def match_regex(string):
    state = 0
    for char in string:
        if state == 0:
            if char == 'a':
                state = 1
            else:
                return False
        elif state == 1:
            if char == 'b' or char == 'c':
                state = 1
            else:
                return False
    return state == 1
 
print(match_regex("a")) # True
print(match_regex("ab")) # True
print(match_regex("ac")) # True
print(match_regex("abc")) # True
print(match_regex("abcb")) # True
print(match_regex("d")) # False

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