When it comes to getting permits for oversize loads, whether or not the load is reducible is typically a major factor in permitting. A reducible load is a load that can be easily made smaller, and a non-reducible load is one that is not easily made smaller. Reducible/non-reducible and divisible/non-divisible are different words for the same concept.
An overwidth piece of equipment can normally be permitted and, along with certain safety restrictions, travel on the highway. If a load is easily reduced in width, though, permits are harder to obtain. This is because oversize loads are dangerous in comparison to normal-sized vehicles, so when possible highway authorities prefer loads to be broken down into smaller dimensions for travel.
As a professional driver, it is useful to understand these terms. It helps shed some light on the permitting process and explain why some commodities have different permit rules.