Amadeus Cafe makes a pre-hysterical music blunder

If you owned a place called the Amadeus Cafe, you might use a musical motif to dress up menus, signs and such. But shouldn't it be something by Wolfgang Amadeus Mozart, not the tune from an old cartoon about a prehistoric family?
See if you can figure out the tune from this viral tweet on the topic:
If you can't figure it out, here's a hint:
It's the theme to The Flintstones — which wasn't composed by Mozart.