In this paper, we prove PSPACE-completeness of the finite satisfiability and model checking problems for the fragment of Halpern and Shoham interval logic with modality 〈E〉, for the “suffix” relation on pairs of intervals, and modality 〈D〉, for the “sub-interval” relation, under the homogeneity assumption. The result significantly improves the EXPSPACE upper bound recently established for the same fragment, and proves the rather surprising fact that the complexity of the considered problems does not change when we add either the modality for suffixes (〈E〉) or, symmetrically, the modality for prefixes (〈B〉) to the logic of sub-intervals (featuring only 〈D〉).
