There is a principle of complementarity a bit like subsidiarity in the EU. It means that if a national court wants to try a case on one of the ICC crimes, it can, and the ICC will only try cases if the country (or countries?) in question dont want to.
This explains why Germany enacted a Völkerstrafgesetzbuch (Code of International Criminal Law).
This, of course, is very similar to the Statute of Rome.
I’ve always preferred the good, old Norse-root word overlap or overlapping to the Latin mouthful of complementarity. Arguably, the point of intersection is on the cusp in the latter case. The usual ‘uncomplimentary’ typo doesn’t help either.
Also, the very word subsidiarity doesn’t exactly lend itself to unambiguous interpretation.