The paper investigates the confluence properties of logically constrained rewrite systems (LCTRSs), which extend plain term rewrite systems with native support for constraints handled by SMT solvers. The main results are:
Local confluence of terminating LCTRSs is undecidable, even when the underlying theory is decidable. This is shown by a reduction from the Post Correspondence Problem.
A simple transformation is presented that maps an LCTRS to a (possibly infinite) term rewrite system (TRS). This allows lifting confluence results for TRSs to the LCTRS setting.
Using the transformation, the authors extend two advanced confluence criteria based on (almost) development closed critical pairs and parallel critical pairs from TRSs to LCTRSs. These results have been formally verified in the Isabelle proof assistant.
The paper highlights the challenges in extending confluence analysis techniques from plain term rewrite systems to the more expressive LCTRS setting, and provides a practical approach to leverage existing TRS confluence results for LCTRSs.
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