YES(?,O(n^2)) Problem: +(-(x,y),z) -> -(+(x,z),y) -(+(x,y),y) -> x Proof: RT Transformation Processor: strict: +(-(x,y),z) -> -(+(x,z),y) -(+(x,y),y) -> x weak: Bounds Processor: bound: 0 enrichment: match-rt automaton: final states: {3} transitions: +0(3,3) -> 3* -0(3,3) -> 3* problem: strict: +(-(x,y),z) -> -(+(x,z),y) weak: -(+(x,y),y) -> x Matrix Interpretation Processor: dimension: 2 interpretation: [1 1] [1 0] [4] [+](x0, x1) = [0 1]x0 + [0 0]x1 + [4], [1 1] [1 8] [2] [-](x0, x1) = [0 1]x0 + [0 0]x1 + [9] orientation: [1 2] [1 8] [1 0] [15] [1 2] [1 8] [1 0] [10] +(-(x,y),z) = [0 1]x + [0 0]y + [0 0]z + [13] >= [0 1]x + [0 0]y + [0 0]z + [13] = -(+(x,z),y) [1 2] [2 8] [10] -(+(x,y),y) = [0 1]x + [0 0]y + [13] >= x = x problem: strict: weak: +(-(x,y),z) -> -(+(x,z),y) -(+(x,y),y) -> x Qed