Hi, I asked something about that a while ago I think it can only mean #2 to native speakers (see MM's post in that thread).
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Debpriya De"I have had a fight with my girlfriend of 14 years."No, it can't have two interpretations. Only your second paraphrase captures the meaning.
Can this sentence have two interpretations:
1. My girlfriend is 14 years old.
2. She has been my girlfriend for 14 years.