The invertible root √BA or √ABA was principally connected to refusal, and its best known derivative was Avari, the group of Elves that refused to travel to Valinor. When Tolkien first introduced the root ᴹ√AB in The Etymologies of the 1930s and other contemporaneous writings on Ancient Quenya, he gave this root the meaning “go away, depart” (Ety/AB; PE19/045); in this sense it may have been a replacement for the early root ᴱ√AVA “go away, depart, leave” (QL/33). Indeed, the first application of Avari was to the Elves that left for Valinor, “the Departing”, rather than those that stayed behind (LR/169-170). But the sense “away” was soon transferred to ᴹ√AWA (Ety/AWA) and √AB was revised in The Etymologies to mean “refuse, deny, say no” (Ety/AB), a sense it retained thereafter.
Tolkien wrote about this root at great length in the 1959 when he decided that √BA was part of the Eldarin system of negation, distinguishing negation of volition (I will not) from negative of fact (it is not so). Tolkien seems to have introduced this notion at the same time he decided to abandon la-negation, so the corresponding negation of fact was the root √Ū (PE17/143). Even when Tolkien considered restoring la-negation in the late 1960s, √BA still retained a role as the negation of volition (PE22/161).
One peculiar feature of √BA is that it represented refusal from the perspective of the speaker. Thus in 1st person, √BA meant “I will not” (refusal), but in 2nd person or 3rd person it meant “do not” (forbiddance). Tolkien discussed this topic at some length in the Quendi and Eldar essay from 1959-60 (WJ/370-2). In 1st person this was Q. ván(ye)/S. avon “I won’t” and Q. vamme/S. avam “we won’t” [using the circa-1960 pronominal suffix -mme; with later pronouns this would be valve and avof]. In 2nd person this used the interjection Q. vá/S. baw “don’t”, or the negative imperative particle Q. áva/S. avo, as in Q. áva care/S. avo garo “don’t do [it]”.
When Tolkien revisited his ideas for negation in 1969, he still kept this notion of 1st person refusal vs. 2nd/3rd person forbiddance (PE22/161-3), so that the system of √BA negation remained more or less the same (barring changes like new pronouns).
A root meaning “go, proceed” appearing as one of the many etymologies of Q. vanwa “gone, departed”. It may have been a partial restoration of the (rejected) meaning of the root ᴹ√AB “go away, depart” from The Etymologies of the 1930s, a root that later was altered in that document to mean “refuse, deny, say no” (Ety/AB). It may also have been intended as a replacement for ᴹ√WAN “depart, go away, disappear, vanish”, also from The Etymologies and the basis for ᴹQ. vanwa in the 1930s.
In the published corpus, the first clear mention of this root is in a discussion of the Quenya future suffix -(u)va from the late 1940s where it was given as √BĀ, BANA “go, proceed” with Q. vanwa “gone, over” as one of its derivatives (PE22/97). It appeared again in a discussion of the Sindarin greeting mae govannen “well met” from the late 1950s, where Tolkien hypothesized that the verb “meet” might be go- “together” + ban- “go” or “meet”, which he again connected to Q. vanwa “gone” (PE17/16). Phonetic complications prompted Tolkien to coin a new verb covad- “assemble, gather together” from a root √KOB, but he was unwilling to commit at this time to the new verb because of the obvious similarity of govannen to √BAN “go” (PE17/16-17).
However, in 1959 when he was overhauling the Eldarin system of negation, it seems Tolkien finally rejected √BA(N) “go” because of the conflict with √BĀ/ABA “refuse”, and he transferred the sense “go” to the root √MEN (PE17/143). In etymological notes contemporaneous with the Quendi and Eldar essay of 1959-60, Tolkien restored √KOB “gather” (PE17/150) though he seems to have eventually settled on the form √KOM for this root along with a restored verb S. covad- “bring together, make meet” (PE17/157-158). Q. vanwa “gone” was also transferred to √WĀ/AWA by the time of the Quendi and Eldar essay (WJ/366). Meanwhile, the Quenya future had been transferred from √BA to the root √UB in the early 1950s (PE22/132).
This left no remaining functions for √BA(N) “go”, and there is no further sign of it starting in the 1960s.