(CNN) Bradley Cooper and Irina Shayk have parted ways after being in a relationship for more than four years, a source close to the couple told CNN.

The relationship has been strained, according to a second insider who has worked with Cooper, over the director and actor's "intense" work-ethic during production and press for "A Star Is Born."

"He's into bettering himself, and his career and doesn't want distractions," this source said. "When he does a role, he stays in character, at least partly, all during filming."

But early in his time together with Shayk, Cooper spoke to friends about wanting to marry her.

"He said she was 'the one'" in 2015," the source said, who added that the couple has been "on and off for about a year now," trying to work on things for the sake of their 2-year-old daughter.

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