User blog:Wythagoras/A good bound for S(7)?

I found here some interesting notes on the record holder for \(\Sigma(6)\). It also says, that when _11 is entered and the head is on the blank and the machine is in state A, it will run for over \(10^{10^{10^{10^{10^7}}}}\) steps. The following machine does this: 0 _ 1 l 4 1 _ 1 r 2 1 1 1 r 5 2 _ 1 l 3 2 1 _ r 1 3 _ 1 r 4 3 1 _ l 2 4 _ 1 l 6 4 1 _ r 3 5 _ 1 r halt 5 1 1 r 2 6 _ 1 r 1 6 1 1 l 4 (note: 6=old state A and 1=old state B, 2=old state C, 3=old state D, etc)

After the first step: _1, head on the blank, state 4

After the second step: _11, head on the blank, state 6, so

\(S(7) > 10^{10^{10^{10^{10^7}}}}\) if it is indeed true what is said on the site and I'm not mistaken.