12.19/3.42 YES 12.19/3.43 12.19/3.43 Problem: 12.19/3.43 strict: 12.19/3.43 f(0()) -> s(0()) 12.19/3.43 f(s(0())) -> s(0()) 12.19/3.43 f(s(s(x))) -> f(f(s(x))) 12.19/3.43 weak: 12.19/3.43 rand(x) -> x 12.19/3.43 rand(x) -> rand(s(x)) 12.19/3.43 12.19/3.43 Proof: 12.19/3.43 Arctic Interpretation Processor: 12.19/3.43 dimension: 2 12.19/3.43 interpretation: 12.19/3.43 [1 1] 12.19/3.43 [rand](x0) = [7 7]x0, 12.19/3.43 12.19/3.43 [0 -&] 12.19/3.43 [s](x0) = [0 0 ]x0, 12.19/3.43 12.19/3.43 [0 0 ] 12.19/3.43 [f](x0) = [-& 0 ]x0, 12.19/3.43 12.19/3.43 [4] 12.19/3.43 [0] = [4] 12.19/3.43 orientation: 12.19/3.43 [4] [4] 12.19/3.43 f(0()) = [4] >= [4] = s(0()) 12.19/3.43 12.19/3.43 [4] [4] 12.19/3.43 f(s(0())) = [4] >= [4] = s(0()) 12.19/3.43 12.19/3.43 [0 0] [0 0] 12.19/3.43 f(s(s(x))) = [0 0]x >= [0 0]x = f(f(s(x))) 12.19/3.43 12.19/3.43 [1 1] 12.19/3.43 rand(x) = [7 7]x >= x = x 12.19/3.43 12.19/3.43 [1 1] [1 1] 12.19/3.43 rand(x) = [7 7]x >= [7 7]x = rand(s(x)) 12.19/3.43 problem: 12.19/3.43 strict: 12.19/3.43 f(0()) -> s(0()) 12.19/3.43 f(s(0())) -> s(0()) 12.19/3.43 f(s(s(x))) -> f(f(s(x))) 12.19/3.43 weak: 12.19/3.43 rand(x) -> rand(s(x)) 12.19/3.43 Matrix Interpretation Processor: dim=2 12.19/3.43 12.19/3.43 interpretation: 12.19/3.43 [1 0] 12.19/3.43 [rand](x0) = [0 2]x0, 12.19/3.43 12.19/3.43 [1 0] 12.19/3.43 [s](x0) = [0 0]x0, 12.19/3.43 12.19/3.43 [1 2] 12.19/3.43 [f](x0) = [0 0]x0, 12.19/3.43 12.19/3.43 [0] 12.19/3.43 [0] = [1] 12.19/3.43 orientation: 12.19/3.43 [2] [0] 12.19/3.43 f(0()) = [0] >= [0] = s(0()) 12.19/3.43 12.19/3.43 [0] [0] 12.19/3.43 f(s(0())) = [0] >= [0] = s(0()) 12.19/3.43 12.19/3.43 [1 0] [1 0] 12.19/3.43 f(s(s(x))) = [0 0]x >= [0 0]x = f(f(s(x))) 12.19/3.43 12.19/3.43 [1 0] [1 0] 12.19/3.43 rand(x) = [0 2]x >= [0 0]x = rand(s(x)) 12.19/3.43 problem: 12.19/3.43 strict: 12.19/3.43 f(s(0())) -> s(0()) 12.19/3.43 f(s(s(x))) -> f(f(s(x))) 12.19/3.43 weak: 12.19/3.43 rand(x) -> rand(s(x)) 12.19/3.43 Arctic Interpretation Processor: 12.19/3.43 dimension: 2 12.19/3.43 interpretation: 12.19/3.43 [0 -&] 12.19/3.43 [rand](x0) = [-& -&]x0, 12.19/3.43 12.19/3.43 [0 -&] 12.19/3.43 [s](x0) = [6 2 ]x0, 12.19/3.43 12.19/3.43 [1 1 ] 12.19/3.43 [f](x0) = [-& 0 ]x0, 12.19/3.43 12.19/3.43 [0] 12.19/3.43 [0] = [6] 12.19/3.43 orientation: 12.19/3.43 [9] [0] 12.19/3.43 f(s(0())) = [8] >= [8] = s(0()) 12.19/3.43 12.19/3.43 [9 5] [8 4] 12.19/3.43 f(s(s(x))) = [8 4]x >= [6 2]x = f(f(s(x))) 12.19/3.43 12.19/3.43 [0 -&] [0 -&] 12.19/3.43 rand(x) = [-& -&]x >= [-& -&]x = rand(s(x)) 12.19/3.43 problem: 12.19/3.43 strict: 12.19/3.43 f(s(0())) -> s(0()) 12.19/3.43 weak: 12.19/3.43 rand(x) -> rand(s(x)) 12.19/3.43 Arctic Interpretation Processor: 12.19/3.43 dimension: 3 12.19/3.43 interpretation: 12.19/3.43 [0 0 0 ] 12.19/3.43 [rand](x0) = [-& -& -&]x0 12.19/3.43 [-& -& -&] , 12.19/3.43 12.19/3.43 [0 -& -&] 12.19/3.43 [s](x0) = [0 0 0 ]x0 12.19/3.43 [0 0 -&] , 12.19/3.43 12.19/3.43 [0 -& 1 ] 12.19/3.43 [f](x0) = [2 -& 3 ]x0 12.19/3.43 [3 0 -&] , 12.19/3.43 12.19/3.43 [3 ] 12.19/3.43 [0] = [-&] 12.19/3.43 [0 ] 12.19/3.43 orientation: 12.19/3.43 [4] [3] 12.19/3.43 f(s(0())) = [6] >= [3] = s(0()) 12.19/3.43 [6] [3] 12.19/3.43 12.19/3.43 [0 0 0 ] [0 0 0 ] 12.19/3.43 rand(x) = [-& -& -&]x >= [-& -& -&]x = rand(s(x)) 12.19/3.43 [-& -& -&] [-& -& -&] 12.19/3.43 problem: 12.19/3.43 strict: 12.19/3.43 12.19/3.43 weak: 12.19/3.43 rand(x) -> rand(s(x)) 12.19/3.43 Qed 12.19/3.43 EOF