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88 alal A-decomposition a0al ala0 arrows indicate edges automata b0 b2 bl b2 bQ b2 b3 b2 bQ b3 b3 bl b5 b3 bQ b5 bl b2 b5 V9 bQ bl bl bQ b2 b5 bQ b3 b1 bQ b5 bQ bQ canonical enumeration canonical mapping construction D-tour define A(W denote directed edges directed Post normal E^-tour edges of Type Eg-tour starting empty word enumeration of F(A exists a lexicon exists a Post exists no node finite set free semigroup input tape integer least common multiple left-component lexica M(W aQ mapping of F(A maps F(A natural numbers node q normal algorithms normal lexicon null productions numerical index order-preserving Post algorithm Post languages Post normal system productions U:V quadruple reads the tape recursive function regular set result right-components sequential machine set of productions starting at q sublist terminal nodes terminal subwords Theorem Let word WeF(A words in F(A XeF(A YeF(B