On the joint subword complexity of automatic sequences

Let the (subword) complexity of a sequence u=(u(n))"n"="0^~ over a finite set @S be the function m@?P"u(m), where P"u(m) denotes the number of distinct blocks u(n)...u(n+m-1) of size m in u. In this paper, we study the complexity of u-(n)=(u"1(n),...,u"r(n))"n"="0^~ when each u"i=(u"i(n))"n"="0^~, i=1,...,r, is a q"i-automatic sequence over a finite set @S"i and q"1,...,q"r=2 are pairwise coprime integers. As an application, we answer a question of Allouche and Shallit regarding morphic real numbers.