Question: Were Operation Nordwind and the Battle of Peleliu both fought in World War II?

full_context: Document 1: Colmar Pocket: The Colmar Pocket (French: "Poche de Colmar" ; German: "Brückenkopf Elsaß" ) was the area held in central Alsace, France, by the German Nineteenth Army from November 1944 to February 1945, against the U.S. 6th Army Group during World War II. It was formed when 6th AG liberated southern and northern Alsace and adjacent eastern Lorraine, but could not clear central Alsace. During Operation Nordwind in December 1944, the 19th Army attacked north out of the Pocket in support of other German forces attacking south from the Saar into northern Alsace. In late January and early February 1945, the French First Army (reinforced by the U.S. XXI Corps) cleared the Pocket of German forces.
Document 2: Battle of Okinawa: The Battle of Okinawa (Japanese: 沖縄戦 , Hepburn: Okinawa-sen ) (Okinawan: 沖縄戦 , "Uchinaa ikusa " ), codenamed Operation Iceberg, was a major battle of the Pacific War fought on the island of Okinawa by United States Marine and Army forces against the Imperial Japanese Army and included the largest amphibious assault in the Pacific War during World War II, the April 1, 1945, invasion of Okinawa itself. The 82-day battle lasted from April 1 until June 22, 1945. After a long campaign of island hopping, the Allies were planning to use Okinawa, a large island only 340 mi away from mainland Japan, as a base for air operations for the planned invasion of the Japanese home islands.
Document 3: Lorraine Campaign: Lorraine Campaign is a term used by U.S. Army historians to describe operations of the U.S. Third Army in Lorraine during World War II from September 1 through December 18, 1944. Official U.S. Army campaign names for this period and location are "Northern France" and "Rhineland". The term was popularized by the publication of a volume of the same name by the U.S. Army in 1950. As written by the volume's author:
Document 4: Battle of Angaur: The Battle of Angaur was a battle of the Pacific campaign in World War II, fought on the island of Angaur in the Palau Islands from 17 September—22 October 1944. This battle was part of a larger offensive campaign known as Operation Forager which ran from June 1944 to November 1944 in the Pacific Theater of Operations, and Operation Stalemate II in particular.
Document 5: Herrlisheim: Herrlisheim is a commune in the Bas-Rhin department in Grand Est in north-eastern France. The town dates from the 8th century. Herrlisheim was the scene of very heavy fighting during "Operation Nordwind", an offensive launched by the German Army during World War II that inflicted considerable damage to the town.
Document 6: Battle of the Bulge: The Battle of the Bulge (16 December 1944 – 25 January 1945) was the last major German offensive campaign on the Western Front during World War II. It was launched through the densely forested Ardennes region of Wallonia in eastern Belgium, northeast France, and Luxembourg, towards the end of World War II. The surprise attack caught the Allied forces completely off guard. American forces bore the brunt of the attack and incurred their highest casualties of any operation during the war. The battle also severely depleted Germany's armored forces, and they were largely unable to replace them. German personnel and, later, Luftwaffe aircraft (in the concluding stages of the engagement) also sustained heavy losses.
Document 7: Order of battle for Operation Nordwind: This is the order of battle of German and Allied forces during Operation Nordwind in World War II
Document 8: Battle of Guam (1944): The Second Battle of Guam (21 July – 10 August 1944) was the American recapture of the Japanese-held island of Guam, a U.S. territory in the Mariana Islands captured by the Japanese from the U.S. in the 1941 First Battle of Guam during the Pacific campaign of World War II.
Document 9: Kunio Nakagawa: Colonel Kunio Nakagawa (中川 州男 , Nakagawa Kunio , 23 January 1898 – 24 November 1944) was the commander of Japanese forces which defended the island of Peleliu in the Battle of Peleliu which took place from 15 September to 27 November 1944. He inflicted heavy losses on attacking U.S. Marines and held Peleliu Island for almost three months. On the evening of 24 November, after the battle was lost, he committed "seppuku" (ritual suicide) in the tradition of Japanese samurai warriors. He was posthumously promoted to lieutenant general.
Document 10: Battle of Peleliu: The Battle of Peleliu, codenamed Operation Stalemate II by the United States military, was fought between the U.S. and the Empire of Japan during the Mariana & Palau Campaign of World War II, from September to November 1944, on the island of Peleliu.
Document 11: Battle of Iwo Jima: The Battle of Iwo Jima (19 February – 26 March 1945) was a major battle in which the United States Marine Corps landed on and eventually captured the island of Iwo Jima from the Imperial Japanese Army during World War II. The American invasion, designated Operation Detachment, had the goal of capturing the entire island, including the three Japanese-controlled airfields (including the South Field and the Central Field), to provide a staging area for attacks on the Japanese main islands. This five-week battle comprised some of the fiercest and bloodiest fighting of the Pacific War of World War II.
Document 12: Peleliu: Peleliu (or Beliliou) is an island in the island nation of Palau. Peleliu forms, along with two small islands to its northeast, one of the sixteen states of Palau. The island is noted as the location of the Battle of Peleliu in World War II.
Document 13: Operation Winter Storm: Operation "Winter Storm" (German: "Unternehmen Wintergewitter" ) was a German offensive in World War II in which the German 4th Panzer Army unsuccessfully attempted to break the Soviet encirclement of the German 6th Army during the Battle of Stalingrad.
Document 14: Battle of Leyte: The Battle of Leyte in the Pacific campaign of World War II was the amphibious invasion of the Gulf of Leyte in the Philippines by American forces and Filipino guerrillas under the command of General Douglas MacArthur, who fought against the Imperial Japanese Army in the Philippines led by General Tomoyuki Yamashita from 17 October - 26 December 1944. The operation code named "King Two" launched the Philippines campaign of 1944–45 for the recapture and liberation of the entire Philippine Archipelago and to end almost three years of Japanese occupation.
Document 15: Operation Nordwind: Operation North Wind (German: "Unternehmen Nordwind" ) was the last major German offensive of World War II on the Western Front. It began on 31 December 1944 in Alsace and Lorraine in northeastern France, and ended on 25 January.
ground_truth: yes