Since the environment for businesses is becoming more competitive by the day, business organizations have to be more adaptive to environmental changes and are constantly in a process of optimization. Fundamental parts of these organizations are their business processes. Discovering and understanding the actual execution flow of the processes deployed in organizations is an important enabler for the management, analysis, and optimization of both, the processes and the business. This has become increasingly difficult since business processes are now often dynamically changing and may produce hundreds of events per second. The basis for this paper is the Constructs Competition Miner (CCM): A divide-and-conquer algorithm which discovers block-structured processes from event logs possibly consisting of exceptional behaviour. In this paper we propose a set of modifications for the CCM to enable dynamic business process discovery of a run-time process model from a stream of events. We describe the different modifications with a particular focus on the influence of individual events, i.e. ageing techniques. We furthermore investigate the behaviour and performance of the algorithm and the ageing techniques on event streams of dynamically changing processes.