No algorithm decides, given a finite list of pairs of strings over $\mathbb{N}$, whether some nonempty sequence of indices makes the two concatenations equal. This is the undecidability of the Post correspondence problem in the index form used by the book Transducers, where it is the source of the undecidability of equivalence of rational relations (Theorem B.1.6). A list of dominos taken from an instance and a list of positions in the instance carry the same information, so the index form is the domino form $PostCorrespondenceUndecidable$ restated.