Algorithms that don't terminate in a lazy language

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According to http://www.reddit.com/r/programming/comments/gwqa2/the_real_point_of_laziness/c1rslxk

Some algorithms don't terminate in an eager language, that do in a lazy one, and (a mild shocker for me to find,) vice-versa.

The former is of course well known, but the latter strikes me as, if true, considerably more than a mild shocker.

Does anyone know an algorithm that terminates in an eager language but not in a lazy one?

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