A phrasal verb did me in.
A phrase verb and his mate,
who was a non-defining relative clause,
did me in.
(In case you don't get the joke: 'to do someone in' is a phrasal verb, and the third line of the poem is itself a non-defining relative clause.)
Presumably I had intended to continue the poem, introducing more grammatical terms as I went. And presumably it would have almost followed the form of (what I've just discovered is called) a cumulative song.
Don't judge me, OK?