Abstract: For a hierarchy of properties of term rewriting systems related to confluence we prove relative undecidability, i.e., for implications X⇒Y in the hierarchy the property X is undecidable for term rewriting systems satisfying Y. For some of the implications either X or ¬X is semi-decidable, for others neither X nor ¬X is semi-decidable. We prove most of these results for linear term rewrite systems.