Let L$1=\{$ an bn ck:$$ n$>=1,$ k$>=0\}.$

a$.$ Use JFLAP to create a npda M$1$ such that L$($M$1)=$ 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.

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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$1.$

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c$.$ Test your machine M$1$ on the following test cases.

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abc,$$ ab$,$ aaabbbcc,$$ aaaabbbb,$$ aaaccbbb,$$ abbcc,$$ cccc$,$ aaabbc,$$ bacabc

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Submit the JFLA diagram that shows your test results.