YES

Problem:
 active(f(f(a()))) -> mark(f(g(f(a()))))
 mark(f(X)) -> active(f(X))
 mark(a()) -> active(a())
 mark(g(X)) -> active(g(mark(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)) -> active#(f(X))
   mark#(a()) -> active#(a())
   mark#(g(X)) -> mark#(X)
   mark#(g(X)) -> g#(mark(X))
   mark#(g(X)) -> active#(g(mark(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(X))
   mark(a()) -> active(a())
   mark(g(X)) -> active(g(mark(X)))
   f(mark(X)) -> f(X)
   f(active(X)) -> f(X)
   g(mark(X)) -> g(X)
   g(active(X)) -> g(X)
  EDG 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)) -> active#(f(X))
    mark#(a()) -> active#(a())
    mark#(g(X)) -> mark#(X)
    mark#(g(X)) -> g#(mark(X))
    mark#(g(X)) -> active#(g(mark(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(X))
    mark(a()) -> active(a())
    mark(g(X)) -> active(g(mark(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)) -> mark#(X) -> mark#(f(X)) -> active#(f(X))
    mark#(g(X)) -> mark#(X) -> mark#(a()) -> active#(a())
    mark#(g(X)) -> mark#(X) -> mark#(g(X)) -> mark#(X)
    mark#(g(X)) -> mark#(X) -> mark#(g(X)) -> g#(mark(X))
    mark#(g(X)) -> mark#(X) -> mark#(g(X)) -> active#(g(mark(X)))
    mark#(g(X)) -> g#(mark(X)) -> g#(mark(X)) -> g#(X)
    mark#(g(X)) -> g#(mark(X)) -> g#(active(X)) -> g#(X)
    mark#(g(X)) -> active#(g(mark(X))) ->
    active#(f(f(a()))) -> g#(f(a()))
    mark#(g(X)) -> active#(g(mark(X))) ->
    active#(f(f(a()))) -> f#(g(f(a())))
    mark#(g(X)) -> active#(g(mark(X))) ->
    active#(f(f(a()))) -> mark#(f(g(f(a()))))
    mark#(f(X)) -> active#(f(X)) -> active#(f(f(a()))) -> g#(f(a()))
    mark#(f(X)) -> active#(f(X)) -> active#(f(f(a()))) -> f#(g(f(a())))
    mark#(f(X)) -> active#(f(X)) -> active#(f(f(a()))) -> mark#(f(g(f(a()))))
    f#(mark(X)) -> f#(X) -> f#(mark(X)) -> f#(X)
    f#(mark(X)) -> f#(X) -> f#(active(X)) -> f#(X)
    f#(active(X)) -> f#(X) -> f#(mark(X)) -> f#(X)
    f#(active(X)) -> f#(X) -> f#(active(X)) -> f#(X)
    g#(mark(X)) -> g#(X) -> g#(mark(X)) -> g#(X)
    g#(mark(X)) -> g#(X) -> g#(active(X)) -> g#(X)
    g#(active(X)) -> g#(X) -> g#(mark(X)) -> g#(X)
    g#(active(X)) -> g#(X) -> g#(active(X)) -> g#(X)
    active#(f(f(a()))) -> mark#(f(g(f(a())))) -> mark#(f(X)) -> active#(f(X))
   SCC Processor:
    #sccs: 4
    #rules: 7
    #arcs: 22/144
    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(X))
     mark(a()) -> active(a())
     mark(g(X)) -> active(g(mark(X)))
     f(mark(X)) -> f(X)
     f(active(X)) -> f(X)
     g(mark(X)) -> g(X)
     g(active(X)) -> g(X)
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [f#](x0) = x0,
      
      [mark](x0) = x0 + 1,
      
      [g](x0) = 1,
      
      [active](x0) = x0,
      
      [f](x0) = x0 + 1,
      
      [a] = 1
     orientation:
      f#(mark(X)) = X + 1 >= X = f#(X)
      
      f#(active(X)) = X >= X = f#(X)
      
      active(f(f(a()))) = 3 >= 3 = mark(f(g(f(a()))))
      
      mark(f(X)) = X + 2 >= X + 1 = active(f(X))
      
      mark(a()) = 2 >= 1 = active(a())
      
      mark(g(X)) = 2 >= 1 = active(g(mark(X)))
      
      f(mark(X)) = X + 2 >= X + 1 = f(X)
      
      f(active(X)) = X + 1 >= X + 1 = f(X)
      
      g(mark(X)) = 1 >= 1 = g(X)
      
      g(active(X)) = 1 >= 1 = g(X)
     problem:
      DPs:
       f#(active(X)) -> f#(X)
      TRS:
       active(f(f(a()))) -> mark(f(g(f(a()))))
       mark(f(X)) -> active(f(X))
       mark(a()) -> active(a())
       mark(g(X)) -> active(g(mark(X)))
       f(mark(X)) -> f(X)
       f(active(X)) -> f(X)
       g(mark(X)) -> g(X)
       g(active(X)) -> g(X)
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [f#](x0) = x0 + 1,
       
       [mark](x0) = x0 + 1,
       
       [g](x0) = 0,
       
       [active](x0) = x0 + 1,
       
       [f](x0) = x0,
       
       [a] = 1
      orientation:
       f#(active(X)) = X + 2 >= X + 1 = f#(X)
       
       active(f(f(a()))) = 2 >= 1 = mark(f(g(f(a()))))
       
       mark(f(X)) = X + 1 >= X + 1 = active(f(X))
       
       mark(a()) = 2 >= 2 = active(a())
       
       mark(g(X)) = 1 >= 1 = active(g(mark(X)))
       
       f(mark(X)) = X + 1 >= X = f(X)
       
       f(active(X)) = X + 1 >= X = f(X)
       
       g(mark(X)) = 0 >= 0 = g(X)
       
       g(active(X)) = 0 >= 0 = g(X)
      problem:
       DPs:
        
       TRS:
        active(f(f(a()))) -> mark(f(g(f(a()))))
        mark(f(X)) -> active(f(X))
        mark(a()) -> active(a())
        mark(g(X)) -> active(g(mark(X)))
        f(mark(X)) -> f(X)
        f(active(X)) -> f(X)
        g(mark(X)) -> g(X)
        g(active(X)) -> g(X)
      Qed
    
    DPs:
     mark#(g(X)) -> mark#(X)
    TRS:
     active(f(f(a()))) -> mark(f(g(f(a()))))
     mark(f(X)) -> active(f(X))
     mark(a()) -> active(a())
     mark(g(X)) -> active(g(mark(X)))
     f(mark(X)) -> f(X)
     f(active(X)) -> f(X)
     g(mark(X)) -> g(X)
     g(active(X)) -> g(X)
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [mark#](x0) = x0,
      
      [mark](x0) = x0,
      
      [g](x0) = x0 + 1,
      
      [active](x0) = x0,
      
      [f](x0) = 1,
      
      [a] = 0
     orientation:
      mark#(g(X)) = X + 1 >= X = mark#(X)
      
      active(f(f(a()))) = 1 >= 1 = mark(f(g(f(a()))))
      
      mark(f(X)) = 1 >= 1 = active(f(X))
      
      mark(a()) = 0 >= 0 = active(a())
      
      mark(g(X)) = X + 1 >= X + 1 = active(g(mark(X)))
      
      f(mark(X)) = 1 >= 1 = f(X)
      
      f(active(X)) = 1 >= 1 = f(X)
      
      g(mark(X)) = X + 1 >= X + 1 = g(X)
      
      g(active(X)) = X + 1 >= X + 1 = g(X)
     problem:
      DPs:
       
      TRS:
       active(f(f(a()))) -> mark(f(g(f(a()))))
       mark(f(X)) -> active(f(X))
       mark(a()) -> active(a())
       mark(g(X)) -> active(g(mark(X)))
       f(mark(X)) -> f(X)
       f(active(X)) -> f(X)
       g(mark(X)) -> g(X)
       g(active(X)) -> g(X)
     Qed
    
    DPs:
     g#(active(X)) -> g#(X)
     g#(mark(X)) -> g#(X)
    TRS:
     active(f(f(a()))) -> mark(f(g(f(a()))))
     mark(f(X)) -> active(f(X))
     mark(a()) -> active(a())
     mark(g(X)) -> active(g(mark(X)))
     f(mark(X)) -> f(X)
     f(active(X)) -> f(X)
     g(mark(X)) -> g(X)
     g(active(X)) -> g(X)
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [g#](x0) = x0,
      
      [mark](x0) = x0 + 1,
      
      [g](x0) = 1,
      
      [active](x0) = x0,
      
      [f](x0) = x0 + 1,
      
      [a] = 1
     orientation:
      g#(active(X)) = X >= X = g#(X)
      
      g#(mark(X)) = X + 1 >= X = g#(X)
      
      active(f(f(a()))) = 3 >= 3 = mark(f(g(f(a()))))
      
      mark(f(X)) = X + 2 >= X + 1 = active(f(X))
      
      mark(a()) = 2 >= 1 = active(a())
      
      mark(g(X)) = 2 >= 1 = active(g(mark(X)))
      
      f(mark(X)) = X + 2 >= X + 1 = f(X)
      
      f(active(X)) = X + 1 >= X + 1 = f(X)
      
      g(mark(X)) = 1 >= 1 = g(X)
      
      g(active(X)) = 1 >= 1 = g(X)
     problem:
      DPs:
       g#(active(X)) -> g#(X)
      TRS:
       active(f(f(a()))) -> mark(f(g(f(a()))))
       mark(f(X)) -> active(f(X))
       mark(a()) -> active(a())
       mark(g(X)) -> active(g(mark(X)))
       f(mark(X)) -> f(X)
       f(active(X)) -> f(X)
       g(mark(X)) -> g(X)
       g(active(X)) -> g(X)
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [g#](x0) = x0 + 1,
       
       [mark](x0) = x0 + 1,
       
       [g](x0) = 0,
       
       [active](x0) = x0 + 1,
       
       [f](x0) = x0,
       
       [a] = 1
      orientation:
       g#(active(X)) = X + 2 >= X + 1 = g#(X)
       
       active(f(f(a()))) = 2 >= 1 = mark(f(g(f(a()))))
       
       mark(f(X)) = X + 1 >= X + 1 = active(f(X))
       
       mark(a()) = 2 >= 2 = active(a())
       
       mark(g(X)) = 1 >= 1 = active(g(mark(X)))
       
       f(mark(X)) = X + 1 >= X = f(X)
       
       f(active(X)) = X + 1 >= X = f(X)
       
       g(mark(X)) = 0 >= 0 = g(X)
       
       g(active(X)) = 0 >= 0 = g(X)
      problem:
       DPs:
        
       TRS:
        active(f(f(a()))) -> mark(f(g(f(a()))))
        mark(f(X)) -> active(f(X))
        mark(a()) -> active(a())
        mark(g(X)) -> active(g(mark(X)))
        f(mark(X)) -> f(X)
        f(active(X)) -> f(X)
        g(mark(X)) -> g(X)
        g(active(X)) -> g(X)
      Qed
    
    DPs:
     active#(f(f(a()))) -> mark#(f(g(f(a()))))
     mark#(f(X)) -> active#(f(X))
    TRS:
     active(f(f(a()))) -> mark(f(g(f(a()))))
     mark(f(X)) -> active(f(X))
     mark(a()) -> active(a())
     mark(g(X)) -> active(g(mark(X)))
     f(mark(X)) -> f(X)
     f(active(X)) -> f(X)
     g(mark(X)) -> g(X)
     g(active(X)) -> g(X)
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [mark#](x0) = x0 + 1,
      
      [active#](x0) = x0,
      
      [mark](x0) = x0 + 1,
      
      [g](x0) = 0,
      
      [active](x0) = x0,
      
      [f](x0) = x0,
      
      [a] = 1
     orientation:
      active#(f(f(a()))) = 1 >= 1 = mark#(f(g(f(a()))))
      
      mark#(f(X)) = X + 1 >= X = active#(f(X))
      
      active(f(f(a()))) = 1 >= 1 = mark(f(g(f(a()))))
      
      mark(f(X)) = X + 1 >= X = active(f(X))
      
      mark(a()) = 2 >= 1 = active(a())
      
      mark(g(X)) = 1 >= 0 = active(g(mark(X)))
      
      f(mark(X)) = X + 1 >= X = f(X)
      
      f(active(X)) = X >= X = f(X)
      
      g(mark(X)) = 0 >= 0 = g(X)
      
      g(active(X)) = 0 >= 0 = g(X)
     problem:
      DPs:
       active#(f(f(a()))) -> mark#(f(g(f(a()))))
      TRS:
       active(f(f(a()))) -> mark(f(g(f(a()))))
       mark(f(X)) -> active(f(X))
       mark(a()) -> active(a())
       mark(g(X)) -> active(g(mark(X)))
       f(mark(X)) -> f(X)
       f(active(X)) -> f(X)
       g(mark(X)) -> g(X)
       g(active(X)) -> g(X)
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [mark#](x0) = 0,
       
       [active#](x0) = 1,
       
       [mark](x0) = 0,
       
       [g](x0) = 0,
       
       [active](x0) = 0,
       
       [f](x0) = 0,
       
       [a] = 0
      orientation:
       active#(f(f(a()))) = 1 >= 0 = mark#(f(g(f(a()))))
       
       active(f(f(a()))) = 0 >= 0 = mark(f(g(f(a()))))
       
       mark(f(X)) = 0 >= 0 = active(f(X))
       
       mark(a()) = 0 >= 0 = active(a())
       
       mark(g(X)) = 0 >= 0 = active(g(mark(X)))
       
       f(mark(X)) = 0 >= 0 = f(X)
       
       f(active(X)) = 0 >= 0 = f(X)
       
       g(mark(X)) = 0 >= 0 = g(X)
       
       g(active(X)) = 0 >= 0 = g(X)
      problem:
       DPs:
        
       TRS:
        active(f(f(a()))) -> mark(f(g(f(a()))))
        mark(f(X)) -> active(f(X))
        mark(a()) -> active(a())
        mark(g(X)) -> active(g(mark(X)))
        f(mark(X)) -> f(X)
        f(active(X)) -> f(X)
        g(mark(X)) -> g(X)
        g(active(X)) -> g(X)
      Qed