The following universe problem for the equality sets is shown to be undecidable: given a weak coding h, and two morphisms g_1, g_2, where g_2 is periodic, determine whether or not h(E_G(g_1, g_2)) = Σ~+, where E_G(g_1, g_2) consists of the solutions w to the equation g_1 (w) = #g_2(w) for a fixed letter #. The problem is trivially decidable, if instead of E_G(g_1, g_2) the equality set E(g_1, g_2) (without a marker symbol #) is chosen.
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