Argumentation theory is an alternative style of formalizing non-monotonic reasoning. It seems, argumentation theory is a suitable framework for practical and uncertain reasoning, where arguments support conclusions. Dung's approach is an unifying framework which has played an influential role on argumentation research and Artificial Intelligence. Even though the success of the argumentation theory, it seems that argumentation theory is so far from being efficiently implemented like the logic programming approach. We present a case of use of the well-known enumerate and eliminate approach to solve the decision problem of the admissible sets and the preferred semantics. By considering this approach, we identify a relationship between the decision problem of the Dung's preferred semantics and the decision problems of the value-based argumentation's preferred semantics. Moreover, we introduce an efficient, clear, and elegant methodology to implement Dung's approach based on the high-level representation of Answer Set Programming (ASP). This methodology is based on the definition of polynomial time mappings from an argumentation framework to logic programs. By using this methodology, we define a direct relationship between the preferred semantics and minimal models of logic programs. On the other hand, our methodology help us to define efficient extensions of the grounded semantics based on extensions of Well-Founded Semantics (WFS). We point out that our extensions of the grounded semantics offer some advantages to solve an open problem in argumentation based semantics.