This question has been updated by the errata.
See Section 9.6. Add the following definition to $(D_1) \ldots (D4)$:
$$ (D_5) \quad x: \mathbb{Z}, y: \mathbb{Z} \triangleright d(x,y) := (x+ y)^2 $$
Let $\Delta ≡D_1, \ldots ,D_5$. Give the full δ-reduction diagram of $d(a(u,v),b(w,w))$.
The following diagram illustrates the δ-reduction of $d(a(u,v),b(w,w))$.
(click to enlarge)
The final result is
$$ d(a(u,v), b(w,w)) \; \triangleq \; (u^2 + v^2 + 2 w^2)^2 $$
