Strength of counting networks

This paper shows that any counting network, made up of balancers whose fan-in and fan-out vary arbitrarily, is, indeed, strong enough to simultaneously support both Fetch&Increment and Fetch&Decrement operations, once each of its balancers is substituted by an elimination balancer. Its proof is purely combinatorial, carried out within the elegant combinatorial framework put forth for the study of balancing networks. Through equivalence theorems, impossibility results, lower bounds, verification algorithms and methodologies to prove correctness carry over to counting networks with enriched operation set.