We consider interacting particle systems on $Z$ which allow five types of pairwise interaction: Annihilation, Birth, Coalescence, Death and Exclusion with corresponding rates a, b,c, d, e . We show that whatever the values of a, c, d, e, if the birthrate is high enough there is a positive probability the particle system will survive starting from any finite occupied set. In particular: an IPS with rates a b c d e has a positive probability of survival if
$$ b > 4d + 6a, \quad c + a \geq d + e$$
$$ b > 7d + 3a - 3c + 3e, \quad c + a < d + e.$$
We create a suitable supermartingale by extending the method used by Holley and Liggett in their treatment of the contact process.
"The survival of nonattractive interacting particle systems on Z." Ann. Probab. 28 (3) 1149 - 1161, July 2000. https://doi.org/10.1214/aop/1019160329