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Following G. Gr\"atzer and E. Knapp (2007), a slim semimodular lattice, SPSlattice for short, is a finite planar semimodular lattice having no $M_3$ as asublattice. An SPS lattice is a slim rectangular lattice if it has exactly twodoubly irreducible elements and these two elements are complements of eachother. A finite poset $P$ is said to be JConSPS-representable if there is anSPS lattice $L$ such that $P$ is isomorphic to the poset J(Con $L$) ofjoin-irreducible congruences of $L$. We prove that if $1<n\in N$ and $P$ is an$n$-element JConSPS-representable poset, then there exists a slim rectangularlattice $L$ such that J(Con $L$) is isomorphic to $P$, the length of $L$ is atmost $2n^2$, and $|L|\leq 4n^4$. This offers an algorithm to decide whether afinite poset $P$ is JConSPS-representable (or a finite distributive lattice is``ConSPS-representable"). This algorithm is slow as G. Cz\'edli, T. D\'ek\'any,G. Gyenizse, and J. Kulin proved in 2016 that there are asymptotically$(k-2)!\cdot e^2/2$ many slim rectangular lattices of a given length $k$, where$e$ is the famous constant $\approx 2.71828$. The known properties andconstructions of JConSPS-representable posets can accelerate the algorithm; wepresent a new construction.

Reducing the lengths of slim planar semimodular lattices without changing their congruence lattices