For discrete BS- and D-Koenigs nets, Laplace degeneracy of the m-th forward transform forces Laplace degeneracy of the (m+1)-th backward transform (or the (m+2)-th for Goursat degeneracy), making every terminating Laplace sequence finite.
Bobenko and Yuri B
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Discrete Koenigs nets and finite Laplace sequences
For discrete BS- and D-Koenigs nets, Laplace degeneracy of the m-th forward transform forces Laplace degeneracy of the (m+1)-th backward transform (or the (m+2)-th for Goursat degeneracy), making every terminating Laplace sequence finite.