"is believed to still be" or "is believed to be still"

I wonder which of the following is correct.

It is believed to still be efficiently solvable.

and

It is believed to be still efficiently solvable.

Solution 1:

I disagee with @RogerK - sentence #1 is best:

It is believed to still be efficiently solvable.

First, it's 100% correct. No problem there. Second, it avoids the "be still" combo in the other sentence. And that's a little weird sounding, to be honest. All those b's one after another, and the expression "be still" is a thing too, so the reader needs to unconsciously disambiguate.

Regardless, I'd do whatever I could to substitute that passive voice "It is believed..." for active voice: Who believes this? In a weak research paper, passive voice is often used to cover up a lack of research...