Structuring a conditional sentence by commata

Solution 1:

Based on comments under the question that provided clarification, I am prepared to provide an answer.

In looking at the sentence, the main part of my personal confusion was this:

… the only relevant information is, if such an unary language part is infinite, and if not, …

To me, I interpreted the meaning of the phrase to be equivalent to this:

The only relevant information is if X, and if not X, then Y.

In short, I took it as a redundancy that could be shortened to simply:

The only relevant information is Y.

However, it was made clear to me that wasn't the intended meaning of the sentence.

Instead, the problem was with the use of and rather than or, and it should have been constructed in a manner similar to this:

I sent you to the store to buy an orange. I see you have a fruit in your bag. Tell me if it is an orange, or, if not, why you bought something else.

Given that this is the correct interpretation of what had been meant to be expressed, the sentence should be rephrased as follows (I have included some additional small edits):

Hence, the only relevant information is [] if such a unary language part is infinite, or, if not, what length has the single unary word it contains.

In short, I did this:

• Removed the comma before if such.
• Changed an unary to a unary
• Changed and if not to or, if not.

The version of the sentence without notation is:

Hence, the only relevant information is if such a unary language part is infinite, or, if not, what length has the single unary word it contains.