YES(?,O(n^1)) 0.15/0.27 YES(?,O(n^1)) 0.15/0.27 0.15/0.27 Problem: 0.15/0.27 a(a(x1)) -> b(b(b(x1))) 0.15/0.27 b(b(b(b(b(x1))))) -> a(a(a(x1))) 0.15/0.27 0.15/0.27 Proof: 0.15/0.27 Complexity Transformation Processor: 0.15/0.27 strict: 0.15/0.27 a(a(x1)) -> b(b(b(x1))) 0.15/0.27 b(b(b(b(b(x1))))) -> a(a(a(x1))) 0.15/0.27 weak: 0.15/0.27 0.15/0.27 Matrix Interpretation Processor: dim=1 0.15/0.27 0.15/0.27 max_matrix: 0.15/0.27 1 0.15/0.27 interpretation: 0.15/0.27 [b](x0) = x0 + 8, 0.15/0.27 0.15/0.27 [a](x0) = x0 + 160 0.15/0.27 orientation: 0.15/0.27 a(a(x1)) = x1 + 320 >= x1 + 24 = b(b(b(x1))) 0.15/0.27 0.15/0.27 b(b(b(b(b(x1))))) = x1 + 40 >= x1 + 480 = a(a(a(x1))) 0.15/0.27 problem: 0.15/0.27 strict: 0.15/0.27 b(b(b(b(b(x1))))) -> a(a(a(x1))) 0.15/0.27 weak: 0.15/0.27 a(a(x1)) -> b(b(b(x1))) 0.15/0.27 Matrix Interpretation Processor: dim=1 0.15/0.27 0.15/0.27 max_matrix: 0.15/0.27 1 0.15/0.27 interpretation: 0.15/0.27 [b](x0) = x0 + 32, 0.15/0.27 0.15/0.27 [a](x0) = x0 + 48 0.15/0.27 orientation: 0.15/0.27 b(b(b(b(b(x1))))) = x1 + 160 >= x1 + 144 = a(a(a(x1))) 0.15/0.27 0.15/0.27 a(a(x1)) = x1 + 96 >= x1 + 96 = b(b(b(x1))) 0.15/0.27 problem: 0.15/0.27 strict: 0.15/0.27 0.15/0.27 weak: 0.15/0.27 b(b(b(b(b(x1))))) -> a(a(a(x1))) 0.15/0.27 a(a(x1)) -> b(b(b(x1))) 0.15/0.27 Qed 0.15/0.27 EOF