Why Are Some Resistors in Parallel While Others Are Not?

[User1265]

Homework Statement

Find the current of i1 and i2

Relevant Equations

V/R = i

E=V+IR

My attempt at a solution:
I can see the two resistors at the bottom are in parallel as shown on the circuit diagram attached, but I'm failing to understand why there's a third resistor in parallel.
So I made it one effective resistance as R/2.
Then I proceded to think the circuit short circuits, as Resitor in the middle + R/2 at the bottom has a lower resistance than resistor at the top + middle resistance. So I though i1 = 0 ... I felt like this was wrong and stopped my solution here.

I have been told in order to determine if resistors are in parallel, you must see if the same pd is applied across them, but struggling to see how I can do this here. How do I indentify which are in parallel in this case?

 

[haruspex]

How do I indentify which are in parallel in this case?

If you can find a path from one side of resistor A to one side of resistor B that does not encounter any components, and similarly for the other sides of the two resistors, then the same PD applies across both.