Decidability of functionality for a single attributed tree transducer

Determine whether the functionality problem for a single attributed tree transducer is decidable; namely, given an attributed tree transducer A, decide whether the relation TA realized by A is a partial function.

Background

While functionality for compositions of top-down tree transducers has been shown decidable, the authors emphasize that even the single-device functionality problem for attributed tree transducers has not been resolved.

Establishing decidability here would have broader implications, connecting to classical open problems in equivalence for deterministic attributed tree transducers.