A Complete Axiomatisation for the Inclusion of Series-Parallel Partial Orders

Series-parallel orders are deened as the least class of partial orders containing the one-element order and closed by ordinal sum and disjoint union. From this inductive deenition, it is almost immediate that any series-parallel order may be represented by an algebraic expression, which is unique up to the associativity of ordinal sum and to the associa-tivivity and commutativity of disjoint union. In this paper, we introduce a rewrite system acting on these algebraic expressions that axiomatises completely the sub-ordering relation for the class of series-parallel orders.