Artificial intelligence (AI) edge devices prefer employing high-capacity nonvolatile compute-in-memory (CIM) to achieve high energy efficiency and rapid wakeup-to-response with sufficient accuracy. Most previous works are based on either memristor-based CIMs, which suffer from accuracy loss and do not support training as a result of limited endurance, or digital static random-access memory (SRAM)-based CIMs, which suffer from large area requirements and volatile storage. We report an AI edge processor that uses a memristor-SRAM CIM-fusion scheme to simultaneously exploit the high accuracy of the digital SRAM CIM and the high energy-efficiency and storage density of the resistive random-access memory memristor CIM. This also enables adaptive local training to accommodate personalized characterization and user environment. The fusion processor achieved high CIM capacity, short wakeup-to-response latency (392 microseconds), high peak energy efficiency (77.64 teraoperations per second per watt), and robust accuracy (<0.5% accuracy loss). This work demonstrates that memristor technology has moved beyond in-lab development stages and now has manufacturability for AI edge processors.