Abstract We report on the new ARI infrastructure that supports tools and competitions in term rewriting. It offers ARI-COPS, a database for confluence problems and competition results, and ARIWeb, a convenient web interface for tools that participate in the annual confluence competition. These are built on top of the new ARI format for rewrite systems, a format converter, certifiers for competition results, and a duplicate checker.

Abstract We present a variant of the multiset path order for untyped applicative term rewriting. Compared to existing work, our variant incorporates two distinctive features, dubbed arity assignment and reification, to overcome difficulties in handling partial and variable application.

Abstract We present a simple criterion for combining reduction pairs lexicographically. The criterion is applicable to arbitrary classes of reduction pairs, such as the polynomial interpretation, the matrix interpretation, and the Knuth–Bendix order. In addition, we investigate a variant of the matrix interpretation where the lexicographic order is employed instead of the usual component-wise order. Effectiveness is demonstrated by experiments and examples, including Touzet’s Hydra Battle.

In this paper, we present an Isabelle/HOL formalization of co-rewrite pairs for non-reachability analysis in term rewriting. In particular, we formalize polynomial interpretations over negative integers as well as the weighted path order (WPO) and its variant co-WPO. With this formalization, the verified certifier CeTA is now able to check such non-reachability proofs, including those for non-reachability problems of a database where existing tools fail to provide certified proofs.