YES

Problem:
 active(f(a(),X,X)) -> mark(f(X,b(),b()))
 active(b()) -> mark(a())
 active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
 f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
 proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
 proper(a()) -> ok(a())
 proper(b()) -> ok(b())
 f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
               [1 0 0]     [0]
   [top](x0) = [0 0 0]x0 + [0]
               [0 0 0]     [1],
   
              [1 0 0]  
   [ok](x0) = [0 0 0]x0
              [0 0 1]  ,
   
                  [1 0 0]  
   [proper](x0) = [0 0 0]x0
                  [0 0 1]  ,
   
                [1 0 0]  
   [mark](x0) = [0 0 0]x0
                [0 0 0]  ,
   
         [0]
   [b] = [0]
         [0],
   
                  [1 0 0]  
   [active](x0) = [0 0 0]x0
                  [0 0 0]  ,
   
                     [1 0 1]     [1 0 0]     [1 0 1]  
   [f](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2
                     [0 0 0]     [0 0 0]     [0 0 0]  ,
   
         [0]
   [a] = [0]
         [1]
  orientation:
                        [2 0 1]    [1]    [1 0 1]                      
   active(f(a(),X,X)) = [0 0 0]X + [0] >= [0 0 0]X = mark(f(X,b(),b()))
                        [0 0 0]    [0]    [0 0 0]                      
   
                 [0]    [0]            
   active(b()) = [0] >= [0] = mark(a())
                 [0]    [0]            
   
                         [1 0 1]     [1 0 0]     [1 0 1]      [1 0 1]     [1 0 0]     [1 0 1]                        
   active(f(X1,X2,X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = f(X1,active(X2),X3)
                         [0 0 0]     [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]     [0 0 0]                        
   
                       [1 0 1]     [1 0 0]     [1 0 1]      [1 0 1]     [1 0 0]     [1 0 1]                      
   f(X1,mark(X2),X3) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = mark(f(X1,X2,X3))
                       [0 0 0]     [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]     [0 0 0]                      
   
                         [1 0 1]     [1 0 0]     [1 0 1]      [1 0 1]     [1 0 0]     [1 0 1]                                        
   proper(f(X1,X2,X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = f(proper(X1),proper(X2),proper(X3))
                         [0 0 0]     [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]     [0 0 0]                                        
   
                 [0]    [0]          
   proper(a()) = [0] >= [0] = ok(a())
                 [1]    [1]          
   
                 [0]    [0]          
   proper(b()) = [0] >= [0] = ok(b())
                 [0]    [0]          
   
                             [1 0 1]     [1 0 0]     [1 0 1]      [1 0 1]     [1 0 0]     [1 0 1]                    
   f(ok(X1),ok(X2),ok(X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = ok(f(X1,X2,X3))
                             [0 0 0]     [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]     [0 0 0]                    
   
                  [1 0 0]    [0]    [1 0 0]    [0]                 
   top(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = top(proper(X))
                  [0 0 0]    [1]    [0 0 0]    [1]                 
   
                [1 0 0]    [0]    [1 0 0]    [0]                 
   top(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = top(active(X))
                [0 0 0]    [1]    [0 0 0]    [1]                 
  problem:
   active(b()) -> mark(a())
   active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
   f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
   proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
   proper(a()) -> ok(a())
   proper(b()) -> ok(b())
   f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [top](x0) = x0,
    
    [ok](x0) = x0,
    
    [proper](x0) = x0,
    
    [mark](x0) = x0 + 1,
    
    [b] = 4,
    
    [active](x0) = x0,
    
    [f](x0, x1, x2) = x0 + x1 + 2x2,
    
    [a] = 2
   orientation:
    active(b()) = 4 >= 3 = mark(a())
    
    active(f(X1,X2,X3)) = X1 + X2 + 2X3 >= X1 + X2 + 2X3 = f(X1,active(X2),X3)
    
    f(X1,mark(X2),X3) = X1 + X2 + 2X3 + 1 >= X1 + X2 + 2X3 + 1 = mark(f(X1,X2,X3))
    
    proper(f(X1,X2,X3)) = X1 + X2 + 2X3 >= X1 + X2 + 2X3 = f(proper(X1),proper(X2),proper(X3))
    
    proper(a()) = 2 >= 2 = ok(a())
    
    proper(b()) = 4 >= 4 = ok(b())
    
    f(ok(X1),ok(X2),ok(X3)) = X1 + X2 + 2X3 >= X1 + X2 + 2X3 = ok(f(X1,X2,X3))
    
    top(mark(X)) = X + 1 >= X = top(proper(X))
    
    top(ok(X)) = X >= X = top(active(X))
   problem:
    active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
    f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
    proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
    proper(a()) -> ok(a())
    proper(b()) -> ok(b())
    f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
    top(ok(X)) -> top(active(X))
   DP Processor:
    DPs:
     active#(f(X1,X2,X3)) -> active#(X2)
     active#(f(X1,X2,X3)) -> f#(X1,active(X2),X3)
     f#(X1,mark(X2),X3) -> f#(X1,X2,X3)
     proper#(f(X1,X2,X3)) -> proper#(X3)
     proper#(f(X1,X2,X3)) -> proper#(X2)
     proper#(f(X1,X2,X3)) -> proper#(X1)
     proper#(f(X1,X2,X3)) -> f#(proper(X1),proper(X2),proper(X3))
     f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3)
     top#(ok(X)) -> active#(X)
     top#(ok(X)) -> top#(active(X))
    TRS:
     active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
     f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
     proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
     proper(a()) -> ok(a())
     proper(b()) -> ok(b())
     f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
     top(ok(X)) -> top(active(X))
    TDG Processor:
     DPs:
      active#(f(X1,X2,X3)) -> active#(X2)
      active#(f(X1,X2,X3)) -> f#(X1,active(X2),X3)
      f#(X1,mark(X2),X3) -> f#(X1,X2,X3)
      proper#(f(X1,X2,X3)) -> proper#(X3)
      proper#(f(X1,X2,X3)) -> proper#(X2)
      proper#(f(X1,X2,X3)) -> proper#(X1)
      proper#(f(X1,X2,X3)) -> f#(proper(X1),proper(X2),proper(X3))
      f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3)
      top#(ok(X)) -> active#(X)
      top#(ok(X)) -> top#(active(X))
     TRS:
      active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
      f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
      proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
      proper(a()) -> ok(a())
      proper(b()) -> ok(b())
      f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
      top(ok(X)) -> top(active(X))
     graph:
      top#(ok(X)) -> top#(active(X)) ->
      top#(ok(X)) -> top#(active(X))
      top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> active#(X)
      top#(ok(X)) -> active#(X) ->
      active#(f(X1,X2,X3)) -> f#(X1,active(X2),X3)
      top#(ok(X)) -> active#(X) ->
      active#(f(X1,X2,X3)) -> active#(X2)
      proper#(f(X1,X2,X3)) -> proper#(X3) ->
      proper#(f(X1,X2,X3)) -> f#(proper(X1),proper(X2),proper(X3))
      proper#(f(X1,X2,X3)) -> proper#(X3) ->
      proper#(f(X1,X2,X3)) -> proper#(X1)
      proper#(f(X1,X2,X3)) -> proper#(X3) ->
      proper#(f(X1,X2,X3)) -> proper#(X2)
      proper#(f(X1,X2,X3)) -> proper#(X3) ->
      proper#(f(X1,X2,X3)) -> proper#(X3)
      proper#(f(X1,X2,X3)) -> proper#(X2) ->
      proper#(f(X1,X2,X3)) -> f#(proper(X1),proper(X2),proper(X3))
      proper#(f(X1,X2,X3)) -> proper#(X2) ->
      proper#(f(X1,X2,X3)) -> proper#(X1)
      proper#(f(X1,X2,X3)) -> proper#(X2) ->
      proper#(f(X1,X2,X3)) -> proper#(X2)
      proper#(f(X1,X2,X3)) -> proper#(X2) ->
      proper#(f(X1,X2,X3)) -> proper#(X3)
      proper#(f(X1,X2,X3)) -> proper#(X1) ->
      proper#(f(X1,X2,X3)) -> f#(proper(X1),proper(X2),proper(X3))
      proper#(f(X1,X2,X3)) -> proper#(X1) ->
      proper#(f(X1,X2,X3)) -> proper#(X1)
      proper#(f(X1,X2,X3)) -> proper#(X1) ->
      proper#(f(X1,X2,X3)) -> proper#(X2)
      proper#(f(X1,X2,X3)) -> proper#(X1) ->
      proper#(f(X1,X2,X3)) -> proper#(X3)
      proper#(f(X1,X2,X3)) -> f#(proper(X1),proper(X2),proper(X3)) ->
      f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3)
      proper#(f(X1,X2,X3)) -> f#(proper(X1),proper(X2),proper(X3)) ->
      f#(X1,mark(X2),X3) -> f#(X1,X2,X3)
      f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3) ->
      f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3)
      f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3) ->
      f#(X1,mark(X2),X3) -> f#(X1,X2,X3)
      f#(X1,mark(X2),X3) -> f#(X1,X2,X3) ->
      f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3)
      f#(X1,mark(X2),X3) -> f#(X1,X2,X3) ->
      f#(X1,mark(X2),X3) -> f#(X1,X2,X3)
      active#(f(X1,X2,X3)) -> f#(X1,active(X2),X3) ->
      f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3)
      active#(f(X1,X2,X3)) -> f#(X1,active(X2),X3) ->
      f#(X1,mark(X2),X3) -> f#(X1,X2,X3)
      active#(f(X1,X2,X3)) -> active#(X2) ->
      active#(f(X1,X2,X3)) -> f#(X1,active(X2),X3)
      active#(f(X1,X2,X3)) -> active#(X2) -> active#(f(X1,X2,X3)) -> active#(X2)
     SCC Processor:
      #sccs: 4
      #rules: 7
      #arcs: 26/100
      DPs:
       proper#(f(X1,X2,X3)) -> proper#(X3)
       proper#(f(X1,X2,X3)) -> proper#(X2)
       proper#(f(X1,X2,X3)) -> proper#(X1)
      TRS:
       active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
       f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
       proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
       proper(a()) -> ok(a())
       proper(b()) -> ok(b())
       f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
       top(ok(X)) -> top(active(X))
      Subterm Criterion Processor:
       simple projection:
        pi(proper#) = 0
       problem:
        DPs:
         
        TRS:
         active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
         f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
         proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
         proper(a()) -> ok(a())
         proper(b()) -> ok(b())
         f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
         top(ok(X)) -> top(active(X))
       Qed
      
      DPs:
       top#(ok(X)) -> top#(active(X))
      TRS:
       active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
       f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
       proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
       proper(a()) -> ok(a())
       proper(b()) -> ok(b())
       f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
       top(ok(X)) -> top(active(X))
      CDG Processor:
       DPs:
        top#(ok(X)) -> top#(active(X))
       TRS:
        active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
        f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
        proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
        proper(a()) -> ok(a())
        proper(b()) -> ok(b())
        f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
        top(ok(X)) -> top(active(X))
       graph:
        
       Qed
      
      DPs:
       active#(f(X1,X2,X3)) -> active#(X2)
      TRS:
       active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
       f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
       proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
       proper(a()) -> ok(a())
       proper(b()) -> ok(b())
       f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
       top(ok(X)) -> top(active(X))
      Subterm Criterion Processor:
       simple projection:
        pi(active#) = 0
       problem:
        DPs:
         
        TRS:
         active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
         f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
         proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
         proper(a()) -> ok(a())
         proper(b()) -> ok(b())
         f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
         top(ok(X)) -> top(active(X))
       Qed
      
      DPs:
       f#(X1,mark(X2),X3) -> f#(X1,X2,X3)
       f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3)
      TRS:
       active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
       f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
       proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
       proper(a()) -> ok(a())
       proper(b()) -> ok(b())
       f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
       top(ok(X)) -> top(active(X))
      Subterm Criterion Processor:
       simple projection:
        pi(f#) = 2
       problem:
        DPs:
         f#(X1,mark(X2),X3) -> f#(X1,X2,X3)
        TRS:
         active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
         f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
         proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
         proper(a()) -> ok(a())
         proper(b()) -> ok(b())
         f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
         top(ok(X)) -> top(active(X))
       Subterm Criterion Processor:
        simple projection:
         pi(f#) = 1
        problem:
         DPs:
          
         TRS:
          active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
          f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
          proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
          proper(a()) -> ok(a())
          proper(b()) -> ok(b())
          f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
          top(ok(X)) -> top(active(X))
        Qed