The third example differs from the first two as the subgroup is not but . At a first glance, adding inverse elements does not lead to any difference. But for ll-CcbaBA the number of cosets enumerated differs between I-ALL and NONE, and for both length-lexicographical orderings there are differences between I-R and NONE and between I-ALL and NONE in the enumeration sequence. Further P-ALL and I-R-P give similar results for all orderings but the length-lexicographic ones. This is not surprising as we get and and almost immediately from the subgroup relators. As in the previous example, no strategy is best for all orderings nor is one ordering best for all strategies.

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