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We demonstrate a simple scheme for mutually coherent dual-comb generation, in which two frequency combs are emitted from a linear polarization maintaining (PM) fiber laser. The employed master laser is simultaneously mode-locked along two cross-polarized axes. The cross-polarized pulses have different repetition rates, since PM fiber has intrinsic birefringence. A theoretical model is established to investigate the pulse generation and interplay between the two pulses. Moreover, excellent mutual coherence of the two cross-polarized mode-locked pulses and overlapping spectra are demonstrated, allowing us to resolve individual comb lines directly in dual-comb spectroscopy (DCS) without active stabilization. Furthermore, due to the compact structure of the setup, the laser has potential as a robust dual-comb source. Keywords: Mode-locked lasers, Fiber, Polarization-maintaining, Simulation, Nonlinear effects, Dual-comb spectroscopy