  We prove that deciding whether a given input word contains as subsequence
every possible permutation of integers $\{1,2,\ldots,n\}$ is coNP-complete. The
coNP-completeness holds even when given the guarantee that the input word
contains as subsequences all of length $n-1$ sequences over the same set of
integers. We also show NP-completeness of a related problem of Partially
Non-crossing Perfect Matching in Bipartite Graphs, i.e. to find a perfect
matching in an ordered bipartite graph where edges of the matching incident to
selected vertices (even only from one side) are non-crossing.
