Are there any complete synonyms in English?

I’m kind of inventing my own linguistic term here (I think), but what I mean by “complete synonyms” are two words that have the exact same meaning (and connotations) and are completely interchangeable. I was thinking about the fact that most examples of synonyms in English have slight differences in meaning or connotations.

Is there such an example in English? I asked my professor this and he gave me the example of “sofa” and “couch” as being the closest he could think of, but the dictionary seems to indicate that while the terms are essentially used interchangeably, a “sofa” can be longer than a couch and always has arms. (To me, however, “sofa” and “couch” did seem to be complete synonyms, as I had never known of any distinction between the two).

Are there any examples of “complete synonyms” in English? Or at least an example of two words having complete synonymy in your mind?