  We study the elliptic inclusion given in the following divergence form
  \begin{align*}
  & -\mathrm{div}\, A(x,\nabla u) \ni f\quad \mathrm{in}\quad \Omega,
  & u=0\quad \mathrm{on}\quad \partial \Omega.
  \end{align*}
  As we assume that $f\in L^1(\Omega)$, the solutions to the above problem are
understood in the renormalized sense. We also assume nonstandard, possibly
nonpolynomial, heterogeneous and anisotropic growth and coercivity conditions
on the maximally monotone multifunction $A$ which necessitates the use of the
nonseparable and nonreflexive Musielak--Orlicz spaces. We prove the existence
and uniqueness of the renormalized solution as well as, under additional
assumptions on the problem data, its relation to the weak solution. The key
difficulty, the lack of a Carath\'{e}odory selection of the maximally monotone
multifunction is overcome with the use of the Minty transform.
