What is Non-adversarial means of dispute resolution?

Answer 1

Non-adversarial adjudication means the legal dispute was solved outside of court, but still within the legal system. It can also be called Alternative Dispute Resolution; maybe the parties went to mediation where they compromised on terms they can both be happy with.

Answer 2

That usually means "mediation", where a court-appointed mediator listens to both sides, looks at 'evidence' and decides the case without tying up the courts time. If either part disagrees with the decision, they have a certain amount of time to file an objection to the mediators decision, in order to be heard by a judge.