Algorithm 1 False Reduction.
Input:      $matrix[N,M]\leftarrow L$ Output:      $L^{\prime }$
1: for $i\leftarrow 0,1,\dots ,N$ do
2:    for $j\leftarrow 0,1,\dots ,M-2$ do
	▹ Excepting the last two clips
3:        if matrix[i, j] ≠ matrix[i, $j+1$] then
4:           if count(matrix[i, j] in matrix[i, $j+2$ to $j+4$]) > 1 then
5:               matrix[i, $j+1$] ← not matrix[i, $j+1$]
6:           end if
7:        end if
8:    end for
	▹ Recheck the first two clips
9:    if matrix[i, 0 to 2] is not identical then
10:        if matrix[i, 1] is not in matrix[i, 2 to 4] then
11:           matrix[i, 1] ← not matrix[i, 1]
12:        end if
13:        if matrix[i, 0] not in matrix[i, 1 to 3] then
14:           matrix[i, 0] ← not matrix[i, 0]
15:        end if
16:    end if
	▹ For the last two clips
17:    if matrix[i, $M-1$] ≠ matrix[i, $M-2$] then
18:        if matrix[i, $M-1$] ≠ matrix[i, $M-3$] then
19:           matrix[i, $M-1$] ← not matrix[i, $M-1$]
20:        end if
21:    end if
22:    if matrix[i, $M-1$] ≠ matrix[i, $M-2$] then
23:        if matrix[i, $M-1$] = matrix[i, $M-3$] then
24:           matrix[i, $M-2$] ← not matrix[i, $M-2$]
25:        end if
26:    end if
27:    if matrix[i, $M-1$] = matrix[i, $M-2$] then
28:        if matrix[i, $M-1$] not in matrix[i, $M-5$ to $M-3$] then
29:           matrix[i, $M-1$] ← not matrix[i, $M-1$]
30:           matrix[i, $M-2$] ← not matrix[i, $M-2$]
31:        end if
32:    end if
33: end for
34: $L^{\prime }\leftarrow matrix$