The Wendt-Abraham criterion [H. R. Wendt and F. F. Abraham, Phys. Rev. Lett. 41,1244 (1978)] is reexamined using computer simulations with an intention to study the kinetic effect in the liquid half arrow right over half arrow left glass transitions. This was carried out by heating an as-quenched glassy metal potassium via (i) a Monte Carlo simulation, which presumably is at an infinite heating rate, and (ii) a molecular-dynamics simulation, which was monitored to run from a finitely high to a lower heating rate. It was found that when the system is heated at a rapid heating rate (relative to cooling), structural relaxation was observed to delay, resulting in an almost linear change in the Wendt-Abraham parameter versus temperature relationship. This delay in structural relaxation was characterized also by virtually unchanged pair-correlation functions for both quenching and heating processes at various temperatures. On the other hand, at a lower heating rate, when the experimental time scale is approaching the average relaxation time, the system undergoes a structural relaxation displaying an anomalous change in the Wendt-Abraham parameter with temperature. In this case structural relaxation was accompanied also by a more orderly structure. These latter behaviors are quite similar to previously related experiments and their interrelation will be discussed in text.