I did this as a history lesson about 4 years ago:
The Anglo-Irish War of 1919-1921:
"Britain's Troubles - Ireland's Opportunities"
John T. Broom, Ph.D.

To comprehend how the Irish struggle involved Compound Warfare, one needs to understand that in the Irish struggle, British "imperial overstretch" (i.e., the effect of imperial commitments) replaced and compensated for Compound Warfare's usual supporting main force. British worldwide military commitments "the overstretch" prevented the British from massing sufficient forces in Ireland to overwhelm the guerrilla forces. This situation was the result of Britain's requirement to garrison a far-flung empire, its provision of forces for the League of Nations newly mandated territories, and the sustaining of an occupation force for the German Rhineland. In addition, the British government faced public pressure to reduce the unprecedented size of the British Army and to control costs in the wake of a very expensive global war. By 19 May 1920, the entire British strategic reserve was thirty-seven battalions, garrisoned in Britain. The theory of Compound War puts for that the synergy achieved when a guerrilla force works in concert with a conventional force against a larger occupying force. The commander of the "compound" force of regulars and guerrillas achieved greater "leverage" that compounds the effects of his massed conventional forces and dispersed unconventional forces against an enemy unprepared to deal with both at the same time. That is to say that the occupying commander must mass his own forces to deal with the rebel conventional threat when at the same time he needs to disperse his forces to maintain control against the unconventional. Put another way, the theory of Compound Warfare reflects much of the underlying tensions in the Contemporary Operational Environment or even much of what challenges U.S. commanders today in Iraq and Afghanistan.

This essay by Dr. John T. Broom on the Anglo-Irish War of 1919-1921 is one section of an anthology by the Combat Studies Institute. It and the remainder of the anthology are available at the CSI web page. That said I will let the author explain why his essay on the Irish Troubles fits the mold for compound war.

This essay describes the successful struggle of Irish nationalists to win their independence from Britain shortly after World War I. The Anglo-Irish War of 1919-21, of all the cases in this volume, is perhaps the least likely candidate for compound warfare analysis. There is no conventional force on the Irish side, no apparent safe haven, no major power ally. From a technical standpoint, some analysts might not wish to characterize the Anglo-Irish conflict as a case of compound war. Nonetheless, the Irish insurgency is fascinating and instructive when considered from a compound warfare perspective. Close inquiry suggests that ultimately it was a combination of pressures much like those of fortified compound warfare that brought the British, though more powerful than the Irish, to capitulate. The British in Ireland faced both a resistant population and flying columns in the countryside. These columns were not a regular force but compelled a degree of concentration that was difficult for British forces to sustain because of the simultaneous need to disperse to control the population throughout the country. British commitments elsewhere in the world also made it hard for the British to concentrate forces on the Irish problem. Public opinion in Britain, opposed to extreme measures, may have functioned as a substitute for a safe haven for the Irish nationalists. Sympathetic world opinion gave the Irish effort some of the leverages of a major power ally. Apparently, the combination of all these pressures, closely akin to the fortified compound warfare pattern, induced the British, despite their far greater resources, to give in.


Best

Tom