This paper presents a series of general properties of the r-Complexity calculus, a complexity measurement for assessing the performance and asymptotic behaviour of real-world algorithms. This research describes characteristics such as reflexivity, transitivity, or symmetry and discusses several conversion rules between different classes of r-Complexity, as well as establishing fundamental arithmetic principles. The work also examines the behaviour of the addition property within this system and compares its characteristics with those frequently used in the traditional Bachmann-Landau notation. Through utilizing these properties, this research seeks to promote the exploration and development of novel applications for r-Complexity, as well as accelerating the adoption rate of calculus in this refined complexity model.

翻译：本文系统阐述了r-复杂性演算的一系列普适性质，该演算体系是用于评估现实世界算法性能与渐近行为的复杂度度量方法。本研究描述了自反性、传递性与对称性等特征，探讨了不同r-复杂性类别之间的若干转换规则，并建立了基本算术原理。研究同时考察了该体系中的加法性质行为，并将其特征与传统巴赫曼-朗道表示法中常用的性质进行了对比分析。通过运用这些性质，本研究旨在推动r-复杂性新型应用场景的探索与发展，并加速该精细化复杂度模型中演算方法的采纳进程。