Correct. S2000 and K Series motors have timing chains. They don't need to be replaced like rubber timing belts.
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if its going through oil try looking into 'krank vents'
the f20c is known to 'drink' oil.
the only thing i can see them inspecting is the timing chain tensioner
Try to avoid S2ks that were run in on the freeway. Quite a few have rings that don't seal well and hence consume oil. Same goes for K-series engines.