The Semantic Web makes an extensive use of the OWL DL ontology language, underlied by the SHOIQ description logic, to formalize its resources. In this paper, we propose a decision procedure for this logic extended with the transitive closure of roles in concept axioms, a feature needed in several application domains. The most challenging issue we have to deal with when designing such a decision procedure is to represent infinitely non-tree-shaped models, which are different from those of SHOIQ ontologies. To address this issue, we introduce a new blocking condition for characterizing models which may have an infinite non-tree-shaped part.