$p-MC(Σ_1) ≤fpt p-MC(Σ_1⁺)$ (Flum–Grohe, Lemma 6.11). The universe is first compressed to the entries of the tuples and $|x|$ further elements (a $Σ_1$-formula of size at most $|x|$ cannot tell the difference); the structure is then expanded by the order $<$ and, per symbol $R$, by its first tuple, its last tuple, its consecutive pairs and $Z_R$ (the universe if $R$ is empty), and every negative literal is replaced by a positive existential formula over these ($¬ x = y$ by $x < y ∨ y < x$). The new parameter is at most $72 k$, and the map is computed by an IMP+ program in $O(|x|³)$ steps.