1RB1LD_1RC1RE_0LA1LB_0LD1LC_1RF0RA_---0RC

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Unsolved problem:
Does this TM run forever?

1RB1LD_1RC1RE_0LA1LB_0LD1LC_1RF0RA_---0RC (bbch) is a probviously non-halting BB(6) Cryptid found by @mxdys and shared on Discord on 20 Aug 2024.


Xl643 Calls this '''Semi-antihydra'''

Analysis by @mxdys

1RB1LD_1RC1RE_0LA1LB_0LD1LC_1RF0RA_---0RC

start: (0,0)

(3x+0,y)   --> (4x+4,y+1)
(3x+1,y+1) --> (4x+5,y+2)
(3x+2,y)   --> (4x+8,max(0,y-1))

(3x+1,0)   --> halt

(x,y) := 0^inf 110 <B 11011 01^x 011^y 0^inf

After simulating the map for 10^6 steps, x was ~10^124940, while y = 331762. This biased pseudo-random walk did not get lucky and recross the origin early in its trajectory.

Plot of y in (x,y) pair described by 1RB1LD_1RC1RE_0LA1LB_0LD1LC_1RF0RA_---0RC. If y = 0 while x is congruent to 1 modulo 3, the TM halts. It is very unlikely that y will ever reach 0 again.