ConfluentMonoidPresentationForGroup variant for permutation groups with short stabilizer chain?

[fingolfin]

For permutation groups other than the symmetric group, ConfluentMonoidPresentationForGroup uses IsomorphismFpGroupByChiefSeries. But if the input group is a permutation group with a small base, it may be better to use a rewriting system derived from the stabilizer chain. Apparently Magma uses that to great effect.

[james-d-mitchell]

How is a confluence rewriting system derived from the stabiliser chain? A reference or brief description of what you had in mind would be interesting to read! @fingolfin