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(f(mark(X1),X2))
                    [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]                           
   
                [2 2 0]    [0]    [2 2 0]    [0]                     
   mark(g(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(g(mark(X)))
                [1 1 1]    [1]    [1 1 1]    [1]                     
   
                    [1 1 0]     [1 0 0]      [1 1 0]     [1 0 0]             
   f(mark(X1),X2) = [0 0 1]X1 + [0 0 0]X2 >= [0 0 1]X1 + [0 0 0]X2 = f(X1,X2)
                    [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]             
   
                    [1 1 0]     [1 1 0]      [1 1 0]     [1 0 0]             
   f(X1,mark(X2)) = [0 0 1]X1 + [0 0 0]X2 >= [0 0 1]X1 + [0 0 0]X2 = f(X1,X2)
                    [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]             
   
                      [1 1 0]     [1 0 0]      [1 1 0]     [1 0 0]             
   f(active(X1),X2) = [0 0 1]X1 + [0 0 0]X2 >= [0 0 1]X1 + [0 0 0]X2 = f(X1,X2)
                      [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]             
   
                      [1 1 0]     [1 1 0]      [1 1 0]     [1 0 0]             
   f(X1,active(X2)) = [0 0 1]X1 + [0 0 0]X2 >= [0 0 1]X1 + [0 0 0]X2 = f(X1,X2)
                      [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]             
   
                [1 1 0]    [0]    [1 1 0]    [0]       
   g(mark(X)) = [1 1 0]X + [0] >= [1 1 0]X + [0] = g(X)
                [1 1 1]    [1]    [1 1 1]    [1]       
   
                  [1 1 0]    [0]    [1 1 0]    [0]       
   g(active(X)) = [1 1 0]X + [0] >= [1 1 0]X + [0] = g(X)
                  [1 1 1]    [1]    [1 1 1]    [1]       
  problem:
   mark(f(X1,X2)) -> active(f(mark(X1),X2))
   mark(g(X)) -> active(g(mark(X)))
   f(mark(X1),X2) -> f(X1,X2)
   f(X1,mark(X2)) -> f(X1,X2)
   f(active(X1),X2) -> f(X1,X2)
   f(X1,active(X2)) -> f(X1,X2)
   g(mark(X)) -> g(X)
   g(active(X)) -> g(X)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [f](x0, x1) = 2x0 + 4x1 + 2,
    
    [mark](x0) = 2x0,
    
    [g](x0) = 4x0,
    
    [active](x0) = x0
   orientation:
    mark(f(X1,X2)) = 4X1 + 8X2 + 4 >= 4X1 + 4X2 + 2 = active(f(mark(X1),X2))
    
    mark(g(X)) = 8X >= 8X = active(g(mark(X)))
    
    f(mark(X1),X2) = 4X1 + 4X2 + 2 >= 2X1 + 4X2 + 2 = f(X1,X2)
    
    f(X1,mark(X2)) = 2X1 + 8X2 + 2 >= 2X1 + 4X2 + 2 = f(X1,X2)
    
    f(active(X1),X2) = 2X1 + 4X2 + 2 >= 2X1 + 4X2 + 2 = f(X1,X2)
    
    f(X1,active(X2)) = 2X1 + 4X2 + 2 >= 2X1 + 4X2 + 2 = f(X1,X2)
    
    g(mark(X)) = 8X >= 4X = g(X)
    
    g(active(X)) = 4X >= 4X = g(X)
   problem:
    mark(g(X)) -> active(g(mark(X)))
    f(mark(X1),X2) -> f(X1,X2)
    f(X1,mark(X2)) -> f(X1,X2)
    f(active(X1),X2) -> f(X1,X2)
    f(X1,active(X2)) -> f(X1,X2)
    g(mark(X)) -> g(X)
    g(active(X)) -> g(X)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [f](x0, x1) = 4x0 + 3x1 + 2,
     
     [mark](x0) = 3x0 + 5,
     
     [g](x0) = 2x0 + 6,
     
     [active](x0) = x0 + 7
    orientation:
     mark(g(X)) = 6X + 23 >= 6X + 23 = active(g(mark(X)))
     
     f(mark(X1),X2) = 12X1 + 3X2 + 22 >= 4X1 + 3X2 + 2 = f(X1,X2)
     
     f(X1,mark(X2)) = 4X1 + 9X2 + 17 >= 4X1 + 3X2 + 2 = f(X1,X2)
     
     f(active(X1),X2) = 4X1 + 3X2 + 30 >= 4X1 + 3X2 + 2 = f(X1,X2)
     
     f(X1,active(X2)) = 4X1 + 3X2 + 23 >= 4X1 + 3X2 + 2 = f(X1,X2)
     
     g(mark(X)) = 6X + 16 >= 2X + 6 = g(X)
     
     g(active(X)) = 2X + 20 >= 2X + 6 = g(X)
    problem:
     mark(g(X)) -> active(g(mark(X)))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                   [1 1 1]  
      [mark](x0) = [0 0 0]x0
                   [1 1 0]  ,
      
                [1 1 0]     [0]
      [g](x0) = [0 0 1]x0 + [0]
                [0 0 0]     [1],
      
                     [1 0 0]  
      [active](x0) = [0 0 0]x0
                     [1 0 0]  
     orientation:
                   [1 1 1]    [1]    [1 1 1]                      
      mark(g(X)) = [0 0 0]X + [0] >= [0 0 0]X = active(g(mark(X)))
                   [1 1 1]    [0]    [1 1 1]                      
     problem:
      
     Qed