if this conjecture were true (it has been shown to be false), then a general decision method would exist; namely, we systematically tile larger and larger square arrays of cells in every possible way with the given set of tiles.
Repeat this setence, but with the correct capitalization.
If this conjecture were true (it has been shown to be false), then a general decision method would exist; namely, we systematically tile larger and larger square arrays of cells in every possible way with the given set of tiles.