Metamorphic testing (MT) is well known for its ability to alleviate the oracle problem in software testing. The main idea of MT is to test a software system by checking whether each identified metamorphic relation (MR) holds among several executions. This alleviates the need for comparing the actual output and the expected output for individual test cases, and thus addresses the oracle problem. At present, MT has already been successfully applied in various fields.

While MT is receiving more and more attention, some challenging issues still deserve substantial effort to address, such as acquisition of good MRs, effective test case generation, and research on foundation theory of MT. Since MRs play an important role in MT, effective and efficient acquisition of MRs is an essential task. Despite their importance, most MRs are still manually or arbitrarily identified. If MRs cannot be identified systematically, the effective application of MT would be affected.

In view of the importance of MRs, METRIC was developed to help software testers identify MRs from a given set of complete test frames (generated using the category-choice framework). Among the existing MR identification techniques, METRIC has the following advantages: (a) wide range of application domains, (b) few restrictions or assumptions, and (c) efficient MR identification process. However, METRIC still has the following limitations: (a) METRIC does not leverage the information of the output domain for MR identification, which may render the identification process less effective. (b) METRIC lacks an effective mechanism for reducing the search space of complete test frames when identifying potential MRs, which could be tedious and inefficient in those complex scenarios. (c) Fault detection effectiveness of MRs identified by METRIC has not been verified by means of experiments.

To address these problems, we propose an enhanced MR identification technique, namely METRIC$^{+}$, which significantly improves the efficacy and automation of METRIC by incorporating an output-domain-guided mechanism. METRIC$^{+}$ is not a simple extension of METRIC. It provides (a) systematic guidelines on identifying the fine-grained relations between the input domain and the output domain, which, in turn, improve the effectiveness of MR identification; and (b) a search space reduction mechanism that enhances the efficiency of MR identification. A supporting tool named MR-GEN$^{+}$ has been developed, which automates most steps of MR identification based on METRIC$^{+}$ (available at: http://www.mt4ws.cc/MR-GEN). Two rounds of experiments, involving four real-life specifications, have been conducted to evaluate the effectiveness and efficiency of METRIC$^{+}$. The results have confirmed that METRIC$^{+}$ is highly effective and efficient in MR identification. Additional experiments have been performed to compare the fault detection capability of the MRs generated by METRIC$^{+}$ and those by $\mu$MT (another MR identification technique). The comparison results have confirmed that the MRs generated by METRIC$^{+}$ are highly effective in fault detection.