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Rigorous - According to Merriam-Webster, rigoroushas to do with something very strict (e.g., The auto industry needs more-rigorous testing). Rigorous often refers to strictly following rules and procedures. It can also mean that something's "scrupulously accurate" or "marked by extremes of temperature or climate."

Vigorous - Merriam-Webster's definition of vigorimplies physical or mental strength or active force (e.g., the benefit of vigorous activity over moderate activity) or the act of carrying something out with force or energy.

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