Problem $2$: Let $L1=\{a^n{b}^n{c}^k$:$n1,k0\}.$

a$.$ Use JFLAP to create a npda M$1$ such that $L(M1)=$ L$1.$ To do this, modify the ndpa in Example $1$ in the instructor's slides from Chap $7\mathrm{.}1($ slide $20).$ Submit graph of M$1$ from JFLAP.

b$.$ Describe in English how you modified the npda from slide $20$ in the Chap $7\mathrm{.}1$ slides. Carefully describe the changes made and why they should work for the language L$1.$

c$.$ Test your machine M$1$ on the following test cases. abc, ab$,$ aaabbbcc, aaaabbbb, aaaccbbb, abbcc, cccc$,$ aaabbc, bacabc

Submit the JFLA diagram that shows your test results.

Show the JFLAP diagram in the answer whuch shows the test results.