YES

Problem:
 active(f(f(a()))) -> mark(f(g(f(a()))))
 active(g(X)) -> g(active(X))
 g(mark(X)) -> mark(g(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:
 DP Processor:
  DPs:
   active#(f(f(a()))) -> g#(f(a()))
   active#(f(f(a()))) -> f#(g(f(a())))
   active#(g(X)) -> active#(X)
   active#(g(X)) -> g#(active(X))
   g#(mark(X)) -> g#(X)
   proper#(f(X)) -> proper#(X)
   proper#(f(X)) -> f#(proper(X))
   proper#(g(X)) -> proper#(X)
   proper#(g(X)) -> g#(proper(X))
   f#(ok(X)) -> f#(X)
   g#(ok(X)) -> g#(X)
   top#(mark(X)) -> proper#(X)
   top#(mark(X)) -> top#(proper(X))
   top#(ok(X)) -> active#(X)
   top#(ok(X)) -> top#(active(X))
  TRS:
   active(f(f(a()))) -> mark(f(g(f(a()))))
   active(g(X)) -> g(active(X))
   g(mark(X)) -> mark(g(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))
  TDG Processor:
   DPs:
    active#(f(f(a()))) -> g#(f(a()))
    active#(f(f(a()))) -> f#(g(f(a())))
    active#(g(X)) -> active#(X)
    active#(g(X)) -> g#(active(X))
    g#(mark(X)) -> g#(X)
    proper#(f(X)) -> proper#(X)
    proper#(f(X)) -> f#(proper(X))
    proper#(g(X)) -> proper#(X)
    proper#(g(X)) -> g#(proper(X))
    f#(ok(X)) -> f#(X)
    g#(ok(X)) -> g#(X)
    top#(mark(X)) -> proper#(X)
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X))
   TRS:
    active(f(f(a()))) -> mark(f(g(f(a()))))
    active(g(X)) -> g(active(X))
    g(mark(X)) -> mark(g(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))
   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)) -> top#(active(X)) ->
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> proper#(X)
    top#(ok(X)) -> active#(X) -> active#(g(X)) -> g#(active(X))
    top#(ok(X)) -> active#(X) -> active#(g(X)) -> active#(X)
    top#(ok(X)) -> active#(X) -> active#(f(f(a()))) -> f#(g(f(a())))
    top#(ok(X)) -> active#(X) -> active#(f(f(a()))) -> g#(f(a()))
    top#(mark(X)) -> top#(proper(X)) ->
    top#(ok(X)) -> top#(active(X))
    top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> active#(X)
    top#(mark(X)) -> top#(proper(X)) ->
    top#(mark(X)) -> top#(proper(X))
    top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> proper#(X)
    top#(mark(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X)
    top#(mark(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X)
    proper#(g(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X))
    proper#(g(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X)
    proper#(g(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X))
    proper#(g(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X)
    proper#(g(X)) -> g#(proper(X)) -> g#(ok(X)) -> g#(X)
    proper#(g(X)) -> g#(proper(X)) -> g#(mark(X)) -> g#(X)
    proper#(f(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X))
    proper#(f(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X)
    proper#(f(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X))
    proper#(f(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X)
    proper#(f(X)) -> f#(proper(X)) -> f#(ok(X)) -> f#(X)
    f#(ok(X)) -> f#(X) -> f#(ok(X)) -> f#(X)
    g#(ok(X)) -> g#(X) -> g#(ok(X)) -> g#(X)
    g#(ok(X)) -> g#(X) -> g#(mark(X)) -> g#(X)
    g#(mark(X)) -> g#(X) -> g#(ok(X)) -> g#(X)
    g#(mark(X)) -> g#(X) -> g#(mark(X)) -> g#(X)
    active#(g(X)) -> g#(active(X)) -> g#(ok(X)) -> g#(X)
    active#(g(X)) -> g#(active(X)) -> g#(mark(X)) -> g#(X)
    active#(g(X)) -> active#(X) -> active#(g(X)) -> g#(active(X))
    active#(g(X)) -> active#(X) -> active#(g(X)) -> active#(X)
    active#(g(X)) -> active#(X) -> active#(f(f(a()))) -> f#(g(f(a())))
    active#(g(X)) -> active#(X) ->
    active#(f(f(a()))) -> g#(f(a()))
    active#(f(f(a()))) -> f#(g(f(a()))) -> f#(ok(X)) -> f#(X)
    active#(f(f(a()))) -> g#(f(a())) -> g#(ok(X)) -> g#(X)
    active#(f(f(a()))) -> g#(f(a())) -> g#(mark(X)) -> g#(X)
   SCC Processor:
    #sccs: 5
    #rules: 8
    #arcs: 41/225
    DPs:
     top#(ok(X)) -> top#(active(X))
     top#(mark(X)) -> top#(proper(X))
    TRS:
     active(f(f(a()))) -> mark(f(g(f(a()))))
     active(g(X)) -> g(active(X))
     g(mark(X)) -> mark(g(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:
      [top#](x0) = [0 1 1]x0,
      
                  [0]
      [top](x0) = [0]
                  [0],
      
                   
      [ok](x0) = x0
                   ,
      
                       
      [proper](x0) = x0
                       ,
      
                   [0 0 0]     [0]
      [mark](x0) = [1 0 0]x0 + [0]
                   [0 1 1]     [1],
      
                [0 0 0]  
      [g](x0) = [0 0 0]x0
                [0 1 1]  ,
      
                     [0 0 0]  
      [active](x0) = [0 0 0]x0
                     [0 1 1]  ,
      
                [0 0 0]  
      [f](x0) = [1 1 0]x0
                [0 1 0]  ,
      
            [1]
      [a] = [1]
            [0]
     orientation:
      top#(ok(X)) = [0 1 1]X >= [0 1 1]X = top#(active(X))
      
      top#(mark(X)) = [1 1 1]X + [1] >= [0 1 1]X = top#(proper(X))
      
                          [0]    [0]                     
      active(f(f(a()))) = [0] >= [0] = mark(f(g(f(a()))))
                          [4]    [1]                     
      
                     [0 0 0]     [0 0 0]                
      active(g(X)) = [0 0 0]X >= [0 0 0]X = g(active(X))
                     [0 1 1]     [0 1 1]                
      
                   [0 0 0]    [0]    [0 0 0]    [0]             
      g(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(g(X))
                   [1 1 1]    [1]    [0 1 1]    [1]             
      
                     [0 0 0]     [0 0 0]                
      proper(f(X)) = [1 1 0]X >= [1 1 0]X = f(proper(X))
                     [0 1 0]     [0 1 0]                
      
                    [1]    [1]          
      proper(a()) = [1] >= [1] = ok(a())
                    [0]    [0]          
      
                     [0 0 0]     [0 0 0]                
      proper(g(X)) = [0 0 0]X >= [0 0 0]X = g(proper(X))
                     [0 1 1]     [0 1 1]                
      
                 [0 0 0]     [0 0 0]            
      f(ok(X)) = [1 1 0]X >= [1 1 0]X = ok(f(X))
                 [0 1 0]     [0 1 0]            
      
                 [0 0 0]     [0 0 0]            
      g(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(g(X))
                 [0 1 1]     [0 1 1]            
      
                     [0]    [0]                 
      top(mark(X)) = [0] >= [0] = top(proper(X))
                     [0]    [0]                 
      
                   [0]    [0]                 
      top(ok(X)) = [0] >= [0] = top(active(X))
                   [0]    [0]                 
     problem:
      DPs:
       top#(ok(X)) -> top#(active(X))
      TRS:
       active(f(f(a()))) -> mark(f(g(f(a()))))
       active(g(X)) -> g(active(X))
       g(mark(X)) -> mark(g(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))
     KBO Processor:
      argument filtering:
       pi(a) = []
       pi(f) = 0
       pi(active) = []
       pi(g) = 0
       pi(mark) = 0
       pi(proper) = []
       pi(ok) = []
       pi(top) = []
       pi(top#) = 0
      weight function:
       w0 = 1
       w(top#) = w(top) = w(ok) = w(proper) = w(mark) = w(g) = w(active) = w(f) = w(a) = 1
      precedence:
       top# ~ top ~ proper > ok > active > mark ~ g ~ f ~ a
      problem:
       DPs:
        
       TRS:
        active(f(f(a()))) -> mark(f(g(f(a()))))
        active(g(X)) -> g(active(X))
        g(mark(X)) -> mark(g(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))
      Qed
    
    DPs:
     active#(g(X)) -> active#(X)
    TRS:
     active(f(f(a()))) -> mark(f(g(f(a()))))
     active(g(X)) -> g(active(X))
     g(mark(X)) -> mark(g(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))
    Subterm Criterion Processor:
     simple projection:
      pi(active#) = 0
     problem:
      DPs:
       
      TRS:
       active(f(f(a()))) -> mark(f(g(f(a()))))
       active(g(X)) -> g(active(X))
       g(mark(X)) -> mark(g(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))
     Qed
    
    DPs:
     proper#(f(X)) -> proper#(X)
     proper#(g(X)) -> proper#(X)
    TRS:
     active(f(f(a()))) -> mark(f(g(f(a()))))
     active(g(X)) -> g(active(X))
     g(mark(X)) -> mark(g(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))
    Subterm Criterion Processor:
     simple projection:
      pi(proper#) = 0
     problem:
      DPs:
       
      TRS:
       active(f(f(a()))) -> mark(f(g(f(a()))))
       active(g(X)) -> g(active(X))
       g(mark(X)) -> mark(g(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))
     Qed
    
    DPs:
     g#(mark(X)) -> g#(X)
     g#(ok(X)) -> g#(X)
    TRS:
     active(f(f(a()))) -> mark(f(g(f(a()))))
     active(g(X)) -> g(active(X))
     g(mark(X)) -> mark(g(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))
    Subterm Criterion Processor:
     simple projection:
      pi(g#) = 0
     problem:
      DPs:
       
      TRS:
       active(f(f(a()))) -> mark(f(g(f(a()))))
       active(g(X)) -> g(active(X))
       g(mark(X)) -> mark(g(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))
     Qed
    
    DPs:
     f#(ok(X)) -> f#(X)
    TRS:
     active(f(f(a()))) -> mark(f(g(f(a()))))
     active(g(X)) -> g(active(X))
     g(mark(X)) -> mark(g(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))
    Subterm Criterion Processor:
     simple projection:
      pi(f#) = 0
     problem:
      DPs:
       
      TRS:
       active(f(f(a()))) -> mark(f(g(f(a()))))
       active(g(X)) -> g(active(X))
       g(mark(X)) -> mark(g(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))
     Qed