Consider the reals ordered by our normal \(\leq\) relation. Do \((1,*)\) as unit and product for a symmetric monoidal structure?
No, monotonicity fails: \(x_1\leq y_1 \land x_2 \leq y_2 \not \implies x_1x_2 \leq y_1y_2\) (Counterexample: \(x_1=x_2=-1, y_1=y_2=0\))