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A 1Kg object traveling at 2/3c "I used around 67% c" would only have 31,999,279,384,000,000 joules in the form of kinetic energy.
The rest mass energy of that object going by E=mc^2 would be 89,875,517,800,000,000 joules.
It's total mass energy would be increased by a little over 1/3.
The kinetic energy will not exceed the rest mass energy until 86.7% c.
Even then this is not an upper limit for an anti matter rocket as the vehicle could have stages.
In the case of the dark energy rocket it's not carrying it's fuel.
Even fusion can top 10% c as in project Daedalus who's goal was to get a probe to 12%c.