As RW suggested, some steps may be eliminated. I have tried to do that, and ends up with 14 steps as given below. I'am not sure, that I could have selected these steps beforehand. Some of the eliminated steps just turned out to be not esential for solving the puzzle.

As RW commented, I choose not to count empty rechtangles, XY-wing etc. as a step.

Step 1, 2, and 3 is as before:

1. X-wing, [r9c1]-3-[r89c3]=3=[r6c3]-3-[r6c9]=3=[r9c9]-3-[r9c13] => r9c1 <> 3 (as RW)

- Code: Select all

2. [r5c8]-3-[r6c9]=3=[r9c9](=1=[r9c5])

=2=[r9c7]-2-[r5c7]=2=[r5c6]=1=[r5c5]

=> r9c5=1 and r5c5=1 - contradiction => r5c8<>3

3. [r6c123](-3-[r6c6])

-3-[r6c9](=3=[r9c9]=1=[r9c5])

=3=[r4c8]-3-[r4c6]=3=[r5c6]=1=[r5c5]

=> r9c5=1 and r5c5=1 - contradiction => r6c123<>3

=> c12 box line reduction => r8c12<>3

(previous step 5)

4b. [r5c1](-6-[r6c123])

(=3=[r4c2]-3-[r4c8])

=3=[r5c6]=1=[r5c5]-1-[r9c5]=1=[r9c9]=2=[r9c7]-2-[r5c7]=2=[r5c8]

-2-[r4c8](-9-[r8c8])

-9-[r7c8](=9=[r8c7]-9-[r8c1]=9=[r9c1]-9-[r9c5])

=9=[r7c5]-9-[r6c5]=9=[r6c4]=6=[r6c5]-6-[r9c5]

=> r9c5 has no candidates => r5c1<>6

=> r6 box line reduction => r6c45<>6

(previous step 6)

5b. [r5c1](=3=[r4c2]-3-[r4c8]=3=[r6c9])

(=3=[r5c6]=1=[r5c5]=6=[r5c4]-6-[r9c4])

-8-[r5c7]=8=[r4c7](-8-[r4c4]-7-[r9c4])

=9=[r4c8]-9-[r7c8]=9=[r7c5]-9-[r6c5]=9=[r6c4]-9-[r9c4]

=> r9c4 has no candidates => r5c1=3

=> single r3c2=3

(previous step 10)

6b. [r9c7]=2=[r9c9](=1=[r9c5]-1-[r5c5]=1=[r5c6])

(=3=[r9c3]-3-[r8c3])

=3=[r6c9]-3-[r4c8]=3=[r4c6]=2=[r6c6]-2-[r6c23]=2=[r4c2]

=7=[r4c4]-7-[r9c4]=7=[r9c1](-7-[r3c1]=7=[r2c3]-7-[r6c3]

-7-[r8c3]-6-[r6c3]

=> r6c3 has no candidates => r9c7<>9

(previous step 11)

7b. [r4c7](-2-[r5c7])

(-2-[r5c8](-4-[r5c4])

(-4-[r5c5])

-4-[r5c7](-8-[r5c4])

-8-[r5c5])

-2-[r9c7]=2=[r9c9]=1=[r9c5]-1-[r5c5]-6-[r5c4]

=> r5c4 has no candidates => r4c7<>2

(previous step 12)

8b. [r2c8](-2-[r45c8])

=6=[r1c8](-6-[r1c2]-2-[r46c2]=2=[r6c3]-2-[r6c9]=2=[r5c7]-2-[r9c7])

-6-[r1c1]-5-[r3c1]-7-[r3c78]=7=[r2c7]-7-[r9c7]

=> r9c7 has no candidates => r2c8<>2

(previous step 13)

9b. [r2c7](-2-[r2c9])

(-2-[r2c3])

-2-[r9c7]=2=[r9c9](=1=[r9c5]-1-[r5c5]=1=[r5c6])

=3=[r6c9]-3-[r4c8]=3=[r4c6]=2=[r6c6]-2-[r6c23]

=2=[r4c2]-2-[r1c2]=2=[r1c3]=4=[r2c3](-4-[r2c9])

-4-[r2c6]-8-[r2c9]

=> r2c9 has no candidates => r2c7<>2

(previous step 14)

10b. [r5c7](-2-[r9c7]-7-[r23c7])

-2-[r45c8]=2=[r1c8](=6=[r2c8])

-2-[r1c23]=2=[r2c3]=7=[r1c3]-7-[r3c78]

=> Box 3 has no candidates for no. 7. => r5c7<>2

=> single r9c7=2

(almost as previous step 9)

11b. [r8c8](-9-[r8c7])

(-9-[r7c8]=9=[r7c5](-9-[r8c5])(-9-[r9c4])-9-[r6c5]=9=[r6c4])

=3=[r9c9](=1=[r9c5](-1-[r8c6])

(-1-[r7c5])

-1-[r5c5]=1=[r5c6])

-3-[r6c9]=3=[r4c8]-3-[r4c6]=3=[r6c6]=2=[r4c6](-2-[r4c2])

=7=[r4c4]

(-7-[r9c4]-6-[r8c5])

-7-[r4c2]-8-[r78c2]=8=[r8c1](-8-[r8c6])

-8-[r8c5](-4-[r8c7])

-4-[r8c6]-7-[r8c7]

=> r8c7 has no candidates => r8c8<>9

(previous step 17 with ekstra eliminations)

12b. [r7c8](=9=[r8c7]-9-[r8c1]=9=[r9c1]-9-[r9c4])

=9=[r4c8](=3=[r6c9]-3-[r9c9]-1-[r9c5]-6-[r9c4])

-9-[r4c7]-8-[r4c4]-7-[r9c4]

=> r9c4 has no candidates => r7c8=9

=> single r4c7=9

=> pointing pair with 7 in r8 => r8c1236<>7

=> empty rectangle box 4 => r6c6<>7

=> empty rectangle box 2 => r5c4<>8

(previous step 20 with ekstra eliminations)

13b. [r5c6]=2=[r5c8]-2-[r4c8]-3-[r6c9]=3=[r9c9]=1=[r9c5]-1-[r5c5]=1=[r5c6]

(continuous nice loop)

=> r5c6<>4, r5c6<>8, r6c9<>2, r78c5<>1

=> pointing pair c8 => r1c8<>2

(previous step 18)

14b. [r6c6]=3=[r4c6]-3-[r4c8]-2-[r5c8]=2=[r5c6]-2-[r6c6] => r6c6<>2

=> box line reduction => r4c2<>2

=> Naked pair 78 r4

=> single r7c6=7

=> box-line-reduction with 7 in c13

=> empty rectangle box 6 => r5c5<>4

=> empty rectangle box 4 => r6c5<>8

=> XY-wing box 5 => r6c4<>9

=> just singles to solution

I have compared the solution with RW's:

Step 1 is the same.

Step 7b eliminates the same candidate as RW's step 6, but in another way.

Step 10b eliminates 9 in r9c7 as RW's step 7, but in another way.

Step 2 eliminates the same candidate as RW's step 8 almost the same way.

Step 12b eliminates 8 in r4c7 as RW's step 9, but in another way.

Step 10b eliminates 2 in r5c7 as RW's step 9, but in another way.

Step 5b eliminates 7 in r3c2 as RW's step 10, but in another way.

Step 14b eliminates 7 in r7c2 as RW's step 11, but in another way.

Step 12b eliminates 7 in r7c8 as RW's step 12, but in another way.

The following graphics illustrate the elimination until the later simpler reductions:

The blue dots represent my "hard" eliminations, and the brown dots represent the implied easier removed candidates. The pink dots represent RW's "hard" eliminations, and the yellow dots are on candidates, where RW's and my eliminations are the same.

In general I'think the two ways, the puzzle is solved, are very different. Except for the first finned X-wing and step 2, all the error nets are different. When other equal candidates are eliminated, the premis are different too. However some of the later simpler reductions are the same.

/Viggo