Hydraulic system for working machine, and working machine

A hydraulic system for a working machine, the hydraulic system comprising:

• a traveling motor to output power to a traveling device in the working machine;
• a first detector to detect a physical quantity that changes in accordance with a traveling state of the working machine and that is detected at intervals of a predetermined period;
• and
• a controller to execute automatic shift-down to automatically shift down a speed stage for a rotational speed of the traveling motor from a second speed stage to a first speed stage in which the rotational speed of the traveling motor is lower than the rotational speed of the traveling motor in the second speed stage;
• wherein
• the controller is configured or programmed to determine a tendency or degree of change in the physical quantity, based on a plurality of values of the physical quantity detected at intervals of the predetermined period by the first detector.