This is what the FAQ section from the ARX website tells us about what kind of oil to use...
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Q: Does it matter what type of oil I use with Auto-Rx®?
A: It does not matter what type of oil you use for the cleaning phase of the Auto-Rx® application. However, for maximum results we recommend that you use plain, non-synthetic oil for the ?rinse? phase. Please see Application Instructions for complete details.
Q: Why do you recommend non-synthetic oil for the rinse" phase of the application?
A: We recommend simple, non-synthetic oil (do not use-semi synthetic or high-mileage oil) for this important step in the Auto-Rx® Application. Synthetic oil has a complex additive package that polarizes the liquefied debris on the engine’s internal oil-lubricated parts. The goal is to rinse all the internal parts of this liquefied debris, and a good ?Dino Oil?, with its simple additive package, does the job very well.
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So there it is, it doesn't matter what kind of oil you clean with, but you're supposed to use only regular dino for the rinse phase.