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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Did you have a look at the second part of Johannes Waldmann's thesis The Combinator S ? He proves that the normalization of Sbased combinators is decidable and provides a procedure. SSS(SS)SS does not normalize. He also refers to Dobouè's combinator S(SS)SSSS which does not normalize. 

