Automatic test case generation plays a key role in automatic testing for web services. Existing testing techniques based on algebraic specifications rely on the creation, initialization, and replication of objects under test to verify the correctness of test results. However, their thirdparty nature means that such operations are not usually available, and thus it is hard to support transforming test cases into executable sequences of operations. One possible solution is to convert the test case into a linear execution sequence that contains only one instance of the service under test, does not include instance initialization, and only modifies and checks the instance states.  We improve the original work and propose to use the test execution graph with inverse terms (TEGI) to describe state changes during the execution of the test case. We design a TEGI construction algorithm and a monic execution sequence generation algorithm, and implement prototype tools.  A case study demonstrates that the proposal is feasible for automatic test case generation and can improve the testability of web services.