User blog comment:Alemagno12/DAN is weaker than R function/@comment-11227630-20170827073324/@comment-11227630-20170902121902

But the "wrong way" doesn't necessary make the whole notation weaker.

For instance, {1{1,,1,,2}2} only reach {1{1,,2}2}, but {1{1,,1,,3}2} can reach {1,,1,,2}, and {1{1,,1,,1,2}2} has the same recursion level as {1,,1,,1,2}.

Another example is the {1{2,,}2}. {1{2,,}2} has the same recursion level as {1{2,,}3} due to unavoidable "wrong ways", and {1{2,,}4} the same as {1{2,,}5}. But it doesn't matter when we get {1{2,,}1,2}.