Based on a new data structure called PATCH Graph, an efficient
completion procedure for finitely presented groups is described.
A PATCH Graph represents rules and their symmetrized forms as 
cycles in a Cayley graph structure.  Completion is easily 
performed directly on the graph, and structure sharing is 
enforced.  The structure of the graph allows us to avoid certain
redundant inferences.  The PATCH Graph data structure and 
inference rules complement other extensions of Knuth-Bendix
completion for finitely presented groups.