Taking a cue from some other ArtistMike/Cayard-animated songs which credit Cayard for songwriting, I perused through Cayard's BMI Repertoire listing, and I found that there are two songs called "Exercise Song":
Work #1878860 -- credited to Cayard and Baron
Work #8750214 -- credited to just Cayard
The former is undoubtedly the one used for the "Exercise Song" covered here under that name, but are we sure that it's this one and not the latter? Unfortunately, Elmocize, which has "Exercise Song," does not list Cayard nor Baron in the song credits. Then again, there is even the possibility that neither "Exercise Song" is "Exercise (That's Right for You)." Anyone have any confirmation on either front?