Trivium is a synchronous stream cipher designed to provide a flexible trade-off between speed and gate count in hardware, and reasonably efficient software implementation. It was designed in 2005 by C. De Cannière and B. Preneel for the European project eSTREAM. It has successfully moved into phase two of the selection process and is currently in the focus group under the hardware category. As of yet there has been no attack on Trivium faster than exhaustive search. Bivium-A and Bivium-B are truncated versions of Trivium that are built on the same design principles. These simplified versions are used for investigating Trivium-like ciphers with a reduced complexity. There have been successful attempts in the cryptanalysis of Bivium ciphers. The goal of this paper is to compare a basic Gröbner basis attack against these ciphers with other known methods. To do so, we present some experimental results.