YES(?,O(n^2)) 7.40/5.71 YES(?,O(n^2)) 7.40/5.71 7.40/5.71 Problem: 7.40/5.71 *(x,*(y,z)) -> *(*(x,y),z) 7.40/5.71 *(x,x) -> x 7.40/5.71 7.40/5.71 Proof: 7.40/5.71 Complexity Transformation Processor: 7.40/5.71 strict: 7.40/5.71 *(x,*(y,z)) -> *(*(x,y),z) 7.40/5.71 *(x,x) -> x 7.40/5.71 weak: 7.40/5.71 7.40/5.71 Matrix Interpretation Processor: dim=1 7.40/5.71 7.40/5.71 max_matrix: 7.40/5.71 1 7.40/5.71 interpretation: 7.40/5.71 [*](x0, x1) = x0 + x1 + 13 7.40/5.71 orientation: 7.40/5.71 *(x,*(y,z)) = x + y + z + 26 >= x + y + z + 26 = *(*(x,y),z) 7.40/5.71 7.40/5.71 *(x,x) = 2x + 13 >= x = x 7.40/5.71 problem: 7.40/5.71 strict: 7.40/5.71 *(x,*(y,z)) -> *(*(x,y),z) 7.40/5.71 weak: 7.40/5.71 *(x,x) -> x 7.40/5.71 Matrix Interpretation Processor: dim=2 7.40/5.71 7.40/5.71 max_matrix: 7.40/5.71 [1 1] 7.40/5.71 [0 1] 7.40/5.71 interpretation: 7.40/5.71 [1 1] [0] 7.40/5.71 [*](x0, x1) = x0 + [0 1]x1 + [1] 7.40/5.71 orientation: 7.40/5.71 [1 1] [1 2] [1] [1 1] [1 1] [0] 7.40/5.71 *(x,*(y,z)) = x + [0 1]y + [0 1]z + [2] >= x + [0 1]y + [0 1]z + [2] = *(*(x,y),z) 7.40/5.71 7.40/5.71 [2 1] [0] 7.40/5.71 *(x,x) = [0 2]x + [1] >= x = x 7.40/5.71 problem: 7.40/5.71 strict: 7.40/5.71 7.40/5.71 weak: 7.40/5.71 *(x,*(y,z)) -> *(*(x,y),z) 7.40/5.71 *(x,x) -> x 7.40/5.72 Qed 7.40/5.72 EOF