Factorize string into Lyndon words

Factorize string into Lyndon words
You are encouraged to solve this task according to the task description, using any language you may know.

Python

def chen_fox_lyndon_factorization(s):
    n = len(s)
    i = 0
    factorization = []
    while i < n:
        j, k = i + 1, i
        while j < n and s[k] <= s[j]:
            if s[k] < s[j]:
                k = i
            else:
                k += 1
            j += 1
        while i <= k:
            factorization.append(s[i:i + j - k])
            i += j - k
    assert ''.join(factorization) == s
    return factorization

m='0'
for i in range(0,7):
     m0=m
     m=m.replace('0','a')
     m=m.replace('1','0')
     m=m.replace('a','1')
     m=m0+m

print(chen_fox_lyndon_factorization(m))