Identifying Sequences for Cellular Automata
Python 2: 93 byte

M,L,n=input();a=[]
while L:z=zip(L,L[1:]);a+=z;L=[M[i][j]for i,j in z]
print len(set(a))==n*n


Straightforward implementation: Find all pairs by zipping, memorize them for later and apply M to L. Repeat. Compare the number of unique pairs found. 

Input is of the form [[0,1],[1,0]], [0,1,0,0], 2.