The chase procedure is a fundamental algorithmic tool in databases that allows us to reason with constraints, such as existential rules, with a plethora of applications. It takes a database and a set of constraints as input and iteratively completes the database as dictated by the constraints. A key challenge, though, is the fact that the chase may not terminate, which leads to the problem of checking whether it terminates given a database and a set of constraints. In this work, we focus on the semi-oblivious version of the chase, which is well-suited for practical implementations, and linear existential rules, a central class of constraints with several applications. In this setting, there is a mature body of theoretical work that provides syntactic characterizations of when the chase terminates, algorithms for checking chase termination, precise complexity results, and worst-case optimal bounds on the size of the result of the chase (whenever it is finite). Our main objective is to experimentally evaluate the existing chase termination algorithms with the aim of understanding which input parameters affect their performance, clarifying whether they can be used in practice, and revealing their performance limitations. Concerning guarded existential rules, a natural generalization of linear existential rules, one can reuse the machinery for linear existential rules by first applying the so-called linearization technique, that is, the technique of converting guarded existential rules into linear existential rules without affecting the termination of the chase. A secondary objective of this work is to understand how realistic is the use of the linearization technique in the context of the semi-oblivious chase termination problem.