The plain Newton-min algorithm to solve the linear complementarity problem (LCP for short) $0\leq x\perp(Mx+q)\geq0$ can be viewed as a nonsmooth Newton algorithm without globalization technique to solve the system of piecewise linear equations $\min(x,Mx+q)=0$, which is equivalent to the LCP. When $M$ is an $\Mmat$-matrix of order~$n$, the algorithm is known to converge in at most $n$ iterations. We show in this paper that this result no longer holds when $M$ is a $\Pmat$-matrix of order~$\geq\nobreak3$, since then the algorithm may cycle. $\Pmat$-matrices are interesting since they are those ensuring the existence and uniqueness of the solution to the LCP for an arbitrary~$q$. Incidentally, convergence occurs for a $\Pmat$-matrix of order~$1$ or~$2$.