Where does “Piripīni” come from?

Piripīni (Rarotongan) comes from English Philippines, from French Philippines, from Spanish Filipinas, from Spanish Felipe, from Latin Philippus, from Ancient Greek φίλιππος, from Ancient Greek φιλέω, from Ancient Greek ἀτέλεια — together, one.

Ancestry of “Piripīni”, step by step

Step	Language	Word	Meaning
1	English	Philippines	—
2	French	Philippines	—
3	Spanish	Filipinas	{{l\|en\|Philippines}}
4	Spanish	Felipe	Philip biblical apostle
5	Latin	Philippus	—
6	Ancient Greek	φίλιππος	fond of horses
7	Ancient Greek	φιλέω	I love, like, regard highly; I treat kindly,...
8	Ancient Greek	ἀτέλεια	exemption from public burdens, immunity
9	Ancient Greek	ἀ-	The alpha privativum, used to make words that...
10	Proto-Hellenic	hə-	same; together
11	Proto-Indo-European	sm̥-	one; with, together
12	Proto-Indo-European	sem-	together, one

Every word from Proto-Indo-European sem- →Every word from Ancient Greek ἀ- →Every word from Ancient Greek ἀτέλεια →