YES(?,O(n^2)) Problem: *(x,*(y,z)) -> *(*(x,y),z) *(x,x) -> x Proof: Complexity Transformation Processor: strict: *(x,*(y,z)) -> *(*(x,y),z) *(x,x) -> x weak: Matrix Interpretation Processor: dimension: 1 max_matrix: 1 interpretation: [*](x0, x1) = x0 + x1 + 1 orientation: *(x,*(y,z)) = x + y + z + 2 >= x + y + z + 2 = *(*(x,y),z) *(x,x) = 2x + 1 >= x = x problem: strict: *(x,*(y,z)) -> *(*(x,y),z) weak: *(x,x) -> x Matrix Interpretation Processor: dimension: 2 max_matrix: [1 1] [0 1] interpretation: [1 1] [1] [*](x0, x1) = x0 + [0 1]x1 + [1] orientation: [1 1] [1 2] [3] [1 1] [1 1] [2] *(x,*(y,z)) = x + [0 1]y + [0 1]z + [2] >= x + [0 1]y + [0 1]z + [2] = *(*(x,y),z) [2 1] [1] *(x,x) = [0 2]x + [1] >= x = x problem: strict: weak: *(x,*(y,z)) -> *(*(x,y),z) *(x,x) -> x Qed