On Modularity of the Completeness in Order-Sorted Term Rewriting Systems

In this paper, we extend the results on the modularity of con uence and termination of single-sorted TRSs[3][6][7] to order-sorted ones. Order-sorted TRSs build a good framework for handling overloaded functions and subtypes. For proving modularity of completeness of ordersorted TRSs, we rst transform a TRS with overloaded functions to a non-overloaded one, and then we demonstrate that our transformation preserves completeness.