Cast Chronomantic Escape by paying {4}{W}{W}, causing creatures to be unable to attack you until your next turn, and exiling Chronomantic Escape with three time counters on it.
At the beginning of your postcombat main phase, Sphinx of the Second Sun triggers, causing you to get an additional beginning phase after this phase.
Move to your additional beginning phase.
At the beginning of your upkeep, Chronomantic Escape triggers, removing a time counter from itself.
At the beginning of your next upkeep, Chronomantic Escape and Paradox Haze trigger.
Resolve the Paradox Haze trigger, causing you to get an additional upkeep step after this one.
Resolve the Chronomantic Escape trigger, removing a time counter from it.
Move to your next upkeep step.
Chronomantic Escape triggers, removing a time counter from itself and causing you to cast it without paying its mana cost.
Resolve Chronomantic Escape,  causing creatures to be unable to attack you until your next turn, and exiling Chronomantic Escape with three time counters on it.
Repeat from step 2.

Creatures cannot attack you

Chronomantic Escape

Sphinx of the Second Sun

Paradox Haze

Move to your postcombat main phase.
Sphinx of the Second Sun triggers, causing you to get an additional beginning phase after this phase.
Activate all lands you control by tapping them, adding at least {6}{R}{R}{R}{R}.
Activate Aggravated Assault by paying {3}{R}{R}, causing you to untap all creatures you control and to get an additional combat and main phase after this one.
Repeat step 4 one additonal time.
Move to the main phase from step 5.
At the beginning of the main phase, Sphinx of the Second Sun triggers, causing you to get an additional beginning phase after this phase.
Move to the beginning phase from step 7, causing you to untap all lands you control and draw a card.
Move to the main phase from step 4.
Repeat from step 2.

Infinite card draw

Infinite draw triggers

Near-infinite combat phases

Near-infinite untap of creatures and lands you control

Aggravated Assault

Cast Chronomantic Escape by paying {4}{W}{W}, causing creatures to be unable to attack you until your next turn, and putting Chronomantic Escape into exile with three time counters on it.
At the beginning of your postcombat main phase, both copies of Sphinx of the Second Sun trigger, causing you to get two additional beginning phases after this phase.
Move to your first additional beginning phase.
At the beginning of your upkeep, Chronomantic Escape triggers, removing a time counter from itself.
Repeat from step 3 one additional time.
At the beginning of your next upkeep, Chronomantic Escape triggers, removing a time counter from itself and causing you to cast it without paying its mana cost.
Resolve Chronomantic Escape,  causing creatures to be unable to attack you until your next turn, and putting Chronomantic Escape into exile with three time counters on it.
Repeat from step 2.

Flesh Duplicate

Cast Rite of Replication by paying {2}{U}{U}, creating a token copy of Sphinx of the Second Sun.
Cast Chronomantic Escape by paying {4}{W}{W}, causing creatures to be unable to attack you until your next turn, and exiling Chronomantic Escape with three time counters on it.
At the beginning of your postcombat main phase, Sphinx of the Second Sun and the Sphinx of the Second Sun token each trigger, causing you to get two additional beginning phases after this phase.
Move to your first additional beginning phase.
At the beginning of your upkeep, Chronomantic Escape triggers, removing a time counter from itself.
Repeat from step 4 one additional time.
At the beginning of your next upkeep, Chronomantic Escape triggers, removing a time counter from itself and causing you to cast it without paying its mana cost.
Resolve Chronomantic Escape,  causing creatures to be unable to attack you until your next turn, and exiling Chronomantic Escape with three time counters on it.
Repeat from step 3.

Rite of Replication

Cast Quasiduplicate by paying {1}{U}{U}, creating a token copy of Sphinx of the Second Sun.
Cast Chronomantic Escape by paying {4}{W}{W}, causing creatures to be unable to attack you until your next turn, and exiling Chronomantic Escape with three time counters on it.
At the beginning of your postcombat main phase, Sphinx of the Second Sun and the Sphinx of the Second Sun token each trigger, causing you to get two additional beginning phases after this phase.
Move to your first additional beginning phase.
At the beginning of your upkeep, Chronomantic Escape triggers, removing a time counter from itself.
Repeat from step 4 one additional time.
At the beginning of your next upkeep, Chronomantic Escape triggers, removing a time counter from itself and causing you to cast it without paying its mana cost.
Resolve Chronomantic Escape,  causing creatures to be unable to attack you until your next turn, and exiling Chronomantic Escape with three time counters on it.
Repeat from step 3.

Quasiduplicate

Cast Cackling Counterpart by paying {1}{U}{U}, creating a token copy of Sphinx of the Second Sun.
Cast Chronomantic Escape by paying {4}{W}{W}, causing creatures to be unable to attack you until your next turn, and exiling Chronomantic Escape with three time counters on it.
At the beginning of your postcombat main phase, Sphinx of the Second Sun and the Sphinx of the Second Sun token each trigger, causing you to get two additional beginning phases after this phase.
Move to your first additional beginning phase.
At the beginning of your upkeep, Chronomantic Escape triggers, removing a time counter from itself.
Repeat from step 4 one additional time.
At the beginning of your next upkeep, Chronomantic Escape triggers, removing a time counter from itself and causing you to cast it without paying its mana cost.
Resolve Chronomantic Escape,  causing creatures to be unable to attack you until your next turn, and exiling Chronomantic Escape with three time counters on it.
Repeat from step 3.

Cackling Counterpart

Cast Fated Infatuation by paying {U}{U}{U}, causing you to scry 2 and create a token copy of Sphinx of the Second Sun.
Cast Chronomantic Escape by paying {4}{W}{W}, causing creatures to be unable to attack you until your next turn, and exiling Chronomantic Escape with three time counters on it.
At the beginning of your postcombat main phase, Sphinx of the Second Sun and the Sphinx of the Second Sun token each trigger, causing you to get two additional beginning phases after this phase.
Move to your first additional beginning phase.
At the beginning of your upkeep, Chronomantic Escape triggers, removing a time counter from itself.
Repeat from step 4 one additional time.
At the beginning of your next upkeep, Chronomantic Escape triggers, removing a time counter from itself and causing you to cast it without paying its mana cost.
Resolve Chronomantic Escape,  causing creatures to be unable to attack you until your next turn, and exiling Chronomantic Escape with three time counters on it.
Repeat from step 3.

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