For the function $f(x)=\cos x - x + 1,; x\in\mathbb{R}$, consider the statements (S1) $f(x)=0$ for only one value of $x$ in $[0,\pi]$. (S2) $f(x)$ is decreasing in $\left[0,\tfrac{\pi}{2}\right]$ and increasing in $\left[\tfrac{\pi}{2},\pi\right]$. Which is/are correct?