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Neural end-to-end (E2E) models have become a promising technique to realize practical automatic speech recognition (ASR) systems. When realizing such a system, one important issue is the segmentation of audio to deal with streaming input or long recording. After audio segmentation, the ASR model with a small real-time factor (RTF) is preferable because the latency of the system can be faster. Recently, E2E ASR based on non-autoregressive models becomes a promising approach since it can decode an $N$-length token sequence with less than $N$ iterations. We propose a system to concatenate audio segmentation and non-autoregressive ASR to realize high accuracy and low RTF ASR. As a non-autoregressive ASR, the insertion-based model is used. In addition, instead of concatenating separated models for segmentation and ASR, we introduce a new architecture that realizes audio segmentation and non-autoregressive ASR by a single neural network. Experimental results on Japanese and English dataset show that the method achieved a reasonable trade-off between accuracy and RTF compared with baseline autoregressive Transformer and connectionist temporal classification.