From the point of Computational Complexity - absolutely right as Collatz function is strongly increasing, moreover it's exponential in base two, which is not so hard to show.

Here is our final paper on Collatz function and its computability:

Preprint Disproof of Collatz Conjecture by using O-notation

Thank you very much professor Syzdykov for your collaboration. I will read your article.

Regards,

Akram Louiz

Still, the conjecture seems to hold:

http://dx.doi.org/10.13140/RG.2.2.30259.54567

Dear professor Esa Säkkinen

Thank you for sharing your work with me.

You know the rules of Mathematics just like me: One of us must be mistaken. This means that the work of at least one of us will be disproven.

I accept this fact and I am self-confident.

Good Luck professor Esa Säkkinen

Best regards,

Akram Louiz

I agree and accept that citation is needed and more rigorous disproof.

Dear Akram Louiz

We can start with any positive natural number - hence all the group N is filled with Collatz-chain members. We can also produce branches backwards.

Dear professor Esa Säkkinen

Since my disproof of the Collatz conjecture is correct, then the Collatz-chain members are not enough to prove that the Collatz conjecture is true for all natural numbers.

Dear Akram Louiz

Yes, the proof must reveal the original structure of Collatz's problem - nothing else is sufficient.

the last version that I updated today seems logically complete to me. I hope you accept it.