The Shalimar Treaty

[AngleWyrm]

If I use the doppler effect of pulsar timings to measure my speed, then these two statements seem to indirectly conflict:

"As a result [of lower time figure], your measurement of light speed relative to yourself will come out exactly the same as the stationary observer's measurement of light speed relative to himself."

"The time dilation due to high speed movement is not linear, so it will generally not exactly cancel the doppler effect."

It would help if we had the formula used for this.
EDIT: Found a derivation of time dilation which is easy to read.