System and information processing apparatus

A system comprising:

• an electronic key;
• a vehicle having a function of a smart key corresponding to the electronic key;
• a server having a controller and a storage;
• a terminal of a user;
• wherein
• the electronic key transmits, to the vehicle in response to an input that causes the transmission of the radio wave to be stopped, first information on the cessation of the transmission of the radio wave;
• in response to receiving the first information from the electronic key, the vehicle transmits to the server second information regarding the electronic key stopping the transmission of the radio wave;
• and
• the controller of the server is configured to:
• calculate, in response to receiving the second information, a number of times the transmission of the radio wave is stopped in the electronic key, and storing the number of times in the storage;
• generate third information for granting the incentive to the user so that the incentive increases as the number of times is increased;
• and
• generate an instruction for causing the display of the generated image according to the third information on the display of the terminal of the user, and transmit the instruction to the terminal of the user;
• and
• the terminal of the user, in response to receiving the command from the server, causes the image to be displayed on the display.