Based on practical observations on rule-based inference on RDF data, we study the problem of redundancy elimination in RDF in the presence of rules (in the form of Datalog rules) and constraints (in the form of so-called tuple-generating dependencies). To this end, we investigate the influence of several problem parameters (like restrictions on the size of the rules and/or the constraints) on the complexity of detecting redundancy. The main result of this paper is a fine-grained complexity analysis of both graph and rule minimisation in various settings.