Statements having non-commutative connection conditions are optimized by replacing the non-commutative connection conditions with equivalent expressions that allow for consideration of additional connection orders that would otherwise violate the ordering rules of the non-commutative connection condition. Elements on the right-hand side of a non-commutative connection condition are converted into distinct results elements, thereby allowing the elements to be used on the left-hand side of a commutative connection operator, while preserving accuracy of the statement results set. This increased set of connection orders is evaluated and the execution plan for the optimal connection order is selected.