CLR cover

Additional Problem 15: Subsequence Covers (Preliminary version)

\( \def\SMot{\mathit{Subs}} \)

A string $x$ is a subsequence cover (subs-cover, in short) of a string $y$ if every position in $y$ belongs to an occurrence of $x$ in $y$ as a subsequence. The subs-covers differ substantially from standard covers:

Write a linear time algorithm checking if a given string $x$ of length $m$ is a subs-cover of a string $y$ of length $n\gt m$. Assume alphabet is a subset of $\{0,1,\ldots,n-1\}$.