Layered transducing term rewriting system and its recognizability preserving property

A term rewriting system which effectively preserves recognizability (EPR-TRS) has good mathematical properties, In this paper, a new subclass of TRSs, layered transducing TRSs (LT-TRSs) is defined and its rccognizability preserving property is discussed. The class of LT-TRSs contains some EPR-TRSs, e.g., {f(x)-f(g(x))} which do not belong to any of the known decidable subclasses of EPR-TRSs. Bottom-up linear tree transducer, which is a well-known computation model in the tree language theory, is a special case of LT-TRS. We present a sufficient condition for an LT-TRS to be an EPR-TRS. Also reachability and joinability are shown to be decidable for LT-TRSs