# Theorem proving with group presentations: Examples and questions

## Abstract

Let *G* be a group on generators *A*. We investigate *C(G,A)*, the class of all t-complete rewrite systems for *G* over *A*, that is convergent inter-reduced rewrite systems for *G* which can be proved terminating with a total division ordering on *A*^{*}. Given *G, A* and an element > of *Tot(A)*, the total division orderings over *A*, there is a unique convergent inter-reduced rewrite system for *G* which can be proved terminating using >. *C(G,A)* induces a partition of *Tot(A)*, where the complete system *T* corresponds to the set of all orderings which prove *T* terminating. We give a collection of examples which illustrate different phenomena which can occur, and indicate some of the natural questions which arise. In particular we investigate how these results extend to subgroups and quotients. [ Rewrite rules, algebra ]

## Keywords

Normal Subgroup Word Problem Complete System Quotient Group Symbolic Computation## Preview

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