1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF
1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch) is a halting BB(7) TM which runs for over Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2 \uparrow^{12} 2 \uparrow^{12} 3}
steps.
Analysis by Shawn Ligocki
Consider general configurations matching the regex:
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0^\infty \; 11 \; (1 \; (01)^*)^* \; 0011100 \; \textrm{A>} \; 0^\infty}
Low level rules
01 1 01^n 0011100 A> 00 --> 1 01^n+2 0011100 A>
01^3 11 01^n 0011100 A> 0^6 --> 1 01^n+5 1 01 0011100 A>
01^3 (1 01)^k+1 11 01^n 0011100 A> 0^6 --> 1 01^n+6 (1 01)^k 11 01 0011100 A>
011 (1 01)^k 11 01^n 0011100 A> 0^2 --> 1 Z> 111 01^n+1 00 101^k+2
Mid level rules
Let
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B(a; b, c, ..., z) = 0^\infty \; 111 \; (01)^{3z+1} \; 1 \; \cdots \; 1 (01)^{3c+1} \; 1 \; (01)^{3b+1} \; 1 \; (01)^0 \; 1 \; (01)^{3a+1} \; 0011100 \; \textrm{A>} \; 0^\infty }
and let B(a; [x]*k, y, ...) = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B(a; \underbrace{x, \cdots, x}_k, y, ...)}
(In other words, [x]*k represents k repeats of the value x in a config).
then
B(a; b+1, ...) -> B(2a+4; b, ...) B(a; [0]*k, 0, n+1, ...) -> B(0; [0]*k, a+2, n, ...) B(a; [0]*k) -> Halt(3a + 2k + 9) Start at step 8178: B(2, [1]*12)
High level rule
Let
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{array}{l} f_0(x) & = & 2x + 4 \\ f_{k+1}(x) & = & f_k^{x+2}(0) \\ \end{array}}
then
Bound
Let
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{array}{l} a_0 & = & 2 \\ a_{k+1} & = & f_k(a_k) \\ \end{array} }
then
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B(a_0; \underbrace{1, \cdots, 1}_k) \to B(a_k, \underbrace{0, \cdots, 0}_k) \to \text{Halt}(3 a_k + 2 k + 9) } and
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \textrm{Start} \to B(a_0; \underbrace{1, \cdots, 1}_{12}) }
and so this TM halts with a sigma score of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma = 3 a_{12} + 33 }
Note that Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f_k(x) = (2 \uparrow^k (x+4)) - 4} and so for Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k \ge 2} ,
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_k + 4 > 2 \uparrow^k 2 \uparrow^k 3 }
and so this TM halts with sigma score Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma > 2 \uparrow^{12} 2 \uparrow^{12} 3} .
This bound is pretty tight: .
