Here are the graphs of first charging and discharging runs. The battery was loaded with 500mA current sink during discharge and supplied from 13V  (1Alimit) voltage source during charging.

During discharge the converter passes trough three modes. First is the constant output voltage. As the battery voltage drops, the battery current rises to the maximum limit. At that point the converter enters into maximum current regulation and the output voltage starts to fall. As the battery voltage reaches minimal value of 2.8V the maximum current starts to be lowered to avoid over discharge at that point the output voltage falls even lower and the test is stopped when the current falls below 10% of maximum value.

During charging similar three modes of operation are visible. The first one is the short period of maximum battery current limit. Then as the battery require more charging power (battery voltage rises and current stays the same) the power supply input start to fall under the input voltage limit (12.1V) and the converter start to lower charging current not to over-load the source. As the battery starts to reach maximal voltage (4.2) the charging current starts to be lowered and the power supply can recover back to initial 13V.