YES

Problem:
 active(f(f(a()))) -> mark(f(g(f(a()))))
 active(f(X)) -> f(active(X))
 f(mark(X)) -> mark(f(X))
 proper(f(X)) -> f(proper(X))
 proper(a()) -> ok(a())
 proper(g(X)) -> g(proper(X))
 f(ok(X)) -> ok(f(X))
 g(ok(X)) -> ok(g(X))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
               [1 0 0]  
   [top](x0) = [0 0 0]x0
               [1 0 1]  ,
   
                
   [ok](x0) = x0
                ,
   
                    
   [proper](x0) = x0
                    ,
   
                     [0]
   [mark](x0) = x0 + [1]
                     [0],
   
             [1 0 0]  
   [g](x0) = [0 0 0]x0
             [0 0 0]  ,
   
                    
   [active](x0) = x0
                    ,
   
             [1 1 0]     [0]
   [f](x0) = [0 1 1]x0 + [0]
             [0 0 0]     [1],
   
         [1]
   [a] = [0]
         [0]
  orientation:
                       [1]    [1]                     
   active(f(f(a()))) = [1] >= [1] = mark(f(g(f(a()))))
                       [1]    [1]                     
   
                  [1 1 0]    [0]    [1 1 0]    [0]               
   active(f(X)) = [0 1 1]X + [0] >= [0 1 1]X + [0] = f(active(X))
                  [0 0 0]    [1]    [0 0 0]    [1]               
   
                [1 1 0]    [1]    [1 1 0]    [0]             
   f(mark(X)) = [0 1 1]X + [1] >= [0 1 1]X + [1] = mark(f(X))
                [0 0 0]    [1]    [0 0 0]    [1]             
   
                  [1 1 0]    [0]    [1 1 0]    [0]               
   proper(f(X)) = [0 1 1]X + [0] >= [0 1 1]X + [0] = f(proper(X))
                  [0 0 0]    [1]    [0 0 0]    [1]               
   
                 [1]    [1]          
   proper(a()) = [0] >= [0] = ok(a())
                 [0]    [0]          
   
                  [1 0 0]     [1 0 0]                
   proper(g(X)) = [0 0 0]X >= [0 0 0]X = g(proper(X))
                  [0 0 0]     [0 0 0]                
   
              [1 1 0]    [0]    [1 1 0]    [0]           
   f(ok(X)) = [0 1 1]X + [0] >= [0 1 1]X + [0] = ok(f(X))
              [0 0 0]    [1]    [0 0 0]    [1]           
   
              [1 0 0]     [1 0 0]            
   g(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(g(X))
              [0 0 0]     [0 0 0]            
   
                  [1 0 0]     [1 0 0]                  
   top(mark(X)) = [0 0 0]X >= [0 0 0]X = top(proper(X))
                  [1 0 1]     [1 0 1]                  
   
                [1 0 0]     [1 0 0]                  
   top(ok(X)) = [0 0 0]X >= [0 0 0]X = top(active(X))
                [1 0 1]     [1 0 1]                  
  problem:
   active(f(f(a()))) -> mark(f(g(f(a()))))
   active(f(X)) -> f(active(X))
   proper(f(X)) -> f(proper(X))
   proper(a()) -> ok(a())
   proper(g(X)) -> g(proper(X))
   f(ok(X)) -> ok(f(X))
   g(ok(X)) -> ok(g(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                [1 1 0]     [0]
    [top](x0) = [0 0 0]x0 + [1]
                [1 1 0]     [0],
    
                 
    [ok](x0) = x0
                 ,
    
                   [1 0 1]  
    [proper](x0) = [0 1 0]x0
                   [0 0 0]  ,
    
                 [1 0 1]  
    [mark](x0) = [0 1 0]x0
                 [0 0 0]  ,
    
              [1 0 0]  
    [g](x0) = [0 0 1]x0
              [0 0 1]  ,
    
                   [1 1 0]  
    [active](x0) = [0 0 0]x0
                   [0 0 1]  ,
    
              [1 0 1]  
    [f](x0) = [0 1 0]x0
              [0 0 0]  ,
    
          [0]
    [a] = [1]
          [0]
   orientation:
                        [1]    [0]                     
    active(f(f(a()))) = [0] >= [0] = mark(f(g(f(a()))))
                        [0]    [0]                     
    
                   [1 1 1]     [1 1 1]                
    active(f(X)) = [0 0 0]X >= [0 0 0]X = f(active(X))
                   [0 0 0]     [0 0 0]                
    
                   [1 0 1]     [1 0 1]                
    proper(f(X)) = [0 1 0]X >= [0 1 0]X = f(proper(X))
                   [0 0 0]     [0 0 0]                
    
                  [0]    [0]          
    proper(a()) = [1] >= [1] = ok(a())
                  [0]    [0]          
    
                   [1 0 1]     [1 0 1]                
    proper(g(X)) = [0 0 1]X >= [0 0 0]X = g(proper(X))
                   [0 0 0]     [0 0 0]                
    
               [1 0 1]     [1 0 1]            
    f(ok(X)) = [0 1 0]X >= [0 1 0]X = ok(f(X))
               [0 0 0]     [0 0 0]            
    
               [1 0 0]     [1 0 0]            
    g(ok(X)) = [0 0 1]X >= [0 0 1]X = ok(g(X))
               [0 0 1]     [0 0 1]            
    
                   [1 1 1]    [0]    [1 1 1]    [0]                 
    top(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = top(proper(X))
                   [1 1 1]    [0]    [1 1 1]    [0]                 
    
                 [1 1 0]    [0]    [1 1 0]    [0]                 
    top(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = top(active(X))
                 [1 1 0]    [0]    [1 1 0]    [0]                 
   problem:
    active(f(X)) -> f(active(X))
    proper(f(X)) -> f(proper(X))
    proper(a()) -> ok(a())
    proper(g(X)) -> g(proper(X))
    f(ok(X)) -> ok(f(X))
    g(ok(X)) -> ok(g(X))
    top(mark(X)) -> top(proper(X))
    top(ok(X)) -> top(active(X))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [top](x0) = 2x0 + 1,
     
     [ok](x0) = 4x0,
     
     [proper](x0) = 4x0,
     
     [mark](x0) = 4x0 + 5,
     
     [g](x0) = 2x0,
     
     [active](x0) = x0,
     
     [f](x0) = 2x0,
     
     [a] = 2
    orientation:
     active(f(X)) = 2X >= 2X = f(active(X))
     
     proper(f(X)) = 8X >= 8X = f(proper(X))
     
     proper(a()) = 8 >= 8 = ok(a())
     
     proper(g(X)) = 8X >= 8X = g(proper(X))
     
     f(ok(X)) = 8X >= 8X = ok(f(X))
     
     g(ok(X)) = 8X >= 8X = ok(g(X))
     
     top(mark(X)) = 8X + 11 >= 8X + 1 = top(proper(X))
     
     top(ok(X)) = 8X + 1 >= 2X + 1 = top(active(X))
    problem:
     active(f(X)) -> f(active(X))
     proper(f(X)) -> f(proper(X))
     proper(a()) -> ok(a())
     proper(g(X)) -> g(proper(X))
     f(ok(X)) -> ok(f(X))
     g(ok(X)) -> ok(g(X))
     top(ok(X)) -> top(active(X))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [top](x0) = x0,
      
      [ok](x0) = 2x0 + 1,
      
      [proper](x0) = 3x0,
      
      [g](x0) = x0,
      
      [active](x0) = 2x0,
      
      [f](x0) = 2x0 + 1,
      
      [a] = 4
     orientation:
      active(f(X)) = 4X + 2 >= 4X + 1 = f(active(X))
      
      proper(f(X)) = 6X + 3 >= 6X + 1 = f(proper(X))
      
      proper(a()) = 12 >= 9 = ok(a())
      
      proper(g(X)) = 3X >= 3X = g(proper(X))
      
      f(ok(X)) = 4X + 3 >= 4X + 3 = ok(f(X))
      
      g(ok(X)) = 2X + 1 >= 2X + 1 = ok(g(X))
      
      top(ok(X)) = 2X + 1 >= 2X = top(active(X))
     problem:
      proper(g(X)) -> g(proper(X))
      f(ok(X)) -> ok(f(X))
      g(ok(X)) -> ok(g(X))
     DP Processor:
      DPs:
       proper#(g(X)) -> proper#(X)
       proper#(g(X)) -> g#(proper(X))
       f#(ok(X)) -> f#(X)
       g#(ok(X)) -> g#(X)
      TRS:
       proper(g(X)) -> g(proper(X))
       f(ok(X)) -> ok(f(X))
       g(ok(X)) -> ok(g(X))
      TDG Processor:
       DPs:
        proper#(g(X)) -> proper#(X)
        proper#(g(X)) -> g#(proper(X))
        f#(ok(X)) -> f#(X)
        g#(ok(X)) -> g#(X)
       TRS:
        proper(g(X)) -> g(proper(X))
        f(ok(X)) -> ok(f(X))
        g(ok(X)) -> ok(g(X))
       graph:
        f#(ok(X)) -> f#(X) -> f#(ok(X)) -> f#(X)
        g#(ok(X)) -> g#(X) -> g#(ok(X)) -> g#(X)
        proper#(g(X)) -> g#(proper(X)) -> g#(ok(X)) -> g#(X)
        proper#(g(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X))
        proper#(g(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X)
       SCC Processor:
        #sccs: 3
        #rules: 3
        #arcs: 5/16
        DPs:
         proper#(g(X)) -> proper#(X)
        TRS:
         proper(g(X)) -> g(proper(X))
         f(ok(X)) -> ok(f(X))
         g(ok(X)) -> ok(g(X))
        Subterm Criterion Processor:
         simple projection:
          pi(proper#) = 0
         problem:
          DPs:
           
          TRS:
           proper(g(X)) -> g(proper(X))
           f(ok(X)) -> ok(f(X))
           g(ok(X)) -> ok(g(X))
         Qed
        
        DPs:
         g#(ok(X)) -> g#(X)
        TRS:
         proper(g(X)) -> g(proper(X))
         f(ok(X)) -> ok(f(X))
         g(ok(X)) -> ok(g(X))
        Subterm Criterion Processor:
         simple projection:
          pi(g#) = 0
         problem:
          DPs:
           
          TRS:
           proper(g(X)) -> g(proper(X))
           f(ok(X)) -> ok(f(X))
           g(ok(X)) -> ok(g(X))
         Qed
        
        DPs:
         f#(ok(X)) -> f#(X)
        TRS:
         proper(g(X)) -> g(proper(X))
         f(ok(X)) -> ok(f(X))
         g(ok(X)) -> ok(g(X))
        Subterm Criterion Processor:
         simple projection:
          pi(f#) = 0
         problem:
          DPs:
           
          TRS:
           proper(g(X)) -> g(proper(X))
           f(ok(X)) -> ok(f(X))
           g(ok(X)) -> ok(g(X))
         Qed