One-piece-type Tetris clearing complexity under SRS

Determine the computational complexity of Tetris clearing under the Super Rotation System (SRS) when the input sequence consists of a single tetromino type only. For each of the seven tetromino types, decide whether Tetris clearing is solvable in polynomial time or is NP-hard, and in particular resolve the case of the O piece type conjectured to be polynomial-time solvable.

Background

The paper proves NP-hardness and #P-hardness for Tetris clearing with SRS using any two tetromino types, resolving a long-standing question for all 2-piece subsets. These results rely on a “blocking bottles” paradigm that uses one piece type to gate access while the other fills structure, inherently requiring at least two types.

For single-piece sequences, that paradigm breaks: the same tetromino would have to both block and fill, which the authors argue cannot be handled by their framework. Prior work (Breukelaar et al., 2004) conjectured polynomial time for the O piece, but no general classification is known for any single piece type under SRS.