Information Processing Letters
Confluence of right ground term rewriting systems is decidable
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
Processes, Terms and Cycles
New Undecidability Results for Properties of Term Rewrite Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
Non-Linear Rewrite Closure and Weak Normalization
Journal of Automated Reasoning
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Just as saturation under an appropriate superposition calculus leads to a convergent presentation of a given equational theory, saturation under a suitable chaining calculus gives, what we call, a rewrite closure. We present a theorem that characterizes confluence of (possibly nonterminating) term rewrite systems that admit a rewrite closure presentation, in terms of local confluence of a related terminating term rewrite system and joinability inclusion between these two rewrite systems. Using constraints to avoid variable chaining, we obtain a finite and computable rewrite closure presentation for right ground systems. This gives an alternate method to decide the reachability and joinability properties for right ground systems. The characterization of confluence, combined with the rewrite closure presentation, is used to obtain a decision procedure for confluence of right ground systems (this problem has been open for quite some time [8]), and a simple decision procedure for the unification problem of confluent right ground systems (result recently obtained in [17). An EXPTIME-hardness result is also proved for reachability and confluence of right ground systems.