The authors examine the solid-fluid equilibrium problem using two computational perspectives: (1) the thermodynamic equilibrium view, wherein the solid phase remains in the system in equilibrium with the fluid phase, and (2) the process sequential view, wherein the solid phase is removed from the equilibrium system as it is formed. The latter view represents the solid-fluid systems in which the solids forming incrementally at successively lower temperatures remain compositionally unchanged as temperature decreases further, i.e. metastable. It is demonstrated for a quadrature-characterized complex system that choice of perspective affects both the compositions and the phenomenological nature of the phase equilibria.