  This paper investigates regex CQs with string equalities (SERCQs), a subclass
of core spanners. As shown by Freydenberger, Kimelfeld, and Peterfreund (PODS
2018), these queries are intractable, even if restricted to acyclic queries.
This previous result defines acyclicity by treating regex formulas as atoms. In
contrast to this, we propose an alternative definition by converting SERCQs
into FC-CQs -- conjunctive queries in FC, a logic that is based on word
equations. We introduce a way to decompose word equations of unbounded arity
into a conjunction of binary word equations. If the result of the decomposition
is acyclic, then evaluation and enumeration of results become tractable. The
main result of this work is an algorithm that decides in polynomial time
whether an FC-CQ can be decomposed into an acyclic FC-CQ. We also give an
efficient conversion from synchronized SERCQs to FC-CQs with regular
constraints. As a consequence, tractability results for acyclic relational CQs
directly translate to a large class of SERCQs.
