Bad Alternator or Battery??

[basit701]

Hello Guys! I own a Toyota Vitz (Yaris) 1KR-FE (CVT). From past few days i am facing problems like dimming lights, vibration when AC or headlights turn on. To diagnose this i checked my battery(approx 2 year old) voltage and DMM was showing about 12.2V. I replaced the battery with new AC Delco sealed maintenance free battery. After changing the battery i am facing these issues.

The engine would crank in the morning and if i turn off and crank again. It would start. But if i drive like 5 6 KM with AC on and turn off the car and start again. The car would take a heavy start like the battery is dead. So i checked the voltage of battery at different instants and these are the results:

Voltage when engine off: 13.08V
Voltage when engine runs after cranking: 13.67V
Voltage after 2 3 minutes of emgine running : 13.34V
Increasing RPM to 2000~2500 voltage after 4 5 minutes of engine running: 13.7V
Turning AC and headlights on @ idle:13.15V and @2000~2500 rpm: 13.28V

I am just confused is the alternator weak or battery is bad(AC Delco is a reputed brand and also the hydrometer on the battery is green which means OK).

Any suggestions???