Pattern detection in sequence of users behaviour for clustering

I need to detect variable-size patterns in a set of fixed-size strings, where each string represents a sequence of activity of a group of users.

As an example, i have a 10 character string or user 1 where each char represents an activity intensity: 'LLMLLMGLML' meaning that the first 2 samples where of a low intensity, the third a medium intensity and then the activity gets lower again. Another example, for user2: 'LMMGMLLMLL'. Both users had a common pattern: 'LLMLL'

My intention is to classify users in terms of their overall activity, defining similarity based on the number of common patterns

Can you recommend an approach to this problem?