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I highly speculate that combinator SSS(SS)SS is not strongly normalizing. What is the argument for the non strong normalization?

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Could you give some motivation for this? Why do you suspect it is not strongly normalizing? Also, why is this particular combinator interesting? –  Noah S May 7 '13 at 21:18
I suspect it is strongly normalizing because it reduces as follows (no room for that) This combinator is interesting because it is the smallest with is no SN. –  Pierre Lescanne May 9 '13 at 6:09
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