We provide an extensive testing on how efficiently state-of-the art solvers are capable of solving credulous and sceptical argument-acceptance for lower-order extensions. In fact, as our benchmark we consider three different random graph-models to represent random Abstract Argumentation Frameworks: Barabasi and Erdos-Renyi networks, and, in addition, we also rework balanced trees by randomise their structure, with the purpose to obtain random trees of different height. Therefore, we test two reasoners, i.e., Con Arg2 and dyn PARTIX, on such benchmark, by comparing their performance on NP/co-NP-complete decision problems related to argument acceptance in admissible, complete, and stable semantics.