We give a complete proof of the fact that the following problem is undecidable:
Given: A term rewriting system, where the termination of its rewrite relation is provable by a total reduction order on ground terms,
Wanted: Does there exist a strictly monotonic interpretation in the positive integers that proves termination?
Keywords: term rewriting, termination, total termination, omega-termination, termination hierarchy, termination type
Ulrike Peiker, Martin Griebl