I heard that rhyme from my grandmother, who BTW was a total racist. She would bounce me on her racist knee and chant,

The grand old duke of York

He had ten thousand men

He marched them up to the top of the hill and he marched them down again

Now when you're up you're up

And when you're down you're down

And when you're only halfway up you're neither up nor down.

I should be grateful. At least she didn’t bounce me to the tune of some racist doggerel!