1RB1RD_0LC1RA_1RA1LC_0RB1LE_1RF0LD_---0RE

1RB1RD_0LC1RA_1RA1LC_0RB1LE_1RF0LD_---0RE (bbch) is a BB(6) potential Cryptid found by Marco Dos Santos using Gemini and reported in his paper At the Limits of Computability: Steps Towards Autonomous AI Discovery on the Busy Beaver Frontier. The probvious behavior of these TMs has not yet been analyzed.

Analysis by Marco Dos Santos

Consider:
P_1(c) = 0^inf C> 0 1^c 0^inf
P_2(a, c) = 0^inf 10^a 1 C> 0 1^c 0^inf
D_1(a, z, w) = 0^inf 10^a 1^z D> 1 1^w 0^inf

P_1(1) -> P_1(4)
P_2(0, 1) -> P_1(5)
P_2(a, 1) -> P_2(a-1, 5) if a >= 1
P_1(c) -> D_1(0, 2, c-2) if c >= 2
P_2(a, c) -> D_1(a, 3, c-2) if c >= 2

D_1(0, 2k+1, w) -> D_1(0, 2k+4, w-2) if w >= 2
D_1(0, 2k+2, w) -> D_1(k+1, 5, w-4) if w >= 4
D_1(a, 2k+1, w) -> D_1(a-1, 2k+5, w-2) if a >= 1 and w >= 2

D_1(0, 2k+1, 0) -> P_1(2k+4)
D_1(0, 2k+1, 1) -> P_1(2k+6)
D_1(0, 2k+2, 0) -> Halt
D_1(0, 2k+2, 1) -> P_2(k, 3)
D_1(0, 2k+2, 2) -> P_2(k, 5)
D_1(0, 2k+2, 3) -> P_2(k, 7)
D_1(1, 2k+1, 0) -> P_1(2k+5)
D_1(1, 2k+1, 1) -> P_1(2k+7)
D_1(a, 2k+1, 0) -> P_2(a-2, 2k+5) if a >= 2
D_1(a, 2k+1, 1) -> P_2(a-2, 2k+7) if a >= 2

Start: P_1(1), reached after 3 raw TM steps

This can be simplified to:

Consider:
D_1(a, z, w) = 0^inf 10^a 1^z D> 1 1^w 0^inf

D_1(0, 2k+1, w) -> D_1(0, 2k+4, w-2) if w >= 2
D_1(0, 2k+2, w) -> D_1(k+1, 5, w-4) if w >= 4
D_1(a, 2k+1, w) -> D_1(a-1, 2k+5, w-2) if a >= 1 and w >= 2

D_1(0, 2k+1, 0) -> D_1(0, 2, 2k+2)
D_1(0, 2k+1, 1) -> D_1(0, 2, 2k+4)
D_1(0, 2k+2, 0) -> Halt
D_1(0, 2k+2, 1) -> D_1(k, 3, 1)
D_1(0, 2k+2, 2) -> D_1(k, 3, 3)
D_1(0, 2k+2, 3) -> D_1(k, 3, 5)
D_1(1, 2k+1, 0) -> D_1(0, 2, 2k+3)
D_1(1, 2k+1, 1) -> D_1(0, 2, 2k+5)
D_1(a, 2k+1, 0) -> D_1(a-2, 3, 2k+3) if a >= 2
D_1(a, 2k+1, 1) -> D_1(a-2, 3, 2k+5) if a >= 2

Start: D_1(0, 2, 2), reached after 16 raw TM steps