1. A memory system comprising: a first non-volatile memory including a plurality of blocks being units of data erasing; a second non-volatile memory; a first volatile memory; a second volatile memory; a power supply circuit having a backup power source, the power supply circuit configured to supply externally supplied electric power to each unit in the memory system; a first processor configured to transmit and receive a command to a host, and configured to store data received from the host into the first volatile memory; and a second processor configured to transfer management information stored in the first non-volatile memory to the first volatile memory at time of startup of the memory system, and configured to store the data stored in the first volatile memory into the first non-volatile memory by using the transferred management information, wherein the power supply circuit is configured to supply the electric power from the backup power source to each unit in the memory system and is configured to notify the first processor of an interruption of external electric supply when detecting the interruption of the external electric power supply, when being notified of the interruption of the external electric power supply from the first processor, the second processor is configured to perform a saving operation for storing the management information and the data stored in the first volatile memory to the first non-volatile memory and is configured to record a progress log, indicating a progress of the saving operation, into the second volatile memory, and when being notified of the interruption of the external electric supply from the power supply circuit, the first processor is configured to notify the second processor of the interruption of the external electric power supply and is configured to check periodically whether or not the progress log is recorded in the second volatile memory, and when the progress log is recorded in the second volatile memory, the first processor is configured to store the progress log into the second non-volatile memory.