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We focus on generating efficient software pipelined schedules for in-order machines, which we call converged trace schedules. For a candidate loop, we form a string of trace block identifiers by hashing together addresses of aggressively scheduled instructions from multiple iterations of a loop. In this process, the loop is unrolled and scheduled until we identify a repeating pattern in the string. Instructions corresponding to this repeating pattern form the kernel for our software pipelined schedule. We evaluate this approach to create aggressive schedules by using it in dynamic hardware and software optimization systems for an in-order architecture.