[en] Numerical simulations of active galactic nuclei (AGNs) feedback in cool-core galaxy clusters have successfully avoided classical cooling flows, but often produce too much cold gas. We perform adaptive mesh simulations that include momentum-driven AGN feedback, self-gravity, star formation, and stellar feedback, focusing on the interplay between cooling, AGN heating, and star formation in an isolated cool-core cluster. Cold clumps triggered by AGN jets and turbulence form filamentary structures tens of kpc long. This cold gas feeds both star formation and the supermassive black hole (SMBH), triggering an AGN outburst that increases the entropy of the intracluster medium (ICM) and reduces its cooling rate. Within 1–2 Gyr, star formation completely consumes the cold gas, leading to a brief shutoff of the AGN. The ICM quickly cools and redevelops multiphase gas, followed by another cycle of star formation/AGN outburst. Within 6.5 Gyr, we observe three such cycles. There is good agreement between our simulated cluster and the observations of cool-core clusters. ICM cooling is dynamically balanced by AGN heating, and a cool-core appearance is preserved. The minimum cooling time to free-fall time ratio typically varies between a few and $\gtrsim <!--\; ???\; -->20$. The star formation rate (SFR) covers a wide range, from 0 to a few hundred $M_{\odot <!--\; ???\; -->}{\mathrm{y}\mathrm{r}}^{-<!--\; ???\; -->1}$, with an average of $\sim <!--\; ???\; -->40M_{\odot <!--\; ???\; -->}{\mathrm{y}\mathrm{r}}^{-<!--\; ???\; -->1}$. The instantaneous SMBH accretion rate shows large variations on short timescales, but the average value correlates well with the SFR. Simulations without stellar feedback or self-gravity produce qualitatively similar results, but a lower SMBH feedback efficiency (0.1% compared to 1%) results in too many stars.