"He’s happy not to be commuting,"

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Is (linking verb)
Happy (adjective complement)
Please explain the use of "to be" here.
Is "not to be commuting" an infinitive phrase functioning adverbially?I

I'd say 'not to be commuting' is a complement of 'happy' and not adverbial. Infinitive constructions are often the complement of 'happy' (or 'glad' or 'sorry', etc.).

happy to be here
happy to help you
glad to see you
glad to be invited
sorry to have missed you
sorry to hear that
happy not to have made a mistake
happy not to be working there anymore


Students: We have free audio pronunciation exercises.


Like an adverb, doesn't it answer the why question (why is or was happy)?

Does complement mean the word or phrase essential to the meaning of the sentence?