  We present a detailed study of the circumstellar gas distribution and
kinematics of the semi-regular variable star RS Cnc on spatial scales ranging
from ~1" (~150 AU) to ~6' (~0.25 pc). New modeling of CO1-0 and CO2-1 imaging
observations leads to a revised characterization of RS Cnc's previously
identified axisymmetric molecular outflow. Rather than a simple disk-outflow
picture, we find that a gradient in velocity as a function of latitude is
needed to fit the spatially resolved spectra, and in our preferred model, the
density and the velocity vary smoothly from the equatorial plane to the polar
axis. In terms of density, the source appears quasi-spherical, whereas in terms
of velocity the source is axi-symmetric with a low expansion velocity in the
equatorial plane and faster outflows in the polar directions. The flux of
matter is also larger in the polar directions than in the equatorial plane. An
implication of our model is that the stellar wind is still accelerated at radii
larger than a few hundred AU, well beyond the radius where the terminal
velocity is thought to be reached in an asymptotic giant branch star. The HI
data show the previously detected head-tail morphology, but also supply
additional detail about the atomic gas distribution and kinematics. We confirm
that the `head' seen in HI is elongated in a direction consistent with the
polar axis of the molecular outflow, suggesting that we are tracing an
extension of the molecular outflow well beyond the molecular dissociation
radius (up to ~0.05 pc). The 6'-long HI `tail' is oriented at a PA of
305{\deg}, consistent with the space motion of the star. We measure a total
mass of atomic hydrogen ~0.0055 solar mass and estimate a lower limit to the
timescale for the formation of the tail to be ~6.4x10^4 years. (abridged)
