User blog:Googleaarex/BMS encoded to 1 symbol system

Introduction
Basicu matrix system is currently the 2nd fastest function that can be computed in the Googology with the notation-type expression.

There are 13 symbols being used in BMS: Today, I can encode to few symbols. I start with 12 symbols.
 * ( and ) brackets (Groups of 2 symbols)
 * A comma
 * Integers (Groups of 10 symbols)

12-symbol system
To encode to 12-symbol system, remove the ( then replace the ) with a period. Then remove the last period to make it shorter by 1 character.

11-symbol system
To encode to 11-symbol system from 12-symbol system, just replace a period with 2 commas.

10-symbol system
To encode to 10-symbol system from 11-symbol system, convert all decimal numbers to base 9 numbers. To go with smaller amount of symbols, convert decimal to the lower base system.

Converting to Unary doesn't work, but I can encode to 2 symbols.

2-symbol system
To encode to 2-symbol system from 11-symbol system, increase the number by 1 each, then convert the number to amount of 0s.

1-symbol system
Finally, to encode to 1-symbol system from 2-symbol system, replace a comma with 1, convert the entire encoded text from binary to decimal, then the result will be the converted number amount of 0s.

Decoding
You can decode easily by reversing the encoding process, but decoding 12-symbol to 13-symbol is hard.

Example

 * \((0,0,0)(1,1,0)(2,2,1)(3,3,1)(4,3,1)\) (Start) =>
 * \(0,0,0.1,1,0.2,2,1.3,3,1.4,3,1\) (12-symbol system) =>
 * \(0,0,0,,1,1,0,,2,2,1,,3,3,1,,4,3,1\) (11-symbol system) =>
 * \(1,1,1,,2,2,1,,3,3,2,,4,4,2,,5,4,2\) (Increase every number by 1) =>
 * \(0,0,0,,00,00,0,,000,000,00,,0000,0000,00,,00000,0000,00\) (Convert to unary, replacing the number to amount of 0s, 2-symbol system) =>
 * \(0101011001001011000100010011000010000100110000010000100\) (Replace every commas with 1) =>
 * \(12144692598825092\) (Convert binary to decimal) =>
 * \(0^{12144692598825092}\) (Convert to unary, replacing the number to amount of 0s, 1-symbol system, end)