This paper discusses how to escape a state in which argumentation can reach no conclusion by offering a new argument. We formalize our approach based on Dung's abstract argumentation framework (AF). When an AF has no stable extension, we have no meaningful conclusion. We address the problem of whether it is possible to revise this situation by adding an argument which attacks an existing one. If possible, how many solutions can we generate and at what position should it be added? We discuss this problem using an AF consisting of a trilemma and show conditions depending on the topology of the AF. We also address the point that a specific argument can be accepted or not by this action. We extend the discussion towards two possible directions: a general N-lemma case and a set of AFs each of which consists of several trilemmas. It follows that when a large size of argumentation becomes stuck in practical situation, the position to which a counter-argument should be added can be detected by a check of the topology of the AF.