YES

Problem:
 a__f(f(a())) -> a__f(g(f(a())))
 mark(f(X)) -> a__f(X)
 mark(a()) -> a()
 mark(g(X)) -> g(mark(X))
 a__f(X) -> f(X)

Proof:
 DP Processor:
  DPs:
   a__f#(f(a())) -> a__f#(g(f(a())))
   mark#(f(X)) -> a__f#(X)
   mark#(g(X)) -> mark#(X)
  TRS:
   a__f(f(a())) -> a__f(g(f(a())))
   mark(f(X)) -> a__f(X)
   mark(a()) -> a()
   mark(g(X)) -> g(mark(X))
   a__f(X) -> f(X)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
    [mark#](x0) = [0 1 1]x0,
    
    [a__f#](x0) = [0 0 1]x0,
    
                 [0 1 1]     [0]
    [mark](x0) = [1 0 1]x0 + [1]
                 [1 1 0]     [1],
    
              [1 0 0]     [1]
    [g](x0) = [0 0 1]x0 + [1]
              [0 1 0]     [0],
    
                 [0 0 1]     [1]
    [a__f](x0) = [0 0 1]x0 + [0]
                 [0 0 1]     [1],
    
              [0 0 1]     [0]
    [f](x0) = [0 0 1]x0 + [0]
              [0 0 0]     [1],
    
          [0]
    [a] = [0]
          [0]
   orientation:
    a__f#(f(a())) = 1 >= 0 = a__f#(g(f(a())))
    
    mark#(f(X)) = [0 0 1]X + [1] >= [0 0 1]X = a__f#(X)
    
    mark#(g(X)) = [0 1 1]X + [1] >= [0 1 1]X = mark#(X)
    
                   [2]    [1]                  
    a__f(f(a())) = [1] >= [0] = a__f(g(f(a())))
                   [2]    [1]                  
    
                 [0 0 1]    [1]    [0 0 1]    [1]          
    mark(f(X)) = [0 0 1]X + [2] >= [0 0 1]X + [0] = a__f(X)
                 [0 0 2]    [1]    [0 0 1]    [1]          
    
                [0]    [0]      
    mark(a()) = [1] >= [0] = a()
                [1]    [0]      
    
                 [0 1 1]    [1]    [0 1 1]    [1]             
    mark(g(X)) = [1 1 0]X + [2] >= [1 1 0]X + [2] = g(mark(X))
                 [1 0 1]    [3]    [1 0 1]    [1]             
    
              [0 0 1]    [1]    [0 0 1]    [0]       
    a__f(X) = [0 0 1]X + [0] >= [0 0 1]X + [0] = f(X)
              [0 0 1]    [1]    [0 0 0]    [1]       
   problem:
    DPs:
     
    TRS:
     a__f(f(a())) -> a__f(g(f(a())))
     mark(f(X)) -> a__f(X)
     mark(a()) -> a()
     mark(g(X)) -> g(mark(X))
     a__f(X) -> f(X)
   Qed