Computation of rewriting systems in finite groups

We present an algorithm computing the rewriting system $R$ of a finite group generated by the fixed set of elements. We have proved that $R$ is confluent and irreducible in this case. A necessary condition for the effective implementation of the algorithm is the availability of a fast procedure for multiplying elements in the group. For example, this group operation can be a composition of permutations, matrix multiplication, calculation of Hall's polynomials, etc. We study rewriting systems in finite two-generator groups of exponent five using the algorithm.