User blog comment:LittlePeng9/Random Turing machines/@comment-5150073-20130402161217/@comment-1605058-20130402162918

Yes, I thought about this, but it seems this method won't be too effective. It requires string copying (quadratic time, I think) and multiplication algorithm (same, quadratic) to perform squaring (that gives quartic time), then string comparison (I think again quadratic). That gives sextic time w.r.t. input. I think my algorithm fits in cubic time. It roots 100 in 12352 steps.