Cast Time Stretch by paying its mana cost, causing you to take two extra turns after this one.
Declare any creature as an attacker. When you do, Doom's Time Platform triggers, exiling Time Stretch from your graveyard with two time counters on it.
Move to your first extra turn. 
At the beginning of your upkeep, Time Stretch's suspend ability triggers, removing a time counter from it.
Move to your second extra turn and repeat step 4 once.
Time Stretch's suspend ability triggers, causing you to cast it without paying its mana cost.
Resolve Time Stretch, causing you to take two extra turns after this one.
Repeat from step 2.

Infinite turns

Lock

Doom's Time Platform

Time Stretch

Cast Time Warp by paying its mana cost, causing you to take an extra turn after this one.
Declare any creature as an attacker. When you do, Doom's Time Platform triggers, exiling Time Warp from your graveyard with two time counters on it.
Move to your next turn. At the beginning of your upkeep, Time Warp's suspend ability triggers, removing a time counter from it.
Cast Clockspinning with buyback by paying {3}{U}, removing a time counter from Time Warp and returning Clockspinning to your hand.
Time Warp's suspend ability triggers, causing you to cast it without paying its mana cost.
Resolve Time Warp, causing you to take an extra turn after this one.
Repeat from step 2 each turn.

Clockspinning

Time Warp

Declare any creature as an attacker. When you do, Doom's Time Platform triggers, exiling Time Warp from your graveyard with two time counters on it.
Activate The Tenth Doctor by paying {7}, removing the time counters from Time Warp.
Time Warp's suspend ability triggers, causing you to cast it without paying its mana cost.
Resolve Time Warp, causing you to take an extra turn after this one.
Repeat each turn.

The Tenth Doctor

Cast Time Warp by paying its mana cost, causing you to take an extra turn after this one.
Declare any creature as an attacker. When you do, Doom's Time Platform triggers, exiling Time Warp from your graveyard with two time counters on it.
Move to your next turn. At the beginning of your upkeep, Time Warp's suspend ability triggers, removing a time counter from it.
Activate Rift Elemental by paying {1}{R} and removing a time counter from Time Warp.
Time Warp's suspend ability triggers, causing you to cast it without paying its mana cost.
Resolve Time Warp, causing you to take an extra turn after this one.
Repeat from step 2.

Rift Elemental

Declare any creature as an attacker. When you do, Doom's Time Platform triggers, exiling Time Warp from your graveyard with two time counters on it.
Blink Shivan Sand-Mage using Elrond.
When Shivan Sand-Mage enters, it triggers, removing two time counters from Time Warp.
Time Warp's suspend ability triggers, causing you to cast it without paying its mana cost.
Resolve Time Warp, causing you to take an extra turn after this one.
Repeat each turn.

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