1.43/0.81 YES 1.43/0.82 1.43/0.82 Problem: 1.43/0.82 strict: 1.43/0.82 f(x,0()) -> s(x) 1.43/0.82 g(x) -> h(x,gen()) 1.43/0.82 h(0(),x) -> f(x,x) 1.43/0.82 a() -> b() 1.43/0.82 weak: 1.43/0.82 gen() -> s(gen()) 1.43/0.82 1.43/0.82 Proof: 1.43/0.82 Matrix Interpretation Processor: dim=3 1.43/0.82 1.43/0.82 interpretation: 1.43/0.82 [0] 1.43/0.82 [b] = [0] 1.43/0.82 [0], 1.43/0.82 1.43/0.82 [0] 1.43/0.82 [a] = [2] 1.43/0.82 [2], 1.43/0.82 1.43/0.82 [1 1 2] [3 1 0] 1.43/0.82 [h](x0, x1) = [1 1 2]x0 + [3 2 3]x1 1.43/0.82 [1 0 0] [2 2 1] , 1.43/0.82 1.43/0.82 [0] 1.43/0.82 [gen] = [0] 1.43/0.82 [0], 1.43/0.82 1.43/0.82 [2 2 2] [0] 1.43/0.82 [g](x0) = [1 2 3]x0 + [2] 1.43/0.82 [1 2 0] [0], 1.43/0.82 1.43/0.82 [1 0 0] 1.43/0.82 [s](x0) = [2 0 0]x0 1.43/0.82 [0 2 0] , 1.43/0.82 1.43/0.82 [1 1 0] [2 0 0] 1.43/0.82 [f](x0, x1) = [2 0 0]x0 + [0 1 3]x1 1.43/0.82 [1 2 0] [1 0 0] , 1.43/0.82 1.43/0.82 [3] 1.43/0.82 [0] = [1] 1.43/0.82 [1] 1.43/0.82 orientation: 1.43/0.82 [1 1 0] [6] [1 0 0] 1.43/0.82 f(x,0()) = [2 0 0]x + [4] >= [2 0 0]x = s(x) 1.43/0.82 [1 2 0] [3] [0 2 0] 1.43/0.82 1.43/0.82 [2 2 2] [0] [1 1 2] 1.43/0.82 g(x) = [1 2 3]x + [2] >= [1 1 2]x = h(x,gen()) 1.43/0.82 [1 2 0] [0] [1 0 0] 1.43/0.82 1.43/0.82 [3 1 0] [6] [3 1 0] 1.43/0.82 h(0(),x) = [3 2 3]x + [6] >= [2 1 3]x = f(x,x) 1.43/0.82 [2 2 1] [3] [2 2 0] 1.43/0.82 1.43/0.82 [0] [0] 1.43/0.82 a() = [2] >= [0] = b() 1.43/0.82 [2] [0] 1.43/0.82 1.43/0.82 [0] [0] 1.43/0.82 gen() = [0] >= [0] = s(gen()) 1.43/0.82 [0] [0] 1.43/0.82 problem: 1.43/0.82 strict: 1.43/0.82 g(x) -> h(x,gen()) 1.43/0.82 a() -> b() 1.43/0.82 weak: 1.43/0.82 gen() -> s(gen()) 1.43/0.82 Matrix Interpretation Processor: dim=5 1.43/0.82 1.43/0.82 interpretation: 1.43/0.82 [0] 1.43/0.82 [0] 1.43/0.82 [b] = [0] 1.43/0.82 [0] 1.43/0.82 [0], 1.43/0.82 1.43/0.82 [1] 1.43/0.82 [0] 1.43/0.82 [a] = [0] 1.43/0.82 [1] 1.43/0.82 [0], 1.43/0.82 1.43/0.82 [1 0 0 0 0] [1 0 0 0 0] 1.43/0.82 [0 0 0 0 0] [0 0 0 0 0] 1.43/0.82 [h](x0, x1) = [0 0 0 0 0]x0 + [0 0 0 0 0]x1 1.43/0.82 [0 0 0 0 0] [0 0 0 0 0] 1.43/0.82 [0 0 0 0 0] [0 0 0 0 0] , 1.43/0.82 1.43/0.82 [0] 1.43/0.82 [0] 1.43/0.82 [gen] = [0] 1.43/0.82 [1] 1.43/0.82 [0], 1.43/0.82 1.43/0.82 [1 0 0 1 0] [1] 1.43/0.82 [0 0 0 1 0] [1] 1.43/0.82 [g](x0) = [0 1 0 0 0]x0 + [1] 1.43/0.82 [0 0 0 0 0] [0] 1.43/0.82 [0 0 0 0 0] [0], 1.43/0.82 1.43/0.82 [1 0 0 0 0] 1.43/0.82 [0 0 0 0 0] 1.43/0.82 [s](x0) = [0 0 0 0 0]x0 1.43/0.82 [0 0 0 0 0] 1.43/0.82 [0 0 0 0 0] 1.43/0.82 orientation: 1.43/0.82 [1 0 0 1 0] [1] [1 0 0 0 0] 1.43/0.82 [0 0 0 1 0] [1] [0 0 0 0 0] 1.43/0.82 g(x) = [0 1 0 0 0]x + [1] >= [0 0 0 0 0]x = h(x,gen()) 1.43/0.82 [0 0 0 0 0] [0] [0 0 0 0 0] 1.43/0.82 [0 0 0 0 0] [0] [0 0 0 0 0] 1.43/0.82 1.43/0.82 [1] [0] 1.43/0.82 [0] [0] 1.43/0.82 a() = [0] >= [0] = b() 1.43/0.82 [1] [0] 1.43/0.82 [0] [0] 1.43/0.82 1.43/0.82 [0] [0] 1.43/0.82 [0] [0] 1.43/0.82 gen() = [0] >= [0] = s(gen()) 1.43/0.82 [1] [0] 1.43/0.82 [0] [0] 1.43/0.82 problem: 1.43/0.82 strict: 1.43/0.82 1.43/0.82 weak: 1.43/0.82 gen() -> s(gen()) 1.43/0.82 Qed 1.43/0.82 EOF