User blog comment:Boboris02/Boris´s sezration notation/@comment-25601061-20161005204243

Here is my analysis.

[a,b] has growth rate w^2

[a|b|a] has growth rate w^2+1

[a||b||a] has growth rate w^2+2

 [a||b||a] has growth rate w^2+2 [a(§c)b(§c)a] has growth rate w^2+c

[a(§a)b(§a)a] has growth rate w^2+w

[a/b] has growth rate w^2+w+1

[a/b/c] has growth rate w^2+w+2

[a//b//c] has growth rate w^2+w+3

[a///b///c] has growth rate w^2+w+4

[a/b]_{c} has growth rate w^2+w+c

[a/b]_{a} has growth rate w^2+w2

[a(@)b]has growth rate w^2+w2+1

[a(@+1)b]has growth rate w^2+w2+2

[a(@+c)b]has growth rate w^2+w2+c

[a(@+a)b]has growth rate w^2+w3

[a(@+@)b]has growth rate w^2+w3+1

[a(@+@+a)b]has growth rate w^2+w4

[a(@+@+@+a)b]has growth rate w^2+w5

[a(@^2)b]has growth rate w^2*2

[a(@^2+b)b]has growth rate w^2*2+w

[a(@^2+@+b)b]has growth rate w^2*2+w2

[a(@^2+@^2)b]has growth rate w^2*3

[a(@^2+@^2 +@^2 )b]has growth rate w^2*4

[a(@^3 )b]has growth rate w^3

[a(@^3+ @^2 )b]has growth rate w^3+w^2

[a(@^3+ @^3 )b]has growth rate w^3*2

[a(@^4 )b]has growth rate w^4

[a(@^a )b]has growth rate w^w

...

And then it pretty much turns into BEAF's array-of and X structures, replacing X with @.

I won't put the whole analysis in this comment, because it's too long and complex, but the notation's limit has growth rate psi(W_w).