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