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Genome sequence alignment is the core of many biological applications. The advancement of sequencing technologies produces a tremendous amount of data, making sequence alignment a critical bottleneck in bioinformatics analysis. The existing hardware accelerators for alignment suffer from limited on-chip memory, costly data movement, and poorly optimized alignment algorithms. They cannot afford to concurrently process the massive amount of data generated by sequencing machines. In this paper, we propose a ReRAM-based accelerator, RAPIDx, using processing in-memory (PIM) for sequence alignment. RAPIDx achieves superior efficiency and performance via software-hardware co-design. First, we propose an adaptive banded parallelism alignment algorithm suitable for PIM architecture. Compared to the original dynamic programming-based alignment, the proposed algorithm significantly reduces the required complexity, data bit width, and memory footprint at the cost of negligible accuracy degradation. Then we propose the efficient PIM architecture that implements the proposed algorithm. The data flow in RAPIDx achieves four-level parallelism and we design an in-situ alignment computation flow in ReRAM, delivering $5.5$-$9.7\times$ efficiency and throughput improvements compared to our previous PIM design, RAPID. The proposed RAPIDx is reconfigurable to serve as a co-processor integrated into existing genome analysis pipeline to boost sequence alignment or edit distance calculation. On short-read alignment, RAPIDx delivers $131.1\times$ and $46.8\times$ throughput improvements over state-of-the-art CPU and GPU libraries, respectively. As compared to ASIC accelerators for long-read alignment, the performance of RAPIDx is $1.8$-$2.9\times$ higher.