  A rewriting system is a set of equations over a given set of terms called
rules that characterize a system of computation and is a powerful general
method for providing decision procedures of equational theories, based upon the
principle of replacing subterms of an expression with other terms.
  In particular, a string rewriting system is usually associated with a monoid
presentation. At the first level the problem is to decide which combinations of
the generators are equivalent under the given rules; Knuth-Bendix completion of
the string rewriting system is one of the most successful mechanisms for
solving this problem. At the second level, the problem involves determining
which combinations of rules are equivalent.
  Logged rewriting is a technique which not only transforms strings but records
the transformation in terms of the original system of rules. The relations
between combinatorial, homotopical and homological finiteness conditions for
monoids prompt us to consider using computer-friendly rewriting systems to
calculate homotopical and homological structure from monoid presentations.
