[tetha]

Yes, but it is not required that a type system has a singular top type. It is entirely valid for a type system to have any number of types which are not in any sub- or supertype relationship.

And once there are two types T1 and T2 which are neither subtypes, nor supertypes of each other, and 2 expressions A1 and A2 of types T1 and T2, and a statically undecideable expression p, then statically typing "if p then A else B" is a problem.

And yes, I agree: Most if not all practical type systems will not accept an if-else statement if they cannot unify both branches of the conditional into a single type. Which makes sense. Because you have to act on the result of the expression, and then it needs to have some common type.

But on a purely theoretical basis, it is entirely possible and valid to have an undecideable type system. Which, btw, happens for a lot of languages: https://3fx.ch/typing-is-hard.html . There are C++ programs which are provably impossible to type at compile time.