1RB1RE 1LC1LD ---1LA 1LB1LE 0RF0RA 1LD1RF

Unsolved problem:

Does this TM halt? If so, how many steps does it take to halt?

1RB1RE_1LC1LD_---1LA_1LB1LE_0RF0RA_1LD1RF (bbch) is a probviously halting tetrational BB(6) Cryptid found by Racheline on 29 July 2024 (Discord link).

1RB1RE_1LC1LD_---1LA_1LB1LE_0RF0RA_1LD1RF
A(m, n+9) = 0^inf 1^m (01)^n 0 A> 0^inf

rules:
A(m+4, 2n) -> A(m, 3n)
A(m+4, 2n+1) -> A(m, 3n+1)
A(0, 2n) -> halt
A(0, 2n+1) -> A(6n-23, 10)
A(1, 2n) -> A(6n-23, 10)
A(1, 2n+1) -> halt
A(2, n) -> halt
A(3, 2n) -> A(6n-20, 10)
A(3, 2n+1) -> A(6n-18, 10)
start from A(1, 10)

B(m) = A(m, 10)
B(4m) -> B(3 * HydraMap^m(10) - 26) if HydraMap^m(10) is odd
B(4m+1) -> B(3 * HydraMap^m(10) - 23) if HydraMap^m(10) is even
B(4m-1) -> B(2 * HydraMap^m(10) - 20)
in all other cases, halt
start from B(1)

iterating HydraMap on 10:
10, 15, 22, 33, 49, 73, 109, 163, 244, 366, 549, 823, 1234, ...
B(1) -> B(3*10-23) = B(7) -> B(2*22-20) = B(24) -> B(3*109-26) = B(301) -> B(3*153090419621086-23) = B(459271258863235) -> B(2*HydraMap^114817814715809(10)-20)