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They get tired because any kind of work uses energy. Breathing is technically considered breathing, so yes they were working.

The height reference in the question shows that you are thinking about potential energy. When something in a gravitational field is raised to a height, the work done against gravity to raise it means it gains potential energy. When something is moved within a gravitational field without gaining height, it does not gain potential energy, but work is done to move it: this work is not necessarily against gravity, but against forces of friction etc, so the energy may be converted into heat etc. rather than into potential energy.

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