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We study the satisfiability of string constraints where context-freemembership constraints may be imposed on variables. Additionally a variable maybe constrained to be a subword of a word obtained by shuffling variables andtheir transductions. The satisfiability problem is known to be undecidable evenwithout rational transductions. It is known to be NExptime-complete withouttransductions, if the subword relations between variables do not have a cyclicdependency between them. We show that the satisfiability problem staysdecidable in this fragment even when rational transductions are added. It is2NExptime-complete with context-free membership, and NExptime-complete withonly regular membership. For the lower bound we prove a technical lemma that isof independent interest: The length of the shortest word in the intersection ofa pushdown automaton (of size $O(n)$) and $n$ finite-state automata (each ofsize $O(n)$) can be double exponential in $n$.

Satisfiability of Context-free String Constraints with Subword-ordering and Transducers