From Seed To Leaf

So the previous post pointed out the problem with a simple extension from a seed : you miss some. In detail, two of the problems are:
Difficulties with growth from a seed
Firstly, A shows the - slightly obvious - idea that for some (seed, leaf) pairs you can only get from one to the other by adding edges and not vertices. This problem is easy enough.

As for B, I show here a detailed (if made up) example of the main problem : augmentation of a seed is not necessarily canonical. Or, to put it another way, the canonical deletion can lead to a sibling of the seed, rather than the seed itself.
I think the way round this might be to restrict the candidate atoms (or bonds, even) for canonical deletion to those outside the original seed. In other words, canonically label the augmentation to give the ordering of atoms/bonds then choose the largest labelled one that is not in the seed.