The grammar is as follows:

$ S rightarrow aaAb | aab | To $

$ A rightarrow aaAb | aAb | epsilon $

I think this grammar has an unequivocal equivalent grammar as follows.

First let's rewrite the grammar in the following way, so that this grammar has the same language as one in question:

$ S rightarrow aaSb | aSb | epsilon $

Because this grammar generates $ L = {a ^ nb ^ m: m le n le 2m } $

This grammar only uses two productions in some order to derive strings and then uses null production to complete the derivation.

So, the idea is that we can order the use of production in such a way that any use of $ S rightarrow aaSb $ Production does not arrive before the use of any production $ S rightarrow aSb $. And following this idea, it is very easy to generate this grammar.

$ S rightarrow aSb | To $

$ A rightarrow aaAb | epsilon $

.

Another argument is as follows:

Why $ 2k_1 + k_2 = n $ Y $ k_1 + k_2 = m $ for some $ not negative spatial integer space k_1, k_2 $. (here $ k_1 $ Y $ k_2 $ corresponds to the production usage number of form $ S rightarrow aSb $ Y $ S rightarrow aaSb $ respectively.)

After solving the previous equations, we find that $ k_1 = m-n $ hence the value of $ k_1 $ It will be unique for any perticular chain. Which means we must use a fixed number of times the production of the form $ S rightarrow aSb $. Which consequently means that in our last rewritten grammar there is a fixed point for a perticular chain where you must perform $ S rightarrow A $.

Please help me with this. I want to know if this language is inherently ambiguous or not?