YES

Problem:
 active(f(f(a()))) -> mark(f(g(f(a()))))
 mark(f(X)) -> active(f(mark(X)))
 mark(a()) -> active(a())
 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 0]     [0]
   [mark](x0) = [0 1 1]x0 + [1]
                [0 0 0]     [0],
   
             [1 0 0]  
   [f](x0) = [0 0 0]x0
             [1 0 0]  ,
   
             [1 1 0]  
   [g](x0) = [0 0 0]x0
             [0 0 0]  ,
   
         [0]
   [a] = [0]
         [0],
   
                  [1 1 0]     [0]
   [active](x0) = [0 0 0]x0 + [1]
                  [0 0 0]     [0]
  orientation:
                       [0]    [0]                     
   active(f(f(a()))) = [1] >= [1] = mark(f(g(f(a()))))
                       [0]    [0]                     
   
                [1 0 0]    [0]    [1 0 0]    [0]                     
   mark(f(X)) = [1 0 0]X + [1] >= [0 0 0]X + [1] = active(f(mark(X)))
                [0 0 0]    [0]    [0 0 0]    [0]                     
   
               [0]    [0]              
   mark(a()) = [1] >= [1] = active(a())
               [0]    [0]              
   
                [1 1 0]    [0]    [1 1 0]    [0]               
   mark(g(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = active(g(X))
                [0 0 0]    [0]    [0 0 0]    [0]               
   
                [1 0 0]     [1 0 0]        
   f(mark(X)) = [0 0 0]X >= [0 0 0]X = f(X)
                [1 0 0]     [1 0 0]        
   
                  [1 1 0]     [1 0 0]        
   f(active(X)) = [0 0 0]X >= [0 0 0]X = f(X)
                  [1 1 0]     [1 0 0]        
   
                [1 1 1]    [1]    [1 1 0]        
   g(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = g(X)
                [0 0 0]    [0]    [0 0 0]        
   
                  [1 1 0]    [1]    [1 1 0]        
   g(active(X)) = [0 0 0]X + [0] >= [0 0 0]X = g(X)
                  [0 0 0]    [0]    [0 0 0]        
  problem:
   active(f(f(a()))) -> mark(f(g(f(a()))))
   mark(f(X)) -> active(f(mark(X)))
   mark(a()) -> active(a())
   mark(g(X)) -> active(g(X))
   f(mark(X)) -> f(X)
   f(active(X)) -> f(X)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                 [1 0 0]  
    [mark](x0) = [0 1 0]x0
                 [0 0 0]  ,
    
              [1 1 0]     [0]
    [f](x0) = [0 0 0]x0 + [1]
              [0 1 0]     [0],
    
              [1 0 0]  
    [g](x0) = [0 0 0]x0
              [0 0 0]  ,
    
          [0]
    [a] = [0]
          [0],
    
                   [1 0 0]  
    [active](x0) = [0 1 0]x0
                   [0 0 0]  
   orientation:
                        [1]    [0]                     
    active(f(f(a()))) = [1] >= [1] = mark(f(g(f(a()))))
                        [0]    [0]                     
    
                 [1 1 0]    [0]    [1 1 0]    [0]                     
    mark(f(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = active(f(mark(X)))
                 [0 0 0]    [0]    [0 0 0]    [0]                     
    
                [0]    [0]              
    mark(a()) = [0] >= [0] = active(a())
                [0]    [0]              
    
                 [1 0 0]     [1 0 0]                
    mark(g(X)) = [0 0 0]X >= [0 0 0]X = active(g(X))
                 [0 0 0]     [0 0 0]                
    
                 [1 1 0]    [0]    [1 1 0]    [0]       
    f(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = f(X)
                 [0 1 0]    [0]    [0 1 0]    [0]       
    
                   [1 1 0]    [0]    [1 1 0]    [0]       
    f(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = f(X)
                   [0 1 0]    [0]    [0 1 0]    [0]       
   problem:
    mark(f(X)) -> active(f(mark(X)))
    mark(a()) -> active(a())
    mark(g(X)) -> active(g(X))
    f(mark(X)) -> f(X)
    f(active(X)) -> f(X)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [mark](x0) = x0 + 1,
     
     [f](x0) = x0,
     
     [g](x0) = x0 + 4,
     
     [a] = 0,
     
     [active](x0) = x0
    orientation:
     mark(f(X)) = X + 1 >= X + 1 = active(f(mark(X)))
     
     mark(a()) = 1 >= 0 = active(a())
     
     mark(g(X)) = X + 5 >= X + 4 = active(g(X))
     
     f(mark(X)) = X + 1 >= X = f(X)
     
     f(active(X)) = X >= X = f(X)
    problem:
     mark(f(X)) -> active(f(mark(X)))
     f(active(X)) -> f(X)
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                   [1 1 0]  
      [mark](x0) = [0 1 0]x0
                   [0 0 0]  ,
      
                [1 0 0]     [0]
      [f](x0) = [0 1 0]x0 + [1]
                [0 0 0]     [0],
      
                     [1 0 0]  
      [active](x0) = [0 1 1]x0
                     [0 0 0]  
     orientation:
                   [1 1 0]    [1]    [1 1 0]    [0]                     
      mark(f(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = active(f(mark(X)))
                   [0 0 0]    [0]    [0 0 0]    [0]                     
      
                     [1 0 0]    [0]    [1 0 0]    [0]       
      f(active(X)) = [0 1 1]X + [1] >= [0 1 0]X + [1] = f(X)
                     [0 0 0]    [0]    [0 0 0]    [0]       
     problem:
      f(active(X)) -> f(X)
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                 [1 0 0]  
       [f](x0) = [1 0 0]x0
                 [0 0 0]  ,
       
                      [1 0 0]     [1]
       [active](x0) = [0 0 0]x0 + [0]
                      [0 0 0]     [0]
      orientation:
                      [1 0 0]    [1]    [1 0 0]        
       f(active(X)) = [1 0 0]X + [1] >= [1 0 0]X = f(X)
                      [0 0 0]    [0]    [0 0 0]        
      problem:
       
      Qed