1RB0RD_0LC1RA_0RA1LB_1RE1LB_1LF1LB_---1LE

1RB0RD_0LC1RA_0RA1LB_1RE1LB_1LF1LB_---1LE (bbch) is a non-halting BB(6) TM discovered by mxdys on 14 Sep 2024 (Discord) and proven non-halting the next day (Discord).

It follows rules similar to 1RB1RE_1LC0RA_0RD1LB_---1RC_1LF1RE_0LB0LE (bbch) (BMO #1) suggesting that it might be a Cryptid, but it turns out that (in this case) it found a stable cycle which guarantees that it will never halt.

Analysis

Analysis by racheline (Discord):

1RB0RD_0LC1RA_0RA1LB_1RE1LB_1LF1LB_---1LE
(a,c) := 0^inf 1^a <B 1 1^c 0^inf

(a,c) -> (2a+2,c-a-1) if a <= c-1
(n,n) -> (2n+2,0)
(n+1,n) -> halt
(a,c) -> (a-c-2,2c+4) if a >= c+2

start: (0,0) at step 3

mxdys discovered that if the TM ever enters a config (n,2n) it would be guaranteed to repeat forever (Discord) since:

(n,2n) -> (2n+2,n-1) -> (n+1,2(n+1))

and in fact it does enter such a config relatively early: (150,300).