On nLab, there are some string diagrams for the triangle identities for the unit and counit of an adjoint pair $(L,R,\eta,\epsilon)$.
and with minimal notation,
I'm confused about how to read these, for in the second and fourth pictures, following the arrow seems to say that $R\epsilon\circ \eta R=1_R$, which is one of the usual triangle identities in equation form, but following the arrow in the third picture, the labels in the first picture seem to indicate an identity where the counit $\epsilon$ is applied before the unit $\eta$ to get $1_L$ somehow, but both triangle identities I know always have the unit coming first. Am I reading the diagrams incorrectly?
Page with the pictures is: https://ncatlab.org/nlab/show/triangle+identities#AsStringDiagrams