We don't have synonyms for relies yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are relief, relics and relied.
(v) :
to rest with confidence, as when fully satisfied of the veracity, integrity, or ability of persons, or of the certainty of facts or of evidence; to have confidence; to trust; to depend; — with on, formerly also with in
(v) :
to rest with confidence, as when fully satisfied of the veracity, integrity, or ability of persons, or of the certainty of facts or of evidence; to have confidence; to trust; to depend; — with on, formerly also with in