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Description
The following GAP session seems to show that the Schreiertree is not updated if
log is not true for the orbit.
gap> LoadPackage("orb");
───────────────────────────────────────────────────────────────────────────────────────────────────────────
Loading orb 4.7.3 (Methods to enumerate orbits)
by Juergen Mueller (http://www.math.rwth-aachen.de/~Juergen.Mueller),
Max Neunhöffer (http://www-groups.mcs.st-and.ac.uk/~neunhoef), and
Felix Noeske (http://www.math.rwth-aachen.de/~Felix.Noeske).
Homepage: http://gap-system.github.io/orb/
───────────────────────────────────────────────────────────────────────────────────────────────────────────
true
gap> gens:=AtlasGenerators("Fi23",1);;
gap> fi23 := Group(gens.generators);
<permutation group with 2 generators>
gap> o:=Orb(fi23, 1, ^, rec(schreier:=true));
<open orbit, 1 points with Schreier tree>
gap> Enumerate(o);
<closed orbit, 31671 points with Schreier tree>
gap> DepthOfSchreierTree(o);
46
gap> dblwords:=Flat(TransposedMat([gens.generators])*[gens.generators]);;
gap> AddGeneratorsToOrbit(o, dblwords);
<closed orbit, 31671 points with Schreier tree>
gap> DepthOfSchreierTree(o);
46
gap> o:=Orb(fi23, 1, ^, rec(schreier:=true,log:=true));
<open orbit, 1 points with Schreier tree with log>
gap> Enumerate(o);
<closed orbit, 31671 points with Schreier tree with log>
gap> DepthOfSchreierTree(o);
46
gap> AddGeneratorsToOrbit(o, dblwords);
<closed orbit, 31671 points with Schreier tree with log>
gap> DepthOfSchreierTree(o);
23
gap> quit;
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