The story of arbitration:

The battle of Siffeen ended with arbitration. 'Ali, may Allah be pleased with him, accepted arbitration and returned to Koofah. Mu'aawiya, may Allah be pleased with him returned to Shaam (an area that included Syria, Lebanon, Palestine, Jordan and parts of Iraq. They agreed that arbitration should be conducted during the month of Ramadan. 'Ali sent Abu Moosaa Al- Asha'ari, while Mu'aawiya sent 'Amr Ibn Al-'Aas, may Allah be pleased with them all.

The famous false story of arbitration was that Amr Ibn Al-'Aas and Abu Moosaa Al-Asha'ari agreed to dethrone 'Ali and Mu'aawiya, may Allah be pleased with them. Abu Moosaa Al-Asha'ari ascended the pulpit and said: "I will take 'Ali off the caliphate in the same way I am taking my ring off. At this point, he took his ring off. 'Amr Ibn Al-'Aas stood and said: "I will take 'Ali off the caliphate in the same manner Abu Moosaa did, and as I am taking my ring off now; meanwhile I am confirming Mu'aawiya as a caliph in the same manner I am wearing this ring of mine! Therefore, there was uproar. Abu Moosaa went out angry. He returned to Koofah. 'Amr Ibn Al-'Aas returned to Sham!
    
This story is fabricated. The true story, however, is that told by people of truth based on right chain of narrators in Al-Bukhari: "When 'Amr Ibn Al-'Aas, may Allah be pleased with him, attended arbitration, he met Abu Moosaa Al-Asha'ari, may Allah be pleased with him, and asked him: 'What do you think?' Abu Moosaa replied: 'I see that ('Ali) was one of the people whom the Prophet (may Allah exalt his mention) was contented with before his demise.'

'Amr Ibn Al-'Aas said: 'How do you rate me and Mu'awiya?' Abu Moosaa said: 'If 'Ali gets your help, then you are helpful. If, however, he does not, then it would be the will of Allah.' The discussion ended at this point, 'Amr Ibn Al-'As went back to brief Mu'aawiya about it and Abu Moosaa returned to 'Ali to do the same.

   
The first version is undoubtedly false for three reasons:

1.     The weak chain of narrators including the name of Abu Mikhnaf, the liar.

2.      Neither Abu Moosaa Al-Asha'ari nor others can dethrone the caliph of Muslims who, according to belief of Ahlus-Sunnah wal-Jamaa'ah could not be dethroned that easily. So how could two men agree on the dethronement of the Leader of the Faithful? This is just rubbish. What happened in the arbitration event was that 'Ali, may Allah be pleased with him, would stay in Koofah, being the caliph of Muslims, while Mu'aawiya, may Allah be pleased with him, would remain in Sham as a prince.

3.     The existence of the sound version which we mentioned above and which contradicts the fabricated one.

The Nahrawaan battle (37 A.H.):

No sooner had 'Ali, may Allah be pleased with him, returned to Koofah, than the Khawaarij (dissidents deviant sect) revolted against him. They refused arbitration and said: 'No judgment but that of Allah.' They started to make a fuss around 'Ali, may Allah be pleased with him, even at the mosque, they used to cry: "No judgment but that of Allah." 'Ali, may Allah be pleased with him, used to comment on that by saying "a word of truth being misused."

'Ali, however, decided to carry out his campaign against Shaam and ignore the insane demand of the Khawaarij, but he was informed of the martyrdom of Abdullaah Ibn Khabbaab, may Allah be pleased with him. The victim passed through Naharwaan during a journey. A group of the Khawaarij came to know that he was a Companion. They came to him and asked about Abu Bakr and 'Umar, may Allah be pleased with them. Abdullaah Ibn Khabbaab said, "Both of them were very pious and true servants of Allah the Almighty." They then inquired of the first and the last parts of the caliphate of 'Uthmaan, may Allah be pleased with him. He replied, "He was truth-loving from beginning to the end." They then wanted to know his opinion about 'Ali, may Allah be pleased with him, before and after the appointment of the arbitrators. He stated, "Ali knows and understands the injunctions of Allah and His Messenger more than you all." Hearing this, the Khawaarij became enraged and killed Khabbaab, may Allah be pleased with hijm, his wife and his fellow travelers.

On being informed of this, 'Ali, may Allah be pleased with him, asked Al-Haarith Ibn Murrah to make an inquiry into the matter. The Khawaarij killed him also. Along with this, it was reported to 'Ali that they were killing all those who disagreed with them. Thus, 'Ali's men grew anxious that the Khawaarij would capture Koofah and Basrah and kill their wives and children in case they advanced towards Shaam.

'Ali, may Allah be pleased with him, himself went to the camp of the Khawaarij and began to preach them to use wisdom and adopt righteousness. Fearing the strength of the impression 'Ali's speech would have on their people, the chieftains asked them not to pay attention to what he said and go to war.

In view of their attitude, 'Ali, may Allah be pleased with him, came back and set himself to the task of organizing his troops and appointing commanding officers of the attacking army. This task being over, 'Ali gave Abu Ayoob Al-Ansaari, may Allah be pleased with him, the flag of peace and asked him to ascend to a raised spot and give a general call saying: "Those who come to us without a fight will get peace, and those who go to Koofah or Madaa'in will also enjoy peace." Having heard this announcement, Farwah Ibn Nawfal Al-Ashja'i moved apart with five hundred horsemen, some people left for Koofah while some others either went to Madaa'in or came to join Ali's troops, with the result less than one-third of the men were left with the Khawaarij. 'Ali, may Allah be pleased with him, then launched a massive attack and put the rest to death.

All the prominent chieftains of the Khawaarij like Abdullaah Ibn Wahb, Zayd Ibn Husayn, Hurqus Ibn Zuhayr, 'Abdullaah Ibn Shajarah, and Shurayh Ibn 'Awfa lost their lives. Only nine of them saved themselves by fleeing from the scene of death.

'Ali's martyrdom (40 A.H.):

Approximately, two years after the battle of An-Nahrawaan, three Kharijites, 'Abdur-Rahmaan Ibn Muljam Muraadi, Burak Ibn 'Abdullaah At-Tameemi and 'Amr Ibn Bakr Tameemi gathered in Makkah and kept expressing profound grief over the men slain in Naharwaan. At last they entered into a pact to do away with the three men in power that had been putting the entire world of Islam to such a great loss and destruction. According to their plan, 'Abdur-Rahmaan Ibn Muljam Muraadi, Burak Ibn 'Abdullaah At-Tameemi, and 'Amr Ibn Bakr At-Tameemi Sa'di each agreed to kill 'Ali, Mu'aawiyah and 'Amr Ibn Al-'Aas, may Allah be pleased with them, respectively. Ramadan 16 and the Morning Prayer were fixed as the date and time of the assassinations.
'Amr Ibn Al 'Aas was in Egypt, Mu'aawiya in Shaam and 'Ali in Koofah. Ibn Muljam killed 'Ali, may Allah be pleased with him, while on his way to Fajr (dawn) prayer using a dagger which he poisoned for a week.  

When 'Ali, may Allah be pleased with him, died, they brought his killer and killed him.    

Al-Barak, who intended to kill Mu'aawiya may Allah be pleased with him, at dawn time, gave Mu'aawiya a stroke. However, this did not kill him. He was cured but caused him sterility.

'Amr had diarrhea that prevented him from going out to perform his prayer. The killer instead murdered the leader of the prayer, Khaarijah Ibn Abi Habeeb, who replaced him. The murder took place during the prayers. When he was asked about his enormous crime, he said: "I relieved people from 'Amr Ibn Al-'Aas." He was told: "But you did not kill 'Amr but killed Khaarijah." His reply was: "I intended to kill 'Amr but Allah willed Khaarijah!!" The murderer was executed as his other two collaborators.  

'Ali's grave is traceless:

'Ali, may Allah be pleased with him, was honored with martyrdom at the age of sixty-three and passed five years as a caliph. Al-Hasan, Al-Husayn and 'Abdullaah bin Ja'far, may Allah be pleased with them, washed his body and shrouded him in three pieces of cloth without a shirt.

Al-Hasan, may Allah be pleased with him, led the funeral prayer. But there is a wide difference of opinion with regard to his burial ground. Some people say that he was buried in the Koofah Mosque while others say that he was buried in his house, or somewhere ten miles away from Koofah.

According to some narratives, Al-Hasan, may Allah be pleased with him, buried him at an unknown place after taking his body out of his grave anticipating an act of desecration from the Khawaarij. Still one more narrative says that his bier was carried to Al-Madeenah to bury him near the grave of Prophet . But the camel carrying the body fled away and remained traceless. Contradicting this narrative, yet another one lends support to the opinion that the camel with the body of 'Ali, may Allah be pleased with him, was traced at Tai and he was buried there. It is a wonder that the grave of such a great personality lies traceless to this day. However, the reason behind his burial at an unknown place was the Khawaarij menace.

Sources:

The History of Islam, by: Akbar Shah Najeebadi

Al-bidayah wa An-Nihayah, by Ibn Katheer

Tareekh At-Tabari

Al-kamel, by Ibn Al-'Atheer

At-Tabaqat Al-kubra, by Ibn S'ad

Al-Isabah fi Tamyeez As-Sahabah, by Ibn Hajar Al-'Asqalany