CSI – A Confluence Tool

Confluence of Non-Left-Linear TRSs via Relative Termination

“…Unjoinability of S-critical pairs can be tested similarly to checking nonconfluence of a TRS with the function TCAP ( [27]). …”

“…This can be automated by first-order theorem provers (for unit equational problems, so-called UEQ) and indeed non-confluence of the above TRS can be proved automatically, see Section 5. Note that in contrast to [27] this approach only requires S-unifiability but not S-unifiers.…”

“…Applications in various domains [16,20,26], resulted in an interest in proving confluence of term rewrite systems (TRSs) automatically [3,10,27,28]. Knuth and Bendix [16] showed that confluence of terminating TRSs is decidable by testing joinability of critical pairs, which are induced by overlaps.…”

Reachability Analysis with State-Compatible Automata

“…In this paper we are largely concerned with over-approximations of the terms reachable from a regular tree language L 0 by rewriting using a term rewrite system R, that is, we are interested in regular tree languages L such that R * (L 0 ) ⊆ L. Such over-approximations have been used, among other things, in the analysis of cryptographic protocols [6], for termination analysis [7,10] and for establishing non-confluence of term rewrite systems [15].…”

“…These results have also been formalized within the theorem prover Isabelle/HOL [13], resulting in a formalized decision procedure for the question R(L) ⊆ L. It is used to certify non-confluence proofs and termination proofs that are using the techniques of [9,10,15]. This paper is structured as follows.…”