YES(?,O(n^2)) 11.27/6.49 YES(?,O(n^2)) 11.27/6.50 11.27/6.50 Problem: 11.27/6.50 average(s(x),y) -> average(x,s(y)) 11.27/6.50 average(x,s(s(s(y)))) -> s(average(s(x),y)) 11.27/6.50 average(0(),0()) -> 0() 11.27/6.50 average(0(),s(0())) -> 0() 11.27/6.50 average(0(),s(s(0()))) -> s(0()) 11.27/6.50 11.27/6.50 Proof: 11.27/6.50 Complexity Transformation Processor: 11.27/6.50 strict: 11.27/6.50 average(s(x),y) -> average(x,s(y)) 11.27/6.50 average(x,s(s(s(y)))) -> s(average(s(x),y)) 11.27/6.50 average(0(),0()) -> 0() 11.27/6.50 average(0(),s(0())) -> 0() 11.27/6.50 average(0(),s(s(0()))) -> s(0()) 11.27/6.50 weak: 11.27/6.50 11.27/6.50 Matrix Interpretation Processor: dim=1 11.27/6.50 11.27/6.50 max_matrix: 11.27/6.50 1 11.27/6.50 interpretation: 11.27/6.50 [0] = 2, 11.27/6.50 11.27/6.50 [average](x0, x1) = x0 + x1 + 133, 11.27/6.50 11.27/6.50 [s](x0) = x0 + 2 11.27/6.50 orientation: 11.27/6.50 average(s(x),y) = x + y + 135 >= x + y + 135 = average(x,s(y)) 11.27/6.50 11.27/6.50 average(x,s(s(s(y)))) = x + y + 139 >= x + y + 137 = s(average(s(x),y)) 11.27/6.50 11.27/6.50 average(0(),0()) = 137 >= 2 = 0() 11.27/6.50 11.27/6.50 average(0(),s(0())) = 139 >= 2 = 0() 11.27/6.50 11.27/6.50 average(0(),s(s(0()))) = 141 >= 4 = s(0()) 11.27/6.50 problem: 11.27/6.50 strict: 11.27/6.50 average(s(x),y) -> average(x,s(y)) 11.27/6.50 weak: 11.27/6.50 average(x,s(s(s(y)))) -> s(average(s(x),y)) 11.27/6.50 average(0(),0()) -> 0() 11.27/6.50 average(0(),s(0())) -> 0() 11.27/6.50 average(0(),s(s(0()))) -> s(0()) 11.27/6.50 Matrix Interpretation Processor: dim=4 11.27/6.50 11.27/6.50 max_matrix: 11.27/6.50 [1 1 1 1] 11.27/6.50 [0 1 1 1] 11.27/6.50 [0 0 0 1] 11.27/6.50 [0 0 0 0] 11.27/6.50 interpretation: 11.27/6.50 [0] 11.27/6.50 [0] 11.27/6.50 [0] = [0] 11.27/6.50 [0], 11.27/6.50 11.27/6.50 [1 1 1 1] [1 0 0 0] 11.27/6.50 [0 1 1 1] [0 1 1 1] 11.27/6.50 [average](x0, x1) = [0 0 0 0]x0 + [0 0 0 0]x1 11.27/6.50 [0 0 0 0] [0 0 0 0] , 11.27/6.50 11.27/6.50 [1 0 0 0] [1] 11.27/6.50 [0 1 1 0] [1] 11.27/6.50 [s](x0) = [0 0 0 1]x0 + [0] 11.27/6.50 [0 0 0 0] [0] 11.27/6.50 orientation: 11.27/6.50 [1 1 1 1] [1 0 0 0] [2] [1 1 1 1] [1 0 0 0] [1] 11.27/6.50 [0 1 1 1] [0 1 1 1] [1] [0 1 1 1] [0 1 1 1] [1] 11.27/6.50 average(s(x),y) = [0 0 0 0]x + [0 0 0 0]y + [0] >= [0 0 0 0]x + [0 0 0 0]y + [0] = average(x,s(y)) 11.27/6.50 [0 0 0 0] [0 0 0 0] [0] [0 0 0 0] [0 0 0 0] [0] 11.27/6.50 11.27/6.50 [1 1 1 1] [1 0 0 0] [3] [1 1 1 1] [1 0 0 0] [3] 11.27/6.50 [0 1 1 1] [0 1 1 1] [3] [0 1 1 1] [0 1 1 1] [2] 11.27/6.50 average(x,s(s(s(y)))) = [0 0 0 0]x + [0 0 0 0]y + [0] >= [0 0 0 0]x + [0 0 0 0]y + [0] = s(average(s(x),y)) 11.27/6.50 [0 0 0 0] [0 0 0 0] [0] [0 0 0 0] [0 0 0 0] [0] 11.27/6.50 11.27/6.50 [0] [0] 11.27/6.50 [0] [0] 11.27/6.50 average(0(),0()) = [0] >= [0] = 0() 11.27/6.50 [0] [0] 11.27/6.50 11.27/6.50 [1] [0] 11.27/6.50 [1] [0] 11.27/6.50 average(0(),s(0())) = [0] >= [0] = 0() 11.27/6.50 [0] [0] 11.27/6.50 11.27/6.50 [2] [1] 11.27/6.50 [2] [1] 11.27/6.50 average(0(),s(s(0()))) = [0] >= [0] = s(0()) 11.27/6.50 [0] [0] 11.27/6.50 problem: 11.27/6.50 strict: 11.27/6.50 11.27/6.50 weak: 11.27/6.50 average(s(x),y) -> average(x,s(y)) 11.27/6.50 average(x,s(s(s(y)))) -> s(average(s(x),y)) 11.27/6.50 average(0(),0()) -> 0() 11.27/6.50 average(0(),s(0())) -> 0() 11.27/6.50 average(0(),s(s(0()))) -> s(0()) 11.27/6.50 Qed 11.37/6.50 EOF