Left: the results of artificial star experiments on the stacked JHK_s images (dashed, dotted, and solid lines) of a  ~24′ × 24′ field of the WIRCam observation. Right: the results of the experiments as a function of the projected radius (R_c) from the center of NGC 205. Only stars brighter than K_s = 18.1 mag were considered because we assumed that AGB stars are brighter than K_s = 18.1 mag in Sect. 3.2. The completeness is the number of recovered artificial stars divided by the total number of added stars. ΔM (mag) is the mean difference between the actual input magnitudes and the measured magnitudes by DAOPHOTII/ALLSTARS, and σ (mag) is the standard deviation of the ΔM.