Numerical computations form an essential part of almost any real-world program. Clearly, in order for a termination analyser to be of practical use it should contain a mechanism for proving termination of such computations. However, this topic attracted relatively little attention of the research community. Moreover, it is well-known that if computations involving real numbers are considered, the actually observed behaviour does not necessarily coincide with the intuitively expected one. The reason for the counter-intuitive behaviour of the computations based on “real numbers” in practice is that real numbers represented by computers are not mathematical objects, but their floating-point approximations. The problem of regarding floating point numbers as real ones and disregarding the rounding errors is not very well-known to programmers of non-scientific codes, but it may have serious and even tragic consequences, as the following example illustrates.