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) = x0 + 2,
   
   [ok](x0) = 6x0 + 2,
   
   [proper](x0) = x0,
   
   [mark](x0) = x0,
   
   [active](x0) = 5x0,
   
   [f](x0, x1) = 2x0 + 4x1,
   
   [g](x0) = 2x0
  orientation:
   active(f(g(X),Y)) = 20X + 20Y >= 18X + 16Y = mark(f(X,f(g(X),Y)))
   
   active(f(X1,X2)) = 10X1 + 20X2 >= 10X1 + 4X2 = f(active(X1),X2)
   
   active(g(X)) = 10X >= 10X = g(active(X))
   
   f(mark(X1),X2) = 2X1 + 4X2 >= 2X1 + 4X2 = mark(f(X1,X2))
   
   g(mark(X)) = 2X >= 2X = mark(g(X))
   
   proper(f(X1,X2)) = 2X1 + 4X2 >= 2X1 + 4X2 = f(proper(X1),proper(X2))
   
   proper(g(X)) = 2X >= 2X = g(proper(X))
   
   f(ok(X1),ok(X2)) = 12X1 + 24X2 + 12 >= 12X1 + 24X2 + 2 = ok(f(X1,X2))
   
   g(ok(X)) = 12X + 4 >= 12X + 2 = ok(g(X))
   
   top(mark(X)) = X + 2 >= X + 2 = top(proper(X))
   
   top(ok(X)) = 6X + 4 >= 5X + 2 = top(active(X))
  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))
   top(mark(X)) -> top(proper(X))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [top](x0) = 5x0,
    
    [proper](x0) = x0,
    
    [mark](x0) = x0 + 3,
    
    [active](x0) = 5x0 + 7,
    
    [f](x0, x1) = x0 + 3x1 + 2,
    
    [g](x0) = x0 + 1
   orientation:
    active(f(g(X),Y)) = 5X + 15Y + 22 >= 4X + 9Y + 14 = mark(f(X,f(g(X),Y)))
    
    active(f(X1,X2)) = 5X1 + 15X2 + 17 >= 5X1 + 3X2 + 9 = f(active(X1),X2)
    
    active(g(X)) = 5X + 12 >= 5X + 8 = g(active(X))
    
    f(mark(X1),X2) = X1 + 3X2 + 5 >= X1 + 3X2 + 5 = mark(f(X1,X2))
    
    g(mark(X)) = X + 4 >= X + 4 = mark(g(X))
    
    proper(f(X1,X2)) = X1 + 3X2 + 2 >= X1 + 3X2 + 2 = f(proper(X1),proper(X2))
    
    proper(g(X)) = X + 1 >= X + 1 = g(proper(X))
    
    top(mark(X)) = 5X + 15 >= 5X = top(proper(X))
   problem:
    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))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [proper](x0) = 2x0 + 1,
     
     [mark](x0) = x0,
     
     [f](x0, x1) = x0 + x1 + 1,
     
     [g](x0) = 2x0 + 2
    orientation:
     f(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(f(X1,X2))
     
     g(mark(X)) = 2X + 2 >= 2X + 2 = mark(g(X))
     
     proper(f(X1,X2)) = 2X1 + 2X2 + 3 >= 2X1 + 2X2 + 3 = f(proper(X1),proper(X2))
     
     proper(g(X)) = 4X + 5 >= 4X + 4 = g(proper(X))
    problem:
     f(mark(X1),X2) -> mark(f(X1,X2))
     g(mark(X)) -> mark(g(X))
     proper(f(X1,X2)) -> f(proper(X1),proper(X2))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [proper](x0) = 2x0 + 1,
      
      [mark](x0) = x0,
      
      [f](x0, x1) = x0 + x1 + 2,
      
      [g](x0) = 4x0 + 2
     orientation:
      f(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(f(X1,X2))
      
      g(mark(X)) = 4X + 2 >= 4X + 2 = mark(g(X))
      
      proper(f(X1,X2)) = 2X1 + 2X2 + 5 >= 2X1 + 2X2 + 4 = f(proper(X1),proper(X2))
     problem:
      f(mark(X1),X2) -> mark(f(X1,X2))
      g(mark(X)) -> mark(g(X))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                         [0]
       [mark](x0) = x0 + [1]
                         [1],
       
                     [1 1 0]     [1 0 1]  
       [f](x0, x1) = [0 1 0]x0 + [0 0 0]x1
                     [0 0 1]     [0 0 0]  ,
       
                 [1 0 1]  
       [g](x0) = [0 1 0]x0
                 [0 1 0]  
      orientation:
                        [1 1 0]     [1 0 1]     [1]    [1 1 0]     [1 0 1]     [0]                 
       f(mark(X1),X2) = [0 1 0]X1 + [0 0 0]X2 + [1] >= [0 1 0]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 0 1]    [1]    [1 0 1]    [0]             
       g(mark(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = mark(g(X))
                    [0 1 0]    [1]    [0 1 0]    [1]             
      problem:
       
      Qed