Bisimulations: Proof that the following LTS are not bisimilar I have the two LTS (labeled transition system) as seen in the following picture:

And the book is telling me that between those two LTS, their $1$ and $1'$ are non-bisimilar.

So I tried to get a bisimilation starting from the pair $\{\{1,1'\}\}$ by continuously extending it whenever I found a conflict, ending up with:
$$\{   \{1,1'\} ,\{2,2'\},\{3,3'\},\{2,4'\},\{4,3'\},\{3,5'\},\{4,5'\}               \}$$

Finally, to check whether it truly was a bisimilation, I checked for each pair each node, and asserted that all possible pairs of derivatives were part of the set.

I am arriving that they are a bisimilation - is the crux in the $a$'s and $b$'s? (They didn't really explain what it means)
The left diagram has a b and the right diagram has a c.  Thus, the pair $(2,4')$ does not satisfy the conditions required to be a bisimulation.  In particular, the book is correct that those two systems are not bisimilar.