Is there a word for "independent of, and not affecting"?

I'm describing a process (let's call it A) that is both unaffected by, and does not affect another separate process (B).

"Independent" doesn't quite seem to cover it. A is indeed "not dependent" on B, but also does not have an impact on it.

"Process/Object A is [mystery word] of Process/Object B"

Is there a better word than "independent" that would fit the bill? I've tried looking up synonyms, but haven't had much luck

Solution 1:

Independent does specifically mean both unaffected by and not having an effect upon the other.

Dependence can be mutual or one way, but independence always works both ways.

Within a larger set of processes, two can be pairwise independent, meaning they don't effect each other but may be affected by other members. Mutual independence extends this idea to all members under consideration.