This paper introduces three different equivalences for processes based on their ability to pass tests. These equivalences are applied to the CCS language, and associated complete proof systems and fully abstract models are provided. The models are represented as trees. The paper discusses the theoretical foundations of process equivalence, the definition of tests, and the derivation of preorders and equivalences. It also presents proof systems for these relations and fully abstract denotational models for CCS. The paper concludes by relating these equivalences to other active research in the field, showing their connections to observational equivalence, failures equivalence, and weak equivalence. The paper also discusses the representation of processes as trees and the use of these trees to model process behavior.This paper introduces three different equivalences for processes based on their ability to pass tests. These equivalences are applied to the CCS language, and associated complete proof systems and fully abstract models are provided. The models are represented as trees. The paper discusses the theoretical foundations of process equivalence, the definition of tests, and the derivation of preorders and equivalences. It also presents proof systems for these relations and fully abstract denotational models for CCS. The paper concludes by relating these equivalences to other active research in the field, showing their connections to observational equivalence, failures equivalence, and weak equivalence. The paper also discusses the representation of processes as trees and the use of these trees to model process behavior.