  Graph bootstrap percolation, introduced by Bollob\'as in 1968, is a cellular
automaton defined as follows. Given a "small" graph $H$ and a "large" graph $G
= G_0 \subseteq K_n$, in consecutive steps we obtain $G_{t+1}$ from $G_t$ by
adding to it all new edges $e$ such that $G_t \cup e$ contains a new copy of
$H$. We say that $G$ percolates if for some $t \geq 0$, we have $G_t = K_n$.
  For $H = K_r$, the question about the size of the smallest percolating graphs
was independently answered by Alon, Frankl and Kalai in the 1980's. Recently,
Balogh, Bollob\'as and Morris considered graph bootstrap percolation for $G =
G(n,p)$ and studied the critical probability $p_c(n,K_r)$, for the event that
the graph percolates with high probability. In this paper, using the same
setup, we determine, up to a logarithmic factor, the critical probability for
percolation by time $t$ for all $1 \leq t \leq C \log\log n$.
