Nested Cascading Hyper Notation (NCHN) is the 10th part of HN.

Rules

An expression is of the form H_m<n,A>, where n is the base, m is the secondary base, and A is an array.

1. If there is no array, H_m<n> = m^n
2. If there is no secondary base, H<n> = H_n<n>
3. If the array's first entry is 1, delete it.
4. If the array is a sequence array, decrease it by one, then nest the whole expression into the base n times.
5. If the array is a limit array, change the array into the nth member of it's FS.

Arrays

As always, this part uses the same definitions as ACHN.

As you can see, the rules have been edited. This is, so we can apply HN expressions to X. So N{x}M is now H_N<M,x>. However, we need to replace N and M into (N) and (M), because else some expressions will have multiple definitions and infinite loops. However, (N) and (M) are still arrays, but any (N)# and (M)# is lower than (1,2)# (where # is rest of array).

So, two more things. If, when solving H_m<n,A>, you find an (N):

If the N is sequence array, ignore N, except for the leftmost entry, then solve like normal.

If the N is limit array, the xth member of (N)'s FS is (FS(N,x)).

Also, (x) = x.

And, to compare arrays, just compare the HN expressions or use ACHN rules.