Cowboy Bebop and the anime adaptation of Trigun both originally aired in 1998, however, unlike Trigun, which used mostly traditional cel animation, Cowboy Bebop made extensive use of computers in its production. Cowboy Bebop is also not something I would consider to be anime, as Cowboy Bebop is good and anime, as a rule, sucks. Ergo Cowboy Bebop does not suck, so it cannot be anime.