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

Knowledge 1: William II, Duke of Aquitaine
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. [SEP] Knowledge 2: Acfred I of Carcassonne
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:
Knowledge 1: William II, Duke of Aquitaine
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. [SEP] Knowledge 2: Princess Marie Frederica of Hesse-Kassel
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.
Knowledge 1: Acfred I of Carcassonne
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: [SEP] Knowledge 2: Princess Marie Frederica of Hesse-Kassel
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.

Answer: Oliba I of Carcassonne