Time transformations in post-Newtonian Lagrangians

We show that the use of time transformations in post-Newtonian Lagrangians is equivalent to using the lowest-order energy-conservation equation in the highest-order terms of the Lagrangian (complementing Schäfer's observation that the use of coordinate transformations is equivalent to using the lowest-order equations of motion in the highest-order terms of the Lagrangian). We also show how identity coordinate or identity time transformations can add double-zero terms to the Lagrangian. Next we use time and coordinate transformations to simplify the Einstein-Infeld-Hoffmann Lagrangian with parametrized-post-Newtonian parameters $\gamma$ and $\beta$.