Assume that there exists at least one NP-intermediate decision problem (which, by Ladner's theorem, is equivalent to P being distinct from NP).


Do there exist two NP-intermediate decision problems, $A$ and $B$, such that neither one is polynomial-time reducible to the other?



Incomparable NPI decision problems
[Balcazar and Diaz](https://www.sciencedirect.com/science/article/pii/0020019082901132) proved that if $P \ne NP$ then there exists an infinite number of non-comparable languages in $NP$.


