  We consider two complementary polymer strands of length $L$ attached by a
common end monomer. The two strands bind through complementary monomers and at
low temperatures form a double stranded conformation (zipping), while at high
temperature they dissociate (unzipping). This is a simple model of DNA (or RNA)
hairpin formation. Here we investigate the dynamics of the strands at the
equilibrium critical temperature $T=T_c$ using Monte Carlo Rouse dynamics. We
find that the dynamics is anomalous, with a characteristic time scaling as
$\tau \sim L^{2.26(2)}$, exceeding the Rouse time $\sim L^{2.18}$. We
investigate the probability distribution function, the velocity autocorrelation
function, the survival probability and boundary behaviour of the underlying
stochastic process. These quantities scale as expected from a fractional
Brownian motion with a Hurst exponent $H=0.44(1)$. We discuss similarities and
differences with unbiased polymer translocation.
