1RB0LE_1LC1LB_0RD0LC_1RA0RE_1RF1RD_0LA---

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1RB0LE_1LC1LB_0RD0LC_1RA0RE_1RF1RD_0LA--- (bbch) is a holdout BB(6) TM.

SAME CONFIG (#4) State  : D Head run : 1 Template : (('0', None), ('0', 'n'), ('1', 1), ('0', None)) FIRST: 

 step 4  params (2)

THEN: 

 step 14  params (4)
 step 86  params (9)

NOW: 

 step 2394  params (21)

Call f(x) := $ 0^x 1 $ Then f(2) at step 4, f(4) at step 14, f(9) at 86, f(21) at 2394

SAME CONFIG (#64) State  : C Head run : 2 Template : (('0', None), ('0', 'n'), ('1', 'n'), ('0', 'n'), ('1', 1), ('0', None)) FIRST: 

 step 80  params (2, 5, 2)

THEN : 

 step 81  params (2, 4, 3)
 step 82  params (2, 3, 4)
 step 83  params (2, 2, 5)
 step 89  params (2, 3, 4)
 step 1226  params (2, 5, 12)
 step 1243  params (2, 7, 10)
 step 1286  params (2, 7, 10)
 step 1309  params (2, 9, 8)
 step 1374  params (2, 9, 8)
 step 2376  params (2, 17, 2)
 step 2377  params (2, 16, 3)
 step 2378  params (2, 15, 4)
 step 2379  params (2, 14, 5)
 step 2380  params (2, 13, 6)
 step 2381  params (2, 12, 7)
 step 2382  params (2, 11, 8)
 step 2383  params (2, 10, 9)
 step 2384  params (2, 9, 10)
 step 2385  params (2, 8, 11)
 step 2386  params (2, 7, 12)
 step 2387  params (2, 6, 13)
 step 2388  params (2, 5, 14)
 step 2389  params (2, 4, 15)
 step 2390  params (2, 3, 16)
 step 2391  params (2, 2, 17)
 step 2397  params (2, 3, 16)
 step 2430  params (2, 6, 13)
 step 2450  params (2, 8, 11)
 step 8224  params (2, 19, 10)
 step 8283  params (2, 21, 8)
 step 10656  params (2, 21, 8)
 step 18088  params (2, 19, 12)
 step 18147  params (2, 21, 10)
 step 20520  params (2, 21, 10)
 step 36576  params (2, 19, 14)
 step 36635  params (2, 21, 12)
 step 39008  params (2, 21, 12)
 step 72990  params (2, 19, 16)
 step 73049  params (2, 21, 14)
 step 75422  params (2, 21, 14) 
 step 145562  params (2, 19, 18)
 step 145621  params (2, 21, 16)
 step 147994  params (2, 21, 16)
 step 288794  params (2, 18, 21)
 step 288850  params (2, 20, 19)
 step 573322  params (2, 5, 36)
 step 573339  params (2, 7, 34)
 step 573382  params (2, 7, 34)
 step 573405  params (2, 9, 32)
 step 573470  params (2, 9, 32)
 step 575518  params (2, 18, 23)
 step 575574  params (2, 20, 21)
 step 1146640  params (2, 41, 2)
 step 1146641  params (2, 40, 3)
 step 1146642  params (2, 39, 4)
 step 1146643  params (2, 38, 5)
 step 1146644  params (2, 37, 6)
 step 1146645  params (2, 36, 7)
 step 1146646  params (2, 35, 8)
 step 1146647  params (2, 34, 9)
 step 1146648  params (2, 33, 10)
 step 1146649  params (2, 32, 11)
 step 1146650  params (2, 31, 12)
 step 1146651  params (2, 30, 13)
 step 1146652  params (2, 29, 14)
 step 1146653  params (2, 28, 15)
 step 1146654  params (2, 27, 16)
 step 1146655  params (2, 26, 17)
 step 1146656  params (2, 25, 18)
 step 1146657  params (2, 24, 19)
 step 1146658  params (2, 23, 20)
 step 1146659  params (2, 22, 21)
 step 1146660  params (2, 21, 22)
 step 1146661  params (2, 20, 23)
 step 1146662  params (2, 19, 24)
 step 1146663  params (2, 18, 25)
 step 1146664  params (2, 17, 26)
 step 1146665  params (2, 16, 27)
 step 1146666  params (2, 15, 28)
 step 1146667  params (2, 14, 29)
 step 1146668  params (2, 13, 30)
 step 1146669  params (2, 12, 31)
 step 1146670  params (2, 11, 32)
 step 1146671  params (2, 10, 33)
 step 1146672  params (2, 9, 34)
 step 1146673  params (2, 8, 35)
 step 1146674  params (2, 7, 36)
 step 1146675  params (2, 6, 37)
 step 1146676  params (2, 5, 38)
 step 1146677  params (2, 4, 39)
 step 1146678  params (2, 3, 40)
 step 1146679  params (2, 2, 41) 
 step 1146685  params (2, 3, 40)
 step 1146718  params (2, 6, 37)
 step 1146738  params (2, 8, 35)
 step 1148978  params (2, 18, 25)
 step 1149034  params (2, 20, 23)
 step 2304354  params (2, 43, 10)
 step 2304485  params (2, 45, 8)
 step 3451146  params (2, 45, 8)
 step 5753106  params (2, 43, 12)

I think the things I've bolded may be the key because they doubles every time and all the start of the new cycle.

NOW : 

 step 5753237  params (2, 45, 10)

Interval (last to now): 131 Interval (first to now): 5753157

Call g(x,y) := $ 0^2 1^x 0^y 1 $ .Since there's a lot of them, I'll sort out the pair. And you might notice, g(x, y) will be g(x-1, y+1) next step until some limit, that is g(2, y). The cycle starts from g(x, 2) to g(2, x)

There's a pattern in f() and g(). We see, f(9) is at 86 and g(2, 5) at 83 with g(3, 4) at 89 f(21) is at 2394 and g(2, 17) at 2391 with g(3, 16) at 2397. I found the pattern: g(2, y) at step a, f(4+y) at step a+3, g(3, y-1) at step a+6

BIG UPDATE: f(45) is confirmed is true and make the statement before more believable!! g(2, 41) at step 1146679, f(41+4) or f(45) at step 1146682 = 1146679 + 3, g(3, 40) at step 1146685 = 1146682 + 3.

CAUTIOUS: the cycle ONLY start when g(2, y) and ONLY when x = 2

This machine PROBABLY is non-halt, because, y always grow larger and larger, there's no point of getting to halt. The macro recurrence y(n+1) = 2y(n) + 7 induces rapidly increasing execution times, with empirical evidence suggesting super-exponential growth between successive f(x) events.

For sufficiently large g(c, d) at step k, regardless of whether c<d or c>d, the machine enters a drain phase that deterministically produces g(c+d, 2) at approx (2 +- 0.1)k. c+d then will be x in the g() function. Then after a deterministic conveyor of length x-2: it will be g(2, y) and starts another chain of patten of +3 steps between g() and f()

The y values in successive g(2, y) appearances seem to follow the recurrence:y(n+1) = 2y(n) + 7

CAUTIOUS: y(1) = 5, not 2

If I am missing, feel free to contribute

(When I skip a line, you know that it's a new message sent from me, updating the progress I've made

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