Complex sentence: The Pakistani Inter-Services Intelligence has allegedly encouraged and aided the Kashmir independence movement through an insurgency due to its dispute on the legitimacy of Indian rule in Kashmir, with the insurgency as an easy way to keep Indian troops distracted and cause international condemnation of India.
Split into simpler sentences: The Pakistani Inter-Services Intelligence has encouraged and aided the Kashmir independence movement, through an insurgency. It has done so because it disputes the legitimacy of Indian rule in Kashmir, sees the insurgency as an easy way to keep Indian troops distracted and cause international condemnation of India.