The algorithms for deciding some properties of finite convergent string rewriting systems(Theory and applications in computer algebra)
Guo Mingchao, Lian Li · Institutional Repositories DataBase (IRDB) · 1993
The following problems are decidable in $O(mn^{2})$ time for con- vergent system $R$ on alphabet $A$ , where $m=|A|,$ $n$ is the length of $R,$ $i.e.$ , the sum of all length of words appeared in $R$ .(1) Is the monoid presented by $R$ finite ?(2) How many elements in the monoid presented by $R$ if it is finite ?and a sofyware is given to decide these properties and some other properties for such monoid.