This is a question regarding Exercise 18 in http://www.math.utah.edu/agtrtg/commutative-algebra/Boocher_lectures.pdf
Let $I$ be the ideal of the polynomial ring $k[a,b,c,d,e,f]$
$I=(a^2+b^2+ab+cd+ef,b^3-6abc+def,c^2e^2+f^4)$.
Krull's altitude theorem gives $\mathrm{ht}\;I\leq 3$. There is a term order such that the height of the initial ideal is 3. Why does this imply that $I$ is generated by a regular sequence?