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