relationship between vladimir and estragon?

It is believed that the two stay together because their personalities meld perfectly; Vladimir complements Estragon and the other way around. The way that one complements the other serves as a source of fulfillment for each of them......... in a way, they're co-dependents.

Not only do they compliment each other, but it is necessary for them to be together. Estragon does not have memories of anything that happened moments before his lines, so he needs Vladimir to be his "historian". Vladimir can remember more than Estragon, but does not trust his knowledge, so he needs Estragon to reassure him. They have been together for what is either literally or feels like 50 years, so if they split up, it would be like taking away 1/2 of a person's identity.