YES(?,O(n^3)) Problem: p(p(b(a(x0)),x1),p(x2,x3)) -> p(p(b(x2),a(a(b(x1)))),p(x3,x0)) Proof: Complexity Transformation Processor: strict: p(p(b(a(x0)),x1),p(x2,x3)) -> p(p(b(x2),a(a(b(x1)))),p(x3,x0)) weak: Matrix Interpretation Processor: dimension: 3 max_matrix: [1 1 1] [0 1 1] [0 0 1] interpretation: [1 0 1] [1 1 0] [0] [p](x0, x1) = [0 0 0]x0 + [0 0 1]x1 + [0] [0 0 0] [0 0 0] [1], [b](x0) = x0 , [1 1 0] [0] [a](x0) = [0 0 0]x0 + [0] [0 0 1] [1] orientation: [1 1 1] [1 1 0] [1 0 1] [1 1 1] [2] [1 1 1] [1 1 0] [1 0 1] [1 0 1] [1] p(p(b(a(x0)),x1),p(x2,x3)) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2 + [0 0 0]x3 + [1] >= [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2 + [0 0 0]x3 + [1] = p(p(b(x2),a(a(b(x1)))),p(x3,x0)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1] problem: strict: weak: p(p(b(a(x0)),x1),p(x2,x3)) -> p(p(b(x2),a(a(b(x1)))),p(x3,x0)) Qed