We aim at finding and understanding dependencies between linguistic structures which differ in terms of constraints and expressive power. It has been shown that studying dependencies between the argu-mentation structure (ARG) and the Rhetorical Structure Theory (RST) is non-trivial and requires a fine methodology. In this paper, we propose to take advantage of the AOC-Poset structure to understand how the subgraphs alignements occur in a small corpus annotated in ARG and RST. We formalize the structures as graphs from which we extract both subgraphs and subgraphs alignments, matching those subgraphs which include the same text segments. Based on these extractions, we build a formal context where the objects are the texts and the attributes are the subgraphs and the subgraphs alignments. We show what we can learn from the dependencies between the structures by mining the AOC-Poset made of these attributes.