\$$R = 0 \text{ if } x \lt0 \$$ gives \$$I(R(-0.2)) = 0.0 \nleq -0.2 \$$ meaning there is no right adjoint.
Simply mapping negative values to 0 is a good mapping, it is called the left adjoint.
There is a right adjoint for \$$I : \mathbb{N} \rightarrow \mathbb{R}^+ \$$ though.
Another, visual, way to think about \$$I(R(x)) \le x \$$ is that red arrows cannot bend to the right [what I was trying to say with the picture].