Cast the self-suspending card by paying its mana cost if its in your hand, or any other spell otherwise if you have not cast a spell this turn.
Cast Time Stretch by paying its mana cost.
Taigam triggers, copying Time Stretch and then exiling it with four time counters on it and giving it suspend.
Resolve the copy of Time Stretch, causing you to take two extra turns after this one.
Move to your first extra turn. At the beginning of that turn's upkeep, Time Stretch and the self-suspending card's suspend abilities trigger, removing a time counter from each of them.
Move to your second extra turn. At the beginning of that turn's upkeep, Time Stretch and the self-suspending card's suspend abilities trigger, removing a time counter from each of them.
Activate The Tenth Doctor by paying {7}, removing three time counters from Time Stretch and the self-suspending card, triggering their suspend abilities.
Resolve the self-suspending card's suspend trigger, causing you to cast it from exile without paying its mana cost, and eventually exile it with time counters on it.
Resolve the Time Stretch's suspend trigger, causing you to cast it from exile without paying its mana cost.
Repeat from step 3.

Infinite turns

Self-Suspending Instant or Sorcery

The Tenth Doctor

Taigam, Master Opportunist

Time Stretch

Cast Time Stretch by paying its mana cost.
Taigam triggers, copying Time Stretch and exiling the original Time Stretch with four time counters on it.
Resolve the Time Stretch copy, causing you to take two extra turns after this one.
Cast Clockspinning with buyback by paying {3}{U}, removing a time counter from Time Stretch and returning Clockspinning to your hand.
Repeat step 4 one additional time.
Move to your next turn. At the beginning of your upkeep, Time Stretch's suspend ability triggers, removing a time counter from it.
Cast Clockspinning with buyback by paying {3}{U}, removing a time counter from Time Stretch and returning Clockspinning to your hand.
Time Stretch's suspend ability triggers, causing you to cast it from exile without paying its mana cost.
Repeat from step 2.

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