I've been assigned to make a traffic light system, and even posted about it in this subreddit, however I'd like some help with making the truth table for it, because I feel like it would help a lot when implementing.Here's what I've got so far:

I want to clarify some terms in case they aren't clear right away: Sn is the current state, Sn+1 is the next state, D are the three D Flip-Flips I believe I'd need to do this project with, and F is the output, F0 is the green light, F1 is the yellow light and F2 is the red light.
So essentially, i'd like for the circuit to behave as follows: green is default and if the I input is pressed, transition to yellow and then red, all the way back to green (until the input is put back to 0 of course).
I feel like my D (for Flip-Flops) may be wrong, although I am positive that I want that behavior for F (Output).
I've also tried making KMaps of the current table but yielded no results, as the behavior was nowhere near the expected.
Any help is appreciated, and thanks in advance!!

Edit #1: These are the KMaps I currently have, the reason I asked for help is that I got confused while making these because I couldn't understand them, and when I tested them out with the expressions I found, I had the wrong light get lit up, or several at once, and I truly believe it was my mistake with either making the KMaps or simplifying them properly.

I am currently working on a traffic light system, the state transition table developed for the project reads as follows: 

I have additionally used Neeman's Digital software to create a table (and K-Maps) for the output F2, F1, and F0.

As I was trying to repeat the process for D2, D1 and D0, with a table that has the following appearance. I would like to clarify that the Input I is being represented by E in the table.

Which returns the following expressions for the output expressions:

I have also tried replacing the x with 0 and get the following output expressions:

Both these aproaches revealed insufficient, because only F0 (the GREEN light) gets lit up, even when Input is true. I would therefore like help resolving this issue.
Thank you very much.

I've been assigned to make a traffic light system, and even posted about it in this subreddit, however I'd like some help with making the truth table for it, because I feel like it would help a lot when implementing.Here's what I've got so far:

I want to clarify some terms in case they aren't clear right away: Sn is the current state, Sn+1 is the next state, D are the three D Flip-Flips I believe I'd need to do this project with, and F is the output, F0 is the green light, F1 is the yellow light and F2 is the red light.
So essentially, i'd like for the circuit to behave as follows: green is default and if the I input is pressed, transition to yellow and then red, all the way back to green (until the input is put back to 0 of course).
I feel like my D (for Flip-Flops) may be wrong, although I am positive that I want that behavior for F (Output).
I've also tried making KMaps of the current table but yielded no results, as the behavior was nowhere near the expected.
Any help is appreciated, and thanks in advance!!

I've been assigned to make a traffic light system, and even posted about it in this subreddit, however I'd like some help with making the truth table for it, because I feel like it would help a lot when implementing.Here's what I've got so far:

I want to clarify some terms in case they aren't clear right away: Sn is the current state, Sn+1 is the next state, D are the three D Flip-Flips I believe I'd need to do this project with, and F is the output, F0 is the green light, F1 is the yellow light and F2 is the red light.
So essentially, i'd like for the circuit to behave as follows: green is default and if the I input is pressed, transition to yellow and then red, all the way back to green (until the input is put back to 0 of course).
I feel like my D (for Flip-Flops) may be wrong, although I am positive that I want that behavior for F (Output).
I've also tried making KMaps of the current table but yielded no results, as the behavior was nowhere near the expected.
Any help is appreciated, and thanks in advance!!

Edit #1: These are the KMaps I currently have, the reason I asked for help is that I got confused while making these because I couldn't understand them, and when I tested them out with the expressions I found, I had the wrong light get lit up, or several at once, and I truly believe it was my mistake with either making the KMaps or simplifying them properly.