View source for 1RB1RC 1LC1LE 1RA1RD 0RF0RE 1LA0LB ---1RA

{{machine|1RB1RC_1LC1LE_1RA1RD_0RF0RE_1LA0LB_---1RA}}{{unsolved|Does this TM run forever?}}
{{TM|1RB1RC_1LC1LE_1RA1RD_0RF0RE_1LA0LB_---1RA}} is a [[BB(6)]] [[Cryptid]] found by @mxdys and shared on Discord on 27 Jul 2024. It's closely related to [[Hydra]] and [[Antihydra]].

== Analysis by @mxdys ==
<pre>
antihydra variant:
1RB1RC_1LC1LE_1RA1RD_0RF0RE_1LA0LB_---1RA

(n,m) := 0^inf C> 01011 01^n 1 01^m 0^inf

start from (3,1)
(2n+1,m) --> (3n+3,m+2)
(2n,m+1) --> (3n+3,m)
(4n,0) --> (9n+6,1)
(4n+2,0) --> halt
</pre>
The rules are proved in [https://github.com/ccz181078/busycoq/blob/BB6/verify/AntiHydra2.v Rocq].

== Analysis by @dyuan01 ==
Using B(a, b) = (3a-6, b), I've come up with these rules:
<pre>
Start from B(3, 1)
B(2n, m+1) → B(3n, m)
B(2n+1, m) → B(3n+1, m+2)
B(4n+2, 0) → B(9n+4, 1)
B(4n, 0) → halt
</pre>
This is actually just Hydra except you start at B(3, 1) instead of B(3, 0) and you don't necessarily halt if you reach -1. In fact, this can only halt if Hydra halts.

[[Category:BB(6)]][[Category:Cryptids]]