For example, the sequence of powers of two (1, 2, 4, 8, ...), the basis of the binary numeral system, is a complete sequence; given any natural number, we can choose the values corresponding to the 1 bits in its binary representation and sum them to obtain that number (e.g. 37 = 1001012 = 1 + 4 + 32).
This sequence is minimal, since no value can be removed from it without making some natural numbers impossible to represent.
The full coding without the trailing one can be found at (sequence A104326 in the OEIS).
In this numeral system, any substring "100" can be replaced by "011" and vice versa due to the definition of the Fibonacci numbers.
[5] Continual application of these rules will translate form the maximal to the minimal, and vice versa.