I will use two flip-flops uv, and two input variables xy, and make the following encodings for states and input:

State encoding:

Input encoding:

I will then transcribe the state-transition table

to the bit values

Finally I will create two Karnaugh maps, one corresponding to next-state value of u and one to v:

Map for next u:

Map for next v:

Now I can derive the simplified logic equations from these maps as:

next u = u + v'xy'

next v = u'x'