HelpMe: added analyses

2026-09-23T12:21:19Z

added analyses

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=== register machine ===
<syntaxhighlight>0-A*

Let A(x) = A:[x]
A(x + 1) --(1)--> A(x)
A(0) --(1)--> *:[0]

A:[0]
= A(0)
--(1)--> *:[0]
MBB(1) ≥ 1</syntaxhighlight><syntaxhighlight>0+B_0-B*

Let A(x) = B:[x]
A(x + 1) --(1)--> A(x)
A(0) --(1)--> *:[0]

A:[0]
--(1)--> A(1)
--(1)--> A(0)
--(1)--> *:[0]
MBB(2) ≥ 3</syntaxhighlight><syntaxhighlight>0+B_1+C_0-BD_1-C*

Let A(x) = C:[0, x]
A(x + 1) --(2)--> A(x)
A(0) --(2)--> *:[0, 0]

A:[0, 0]
--(4)--> A(2)
--(2)--> A(1)
--(2)--> A(0)
--(2)--> *:[0, 0]
MBB(4) ≥ 10</syntaxhighlight><syntaxhighlight>0-DB_0+C_1-ED_1+A_1-B*

Let A(x) = D:[x, 0]
A(2k) --(7k + 5)--> *:[k + 1, 0]
A(2k + 1) --(7k + 9)--> A(k + 2)

A:[0, 0]
--(3)--> A(1)
--(9)--> A(2)
--(12)--> *[2, 0]
MBB(5) ≥ 24</syntaxhighlight><syntaxhighlight>0+B_1-FC_1+D_0-CE_0+A_1-A*

Let A(x) = C:[x, 0]
A(2k) --(7k + 6)--> *:[k + 2, 0]
A(2k + 1) --(7k + 10)--> A(k + 3)

A:[0, 0]
--(2)--> A(1)
--(10)--> A(3)
--(17)--> A(4)
--(20)--> *:[4, 0]
MBB(6) ≥ 49</syntaxhighlight><syntaxhighlight>0+B_0+C_0+D_1-GE_1+F_0-EC_1-A*

Let A(x) = C:[0, x]
A(2k) --(11k + 6)--> A(3k + 2)
A(2k + 1) --(5k + 3)--> *:[3k + 1, 0]

A:[0, 0]
--(12)--> A(4)
--(28)--> A(8)
--(50)--> A(14)
--(83)--> A(23)
--(58)--> *:[34, 0]
MBB(7) ≥ 231</syntaxhighlight><syntaxhighlight>0+B_0+C_1-GD_1+E_0-DF_2-HG_2+A_2-D*

Let A(x) = G:[0, x, 0]
A(2k) --(20k + 12)--> *:[0, 5k + 3, 0]
A(2k + 1) --(20k + 23)--> A(5k + 6)

A:[0, 0]
--(10)--> A(3)
--(43)--> A(11)
--(123)--> A(31)
--(323)--> A(81)
--(823)--> A(206)
--(2.072)--> *:[0, 518, 0]
MBB(8) ≥ 3.394</syntaxhighlight><syntaxhighlight>0+B_0+C_1-HD_0-EG_0-FI_1+D_2+H_0+A_2-B*

Let A(x, y) = D:[x, 0, y]
A(2k, y) –(7k + 6)–> A(3k + 3, y + 1)
A(2k + 1, y + 1) –(7k + 5)–> A(3k + 1, y)
A(2k + 1, 0) –(3k + 3)–> *:[0, k, 0]

A:[0, 0, 0]
–(3)–> A(2, 0)
–(13)–> A(6, 1)
–(27)–> A(12, 2)
...
–(2.753.550.047.052.785.432.549)–> A(1.180.092.877.308.336.613.950, 31)
–(4.130.325.070.579.178.148.831)–> A(1.770.139.315.962.504.920.928, 32)
–(6.195.487.605.868.767.223.254)–> A(2.655.208.973.943.757.381.395, 33)
...
–(123.361.440.505.394.191.838.159.894.807.429.323.394.336.791.980.165.278.392.551.786.831.696.080.997)–> A(52.869.188.788.026.082.216.354.240.631.755.424.311.858.625.134.356.547.882.522.194.356.441.177.569, 0)
–(79.303.783.182.039.123.324.531.360.947.633.136.467.787.937.701.534.821.823.783.291.534.661.766.355)–> *[0, 26.434.594.394.013.041.108.177.120.315.877.712.155.929.312.567.178.273.941.261.097.178.220.588.784, 0]
MBB(9) ≥ holy fuck 449.388.104.698.221.698.839.011.045.369.921.106.650.798.313.642.030.657.001.438.652.029.750.007.257</syntaxhighlight>idk what to do in MBB(10)<syntaxhighlight>0+B_0+C_0+D_0+E_1-IF_2+G_1+H_0-GI_0+J_1-AK_2-G*

Let A(x, y) = I:[0, x, y]
A(2k, y + 1) --(17k + 7)--> A(5k + 2, y)
A(2k, 0) --(7x + 3)--> *:[5k + 1, 0, 0]
A(2k + 1, y) --(17k + 20)--> A(5k + 6, y + 1)

A:[0, 0, 0]
–(16)–> A(5, 1)
–(54)–> A(16, 2)
–(143)–> A(42, 1)
...
–(3'033 * 10^6.703)–> A(8'920 * 10^6.702, 375)
–(7'582 * 10^6.703)–> A(2'230 * 10^6.703, 376)
–(1'895 * 10^6.704)–> A(5'575 * 10^6.703, 375)
...
–(4'149 * 10^21.242)–> A(1'220 * 10^21.242, 1)
–(1'037 * 10^21.243)–> A(3'051 * 10^21.242, 0)
–(1'067 * 10^21.243)–> *:[7'628 * 10^21.242, 0, 0]
MBB(11) > 2'797 * 10^21.243</syntaxhighlight>

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HelpMe: added analyses