Improving Homeomorphic Embedding for Online Termination

Well-quasi orders in general, and homeomorphic embedding in particular, have gained popularity to ensure online termination of program analysis, specialisation and transformation techniques. It has been recently shown that the homeomorphic embedding relation is strictly more powerful than a large class of involved well-founded approaches. In this paper we provide some additional investigations on the power of homeomorphic embedding. We, however, also illustrate that the homeomorphic embedding relation suffers from several inadequacies in contexts where logical variables arise. We therefore present new, extended homeomorphic embedding relations to remedy this problem.