You think it's like that but:
when we first see them, they meet on a train, but when he start wiping his memories the train is nowhere to be seen so they both had to have their memories wiped before, and then met, and then she wiped her memories AGAIN only to have the guy wipe HIS memories AGAIN in retaliation, but the Kirsten Dunst chick who performed the whole thing also had her memory wiped because she had an affair with the owner of the mind-wiping company but that other guy is in love with her and Elijah Wood is in love with Jim Carrey's girlfriend and then it's all useless anyway because Kirsten Dunst restores everyone's memory and....
As you see, the plot is WAY too complicated for me to follow.