Does Ayu come up with song titles?

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She probably either writes the lyrics, then comes up with a title that fit them or she has an idea of a subject she wants to write about, writes down some possible titles and then write lyrics for it.

She could also get titles from the composers. They might call the track they've made something, before they pass it on to ayu and she could go with that title if she likes it. I think this might be the case for some of the interludes.