Unique normal form property of compatible term rewriting systems: a new proof of Chew's theorem

We present a new proof of Chew's theorem, which states that normal forms are unique up to conversion in compatible term rewriting systems. We apply the technique of left-right separated conditional term rewriting systems (LRCTRSs), in which the unique normal form property of a term rewriting system is reduced to the Church-Rosser property of its conditional linearization. In contrast to traditional techniques, such as strong con uence, we introduce a binary relation, called an independence, to prove the Church-Rosser property of the conditional systems. Finally, a suitable independence is constructed for a compatible LRCTRS.