2.51/0.93 YES 2.51/0.94 2.51/0.94 Problem: 2.51/0.94 strict: 2.51/0.94 f(g(x),y,z) -> f(x,y,g(z)) 2.51/0.94 weak: 2.51/0.94 f(x,y,g(z)) -> f(x,g(y),z) 2.51/0.94 f(x,a(),z) -> f(x,g(a()),z) 2.51/0.94 f(x,y,z) -> f(x,y,g(z)) 2.51/0.94 2.51/0.94 Proof: 2.51/0.94 Matrix Interpretation Processor: dim=2 2.51/0.94 2.51/0.94 interpretation: 2.51/0.94 [0] 2.51/0.94 [a] = [0], 2.51/0.94 2.51/0.94 [2 1] [2 0] [1 0] [0] 2.51/0.94 [f](x0, x1, x2) = [0 0]x0 + [0 0]x1 + [0 0]x2 + [2], 2.51/0.94 2.51/0.94 [1 0] [0] 2.51/0.94 [g](x0) = [1 1]x0 + [2] 2.51/0.94 orientation: 2.51/0.94 [3 1] [2 0] [1 0] [2] [2 1] [2 0] [1 0] [0] 2.51/0.94 f(g(x),y,z) = [0 0]x + [0 0]y + [0 0]z + [2] >= [0 0]x + [0 0]y + [0 0]z + [2] = f(x,y,g(z)) 2.51/0.94 2.51/0.94 [2 1] [2 0] [1 0] [0] [2 1] [2 0] [1 0] [0] 2.51/0.94 f(x,y,g(z)) = [0 0]x + [0 0]y + [0 0]z + [2] >= [0 0]x + [0 0]y + [0 0]z + [2] = f(x,g(y),z) 2.51/0.94 2.51/0.94 [2 1] [1 0] [0] [2 1] [1 0] [0] 2.51/0.94 f(x,a(),z) = [0 0]x + [0 0]z + [2] >= [0 0]x + [0 0]z + [2] = f(x,g(a()),z) 2.51/0.94 2.51/0.94 [2 1] [2 0] [1 0] [0] [2 1] [2 0] [1 0] [0] 2.51/0.94 f(x,y,z) = [0 0]x + [0 0]y + [0 0]z + [2] >= [0 0]x + [0 0]y + [0 0]z + [2] = f(x,y,g(z)) 2.51/0.94 problem: 2.51/0.94 strict: 2.51/0.94 2.51/0.94 weak: 2.51/0.94 f(x,y,g(z)) -> f(x,g(y),z) 2.51/0.94 f(x,a(),z) -> f(x,g(a()),z) 2.51/0.94 f(x,y,z) -> f(x,y,g(z)) 2.51/0.94 Qed 2.51/0.94 EOF