Ari-ari
Ari-ari 「アリ アリ」 refers to a ruleset which allows kuitan (open tanyao) and allows atozuke (winning without confirmed yaku). It is generally the most commonly accepted ruleset pertaining to Japanese mahjong.
Conversely, nashi-nashi forbids kuitan and atozuke. Nashi-ari would forbid kuitan but allow atozuke, and vice versa for ari-nashi.