1) You describe only the linear step-by-step use of Memory\Elements Interaction.
2) Memory is also the simultaneity of the connection of more than a one element.
3) Time is not necessarily involved here, so concepts like “process” are not fundamentals of Memory\Elements Interaction.
4) Again, please think again about the String\Beads analogy, the amount of elements is a simultaneous result of the String(Non-locality)\Bead(Locality) Interaction, which is independent of any step-by-step linear addition.
5) Usually addition is taken as a linear form because of the representation style that is based of x+y+z+... form.
6) But addition is independent of this particular representation, for example, by using Lisp programming language, addition is represented as
(+ x y z ...) where + is equivalent to the String and x y z ... are equivalent to Elements in String\Elements analogy.
7) In other words, please follow the notion and not any particular representation of it.