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Agents often repeatedly solve similar task instances from scratch, leading to unnecessary reasoning cost and long execution traces. Prior work has explored workflow reuse and executable skill induction, but it remains unclear which task scenarios admit procedural skills and how the shared procedural structure should be represented across successful traces. We study this problem in FSM-defined scenarios, where successful traces can be viewed as paths in an unknown transition graph, and formulate procedural skills as reusable parameterized control-flow subgraphs. Based on this view, we introduce SkillDisCo, a distillation-and-compilation framework that distills reusable PFSM subgraphs from successful traces and compiles them into callable, executable, and verifiable procedural skills. Experiments on ALFWorld and WebArena show that SkillDisCo improves success rates and reduces agent turns across benchmarks and model scales, demonstrating the benefits of representing shared experience as reusable execution structures.