View source for 1RB0LD 0RC1RB 0RD0RA 1LE0RD 1LF--- 0LA1LA

{{machine|1RB0LD_0RC1RB_0RD0RA_1LE0RD_1LF---_0LA1LA}}
{{TM|1RB0LD_0RC1RB_0RD0RA_1LE0RD_1LF---_0LA1LA}} (and its equivalent {{TM|1RB0LD_0RC0RF_0RD0RA_1LE0RD_1LF---_0LA1LA}}) is an unsolved [[BB(6)]] TM. It is the 8th [[Beaver Math Olympiad]] problem.

== Analysis by mxdys ==
https://discord.com/channels/960643023006490684/1239205785913790465/1402211374565953609
<pre>
1RB0LD_0RC0RF_0RD0RA_1LE0RD_1LF---_0LA1LA

(n+a,b,2n+c) --> (a,n+b,c)

(0,b,c) --> (5+3b,0,c)

(1,10+b,0) --> halt
(1,10+b,1) --> halt

(2,b,0) --> (2,0,8+3b)
(2,b,1) --> (2,0,11+3b)

(3+a,b,0) --> (a,0,6+3b)
(3+a,b,1) --> (a,0,9+3b)

start: (10,0,12)

this machine is weird
it does't halt in 8.9e12 rules (the first rule doesn't count)
for small (a,0,c), none of them halts between 1e5 and 1e8 rules (use the simplified model that (1,b,0) and (1,b,1) halts)
for each visited (a,0,c), log(c/a) seems to have a good distribution, which means that it doesn't fall into a fixpoint quickly
and the (2,b,0),(2,b,1) rules are used for several times:
T=462: 2 673 1
T=41231: 2 59502 0
T=6056795: 2 8748186 1
T=45863796: 2 66242895 0
T=2012212661: 2 2906495658 1
T=10335020887: 2 14928329409 1
T=468871071868: 2 677258129269 1
</pre>

== Analysis by dyuan ==
https://discord.com/channels/960643023006490684/1468065303278911613
<pre>
1RB0LD_0RC1RB_0RD0RA_1LE0RD_1LF---_0LA1LA 

A(a, b, c) = 1^4 0^a <A 1^3b 0 1^c 0 1^2
A(a+1, b, c+2) → A(a, b+1, c)
A(0, b, c) → A(3b+3, 0, c+2)
A(a+2, b, 0) → A(a, 0, 3b+5)
A(a+2, b, 1) → A(a, 0, 3b+8)
A(1, b+5, 0) → Halt (after some time)
A(1, b+4, 1) → Halt (after some time)

Start: A(4, 0, 11)


B(a, b) = A(a, 0, b)

B(a+b+2, 2b+1) → B(a, 3b+8)
B(b+1, 2b+1) → Halt
B(a+b+2, 2b) → B(a, 3b+5)
B(b+1, 2b) → Halt
B(a, 2a+b) → B(3a+3, b+2)

Start: B(4, 11)
</pre>