Lower bounds for critical values of a cancellative model

We consider the following one-dimensional discrete-time cancellative model whose evolution is given by n +1 (x ) = n (x +1)+ n (x -1) (mod 2) with probability p and n +1 = 0 with probability 1-p . Concerning critical probabilities pc and pc * on a survival probability, it is known that 0.706 pc pc *