Process mining techniques allow for extracting information from event logs. In general, there are two steps in process mining, correlation definition or discovery and then process inference or composition. Firstly, the work consists to mine small patterns from a log traces; those patterns are the representation of the traces execution from a log file of a business process. In this step, the authors use existing techniques. The patterns are represented by finite state automaton or their regular expression. The final model is the combination of only two types of small patterns that are represented by the regular expressions. Secondly, they compute these patterns in parallel and then combine those small patterns using the MapReduce framework. They have two parties the first is the map step. They mine patterns from execution traces, and the second is the combination of these small patterns as reduce step. The results are promising; they show that the approach is scalable, general, and precise. It minimizes the execution time by the use of the MapReduce framework.