= Solution
On the universe $\mathbb Z$, interpret the <first-order signature> by
$$
\boxed{c_1^{\mathcal A}=c_2^{\mathcal A}=0,\quad f^{\mathcal A}(x,y)=x+y,\quad R_2^{\mathcal A}=\mathbb Z_{\geq0},\quad R_1^{\mathcal A}=\{(u,v)\in\mathbb Z^2:u\leq v\}.}
$$
This assigns both constants, a total binary function, a unary relation and a binary relation, so it specifies a complete <first-order structure>. If $R_2(x)$ and $R_2(y)$ both hold, then $x,y\geq0$, and hence $f(c_1,c_2)=0\leq x+y=f(x,y)$, proving the consequent. If either premise fails, the implication is true. Thus the universally quantified implication holds for every pair of <integers>, nonvacuously for every pair of nonnegative <integers>. Distinct constant symbols need not denote distinct objects unless a separate axiom requires it.
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