Drawing a Mealy FSM for Detecting the Pattern PARTY Step by Step

Let’s say I want to detect the pattern “PARTY”. 
First State: waiting for ‘P’.If I got P, I go to second State.Second State: got ‘P’.
Now...(Here’s my question)If I got A..I’ll go to third state.If not...I’ll have two options..if I got ‘P’.. I’ll go back to second State. If not, I’ll go back to first state.
Is this how it is supposed to be done?

Either option may be correct -- it all depends on how the problem has been defined.
#1 Assume the problem is to find "PARTY" as consecutive letters -- consider the following string:
      xxPAxxRxxTxxxxYxxPARTxxPARTYxxxxIn this case, you would wait for a P -- when you get a P you would wait for an A -- when you get an A you would wait for a R and so on. If you see anything other than the letter you are looking for, you go back to the first state. So if you are looking for PARTY as consecutive letters, then you wouldn't reach your end state until the final PARTY in the above.
NOTE: One tricky case here would be a string like:      xxxxxxxPPARTYxxxxxxxx
In this case you detect the first P, so now you are looking for A. When you don't get A (on the second P) if you haven't thought this out, then you'll go back to waiting for a P again -- but in fact you just got the P you were looking for... it's these little "gotcha's" that can trip you up.

#2 If the problem says that you have to detect the sequence P A R T Y but not as consecutive letters, then you wait for a P, then for an A, then for a T...etc. But you don't reset if you don't get the letter you are looking for -- you just loop around waiting for that letter to appear

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