Running time question If I have two kinds of LinkedList $A$ and $B$.

$A$ is a move to front one which means:
&gt;&gt;&gt; lst1 = 1, 2, 3, 4, 5, 6, 7, 8, 9
&gt;&gt;&gt; lst1.contain(7)
True
&gt;&gt;&gt; lst1.to_list
7, 1, 2, 3, 4, 5, 6, 8, 9
$B$ is a swap list, which means:
&gt;&gt;&gt; lst2 = 1, 2, 3, 4, 5, 6, 7, 8, 9
&gt;&gt;&gt; lst2.contain(7)
True
&gt;&gt;&gt; lst2.to_list
1, 2, 3, 4, 5, 7, 6, 8, 9

I want to find a searching sequence such that the running time of $B$ is faster than $A$. I mean the Theta of them would be different. The length of lst1 and lst2 are both $n$. We search $m$ times and can search different elements for different times.
The move-to-front heuristic is 4-competitive in the model where swapping adjacent elements costs one unit. This means that if the optimal strategy has cost $N$, then move-to-front has cost at most $4N$. In particular, if a swap list has cost $N$ on some searching sequence, then move-to-front will have cost at most $4N$.
See for example MIT OpenCourseWare or Princeton Slides.