Controller and control method for internal combustion engine

A controller for an internal combustion engine, wherein

• an exhaust purification device is disposed in an exhaust passage of the internal combustion engine,
• the internal combustion engine is configured to execute a fuel cutoff operation in which an engine output shaft is rotated with fuel supply stopped,
• the controller comprises processing circuitry,
• the processing circuitry is configured to execute a first change amount calculating process, a second change amount calculating process, a determination process, and an anomaly diagnosing process,
• the first change amount calculating process is a process of calculating a first change amount that is a change amount per unit time of an upstream-side temperature, the upstream-side temperature being a temperature of exhaust gas on an upstream side of the exhaust purification device,
• the second change amount calculating process is a process of calculating a second change amount that is a change amount per unit time of a downstream-side temperature, the downstream-side temperature being a temperature of exhaust gas on a downstream side of the exhaust purification device,
• the determination process is a process of determining that a deviation between the first change amount during the fuel cutoff operation and the second change amount during the fuel cutoff operation is less than or equal to a threshold,
• the anomaly diagnosing process is a process of determining that the exhaust purification device is in a detached state when it is determined in the determination process that the deviation is less than or equal to the threshold,
• the processing circuitry is configured to interrupt the determination process when the upstream-side temperature increases within a determination period, and
• the determination period is a period from when the determination process is started to when the upstream-side temperature decreases by a specified temperature from a value at the start of the determination process.