Even, Itai & Shamir's limited backtracking algorithm for 2-SAT: is it really linear?

Question

I have read in Wikipedia (and other sources) about the limited backtracking algorithm of Even, Itai & Shamir for solving 2-SAT problem in a linear time, but the approach doesn't seem to be linear, there is no demonstration nor algorithm implementation to check it.

Here is the algorithm description from Wikipedia: Even, Itai & Shamir - Limited backtracking.

Has anyone heard about this algorithm? Does anyone have its implementation/demonstration?

PS: I am not searching for an algorithm to solve 2-SAT problem in a linear time since I have read about the Aspvall, Plass & Tarjan approach. I am just interested in the former algorithm.