User blog:Alemagno12/DAN is weaker than R function

Aarex found out in the Googology Server Discord that {1{1,,,1,,,2}2} is 1-separator of {1,,,__}, not {1{1,,,1{1,,,1,,,2}2}2}. Here is the proof:



This makes DAN < R Function. Here's the analysis of R function and SAN beyond {1,,,1{1,,,1{...}2}2}:
 * {0,,0{0,,0,,1}1} = {1,,,1,,,2}
 * {0,,0{0,,0,,1}2} = {1,,,1,,,3}
 * {0,,0{0,,0,,1}0{0,,0,,1}1} = {1,,,1,,,1,,,2}
 * {0,,0,,1} = ,,,
 * {0,,0,,2} = {1,,,,3}
 * {0,,0,,0{0,,0,,0,,1}1} = {1{1,,,,1,,,,2}2}
 * {0,,0,,0{0,,0,,0,,1}0{0,,0,,0,,1}1} = {1{1,,,,1,,,,1,,,,2}2}
 * {0,,0,,0,,1} = ,,,,
 * {0,,0,,0,,0,,1} = ,,,,,
 * [WIP]