  We solve two open problems concerning syntactic complexity: We prove that the
cardinality of the syntactic semigroup of a left ideal or a suffix-closed
language with $n$ left quotients (that is, with state complexity $n$) is at
most $n^{n-1}+n-1$, and that of a two-sided ideal or a factor-closed language
is at most $n^{n-2}+(n-2)2^{n-2}+1$. Since these bounds are known to be
reachable, this settles the problems.
