8.3 $G^{3, 7, 17} \vert <ab, c>$

The third example differs from the first two as the subgroup is not $E$ but $<ab, c>$. 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 $c = C = \lambda$ and $a = B$ and $b = A$ 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.