Generalized pseudostandard words were introduced by de Luca and De Luca in 2006. In comparison to the palindromic and pseudopalindromic closure, only little is known about the generalized pseudopalindromic closure and the associated generalized pseudostandard words. We present a counterexample to a conjecture by Blondin Mass′e et al. from 2013 that estimated the complexity of binary generalized pseudostandard words as C(n) ? 4n for all suciently large n. We conjecture that C(n) < 6n for all n 2 N.
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