A polynomial upper bound on Reidemeister moves

We prove that any diagram of the unknot with c crossings may be reduced to
the trivial diagram using at most (236 c)^{11} Reidemeister moves. Moreover,
every diagram in this sequence has at most (7 c)^2 crossings. We also prove a
similar theorem for split links, which provides a polynomial upper bound on the
number of Reidemeister moves required to transform a diagram of the link into a
disconnected diagram.