Greenberg, now 91, took a pair of silver-rimmed glass from his dark suit jacket and dug into document after document placed before him by Nachman, reading the court exhibits carefully and then verbally jousting with Nachman over his actions, his true intentions in 1999 and 2000, and just how concerned he really was about the auto-warranty segment of the giant insurance company.

"I think what you're not covering here," he told Nachman from the stand at one point, "is that this [auto-warranty line] was only a small part of our business. Our business was huge. … This was insignificant."

Stressing repeatedly that AIG, which under Greenberg's direction grew to become the world's largest insurance company, operating in 137 countries, Greenberg also said that a major reason why he kept up his interest in the auto-warranty segment was to teach his subordinates a lesson about not entering into a bad business in the future.

"I wanted to teach people a lesson," he said. "I thought their judgment going into that [auto-warranty program] was bad."

But Nachman gave no quarter. Throughout the day, he read from and entered into evidence memo after memo sent directly from senior deputies throughout 1999 and 2000 to Greenberg.

Trying to contain auto-warranty losses

The memos and reports sought to detail the progress they were making in trying to contain the auto-warranty losses, which an actuary had told Greenberg and senior AIG management would run into hundreds of millions of dollars.

Reading from the correspondence of one senior deputy, Nachman had Greenberg confirm that he had called the deputy on weekends about the problem. Early in the day, Nachman pointed out that Greenberg's son, Evan, who was a chief operating officer at AIG, had supported the idea of the auto-warranty business.

It all raised the spectre of why Greenberg did become so intimately involved in the failing segment, even as he testified that the millions in losses would only add up to a "half point" of the massive company's combined ratio, which measured the company's underwriting profitability.

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Sham financial transaction

Late in the day, Nachman moved more directly into tying Greenberg to the sham financial transaction — referred to as CAPCO — in which a deputy at AIG specializing in reinsurance allegedly created a transaction that would convert underwriting losses into investment losses.

Nachman read from the deposition of Greenberg's co-defendant, former AIG chief financial officer Howard Smith, recalling a 1999 meeting at which Smith, Greenberg and others at AIG discussed a potential reinsurance vehicle meant to reclassify the losses.

Greenberg pushed back. He said that "there may be a method of converting underwriting losses to investment losses, that was what I was interested in." He said it was hypothetical, was not to involve reinsurance, and "it may come in the future." He did not say or hint that he ordered any wrongful transactions, but rather that they were looking into a potential legal maneuver.

Bench trial

The bench trial is being held before state Supreme Court Justice Charles Ramos, who has been presiding over the lawsuit since its 2005 inception. He listened intently on Tuesday, asking Greenberg or Nachman to further explain aspects of the auto warranty insurance business, and at other times making light of the complicated testimony.

"This is a great college course in business management," he quipped at one point, not long after Nachman had spent the better part of an hour asking Greenberg to testify about the central importance of underwriting to the property and casualty insurance line's success.

Nachman read from a book Greenberg had co-authored in 2013, called "The AIG Story," to help make the point about the emphasis Greenberg had placed on underwriting profits.

The civil fraud trial of Greenberg has been coming for 11 years, winding its way through seven pretrial appeals and narrowing in scope as government lawyers abandoned parts of their case against the prominent insurance executive.

Former New York Attorney General Eliot Spitzer brought the case in 2005, alleging nine different wrongful financial acts.

Today, the lawsuit focuses on just two alleged sham transactions and seeks disgorgement of $52 million in total from Greenberg and Smith. David Boies of Boies Schiller & Flexner is representing Greenberg; Vincent Sama, a partner at Kaye Scholer, is leading Smith's defense.

Fraudulent reinsurance deal

In the second alleged transaction — which was not part of Tuesday's questioning — Schneiderman's office claims Greenberg and Smith helped orchestrate a fraudulent reinsurance deal between AIG and General Reinsurance Corp. The transaction allegedly pumped up AIG's reserves by $500 million in 2000 and 2001, deceiving Wall Street analysts and investors about the level of losses AIG could handle.

Under state law, Greenberg and Smith are not afforded a jury trial because the government is not asking for damages but rather a forfeit of past bonuses from Greenberg and Smith.

Six billion dollars in damages were once sought in the long-running case. But in 2013, both Greenberg and Smith were included as parties in a $115 million settlement in a federal class action suit brought by former AIG stockholders that included similar allegations as those made in this case. Under res judicata legal principles, the government cannot seek damages already paid out in the class action.

Related: Ex-AIG chairman Greenberg ordered to fact trial in N.Y. suit