Alchemist's Retrieval

one blue mana Instant

Cleave one generic mana one blue mana (You may cast this spell for its cleave cost. If you do, remove the words in square brackets.)

Return target nonland permanent [you control] to its owner's hand.

To most, a terrifying apparition. To a necro-alchemist, a potent fuel source.

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Alchemist's Retrieval rulings

2021-11-19
If you cast a spell for its cleave cost, that spell doesn't have any of the text in square brackets while it's on the stack.
2021-11-19
A cleave cost is an alternative cost that's paid instead of the spell's mana cost. Casting a spell for its cleave cost doesn't change the spell's mana value.
2021-11-19
You can't cast a spell for both its cleave cost and another alternative cost. For example, if an effect gives an Alchemist's Retrieval in your graveyard a flashback cost of , you can't cast it from your graveyard for its cleave cost.
2021-11-19
If an effect allows you to “cast a spell without paying its mana cost,” you can't cast that spell for its cleave cost.

Alchemist's Retrieval keyword rules

Cleave Rule 702.148

Cleave is a keyword that represents two static abilities that function while a spell with cleave is on the stack. “Cleave [cost]” means “You may cast this spell by paying [cost] rather than paying its mana cost” and “If this spell’s cleave cost was paid, change its text by removing all text found within square brackets in the spell’s rules text.” Casting a spell for its cleave cost follows the rules for paying alternative costs in rules and –h.

Cleave’s second ability is a text-changing effect. See rule , “Text-Changing Effects.”