Finite abstraction helps program analysis cope with the huge state space of programs. We wish to use abstraction in the process of error detection. Such a detection involves reachability analysis of the program. Reachability in an abstraction that under-approximates the program implies reachability in the concrete system. Under-approximation techniques, however, lose precision in the presence of loops, and cannot detect their termination. This causes reachability analysis that is done with respect to an abstraction to miss states of the program that are reachable via loops. Current solutions to this loop-termination challenge are based on fair termination and involve the use of well-founded sets and ranking functions. In many cases, the concrete system has a huge, but still finite set of states. Our contribution is to show how, in such cases, it is possible to analyze termination of loops without refinement and wimout well-founded sets and ranking functions. Instead, our method is based on conditions on the structure of the graph that corresponds to the concrete system - conditions that can be checked with respect to the abstraction. We describe our method, demonstrate its usefulness and show how its application can be automated by means of a theorem prover.