On
page 525, Eq. (18.3), you assume M1
is in saturation when the Schmitt trigger switches. However,

for
M1 to be in saturation

*V _{x}*
>=

Since
*V _{THN2}*
increases due to the body effect we can write

0
>= to a positive number (so M1 is
NOT operating in the saturation region).

The
connection of M1 and M2 is a
split-length device; see Problem 6.14 on page 160. So, M1 operates

in
either the cutoff or triode regions.
Your conclusion appears to be correct. However, as discussed

in
section 6.3.2 starting on page 143,
on the border between the saturation and triode regions (when *V _{DS}*

= *V _{DS,sat}*

what
we need to show is that M1 is
operating with *V _{x}*
=

to
use the saturation equation as seen
in Eq. (18.3). As pointed out above and in the book this is indeed

the
case since *V _{THN1}*
=

6.14).