Paired Counter Automata

Consider a DFA $A$ together with $d$ pairs off counters $(x_1,y_1),\dots,(x_d,y_d)$. Each transition of $A$ is labelled with an update function for all counters. The update functions for the x-counters are $id:n\rightarrow n$ and $++ : n\rightarrow n+1$. The update function for the y-counters are $id:n\rightarrow n$, $\times 2:n\rightarrow 2n$ and $\times 2+1:n\rightarrow 2n+1$. An accepting configuration is a configuration in which we are in an accepting state and all the counter pairs have the same value, i.e. $x_1=y_1,\dots,x_d=y_d$. Question: is the emptiness problem for this class of automata decidable?