User blog comment:Alemagno12/DAN is weaker than R function/@comment-11227630-20170827073324/@comment-11227630-20170827143758

Well, {1{1,,,1{1,,,1,,,2}2}2} is a kind of "wrong way", similar to {1{1,,1,,2}2}, where {1,,1,,2} is 1-separator of {1,, ____ } instead of { ____ }.

And s(n,n{1{1,,,1{1,,,1,,,2}2}2}2) = s(n,n{1`2}2), which is much smaller than s(n,n{1,,,1{1,,,1,,,2}2}2).