YES(?,O(n^1)) 0.16/0.24 YES(?,O(n^1)) 0.16/0.24 0.16/0.24 Problem: 0.16/0.24 a(x1) -> b(b(x1)) 0.16/0.24 b(b(b(x1))) -> a(x1) 0.16/0.24 0.16/0.24 Proof: 0.16/0.24 Complexity Transformation Processor: 0.16/0.24 strict: 0.16/0.24 a(x1) -> b(b(x1)) 0.16/0.24 b(b(b(x1))) -> a(x1) 0.16/0.24 weak: 0.16/0.24 0.16/0.24 Matrix Interpretation Processor: dim=1 0.16/0.24 0.16/0.24 max_matrix: 0.16/0.24 1 0.16/0.24 interpretation: 0.16/0.24 [b](x0) = x0 + 154, 0.16/0.24 0.16/0.24 [a](x0) = x0 0.16/0.24 orientation: 0.16/0.24 a(x1) = x1 >= x1 + 308 = b(b(x1)) 0.16/0.24 0.16/0.24 b(b(b(x1))) = x1 + 462 >= x1 = a(x1) 0.16/0.24 problem: 0.16/0.24 strict: 0.16/0.24 a(x1) -> b(b(x1)) 0.16/0.24 weak: 0.16/0.24 b(b(b(x1))) -> a(x1) 0.16/0.24 Matrix Interpretation Processor: dim=1 0.16/0.24 0.16/0.24 max_matrix: 0.16/0.24 1 0.16/0.24 interpretation: 0.16/0.24 [b](x0) = x0 + 64, 0.16/0.24 0.16/0.24 [a](x0) = x0 + 136 0.16/0.24 orientation: 0.16/0.24 a(x1) = x1 + 136 >= x1 + 128 = b(b(x1)) 0.16/0.24 0.16/0.24 b(b(b(x1))) = x1 + 192 >= x1 + 136 = a(x1) 0.16/0.24 problem: 0.16/0.24 strict: 0.16/0.24 0.16/0.24 weak: 0.16/0.24 a(x1) -> b(b(x1)) 0.16/0.24 b(b(b(x1))) -> a(x1) 0.16/0.24 Qed 0.16/0.25 EOF