All - Termination ( SCP )

We recently introduced the All-Termination(T ) problem: given a termination solver T and a function F , find every subset of the formal parameters to F whose consideration is sufficient to show, using T , that F terminates. These subsets can be harnessed by a theorem prover to locate and justify induction schemes, and are also useful for guiding rewriting heuristics and ensuring their termination. In this paper, we study the All-Termination problem for SCP (polynomial size-change analysis), a powerful, cubic-time termination analysis. SCP is the first nonmonotonic termination analysis studied in the context of All-Termination, making its analysis both challenging and informative. We develop an algorithm for solving the All-Termination(SCP) problem, and briefly report on initial experimental results obtained on the ACL2 regression suite.