View source for 1RB0RD 0LC1RA 0RA1LB 1RE1LB 1LF1LB ---1LE

{{machine|1RB0RD_0LC1RA_0RA1LB_1RE1LB_1LF1LB_---1LE}}
{{TM|1RB0RD_0LC1RA_0RA1LB_1RE1LB_1LF1LB_---1LE}} is a non-halting [[BB(6)]] TM discovered by mxdys on 14 Sep 2024 ([https://discord.com/channels/960643023006490684/1239205785913790465/1284419946759323700 Discord]) and proven non-halting the next day ([https://discord.com/channels/960643023006490684/1239205785913790465/1284838151348551795 Discord]).

It follows rules similar to {{TM|1RB1RE_1LC0RA_0RD1LB_---1RC_1LF1RE_0LB0LE}} ([[BMO]] #1) suggesting that it might be a [[Cryptid]], but it turns out that (in this case) it enters a cycle which guarantees that it will never halt.

== Analysis ==
Analysis by racheline ([https://discord.com/channels/960643023006490684/1239205785913790465/1284425417704341549 Discord]):
<pre>
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
</pre>

mxdys discovered that if the TM ever enters a config <code>(n,2n)</code> it would be guaranteed to repeat forever ([https://discord.com/channels/960643023006490684/1239205785913790465/1284838151348551795 Discord]) since:
<pre>
(n,2n) -> (2n+2,n-1) -> (n+1,2(n+1))
</pre>

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

[[Category:BB(6)]]