SCT and the idempotence condition Draft

These notes show how to get rid of the idempotence condition (G = G;G) in (δ)-Size Change Termination. Both the “graph algorithm” of the original SCT paper [LJBA01] and the δSCT criterion of BenAmram [BA06] use some kind of idempotence on the potential cycles. This idempotence condition can be replaced by a more semantical condition on the cycles. The new condition is probably not easier to compute. In the case of the original SCT, it is probably not even easier to express. In the case of the δSCT, however, the new condition is much easier to express (and, hopefully, understand) while the idempotence condition was more contrived. I mostly explain how things work on the δSCT, and then briefly explain how to restrict this to basic SCT. This is also likely to work on many extensions of SCT. The main part of the result holds on a key Lemma (Lemma 8).