1RB0LD_1RC1RF_1LA0RA_0LA0LE_1LD1LA_0RB---

Unsolved problem:

Does this TM run forever?

This is a probviously non-halting BB(6) Cryptid found by @dyuan01 and shared on Discord on 04 Sep 2024.

Rules

start: (1,0)
(3b+0,c+1) --> (4b+5,c)
(3b+1,c) --> (4b+2,c+4)
(3b+2,c+1) --> (4b+6,c+7)
(3(3(3(3b+2)+1)+1)+0,0) --> halt

(b,c) := 0^inf 110 A> 0^b 10^c 01 0^inf

Plot of the second entry in (b,c) over the first 100k steps of this TM. The TM halts or enters a new phase if x hits 0. This is extremely unlikely.

For simplicity only one potential halting rule is shown.