I don't see how it's just arithmetic, since there is no free flow of goods and labor across national boundaries and the prices of goods and services at market exchange rates vary widely across countries. Can you explain your thinking?
Also, how about Canada for another counterexample, albeit not as dramatic as Japan? In the 15 years from May 8, 2009 to May 8, 2024 the Loonie has depreciated from 0.87 USD to 0.73 USD. But inflation in Canada was slightly less than in the US (39% vs 46% according to ChatGPT).