YES

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

Proof:
 DP Processor:
  DPs:
   mark#(f(X)) -> mark#(X)
   mark#(f(X)) -> a__f#(mark(X))
   mark#(h(X)) -> mark#(X)
  TRS:
   a__f(X) -> g(h(f(X)))
   mark(f(X)) -> a__f(mark(X))
   mark(g(X)) -> g(X)
   mark(h(X)) -> h(mark(X))
   a__f(X) -> f(X)
  Matrix Interpretation Processor: dim=4
   
   interpretation:
    [mark#](x0) = [1 1 0 0]x0,
    
    [a__f#](x0) = [1 1 0 0]x0,
    
                 [1 0 0 0]  
                 [0 1 0 0]  
    [mark](x0) = [0 0 1 0]x0
                 [0 0 0 0]  ,
    
              [0 0 0 0]  
              [0 0 1 0]  
    [g](x0) = [0 0 0 0]x0
              [0 0 0 0]  ,
    
              [0 0 0 0]     [1]
              [1 1 0 0]     [0]
    [h](x0) = [0 1 0 0]x0 + [0]
              [0 0 0 0]     [0],
    
              [0 0 0 0]     [0]
              [1 1 0 0]     [1]
    [f](x0) = [0 0 0 0]x0 + [0]
              [0 0 0 0]     [0],
    
                 [0 0 0 0]     [0]
                 [1 1 0 0]     [1]
    [a__f](x0) = [0 0 0 0]x0 + [0]
                 [0 0 0 0]     [0]
   orientation:
    mark#(f(X)) = [1 1 0 0]X + [1] >= [1 1 0 0]X = mark#(X)
    
    mark#(f(X)) = [1 1 0 0]X + [1] >= [1 1 0 0]X = a__f#(mark(X))
    
    mark#(h(X)) = [1 1 0 0]X + [1] >= [1 1 0 0]X = mark#(X)
    
              [0 0 0 0]    [0]    [0 0 0 0]    [0]             
              [1 1 0 0]    [1]    [1 1 0 0]    [1]             
    a__f(X) = [0 0 0 0]X + [0] >= [0 0 0 0]X + [0] = g(h(f(X)))
              [0 0 0 0]    [0]    [0 0 0 0]    [0]             
    
                 [0 0 0 0]    [0]    [0 0 0 0]    [0]                
                 [1 1 0 0]    [1]    [1 1 0 0]    [1]                
    mark(f(X)) = [0 0 0 0]X + [0] >= [0 0 0 0]X + [0] = a__f(mark(X))
                 [0 0 0 0]    [0]    [0 0 0 0]    [0]                
    
                 [0 0 0 0]     [0 0 0 0]        
                 [0 0 1 0]     [0 0 1 0]        
    mark(g(X)) = [0 0 0 0]X >= [0 0 0 0]X = g(X)
                 [0 0 0 0]     [0 0 0 0]        
    
                 [0 0 0 0]    [1]    [0 0 0 0]    [1]             
                 [1 1 0 0]    [0]    [1 1 0 0]    [0]             
    mark(h(X)) = [0 1 0 0]X + [0] >= [0 1 0 0]X + [0] = h(mark(X))
                 [0 0 0 0]    [0]    [0 0 0 0]    [0]             
    
              [0 0 0 0]    [0]    [0 0 0 0]    [0]       
              [1 1 0 0]    [1]    [1 1 0 0]    [1]       
    a__f(X) = [0 0 0 0]X + [0] >= [0 0 0 0]X + [0] = f(X)
              [0 0 0 0]    [0]    [0 0 0 0]    [0]       
   problem:
    DPs:
     
    TRS:
     a__f(X) -> g(h(f(X)))
     mark(f(X)) -> a__f(mark(X))
     mark(g(X)) -> g(X)
     mark(h(X)) -> h(mark(X))
     a__f(X) -> f(X)
   Qed