@article {IOPORT.00896572, author = {Needham, Roger E.}, title = {Infinite complete group presentations.}, year = {1996}, journal = {Journal of Pure and Applied Algebra}, volume = {110}, number = {2}, issn = {0022-4049}, pages = {195-218}, publisher = {Elsevier Science B.V. (North-Holland), Amsterdam}, doi = {10.1016/0022-4049(95)00108-5}, abstract = {Author's abstract: Knuth-Bendix for strings, when applied to a presentation for a group $G$, often diverges. In this paper we develop a Knuth-Bendix procedure for equational term rewriting which can find an infinite, complete presentation for $G$ in certain cases where previous procedures fail. These presentations yield an efficient solution for the word problem for $G$ in the same way as finite ones, by reducing any word to a unique normal form. Our presentations consist of finitely many families, each of which is parametrized by a single term rewrite rule. The parameters are formal variables which occur in exponents, and take all positive integer values. We give an example of a group which is not $\text{FP}_\infty$, hence which has no finite complete rewrite system, and is not automatic, but which has a complete presentation in our sense.}, reviewer = {S.C.Althoen (Flint)}, identifier = {00896572}, }