Ok. First of all, a lot of the “breeding terms” used in the cannabis seed game are made up. Outside of filial generations and backcrosses (F1, F2, bx), these terms aren’t used by real geneticists. For example, incross, is not a real genetics term, but breeders use it all the time for all kinds of different crosses.
Side note - I’ve seen a lot of people, particularly on icmag, say that you need to understand Mendelian genetics to be a good breeder. No you don’t. Mendelian genetics is only useful for discrete traits that are controlled by a few loci. Almost every relevant trait in cannabis is a quantitative trait. Mendelian genetics is not useful in those situations. Good breeding is about good selections and nothing else.
The most important thing is having a standardized nomenclature that is consistent so other people understand what you are referring to. S1 is a first generation selfed plant. The original clone was selfed. Those offspring are S1’s. If an S1 is selfed again, it’s called an S2. The second number is used to represent how many generations of selfing has occurred between these offspring and the original clone. Heisen is right. That is how the terms are used, and it should remain that way or else things will get confusing.
The alternative is saying something ridiculous like “s1 of a gg4 s1” or “gg4 s1 s1”.
Is there any benefit to searching further down selfed generations? I would argue not. Each generation, the plants become further and further inbred. Inbreeding depression can ramp up very quickly.