1RB3RB1LB---2RB_2LA1RA4LB2LA2RA

1RB3RB1LB---2RB_2LA1RA4LB2LA2RA (bbch) is a BB(2,5) machine whose behavior is similar to Skelet 17. A proof was given by Daniel Yuan (@dyuan01) of the machine's nonhalting on July 30th 2024. 1RB3RA2LB1LB1RB_2LA2RA4LA1LA--- (bbch) is equivalent to this machine.

Analysis shared by Daniel Yuan (@dyuan01) on Discord, on June 14th 2024:

I just checked whenever the beaver reaches the 1 on the left side, and calculated the tape for when it next reaches the left side. It would be nice if someone can verify these rules.

[x, y, z] := 1 <B 4^x 12 4^y 12 4^z

[0, a, b, …] -> [a+3, b, …]
[2n+1, 2a, 2b, …, 0] -> Halt 
[2n+1, 2a, 2b, …, 2m+2] -> [2n, 2a, 2b, …, 2m+2, 0]
[2n+1, 2a, 2b, …, 2m+1] -> [2n, 2a, 2b, …, 2m+1, 1]
[2n+1, 2a, 2b, …, 2m+1, x, …] -> [2n, 2a, 2b, …, 2m+1, x+1, …]
[2n+2, a, b, …] -> [2n+1, a+1, b, …]

And you should start at [1, 1].

Review

Matthew House (@LegionMammal978) reviewed the above analysis on June 14th 2024 and agrees with it.

The proof given by @dyuan01 is not yet verified.