Chapter I. Conditions for Authority of Penalties, Sphere of Application of Penal Law et al.
Art. 8 a.
A person who has been sentenced in a State where his/her offence was committed, cf. Art. 5, para.1, clause 2, or in a State being party to the Convention on the International Validity of Criminal Judgments of 28 May 1970 or international agreements applying to the Schengen co-operation shall not be indicted or sentenced in Iceland, or any sentence enforced against such person on account of the offence in respect of which Judgment was rendered in that State, if
1. the person was acquitted ;
2. the sanctions ordered have already been enforced, these are being enforced, have been cancelled or abandoned in accordance with the Law of the State where the Judgment was rendered ;
3. the person has been found guilty without a penalty or other sanctions having been ordered.
Ne bis in idem
Ne bis in idem - State's own court
EDIT.