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This paper presents SOAR: the first oblivious atomicity assertion with polynomial complexity. SOAR enables to check atomicity of a single-writer multi-reader register implementation. The basic idea underlying the low overhead induced by SOAR lies in greedily checking, in a backward manner, specific points of an execution where register operations could be linearized, rather than exploring all possible precedence relations among these. We illustrate the use of SOAR by implementing it in +CAL. The performance of the resulting automatic verification outperforms comparable approaches by more than an order of magnitude already in executions with only 6 read/write operations. This difference increases to 3-4 orders of magnitude in the ``negative'' scenario, i.e., when checking some non-atomic execution, with only 5 operations. For example, checking atomicity of every possible execution of a single-writer single-reader (SWSR) register with at most 2 write and 3 read operations with the state of the art oblivious assertion takes more than 58 hours to complete, whereas SOAR takes just 9 seconds.