I. The boundedness of all products of a pair of matrices is undecidable, Systems & Control Letters 41 (2000) 135-140 by Vincent D. Blondela & John N. Tsitsiklis http://web.mit.edu/jnt/www/Papers/J081-00-vb-products.pdf
--and as a result of this, Lunnon's problem of finding a sharp upper bound on c, is undecidable, in particular it is undecidable whether c<=1. So you will in general have to be satisfied with non-sharp upper bounds got by e.g. matrix-norm techniques -- lower bounds are also producable by computer exploration of many words -- or hope for miracles e.g. if you have a particularly nice set of generators in mind, you may be able to solve it. As some joker once said, "I solve undecidable problems all the time." (Actually I think the joker was Roger Penrose, who had the asinine utterly incorrect idea that this "proved" human minds had super-Turing power.)