From theoretical computational perspectives, decision problems in Dung's abstract argumentation frameworks (AFs) are either polynomial solvable or intractable. To investigate practical efficiency, theoretical evaluation of applied algorithms does not necessarily reveal performance dissimilarities. Although experimental analysis of algorithms is a well-established alternative exploited in other domains, such methodology is given a little attention in the context of AFs. The main purpose of this paper is to give an example of how such experiments can be conducted to get meaningful conclusions about algorithms' behavior in situations where theoretical analysis might be of little help. To this end, we pick an extended model of AFs as a case study to empirically examine the efficiency of algorithms related to the acceptability of arguments.