In recent years a large corpus of studies has arisen from Dung’s seminal abstract model of argumentation, including several extensions aimed at increasing its expressiveness. Most of these works focus on the case of finite argumentation frameworks, leaving the potential practical applications of infinite frameworks largely unexplored. In the context of a recently proposed extension of Dung’s framework called AFRA (Argumentation Framework with Recursive Attacks), this paper makes a first step to fill this gap. It is shown that, under some reasonable restrictions, infinite frameworks admit a compact finite specification and that, on this basis, computational problems which are tractable for finite frameworks may preserve the same property in the infinite case. In particular we provide a polynomial-time algorithm to compute the finite representation of the (possibly infinite) grounded extension of an AFRA with infinite attacks. An example concerning the representation of a moral dilemma is introduced to illustrate and instantiate the proposal and gives a preliminary idea of its potential applicability.