Can the Chase test algorithm only modify attributes on the right side of a functional dependency


I'm attempting to apply the Chase Algorithm to determine if a decomposition is a lossless join decomposition.

Functional Dependencies = {A → C, B → D, C → D, DE → C, CE → A}

Here is my initial matrix:

Initial Matrix

Can I apply DE → C to remove the subscript from e on the first two rows? Since all c1's are the same, then this means that e1 and e2 must be equivalent to e, correct?

Second Matrix

At this point, I would be able to set all c1's equal to c, correct? (Since, again, DE → C.)