No, that is because that matrix is not in reduced row echelon form. You need to divide the first row by 2 and then subtract 2.5 times the second row from the first row to make it row reduced, at which point you get:
1 0.5 0 0.5
0 0 1 0
Which is rref as it is in row echelon form, has leading coefficient 1 in every row, and every leading coefficient is the only nonzero entry in its coumn.
The definition seems to not be universal, though, according to Wikipedia some authors let a row echelon form matrix have leading coefficients that aren't 1, while others require them to be 1. Either way however a reduced row echelon form matrix (like the one above in my post) must have leading coefficients of 1 as that representation is unique.
The slowsort algorithm is a perfect illustration of the multiply and surrender paradigm, which is perhaps the single most important paradigm in the development of reluctant algorithms. The basic multiply and surrender strategy consists in replacing the problem at hand by two or more subproblems, each slightly simpler than the original, and continue multiplying subproblems and subsubproblems recursively in this fashion as long as possible. At some point the subproblems will all become so simple that their solution can no longer be postponed, and we will have to surrender. Experience shows that, in most cases, by the time this point is reached the total work will be substantially higher than what could have been wasted by a more direct approach.
- Pessimal Algorithms and Simplexity Analysis