One of the most representative semantics of Dung's approach is the grounded semantics. This semantics captures a skeptical approach, this means that given an argumentation framework the grounded semantics always identifies a single set of arguments, called grounded extension. It worth mentioning that the grounded semantics approach is one of the most useful argumentation approaches in real argumentation-based systems As argumentation can be abstractly defined as the interaction of arguments for and against some conclusion, a reasoning based on an abstract argumentation semantics for describing the interaction arguments is as important as to find an extension of an argumentation framework. In this paper, we introduce a novel formal argumentation method based on normal programs and rewriting systems which is able to - describe the interaction of arguments during the process of inferring an extension, and -define extensions of the grounded semantics based on specific rewriting rules which perform particular kind of reasoning as in reasoning by cases. Moreover, we point out that our codification of an argumentation framework as a normal program is a suitable codification for studying other abstract argumentation semantics as are the stable semantics and the preferred semantics.