  We study the local dynamics of a thixotropic yield stress fluid that shows a
pronounced non-monotonic flow curve. This mechanically unstable behavior is
generally not observable from standard rheometry tests, resulting in a stress
plateau that stems from the coexistence of a flowing band with an unyielded
region below a critical shear rate $\dot \gamma_c$. Combining ultrasound
velocimetry with standard rheometry, we discover an original shear-banding
scenario in the decreasing branch of the flow curve of model paraffin gels, in
which the flow profile of the flowing band is set by the applied shear rate
$\gd$ instead of $\dot \gamma_c$. As a consequence, the material slips at the
walls with a velocity that shows a non-trivial dependence on the applied shear
rate. To capture our observations, we propose a differential version of the
so-called lever rule, describing the extent of the flowing band and the
evolution of wall slip with shear rate. This phenomenological model holds down
to very low shear rates, at which the dimension of the flowing band becomes
comparable to the size of the wax particles that constitute the gel
microstructure, leading to cooperative effects. Our approach provides a
framework where constraints imposed in the classical shear-banding scenario can
be relaxed, with wall slip acting as an additional degree of freedom.
