Abstract
In this paper, we study the reachability problem for conditional term rewriting systems. Given two ground terms s and t, our practical aim is to prove s ↛R∗t for some join conditional term rewriting system R (possibly not terminating and not confluent). The proof method we propose relies on an over approximation of reachable terms for unrestricted join conditional term rewriting systems. This approximation is computed using an extension of the tree automata completion algorithm to the conditional case.
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