Relay model for controlling the Air Conditioner power supply
Assuming you are using a 220VAC mains supply, 1126 Watts will consume about 6 Amps of current, you can calculate it from the following Online Calculator.

Average mechanical relay have a life cycle of 100,000 cycles which means it can be used for a long period of time. Also its not mandatory to use the fast response of the solid state relay. Because your application is going to switch the air conditioner on and back off once every half an hour. 

The starting current of AC motor is usually 2 - 2.5 times the running current, which is equal to 15 Amp.

So a typical 220VAC 20Amp mechanical relay will fit your application well.