Question: Who is the paternal grandfather of William Ii, Duke Of Aquitaine?

Context paragraphs:
title: Acfred I of Carcassonne
paragraph_text: Acfred I (died 906) was the Count of Razès from 837 and Count of Carcassonne from 877. Acfred was the younger son of Oliba I of Carcassonne. He inherited Razès on his father's death, while his elder brother Oliba II inherited Carcassonne. Acfred and Oliba probably shared authority with each other in their two counties until the elder's death in 877, when Acfred inherited both counties, probably as the regent for his nephew Bencion I, but actually as count in his own right. Bencion nevertheless succeeded him on his death. Acfred married Adelinda, daughter of Bernard Plantapilosa and sister of William I of Aquitaine. He had three sons:
title: Maria of Brabant, Duchess of Bavaria
paragraph_text: Maria of Brabant( 1226–1256) was a daughter of Henry II, Duke of Brabant, and Maria of Swabia. She married Louis II, Duke of Bavaria, being the first of three wives.
title: Frederick William II, Duke of Schleswig-Holstein-Sonderburg-Beck
paragraph_text: Frederick William II, Duke of Schleswig-Holstein- Sonderburg- Beck( 18 June 1687 – 11 November 1749) was a Duke of Schleswig- Holstein- Sonderburg- Beck. He served as Prussian field marshal and was appointed Governor of Berlin, but never filled the latter position. Frederick William II was the eldest son of Duke Frederick Louis( 1653 – 1728) and his wife Louise Charlotte of Schleswig- Holstein- Sonderburg- Augustenburg( 1658 – 1740). His siblings included Dorothea, Peter August, Charles Louis. In 1728, Frederick William II succeeded his father as Duke of Beck. After his death, he was succeeded by his son Frederick William III, who fell in battle in 1757. The title was then inherited by Frederick William II's brother, Charles Louis.
title: William II, Duke of Aquitaine
paragraph_text: William II the Young (died 12 December 926) was the Count of Auvergne and Duke of Aquitaine from 918 to his death, succeeding his uncle William I. William was son of the Acfred I of Carcassonne and Adelinde, William I's sister and Bernard Plantapilosa's daughter. Immediately after succeeding his uncle, he made war on the Burgundians and Normans, who refused to accept Rudolph as king of France. His support of the king, however, was insincere. He later revolted and Rudolph led an army into Aquitaine, but was called back to defend the Rhine from the Magyars. William died soon after. In 924 the duke Raoul of Burgundy came up to the Loire river and William was forced to make his submission to him. Upon which Raoul, relieved that such a powerful vassal accepted his suzerainty, gave him back the counties of Berry and Macon and the town of Bourges.
title: Princess Marie Frederica of Hesse-Kassel
paragraph_text: Princess Marie Frederica Wilhelmina of Hesse-Kassel (6 September 1804 – 1 January 1888) was a Duchess consort of Saxe-Meiningen by marriage to Bernhard II, Duke of Saxe-Meiningen. She was the daughter of William II, Elector of Hesse and Princess Augusta of Prussia.
title: John Mackay (poet)
paragraph_text: John Mackay( 1656–1754), known as( The Blind Piper), was a Scottish Gaelic poet and composer, and the grandfather of William Ross.
title: William II, Duke of Brunswick-Lüneburg
paragraph_text: William II, Duke of Brunswick- Lüneburg( about 1300 – 1369) was the Prince of Lüneburg from 1330 to 1369.
title: Emma of Blois
paragraph_text: Emma of Blois( 950–27 December 1003) was Duchess consort of Aquitaine by marriage to William IV, Duke of Aquitaine. She ruled Aquitaine as regent for her son, William V, Duke of Aquitaine, from 996 until 1004.
title: William II of the Netherlands
paragraph_text: William II( Willem Frederik George Lodewijk, anglicized as William Frederick George Louis; 6 December 1792 – 17 March 1849) was King of the Netherlands, Grand Duke of Luxembourg, and Duke of Limburg. William II was the son of William I and Wilhelmine of Prussia. When his father, who up to that time ruled as sovereign prince, proclaimed himself king in 1815, he became Prince of Orange as heir apparent of the Kingdom of the Netherlands. With the abdication of his father on 7 October 1840, William II became king. During his reign, the Netherlands became a parliamentary democracy with the new constitution of 1848. William II was married to Anna Pavlovna of Russia. They had four sons and one daughter. William II died on 17 March 1849 and was succeeded by his son William III.
title: William II of Baux
paragraph_text: William II of Baux( died 1239) was a son of William of Baux. Following his father, William II carried the title of prince of Orange. The title had come to the House of Baux through a brother, Raimbaut of Orange, of William II's paternal grandmother, Tiburge de Sarenom, the latter also referred to as Tiburge princess of Orange.

Reasoning steps:
William II, Duke of Aquitaine father Acfred I of Carcassonne
Acfred I of Carcassonne father Oliba I of Carcassonne

Answer: spans: Oliba I of Carcassonne