Unfortunately I'm not an expert on AMD graphics. Except for a 2014 low-cost HP notebook with AMD APU (equivalent to R2 graphics) where I installed the recommended drivers and everything works fine, my last experience with AMD graphics was in the time they were still called ATI (circa 2005).
Nevertheless, I have a question: Is there some reason why you kept the 12.04? The machine is new enough to perhaps work better with newer releases. 14.04 is also LTS.
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