ENHANCE: Use DAG structure for rewriting

Utility functions/data structure for finding rewriting rule that would apply
to word at give position. This is faster (and cleaner) than the
caching/sorting kludges used before.

If code manipulates the `tzrules` entry (as the `fr` package does), the
functionality is disabled.

lib/gpfpiso.gi

@@ -1904,6 +1904,7 @@ local isob,isos,iso,gens,u,a,rels,l,i,j,bgens,cb,cs,b,f,k,w,monoid,
   rels:=[];
   mytzf:=maketzf(rels);
 
+  directerr:=false;
   if newstyle then directerr:=true;fi;
 
   addrule:=function(rule)

lib/kbsemi.gd

@@ -131,3 +131,37 @@ DeclareGlobalFunction("ReduceWordUsingRewritingSystem");
 ##  </ManSection>
 ##
 DeclareAttribute( "TzRules", IsKnuthBendixRewritingSystem );
+
+# utility functions for identifying applicable rules through a DAG
+############################################################################
+##
+#F  EmptyKBDAG(<genids>)
+##
+## takes a list of generator id's (signed integers, used to check how far
+## indices have to be shifted) and returns a record that represents such
+## a DAG. 
+DeclareGlobalFunction("EmptyKBDAG");
+
+############################################################################
+##
+#F  AddRuleKBDAG(<dag>,<left>,<index>)
+##
+##  Adds rule with given left side to the DAG at given index position 
+DeclareGlobalFunction("AddRuleKBDAG");
+
+############################################################################
+##
+#F  DeleteRuleKBDAG(<dag>,<left>,<index>)
+##
+## removes a rule with given left side (sgtored at position <index> from the
+## DAG. Index numbers of all rules with higher index number will be shifted
+##  one down.
+DeclareGlobalFunction("DeleteRuleKBDAG");
+
+############################################################################
+##
+#F  RuleAtPosKBDAG(<dag>,<w>,<p>)
+##
+## returns the index position of the rule that applies at position <p> in
+##  word <w> (or `fail` if no rule applies.
+DeclareGlobalFunction("RuleAtPosKBDAG");