Datatype defining rewrite systems for the ring of integers, and for natural and integer arithmetic in unary view

A datatype defining rewrite system (DDRS) is a ground-complete term rewriting system, intended to be used for the specification of datatypes. As a follow-up of an earlier paper we define two concise DDRSes for the ring of integers, each comprising only twelve rewrite rules, and prove their ground-completeness. Then we introduce DDRSes for a concise specification of natural number arithmetic and integer arithmetic in unary view, that is, arithmetic based on unary append (a form of tallying) or on successor function. Finally, we relate one of the DDRSes for the ring of integers to the above-mentioned DDRSes for natural and integer arithmetic in unary view.