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CR-SISTEM models lunar orbital and rotational dynamics, taking into account the effects of a liquid core. Orbits of the Moon and Earth are fully integrated, and other planets (or additional point-mass satellites) may be included in the integration. Lunar and solar tides on Earth, eccentricity and obliquity tides on the Moon, and lunar core-mantle friction are included. The integrator is one file (crsistem5.for) written in FORTRAN 90, uses seven input files (settings.in, planets.in, moons.in, tidal.in, lunar.in, precess.in and core.in), and has at least eight output files (planet101.out, moon101.out, pole.out, spin_orb.out, spin_ecl.out, cspin_ecl.out, long.out and clong.out); additional moons and planets would add more output. The input files provided with the code set up a 1 Myr simulation of a slow-spinning Moon on an orbit of 40 Earth radii, which will then dynamically relax to the lowest-energy state (in this case it is a synchronous rotation with a core spinning separately from the mantle).