Unified Software Development Life Cycle. Iterative and Incremental. RUP is a specific implementation of the Unified.
However to get the most benefit from the UML you should consider a process that is. The software development lifecycle SDLC is the series of steps an organization follows to develop and deploy its software. Iterative and Incremental.
Use case driven Architecture centric Iterative and incremental.
Each of these phases consists of several iterations. RUP is not a single concrete prescriptive process but rather an adaptable process framework intended to be tailored by the development organizations and software project teams that will select the elements of the process that are appropriate for their needs. The unified process occurs over four phases which include Inception Elaboration Construction and Transition. There isnt a single unified software development lifecycle.