Confluence Competition 2015

Abstract

Confluence is one of the central properties of rewriting. Our competition aims to foster the development of techniques for proving/disproving confluence of various formalisms of rewriting automatically. We explain the background and setup of the 4th Confluence Competition.

Certifying Confluence of Quasi-Decreasing Strongly Deterministic Conditional Term Rewrite Systems

“…Our experiments ran on the StarExec [29] platform with a timeout of 60 seconds per problem. The outcome is summarized in Table 1, 3 where columns labeled A, N, and T contain the results of applying Theorem 3, using non-confluence methods, and trying all methods implemented in ConCon concurrently, respectively. A suffix '+ i' indicates preprocessing by exhaustive inlining of conditions (Lemma 3).…”

“…Among these, there are 119 oriented 3-CTRSs from which exactly 100 are also ADTRSs. We compare ConCon 1.3.2, which participated in last years confluence competition (CoCo 2016) [3], to ConCon 1.4.0, the current version which implements the results of the paper at hand. Our experiments ran on the StarExec [29] platform with a timeout of 60 seconds per problem.…”

“…Here, the output of an automated tool-the certificateis checked by a formally verified certifier that is code generated from a formalization inside a proof assistant. This approach was already quite successful for termination and confluence of TRSs, where state-of-the-art certifiers cover more than 80% of all generated certificates in the respective tool competitions [3,13].…”

“…= x min (x:xs) | x < y = x | otherwise = y where y = min xs min(cons(x, nil)) → x (1) min(cons(x, xs)) → x ⇐ min(xs) ≈ y, x < y ≈ true (2) min(cons(x, xs)) → y ⇐ min(xs) ≈ y, x < y ≈ false (3) x < 0 → false (4) 0 < s(y) → true (5) s(x) < s(y) → x< y (6) Issue. Alas, even in the presence of termination, confluence is in general still undecidable for conditional term rewrite systems (CTRSs).…”

Inductive Theorem Proving in Non-terminating Rewriting Systems and Its Application to Program Transformation

“…The confluence property, a general notion of determinism, has a long history for its study in the fields of lambda calculus and term rewriting. Recently, renewed interest for proving confluence of term rewriting systems automatically arises by development of several confluence tools and starting of confluence competitions [2], which have been held yearly from 2012. We can benefit from availability of such confluence tools to verify the confluence property, which plays a key role in inductionless induction methods.…”