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:
 DP Processor:
  DPs:
   active#(f(f(a()))) -> g#(f(a()))
   active#(f(f(a()))) -> f#(g(f(a())))
   active#(f(f(a()))) -> mark#(f(g(f(a()))))
   mark#(f(X)) -> mark#(X)
   mark#(f(X)) -> f#(mark(X))
   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)
  TRS:
   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)
  TDG Processor:
   DPs:
    active#(f(f(a()))) -> g#(f(a()))
    active#(f(f(a()))) -> f#(g(f(a())))
    active#(f(f(a()))) -> mark#(f(g(f(a()))))
    mark#(f(X)) -> mark#(X)
    mark#(f(X)) -> f#(mark(X))
    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)
   TRS:
    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)
   graph:
    mark#(g(X)) -> active#(g(X)) ->
    active#(f(f(a()))) -> mark#(f(g(f(a()))))
    mark#(g(X)) -> active#(g(X)) -> active#(f(f(a()))) -> f#(g(f(a())))
    mark#(g(X)) -> active#(g(X)) -> active#(f(f(a()))) -> g#(f(a()))
    mark#(f(X)) -> mark#(X) -> mark#(g(X)) -> active#(g(X))
    mark#(f(X)) -> mark#(X) -> mark#(a()) -> active#(a())
    mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> active#(f(mark(X)))
    mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> f#(mark(X))
    mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> mark#(X)
    mark#(f(X)) -> f#(mark(X)) -> f#(active(X)) -> f#(X)
    mark#(f(X)) -> f#(mark(X)) -> f#(mark(X)) -> f#(X)
    mark#(f(X)) -> active#(f(mark(X))) ->
    active#(f(f(a()))) -> mark#(f(g(f(a()))))
    mark#(f(X)) -> active#(f(mark(X))) ->
    active#(f(f(a()))) -> f#(g(f(a())))
    mark#(f(X)) -> active#(f(mark(X))) ->
    active#(f(f(a()))) -> g#(f(a()))
    mark#(a()) -> active#(a()) ->
    active#(f(f(a()))) -> mark#(f(g(f(a()))))
    mark#(a()) -> active#(a()) -> active#(f(f(a()))) -> f#(g(f(a())))
    mark#(a()) -> active#(a()) -> active#(f(f(a()))) -> g#(f(a()))
    f#(mark(X)) -> f#(X) -> f#(active(X)) -> f#(X)
    f#(mark(X)) -> f#(X) -> f#(mark(X)) -> f#(X)
    f#(active(X)) -> f#(X) -> f#(active(X)) -> f#(X)
    f#(active(X)) -> f#(X) -> f#(mark(X)) -> f#(X)
    g#(mark(X)) -> g#(X) -> g#(active(X)) -> g#(X)
    g#(mark(X)) -> g#(X) -> g#(mark(X)) -> g#(X)
    g#(active(X)) -> g#(X) -> g#(active(X)) -> g#(X)
    g#(active(X)) -> g#(X) -> g#(mark(X)) -> g#(X)
    active#(f(f(a()))) -> mark#(f(g(f(a())))) ->
    mark#(g(X)) -> active#(g(X))
    active#(f(f(a()))) -> mark#(f(g(f(a())))) ->
    mark#(a()) -> active#(a())
    active#(f(f(a()))) -> mark#(f(g(f(a())))) ->
    mark#(f(X)) -> active#(f(mark(X)))
    active#(f(f(a()))) -> mark#(f(g(f(a())))) ->
    mark#(f(X)) -> f#(mark(X))
    active#(f(f(a()))) -> mark#(f(g(f(a())))) ->
    mark#(f(X)) -> mark#(X)
    active#(f(f(a()))) -> f#(g(f(a()))) ->
    f#(active(X)) -> f#(X)
    active#(f(f(a()))) -> f#(g(f(a()))) -> f#(mark(X)) -> f#(X)
    active#(f(f(a()))) -> g#(f(a())) -> g#(active(X)) -> g#(X)
    active#(f(f(a()))) -> g#(f(a())) -> g#(mark(X)) -> g#(X)
   SCC Processor:
    #sccs: 3
    #rules: 9
    #arcs: 33/144
    DPs:
     mark#(g(X)) -> active#(g(X))
     active#(f(f(a()))) -> mark#(f(g(f(a()))))
     mark#(f(X)) -> mark#(X)
     mark#(f(X)) -> active#(f(mark(X)))
     mark#(a()) -> active#(a())
    TRS:
     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)
    EDG Processor:
     DPs:
      mark#(g(X)) -> active#(g(X))
      active#(f(f(a()))) -> mark#(f(g(f(a()))))
      mark#(f(X)) -> mark#(X)
      mark#(f(X)) -> active#(f(mark(X)))
      mark#(a()) -> active#(a())
     TRS:
      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)
     graph:
      mark#(g(X)) -> active#(g(X)) ->
      active#(f(f(a()))) -> mark#(f(g(f(a()))))
      mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> mark#(X)
      mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> active#(f(mark(X)))
      mark#(f(X)) -> mark#(X) -> mark#(a()) -> active#(a())
      mark#(f(X)) -> mark#(X) -> mark#(g(X)) -> active#(g(X))
      mark#(f(X)) -> active#(f(mark(X))) ->
      active#(f(f(a()))) -> mark#(f(g(f(a()))))
      active#(f(f(a()))) -> mark#(f(g(f(a())))) ->
      mark#(f(X)) -> mark#(X)
      active#(f(f(a()))) -> mark#(f(g(f(a())))) -> mark#(f(X)) -> active#(f(mark(X)))
     CDG Processor:
      DPs:
       mark#(g(X)) -> active#(g(X))
       active#(f(f(a()))) -> mark#(f(g(f(a()))))
       mark#(f(X)) -> mark#(X)
       mark#(f(X)) -> active#(f(mark(X)))
       mark#(a()) -> active#(a())
      TRS:
       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)
      graph:
       mark#(f(X)) -> mark#(X) -> mark#(g(X)) -> active#(g(X))
       mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> active#(f(mark(X)))
       mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> mark#(X)
       mark#(f(X)) -> active#(f(mark(X))) ->
       active#(f(f(a()))) -> mark#(f(g(f(a()))))
       active#(f(f(a()))) -> mark#(f(g(f(a())))) ->
       mark#(f(X)) -> active#(f(mark(X)))
       active#(f(f(a()))) -> mark#(f(g(f(a())))) -> mark#(f(X)) -> mark#(X)
      SCC Processor:
       #sccs: 1
       #rules: 3
       #arcs: 6/25
       DPs:
        mark#(f(X)) -> mark#(X)
        mark#(f(X)) -> active#(f(mark(X)))
        active#(f(f(a()))) -> mark#(f(g(f(a()))))
       TRS:
        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)
       Arctic Interpretation Processor:
        dimension: 1
        interpretation:
         [mark#](x0) = x0 + 0,
         
         [active#](x0) = x0 + 0,
         
         [mark](x0) = x0 + 6,
         
         [g](x0) = 3,
         
         [active](x0) = x0 + 6,
         
         [f](x0) = x0 + 6,
         
         [a] = 7
        orientation:
         mark#(f(X)) = X + 6 >= X + 0 = mark#(X)
         
         mark#(f(X)) = X + 6 >= X + 6 = active#(f(mark(X)))
         
         active#(f(f(a()))) = 7 >= 6 = mark#(f(g(f(a()))))
         
         active(f(f(a()))) = 7 >= 6 = mark(f(g(f(a()))))
         
         mark(f(X)) = X + 6 >= X + 6 = active(f(mark(X)))
         
         mark(a()) = 7 >= 7 = active(a())
         
         mark(g(X)) = 6 >= 6 = active(g(X))
         
         f(mark(X)) = X + 6 >= X + 6 = f(X)
         
         f(active(X)) = X + 6 >= X + 6 = f(X)
         
         g(mark(X)) = 3 >= 3 = g(X)
         
         g(active(X)) = 3 >= 3 = g(X)
        problem:
         DPs:
          mark#(f(X)) -> mark#(X)
          mark#(f(X)) -> active#(f(mark(X)))
         TRS:
          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)
        SCC Processor:
         #sccs: 1
         #rules: 1
         #arcs: 5/4
         DPs:
          mark#(f(X)) -> mark#(X)
         TRS:
          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)
         Subterm Criterion Processor:
          simple projection:
           pi(mark#) = 0
          problem:
           DPs:
            
           TRS:
            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)
          Qed
    
    DPs:
     f#(mark(X)) -> f#(X)
     f#(active(X)) -> f#(X)
    TRS:
     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)
    Subterm Criterion Processor:
     simple projection:
      pi(f#) = 0
     problem:
      DPs:
       
      TRS:
       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)
     Qed
    
    DPs:
     g#(mark(X)) -> g#(X)
     g#(active(X)) -> g#(X)
    TRS:
     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)
    Subterm Criterion Processor:
     simple projection:
      pi(g#) = 0
     problem:
      DPs:
       
      TRS:
       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)
     Qed