YES(?,O(n^2)) 9.34/5.98 YES(?,O(n^2)) 9.34/5.98 9.34/5.98 Problem: 9.34/5.98 rev(a()) -> a() 9.34/5.98 rev(b()) -> b() 9.34/5.98 rev(++(x,y)) -> ++(rev(y),rev(x)) 9.34/5.98 rev(++(x,x)) -> rev(x) 9.34/5.98 9.34/5.98 Proof: 9.34/5.98 Complexity Transformation Processor: 9.34/5.98 strict: 9.34/5.98 rev(a()) -> a() 9.34/5.98 rev(b()) -> b() 9.34/5.98 rev(++(x,y)) -> ++(rev(y),rev(x)) 9.34/5.98 rev(++(x,x)) -> rev(x) 9.34/5.98 weak: 9.34/5.98 9.34/5.98 Matrix Interpretation Processor: dim=1 9.34/5.98 9.34/5.98 max_matrix: 9.34/5.98 1 9.34/5.98 interpretation: 9.34/5.98 [++](x0, x1) = x0 + x1 + 193, 9.34/5.98 9.34/5.98 [b] = 30, 9.34/5.98 9.34/5.98 [rev](x0) = x0 + 4, 9.34/5.98 9.34/5.98 [a] = 32 9.34/5.98 orientation: 9.34/5.98 rev(a()) = 36 >= 32 = a() 9.34/5.98 9.34/5.98 rev(b()) = 34 >= 30 = b() 9.34/5.98 9.34/5.98 rev(++(x,y)) = x + y + 197 >= x + y + 201 = ++(rev(y),rev(x)) 9.34/5.98 9.34/5.98 rev(++(x,x)) = 2x + 197 >= x + 4 = rev(x) 9.34/5.98 problem: 9.34/5.98 strict: 9.34/5.98 rev(++(x,y)) -> ++(rev(y),rev(x)) 9.34/5.98 weak: 9.34/5.98 rev(a()) -> a() 9.34/5.98 rev(b()) -> b() 9.34/5.98 rev(++(x,x)) -> rev(x) 9.34/5.98 Matrix Interpretation Processor: dim=2 9.34/5.98 9.34/5.98 max_matrix: 9.34/5.98 [1 1] 9.34/5.98 [0 1] 9.34/5.98 interpretation: 9.34/5.98 [2] 9.34/5.98 [++](x0, x1) = x0 + x1 + [4], 9.34/5.98 9.34/5.98 [0] 9.34/5.98 [b] = [0], 9.34/5.98 9.34/5.98 [1 1] 9.34/5.98 [rev](x0) = [0 1]x0, 9.34/5.98 9.34/5.98 [0] 9.34/5.98 [a] = [0] 9.34/5.98 orientation: 9.34/5.98 [1 1] [1 1] [6] [1 1] [1 1] [2] 9.34/5.98 rev(++(x,y)) = [0 1]x + [0 1]y + [4] >= [0 1]x + [0 1]y + [4] = ++(rev(y),rev(x)) 9.34/5.98 9.34/5.98 [0] [0] 9.34/5.98 rev(a()) = [0] >= [0] = a() 9.34/5.98 9.34/5.98 [0] [0] 9.34/5.98 rev(b()) = [0] >= [0] = b() 9.34/5.98 9.34/5.98 [2 2] [6] [1 1] 9.34/5.98 rev(++(x,x)) = [0 2]x + [4] >= [0 1]x = rev(x) 9.34/5.98 problem: 9.34/5.98 strict: 9.34/5.98 9.34/5.98 weak: 9.34/5.98 rev(++(x,y)) -> ++(rev(y),rev(x)) 9.34/5.98 rev(a()) -> a() 9.34/5.98 rev(b()) -> b() 9.34/5.98 rev(++(x,x)) -> rev(x) 9.34/5.98 Qed 9.34/5.98 EOF