The following persons are not entitled to prosecute such writ: persons committed or detained by virtue of the final judgment, conviction or decree of any competent tribunal or by virtue of an execution issued upon such judgment or decree; but no order of commitment for any alleged contempt, or upon proceedings as for contempt, to enforce the rights or remedies of any party shall be deemed a judgment, conviction or decree within the meaning of this section; nor shall any attachment or other process issued upon any such order be deemed an execution within the meaning of this section.
NMS § 44-1-2