I try to some how stuck my state machine. As you can see on pic I have state S0 and then when I pressed button (GPIO_SW_W) then i have all changes of states. when I press again in random moment then I get S5 which is results of mixing states.
I find some resulution on my problem- to do time delay, but it’s risky, because this program will be on board and i don’t know how fast or slowly someone will press button. I did debouncer and also shift register to this. I stuck in this problem and I don’t know how to fix it.
Here is screen of my simulation and also part of code.

process [..]
elsif rising_edge(sys_clock) then 
        if output = '1' then                                                                                            
            state <= nstate;
[...] 
end process;
process([..]) 
begin
     case state is     
        when S0 =>   
            if output = '1'then      
                nstate <= S1;
            else
                nstate <= S0;
            end if;

        when S1 =>      
            if output = '1' then
                nstate <= S2;
            else
                nstate <= S1;
            end if;

        when S2 =>      
            if output = '1' then
                nstate <= S3;
            else
                nstate <= S2;
            end if;
[...]

I will be really gratefull for your help!

enter image description here

All what I want is when I press button then will next state for example:

1. started program is on S0
2. button = ‘1’ -> S1
3. button = ‘0’ -> S1
4. button = ‘1’ -> S2
5. button = ‘0’ -> S2