View source for 1RB0LE 1LC1RA ---1LD 0RB1LF 1RD1LA 0LA0RD

{{machine|1RB0LE_1LC1RA_---1LD_0RB1LF_1RD1LA_0LA0RD}}
{{TM|1RB0LE_1LC1RA_---1LD_0RB1LF_1RD1LA_0LA0RD}} is a non-halting [[BB(6)]] Turing machine.

== Analysis by @racheline on 29 July 2024 ==

From [https://discord.com/channels/960643023006490684/1239205785913790465/1267551868997992652 Discord link]:

<pre>
1RB0LE_1LC1RA_---1LD_0RB1LF_1RD1LA_0LA0RD
A(n) = 0^inf <A 0 1^n

rules:
A(6n) -> A(12n+3)
A(6n+1) -> A(12n+6)
A(6n+2) -> halt
A(6n+3) -> A(9n+9)
A(6n+4) -> halt
A(6n+5) -> A(9n+12)
start from A(3)

as we can see, everything that doesn't halt goes to A(6m) or A(6m+3) for some m, so halting is unreachable

the next two (1RB0LE_1LC1RA_---1LD_0RB1LF_1RD1LA_1RD0LA and 1RB0LE_1LC1RA_---1LD_0RB1LF_1RD1LA_0LA0LA) are clearly equivalent to it, so also non-halting
</pre>

==== Incorrect probviously halting argument ====
Assuming that the remainders mod 6 are independent and uniformly distributed from 0 to 5 predicts that the machine must halt with probability 1. But, the machine is non-halting.

== Analysis by mxdys on Nov 2 2024 ==

mxdys gave a Rocq proof that this TM does not halt: https://github.com/ccz181078/busycoq/blob/256b1916a325cef4d9f904bc61398e1d97b02c9e/verify/RWL_mod_v5.v#L2357-L2358

[[Category:BB(6)]]