9.90/2.81 YES 9.90/2.82 9.90/2.82 Problem: 9.90/2.82 strict: 9.90/2.82 a(b(x1)) -> a(x1) 9.90/2.82 d(b(x1)) -> b(x1) 9.90/2.82 d(c(x1)) -> c(x1) 9.90/2.82 weak: 9.90/2.82 a(x1) -> d(a(x1)) 9.90/2.82 c(x1) -> c(b(x1)) 9.90/2.82 9.90/2.82 Proof: 9.90/2.82 Matrix Interpretation Processor: dim=2 9.90/2.82 9.90/2.82 interpretation: 9.90/2.82 [1 0] [2] 9.90/2.82 [c](x0) = [2 0]x0 + [0], 9.90/2.82 9.90/2.82 9.90/2.82 [d](x0) = x0, 9.90/2.82 9.90/2.82 [1 1] 9.90/2.82 [a](x0) = [0 1]x0, 9.90/2.82 9.90/2.82 [1 0] [0] 9.90/2.82 [b](x0) = [1 2]x0 + [1] 9.90/2.82 orientation: 9.90/2.82 [2 2] [1] [1 1] 9.90/2.82 a(b(x1)) = [1 2]x1 + [1] >= [0 1]x1 = a(x1) 9.90/2.82 9.90/2.82 [1 0] [0] [1 0] [0] 9.90/2.82 d(b(x1)) = [1 2]x1 + [1] >= [1 2]x1 + [1] = b(x1) 9.90/2.82 9.90/2.82 [1 0] [2] [1 0] [2] 9.90/2.82 d(c(x1)) = [2 0]x1 + [0] >= [2 0]x1 + [0] = c(x1) 9.90/2.82 9.90/2.82 [1 1] [1 1] 9.90/2.82 a(x1) = [0 1]x1 >= [0 1]x1 = d(a(x1)) 9.90/2.82 9.90/2.82 [1 0] [2] [1 0] [2] 9.90/2.82 c(x1) = [2 0]x1 + [0] >= [2 0]x1 + [0] = c(b(x1)) 9.90/2.82 problem: 9.90/2.82 strict: 9.90/2.82 d(b(x1)) -> b(x1) 9.90/2.82 d(c(x1)) -> c(x1) 9.90/2.82 weak: 9.90/2.82 a(x1) -> d(a(x1)) 9.90/2.82 c(x1) -> c(b(x1)) 9.90/2.82 Arctic Interpretation Processor: 9.90/2.82 dimension: 2 9.90/2.82 interpretation: 9.90/2.82 [0 0] 9.90/2.82 [c](x0) = [1 1]x0, 9.90/2.82 9.90/2.82 [0 0 ] 9.90/2.82 [d](x0) = [-& 2 ]x0, 9.90/2.82 9.90/2.82 [0 4 ] 9.90/2.82 [a](x0) = [-& -&]x0, 9.90/2.82 9.90/2.82 [0 0 ] 9.90/2.82 [b](x0) = [-& -&]x0 9.90/2.82 orientation: 9.90/2.82 [0 0 ] [0 0 ] 9.90/2.82 d(b(x1)) = [-& -&]x1 >= [-& -&]x1 = b(x1) 9.90/2.82 9.90/2.82 [1 1] [0 0] 9.90/2.82 d(c(x1)) = [3 3]x1 >= [1 1]x1 = c(x1) 9.90/2.82 9.90/2.82 [0 4 ] [0 4 ] 9.90/2.82 a(x1) = [-& -&]x1 >= [-& -&]x1 = d(a(x1)) 9.90/2.82 9.90/2.82 [0 0] [0 0] 9.90/2.82 c(x1) = [1 1]x1 >= [1 1]x1 = c(b(x1)) 9.90/2.82 problem: 9.90/2.82 strict: 9.90/2.82 d(b(x1)) -> b(x1) 9.90/2.82 weak: 9.90/2.82 a(x1) -> d(a(x1)) 9.90/2.82 c(x1) -> c(b(x1)) 9.90/2.82 String Reversal Processor: 9.90/2.82 strict: 9.90/2.82 b(d(x1)) -> b(x1) 9.90/2.82 weak: 9.90/2.82 a(x1) -> a(d(x1)) 9.90/2.82 c(x1) -> b(c(x1)) 9.90/2.82 Arctic Interpretation Processor: 9.90/2.82 dimension: 2 9.90/2.82 interpretation: 9.90/2.82 [4 2 ] 9.90/2.82 [c](x0) = [2 -&]x0, 9.90/2.82 9.90/2.82 [0 -&] 9.90/2.82 [d](x0) = [0 1 ]x0, 9.90/2.82 9.90/2.82 [0 -&] 9.90/2.82 [a](x0) = [-& -&]x0, 9.90/2.82 9.90/2.82 [0 2 ] 9.90/2.82 [b](x0) = [-& 0 ]x0 9.90/2.82 orientation: 9.90/2.82 [2 3] [0 2 ] 9.90/2.82 b(d(x1)) = [0 1]x1 >= [-& 0 ]x1 = b(x1) 9.90/2.82 9.90/2.82 [0 -&] [0 -&] 9.90/2.82 a(x1) = [-& -&]x1 >= [-& -&]x1 = a(d(x1)) 9.90/2.82 9.90/2.82 [4 2 ] [4 2 ] 9.90/2.82 c(x1) = [2 -&]x1 >= [2 -&]x1 = b(c(x1)) 9.90/2.82 problem: 9.90/2.82 strict: 9.90/2.82 9.90/2.82 weak: 9.90/2.82 a(x1) -> a(d(x1)) 9.90/2.82 c(x1) -> b(c(x1)) 9.90/2.82 Qed 9.90/2.82 EOF