A. An owner's claim for an increase in the compensation is abandoned when he fails to take any step in the prosecution of that claim for a period of five years. This provision shall be operative without formal order, but on ex parte motion of the levee district or levee and drainage district, the trial court shall render final judgment fixing just compensation in the amount deposited in the registry of the court and awarding that sum to the defendant and dismissing with prejudice any claim for any increase in compensation.
B. An appeal is abandoned when the parties fail to take any step in its prosecution or disposition for the period provided in the rules of the appellate court, which shall be not less than one year.