1RB1RF_0RC0RD_1LC1LD_1LE0RB_0RA1LG_1LC1RA_---0RF

1RB1RF_0RC0RD_1LC1LD_1LE0RB_0RA1LG_1LC1RA_---0RF (bbch) is a non-halting BB(7) TM with an infinite tetrational rule.

Analysis by Shawn Ligocki

Low level rules:

  11 00^n C> 0^2  -->  00^n+2 C>
1101 00^n C> 0^3  -->  0 11^n+1 00^2 C>
0010 00^n C> 0^8  -->  01 11^n+1 0^3 1 00^2 C>
 001 00^n C> 0^3  -->  01 11^n 00^2 C>
 110 00^n C> 0^5  -->  0^2n+3 1 00^2 C>
0101 00^n C> 0    -->  1 Z> 1^2n+4

Higher level rules:

C(a, b, c, d) = 0^inf 1^d 0^c 1^b 00^a C> 0^inf

C(a, b+2, ...) -> C(a+2, b, ...)
C(a, 2b+r, ...) -> C(a+2b, r, ...)

C(a, b, c, 0) = C(a, b, inf)
C(a, 0, 2c+r, ...) = C(a+c, 0, r, ...)

C(a, 0, 0, d) = C(a, d, inf)
C(a, 0, 1, 1) -> C(2, 1, 3, 2a+3) -> C(14, 1, 1, 2a+3)
C(a, 0, 1, d+2) -> C(2, 1, 2a+3, d) -> C(2^{2a+4} - 2, 1, 1, d)

C(a, 1, c+2, ...) -> C(2, 2a+1, c+1, ...) -> C(2a+2, 1, c+1, ...)
C(a, 1, c+1, ...) -> C((a+2) 2^c - 2, 1, 1, ...)

C(a, 1, 1, d+2) -> C(2, 2a+2, 1, d) -> C(2a+4, 0, 1, d)
C(a, 1, 1, d+4) -> C(2^{4a+12} - 2, 1, 1, d)
C(a, 1, 1, 3) -> C(2a+4, 0, 1, 1) -> C(14, 1, 1, 4a+11)
C(a, 1, 1, 1) -> Halt(2a+5)

g_2(n) = 2^{4n+12} - 2

C(a, 1, 1, 4k+r) -> C(g_2^k(a), 1, 1, r)

C(14, 1, 1, 4k+3) -> C(14, 1, 1, 4 g_2^k(a) + 11)

Note: the last rule is infinite since 4 g_2^k(a) + 11 is of the form 4k+3. The TM enters this config at step 334: C(14, 1, 1, 3)