log

gistfile1.txt

USER: ismellpillows
MODEL: gpt-4-0314
PROMPT:
You will be given tokens [ A# , #A , B# , #B ] in a <problem> tag.
Translate the tokens according to
A# = X
#A = Y
B# = N
#B = M

Remove: consecutive pairs X Y or N M
Swap: consecutive pairs X M or N Y
Repeat until no more pairs can be removed or swapped.

Translate the tokens back according to
X = A#
Y = #A
N = B#
M = #B
Output the tokens in a <solution> tag.

EXAMPLE:
<problem>#A A# A# #A B# B# #A</problem>

Translate the tokens
1. Y
2. X
3. X
4. Y
5. N
6. N
7. Y

Remove: consecutive pairs X Y or N M
1. Y> no
2. X> Y and 3 is X, Y!=X
3. X> Y and 4 is Y, Y==Y remove 3 4
4. Y> no
5. N> M and 6 is N, M!=N
6. N> M and 7 is Y, M!=Y
7. Y> no
REMOVE [ 3 4 , ]
1. Y
2. X
3. _
4. _
5. N
6. N
7. Y

Cleanup removed
1. Y
2. X
3. N
4. N
5. Y

Swap: consecutive pairs X M or N Y
1. Y> no
2. X> M and 3 is N, M!=N
3. N> Y and 4 is N, Y!=N
4. N> Y and 5 is Y, Y==Y swap 4 5
5. Y> no
SWAP [ 4 5 , ]
1/5. Y
2. X
3. N
4. Y
5. N

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. X> Y and 3 is N, Y!=N
3. N> M and 4 is Y, M!=Y
4. Y> no
5. N> M and 6 is None, M!=None
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. X> M and 3 is N, M!=N
3. N> Y and 4 is Y, Y==Y swap 3 4
4. Y> no
5. N> Y and 6 is None, Y!=None
SWAP [ 3 4 , ]
1/5. Y
2. X
3. Y
4. N
5. N

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. X> Y and 3 is Y, Y==Y remove 2 3
3. Y> no
4. N> M and 5 is N, M!=N
5. N> M and 6 is None, M!=None
REMOVE [ 2 3 , ]
1. Y
2. _
3. _
4. N
5. N

Cleanup removed
1. Y
2. N
3. N

Swap: consecutive pairs X M or N Y
1. Y> no
2. N> Y and 3 is N, Y!=N
3. N> Y and 4 is None, Y!=None
no swap

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. N> M and 3 is N, M!=N
3. N> M and 4 is None, M!=None
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. N> Y and 3 is N, Y!=N
3. N> Y and 4 is None, Y!=None
no swap

Repeat if did cleanup or did swap: no

Final result
1. Y
2. N
3. N

Translate the tokens back
1. Y = #A
2. N = B#
3. N = B#

Output the tokens
<solution>#A B# B#</solution>

END OF EXAMPLE
## Instance 0:
Term: #A #A #B #B A# B# A# B# B# B# B# A# 
Norm: #A #A #B #B A# B# A# B# B# B# B# A# 
Rwts: 0
AI-RESPONSE:
Translate the tokens
1. Y
2. Y
3. M
4. M
5. X
6. N
7. X
8. N
9. N
10. N
11. N
12. X

Remove: consecutive pairs X Y or N M
1. Y> no
2. Y> no
3. M> no
4. M> no
5. X> Y and 6 is N, Y!=N
6. N> M and 7 is X, M!=X
7. X> Y and 8 is N, Y!=N
8. N> M and 9 is N, M!=N
9. N> M and 10 is N, M!=N
10. N> M and 11 is N, M!=N
11. N> M and 12 is X, M!=X
12. X> Y and 13 is None, Y!=None
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. Y> no
3. M> no
4. M> no
5. X> M and 6 is N, M!=N
6. N> Y and 7 is X, Y!=X
7. X> M and 8 is N, M!=N
8. N> Y and 9 is N, Y!=N
9. N> Y and 10 is N, Y!=N
10. N> Y and 11 is N, Y!=N
11. N> Y and 12 is X, Y!=X
12. X> M and 13 is None, M!=None
no swap

Repeat if did cleanup or did swap: no

Final result
1. Y
2. Y
3. M
4. M
5. X
6. N
7. X
8. N
9. N
10. N
11. N
12. X

Translate the tokens back
1. Y = #A
2. Y = #A
3. M = #B
4. M = #B
5. X = A#
6. N = B#
7. X = A#
8. N = B#
9. N = B#
10. N = B#
11. N = B#
12. X = A#

Output the tokens
<solution>#A #A #B #B A# B# A# B# B# B# B# A#</solution>

AI-Solution: #A #A #B #B A# B# A# B# B# B# B# A# 

<<correct>>

## Instance 1:
Term: #B B# A# B# #B B# A# B# #B A# B# B# 
Norm: #B B# A# B# A# A# B# B# 
Rwts: 2
AI-RESPONSE:
Translate the tokens
1. M
2. N
3. X
4. N
5. M
6. N
7. X
8. N
9. M
10. X
11. N
12. N

Remove: consecutive pairs X Y or N M
1. M> no
2. N> M and 3 is X, M!=X
3. X> Y and 4 is N, Y!=N
4. N> M and 5 is M, M==M remove 4 5
5. M> no
6. N> M and 7 is X, M!=X
7. X> Y and 8 is N, Y!=N
8. N> M and 9 is M, M==M remove 8 9
9. M> no
10. X> Y and 11 is N, Y!=N
11. N> M and 12 is N, M!=N
12. N> M and 13 is None, M!=None
REMOVE [ 4 5 , 8 9 , ]
1. M
2. N
3. X
4. _
5. _
6. N
7. X
8. _
9. _
10. X
11. N
12. N

Cleanup removed
1. M
2. N
3. X
4. N
5. X
6. X
7. N
8. N

Swap: consecutive pairs X M or N Y
1. M> no
2. N> Y and 3 is X, Y!=X
3. X> M and 4 is N, M!=N
4. N> Y and 5 is X, Y!=X
5. X> M and 6 is X, M!=X
6. X> M and 7 is N, M!=N
7. N> Y and 8 is N, Y!=N
8. N> Y and 9 is None, Y!=None
no swap

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. M> no
2. N> M and 3 is X, M!=X
3. X> Y and 4 is N, Y!=N
4. N> M and 5 is X, M!=X
5. X> Y and 6 is X, Y!=X
6. X> Y and 7 is N, Y!=N
7. N> M and 8 is N, M!=N
8. N> M and 9 is None, M!=None
no remove

Swap: consecutive pairs X M or N Y
1. M> no
2. N> Y and 3 is X, Y!=X
3. X> M and 4 is N, M!=N
4. N> Y and 5 is X, Y!=X
5. X> M and 6 is X, M!=X
6. X> M and 7 is N, M!=N
7. N> Y and 8 is N, Y!=N
8. N> Y and 9 is None, Y!=None
no swap

Repeat if did cleanup or did swap: no

Final result
1. M
2. N
3. X
4. N
5. X
6. X
7. N
8. N

Translate the tokens back
1. M = #B
2. N = B#
3. X = A#
4. N = B#
5. X = A#
6. X = A#
7. N = B#
8. N = B#

Output the tokens
<solution>#B B# A# B# A# A# B# B#</solution>

AI-Solution: #B B# A# B# A# A# B# B# 

<<correct>>

## Instance 2:
Term: A# #B A# A# A# #A B# #B B# #B B# A# 
Norm: #B A# A# A# B# A# 
Rwts: 4
AI-RESPONSE:
Translate the tokens
1. X
2. M
3. X
4. X
5. X
6. Y
7. N
8. M
9. N
10. M
11. N
12. X

Remove: consecutive pairs X Y or N M
1. X> Y and 2 is M, Y!=M
2. M> no
3. X> Y and 4 is X, Y!=X
4. X> Y and 5 is X, Y!=X
5. X> Y and 6 is Y, Y==Y remove 5 6
6. Y> no
7. N> M and 8 is M, M==M remove 7 8
8. M> no
9. N> M and 10 is M, M==M remove 9 10
10. M> no
11. N> M and 12 is X, M!=X
12. X> Y and 13 is None, Y!=None
REMOVE [ 5 6 , 7 8 , 9 10 , ]
1. X
2. M
3. X
4. X
5. _
6. _
7. _
8. _
9. _
10. _
11. N
12. X

Cleanup removed
1. X
2. M
3. X
4. X
5. N
6. X

Swap: consecutive pairs X M or N Y
1. X> M and 2 is M, M==M swap 1 2
2. M> no
3. X> M and 4 is X, M!=X
4. X> M and 5 is N, M!=N
5. N> Y and 6 is X, Y!=X
6. X> Y and 7 is None, Y!=None
SWAP [ 1 2 , ]
1. M
2. X
3. X
4. X
5. N
6. X

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. M> no
2. X> Y and 3 is X, Y!=X
3. X> Y and 4 is X, Y!=X
4. X> Y and 5 is N, Y!=N
5. N> M and 6 is X, M!=X
6. X> Y and 7 is None, Y!=None
no remove

Swap: consecutive pairs X M or N Y
1. M> no
2. X> M and 3 is X, M!=X
3. X> M and 4 is X, M!=X
4. X> M and 5 is N, M!=N
5. N> Y and 6 is X, Y!=X
6. X> Y and 7 is None, Y!=None
no swap

Repeat if did cleanup or did swap: no

Final result
1. M
2. X
3. X
4. X
5. N
6. X

Translate the tokens back
1. M = #B
2. X = A#
3. X = A#
4. X = A#
5. N = B#
6. X = A#

Output the tokens
<solution>#B A# A# A# B# A#</solution>

AI-Solution: #B A# A# A# B# A# 

<<correct>>

## Instance 3:
Term: A# #B B# B# #B #A #B A# #A #A #B #A 
Norm: #B #A #B #A 
Rwts: 6
AI-RESPONSE:
Translate the tokens
1. X
2. M
3. N
4. N
5. M
6. Y
7. M
8. X
9. Y
10. Y
11. M
12. Y

Remove: consecutive pairs X Y or N M
1. X> Y and 2 is M, Y!=M
2. M> no
3. N> M and 4 is N, M!=N
4. N> M and 5 is M, M==M remove 4 5
5. M> no
6. Y> no
7. M> no
8. X> Y and 9 is Y, Y==Y remove 8 9
9. Y> no
10. Y> no
11. M> no
12. Y> no
REMOVE [ 4 5 , 8 9 , ]
1. X
2. M
3. N
4. _
5. _
6. Y
7. M
8. _
9. _
10. Y
11. M
12. Y

Cleanup removed
1. X
2. M
3. N
4. Y
5. M
6. Y
7. M
8. Y

Swap: consecutive pairs X M or N Y
1. X> M and 2 is M, M==M swap 1 2
2. M> no
3. N> Y and 4 is Y, Y==Y swap 3 4
4. Y> no
5. M> no
6. Y> no
7. M> no
8. Y> no
SWAP [ 1 2 , 3 4 , ]
1. M
2. X
3. Y
4. N
5. M
6. Y
7. M
8. Y

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. M> no
2. X> Y and 3 is Y, Y==Y remove 2 3
3. Y> no
4. N> M and 5 is M, M==M remove 4 5
5. M> no
6. Y> no
7. M> no
8. Y> no
REMOVE [ 2 3 , 4 5 , ]
1. M
2. _
3. _
4. _
5. _
6. Y
7. M
8. Y

Cleanup removed
1. M
2. Y
3. M
4. Y

Swap: consecutive pairs X M or N Y
1. M> no
2. Y> no
3. M> no
4. Y> no
no swap

Repeat if did cleanup or did swap: no

Final result
1. M
2. Y
3. M
4. Y

Translate the tokens back
1. M = #B
2. Y = #A
3. M = #B
4. Y = #A

Output the tokens
<solution>#B #A #B #A</solution>

AI-Solution: #B #A #B #A 

<<correct>>

## Instance 4:
Term: B# #B A# #B #B #B #B #B A# B# #B #A 
Norm: #B #B #B #B #B A# 
Rwts: 8
AI-RESPONSE:
Translate the tokens
1. N
2. M
3. X
4. M
5. M
6. M
7. M
8. M
9. X
10. N
11. M
12. Y

Remove: consecutive pairs X Y or N M
1. N> M and 2 is M, M==M remove 1 2
2. M> no
3. X> Y and 4 is M, Y!=M
4. M> no
5. M> no
6. M> no
7. M> no
8. M> no
9. X> Y and 10 is N, Y!=N
10. N> M and 11 is M, M==M remove 10 11
11. M> no
12. Y> no
REMOVE [ 1 2 , 10 11 , ]
1. _
2. _
3. X
4. M
5. M
6. M
7. M
8. M
9. X
10. _
11. _
12. Y

Cleanup removed
1. X
2. M
3. M
4. M
5. M
6. M
7. X
8. Y

Swap: consecutive pairs X M or N Y
1. X> M and 2 is M, M==M swap 1 2
2. M> no
3. M> no
4. M> no
5. M> no
6. M> no
7. X> M and 8 is Y, M!=Y
8. Y> no
SWAP [ 1 2 , ]
1. M
2. X
3. M
4. M
5. M
6. M
7. X
8. Y

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. M> no
2. X> Y and 3 is M, Y!=M
3. M> no
4. M> no
5. M> no
6. M> no
7. X> Y and 8 is Y, Y==Y remove 7 8
8. Y> no
REMOVE [ 7 8 , ]
1. M
2. X
3. M
4. M
5. M
6. M
7. _
8. _

Cleanup removed
1. M
2. X
3. M
4. M
5. M
6. M

Swap: consecutive pairs X M or N Y
1. M> no
2. X> M and 3 is M, M==M swap 2 3
3. M> no
4. M> no
5. M> no
6. M> no
SWAP [ 2 3 , ]
1. M
2. M
3. X
4. M
5. M
6. M

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. M> no
2. M> no
3. X> Y and 4 is M, Y!=M
4. M> no
5. M> no
6. M> no
no remove

Swap: consecutive pairs X M or N Y
1. M> no
2. M> no
3. X> M and 4 is M, M==M swap 3 4
4. M> no
5. M> no
6. M> no
SWAP [ 3 4 , ]
1. M
2. M
3. M
4. X
5. M
6. M

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. M> no
2. M> no
3. M> no
4. X> Y and 5 is M, Y!=M
5. M> no
6. M> no
no remove

Swap: consecutive pairs X M or N Y
1. M> no
2. M> no
3. M> no
4. X> M and 5 is M, M==M swap 4 5
5. M> no
6. M> no
SWAP [ 4 5 , ]
1. M
2. M
3. M
4. M
5. X
6. M

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. M> no
2. M> no
3. M> no
4. M> no
5. X> Y and 6 is M, Y!=M
6. M> no
no remove

Swap: consecutive pairs X M or N Y
1. M> no
2. M> no
3. M> no
4. M> no
5. X> M and 6 is M, M==M swap 5 6
6. M> no
SWAP [ 5 6 , ]
1. M
2. M
3. M
4. M
5. M
6. X

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. M> no
2. M> no
3. M> no
4. M> no
5. M> no
6. X> Y and 7 is None, Y!=None
no remove

Swap: consecutive pairs X M or N Y
1. M> no
2. M> no
3. M> no
4. M> no
5. M> no
6. X> M and 7 is None, M!=None
no swap

Repeat if did cleanup or did swap: no

Final result
1. M
2. M
3. M
4. M
5. M
6. X

Translate the tokens back
1. M = #B
2. M = #B
3. M = #B
4. M = #B
5. M = #B
6. X = A#

Output the tokens
<solution>#B #B #B #B #B A#</solution>

AI-Solution: #B #B #B #B #B A# 

<<correct>>

## Instance 5:
Term: A# #B #B B# B# B# #A #B A# #A #B #A 
Norm: #B #B #A B# 
Rwts: 10
AI-RESPONSE:
Translate the tokens
1. X
2. M
3. M
4. N
5. N
6. N
7. Y
8. M
9. X
10. Y
11. M
12. Y

Remove: consecutive pairs X Y or N M
1. X> Y and 2 is M, Y!=M
2. M> no
3. M> no
4. N> M and 5 is N, M!=N
5. N> M and 6 is N, M!=N
6. N> M and 7 is Y, M!=Y
7. Y> no
8. M> no
9. X> Y and 10 is Y, Y==Y remove 9 10
10. Y> no
11. M> no
12. Y> no
REMOVE [ 9 10 , ]
1. X
2. M
3. M
4. N
5. N
6. N
7. Y
8. M
9. _
10. _
11. M
12. Y

Cleanup removed
1. X
2. M
3. M
4. N
5. N
6. N
7. Y
8. M
9. M
10. Y

Swap: consecutive pairs X M or N Y
1. X> M and 2 is M, M==M swap 1 2
2. M> no
3. M> no
4. N> Y and 5 is N, Y!=N
5. N> Y and 6 is N, Y!=N
6. N> Y and 7 is Y, Y==Y swap 6 7
7. Y> no
8. M> no
9. M> no
10. Y> no
SWAP [ 1 2 , 6 7 , ]
1/2. M
2/1. X
3. M
4. N
5. N
6/7. Y
7/6. N
8. M
9. M
10. Y

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. M> no
2. X> Y and 3 is M, Y!=M
3. M> no
4. N> M and 5 is N, M!=N
5. N> M and 6 is Y, M!=Y
6. Y> no
7. N> M and 8 is M, M==M remove 7 8
8. M> no
9. M> no
10. Y> no
REMOVE [ 7 8 , ]
1. M
2. X
3. M
4. N
5. N
6. Y
7. _
8. _
9. M
10. Y

Cleanup removed
1. M
2. X
3. M
4. N
5. N
6. Y
7. M
8. Y

Swap: consecutive pairs X M or N Y
1. M> no
2. X> M and 3 is M, M==M swap 2 3
3. M> no
4. N> Y and 5 is N, Y!=N
5. N> Y and 6 is Y, Y==Y swap 5 6
6. Y> no
7. M> no
8. Y> no
SWAP [ 2 3 , 5 6 , ]
1. M
2/3. M
3/2. X
4. N
5/6. Y
6/5. N
7. M
8. Y

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. M> no
2. M> no
3. X> Y and 4 is N, Y!=N
4. N> M and 5 is Y, M!=Y
5. Y> no
6. N> M and 7 is M, M==M remove 6 7
7. M> no
8. Y> no
REMOVE [ 6 7 , ]
1. M
2. M
3. X
4. N
5. Y
6. _
7. _
8. Y

Cleanup removed
1. M
2. M
3. X
4. N
5. Y
6. Y

Swap: consecutive pairs X M or N Y
1. M> no
2. M> no
3. X> M and 4 is N, M!=N
4. N> Y and 5 is Y, Y==Y swap 4 5
5. Y> no
6. Y> no
SWAP [ 4 5 , ]
1. M
2. M
3. X
4/5. Y
5/4. N
6. Y

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. M> no
2. M> no
3. X> Y and 4 is Y, Y==Y remove 3 4
4. Y> no
5. N> M and 6 is Y, M!=Y
6. Y> no
REMOVE [ 3 4 , ]
1. M
2. M
3. _
4. _
5. N
6. Y

Cleanup removed
1. M
2. M
3. N
4. Y

Swap: consecutive pairs X M or N Y
1. M> no
2. M> no
3. N> Y and 4 is Y, Y==Y swap 3 4
4. Y> no
SWAP [ 3 4 , ]
1. M
2. M
3/4. Y
4/3. N

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. M> no
2. M> no
3. Y> no
4. N> M and 5 is None, M!=None
no remove

Swap: consecutive pairs X M or N Y
1. M> no
2. M> no
3. Y> no
4. N> Y and 5 is None, Y!=None
no swap

Repeat if did cleanup or did swap: no

Final result
1. M
2. M
3. Y
4. N

Translate the tokens back
1. M = #B
2. M = #B
3. Y = #A
4. N = B#

Output the tokens
<solution>#B #B #A B#</solution>

AI-Solution: #B #B #A B# 

<<correct>>

## Instance 6:
Term: A# B# B# #A #A #A A# A# #B B# A# #B 
Norm: #A #A B# A# A# A# 
Rwts: 12
AI-RESPONSE:
Translate the tokens
1. X
2. N
3. N
4. Y
5. Y
6. Y
7. X
8. X
9. M
10. N
11. X
12. M

Remove: consecutive pairs X Y or N M
1. X> Y and 2 is N, Y!=N
2. N> M and 3 is N, M!=N
3. N> M and 4 is Y, M!=Y
4. Y> no
5. Y> no
6. Y> no
7. X> Y and 8 is X, Y!=X
8. X> Y and 9 is M, Y!=M
9. M> no
10. N> M and 11 is X, M!=X
11. X> Y and 12 is M, Y!=M
12. M> no
no remove

Swap: consecutive pairs X M or N Y
1. X> M and 2 is N, M!=N
2. N> Y and 3 is N, Y!=N
3. N> Y and 4 is Y, Y==Y swap 3 4
4. Y> no
5. Y> no
6. Y> no
7. X> M and 8 is X, M!=X
8. X> M and 9 is M, M==M swap 8 9
9. M> no
10. N> Y and 11 is X, Y!=X
11. X> M and 12 is M, M==M swap 11 12
SWAP [ 3 4 , 8 9 , 11 12 , ]
1. X
2. N
3. Y
4. N
5. Y
6. Y
7. M
8. X
9. X
10. N
11. M
12. X

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. X> Y and 2 is N, Y!=N
2. N> M and 3 is Y, M!=Y
3. Y> no
4. N> M and 5 is Y, M!=Y
5. Y> no
6. Y> no
7. M> no
8. X> Y and 9 is X, Y!=X
9. X> Y and 10 is N, Y!=N
10. N> M and 11 is M, M==M remove 10 11
11. M> no
12. X> Y and 13 is None, Y!=None
REMOVE [ 10 11 , ]
1. X
2. N
3. Y
4. N
5. Y
6. Y
7. M
8. X
9. X
10. _
11. _
12. X

Cleanup removed
1. X
2. N
3. Y
4. N
5. Y
6. Y
7. M
8. X
9. X
10. X

Swap: consecutive pairs X M or N Y
1. X> M and 2 is N, M!=N
2. N> Y and 3 is Y, Y==Y swap 2 3
3. Y> no
4. N> Y and 5 is Y, Y==Y swap 4 5
5. Y> no
6. Y> no
7. M> no
8. X> M and 9 is X, M!=X
9. X> M and 10 is X, M!=X
10. X> M and 11 is None, M!=None
SWAP [ 2 3 , 4 5 , ]
1. X
2. Y
3. N
4. Y
5. N
6. Y
7. M
8. X
9. X
10. X

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. X> Y and 2 is Y, Y==Y remove 1 2
2. Y> no
3. N> M and 4 is Y, M!=Y
4. Y> no
5. N> M and 6 is Y, M!=Y
6. Y> no
7. M> no
8. X> Y and 9 is X, Y!=X
9. X> Y and 10 is X, Y!=X
10. X> Y and 11 is None, Y!=None
REMOVE [ 1 2 , ]
1. _
2. _
3. N
4. Y
5. N
6. Y
7. M
8. X
9. X
10. X

Cleanup removed
1. N
2. Y
3. N
4. Y
5. M
6. X
7. X
8. X

Swap: consecutive pairs X M or N Y
1. N> Y and 2 is Y, Y==Y swap 1 2
2. Y> no
3. N> Y and 4 is Y, Y==Y swap 3 4
4. Y> no
5. M> no
6. X> M and 7 is X, M!=X
7. X> M and 8 is X, M!=X
8. X> M and 9 is None, M!=None
SWAP [ 1 2 , 3 4 , ]
1. Y
2. N
3. Y
4. N
5. M
6. X
7. X
8. X

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. N> M and 3 is Y, M!=Y
3. Y> no
4. N> M and 5 is M, M==M remove 4 5
5. M> no
6. X> Y and 7 is X, Y!=X
7. X> Y and 8 is X, Y!=X
8. X> Y and 9 is None, Y!=None
REMOVE [ 4 5 , ]
1. Y
2. N
3. Y
4. _
5. _
6. X
7. X
8. X

Cleanup removed
1. Y
2. N
3. Y
4. X
5. X
6. X

Swap: consecutive pairs X M or N Y
1. Y> no
2. N> Y and 3 is Y, Y==Y swap 2 3
3. Y> no
4. X> M and 5 is X, M!=X
5. X> M and 6 is X, M!=X
6. X> M and 7 is None, M!=None
SWAP [ 2 3 , ]
1. Y
2. Y
3. N
4. X
5. X
6. X

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. Y> no
3. N> M and 4 is X, M!=X
4. X> Y and 5 is X, Y!=X
5. X> Y and 6 is X, Y!=X
6. X> Y and 7 is None, Y!=None
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. Y> no
3. N> Y and 4 is X, Y!=X
4. X> M and 5 is X, M!=X
5. X> M and 6 is X, M!=X
6. X> M and 7 is None, M!=None
no swap

Repeat if did cleanup or did swap: no

Final result
1. Y
2. Y
3. N
4. X
5. X
6. X

Translate the tokens back
1. Y = #A
2. Y = #A
3. N = B#
4. X = A#
5. X = A#
6. X = A#

Output the tokens
<solution>#A #A B# A# A# A#</solution>

AI-Solution: #A #A B# A# A# A# 

<<correct>>

## Instance 7:
Term: A# B# B# B# #A #A #B #A B# B# #A B# 
Norm: #A #A #A B# B# B# B# B# 
Rwts: 14
AI-RESPONSE:
Translate the tokens
1. X
2. N
3. N
4. N
5. Y
6. Y
7. M
8. Y
9. N
10. N
11. Y
12. N

Remove: consecutive pairs X Y or N M
1. X> Y and 2 is N, Y!=N
2. N> M and 3 is N, M!=N
3. N> M and 4 is N, M!=N
4. N> M and 5 is Y, M!=Y
5. Y> no
6. Y> no
7. M> no
8. Y> no
9. N> M and 10 is N, M!=N
10. N> M and 11 is Y, M!=Y
11. Y> no
12. N> M and 13 is None, M!=None
no remove

Swap: consecutive pairs X M or N Y
1. X> M and 2 is N, M!=N
2. N> Y and 3 is N, Y!=N
3. N> Y and 4 is N, Y!=N
4. N> Y and 5 is Y, Y==Y swap 4 5
5. Y> no
6. Y> no
7. M> no
8. Y> no
9. N> Y and 10 is N, Y!=N
10. N> Y and 11 is Y, Y==Y swap 10 11
11. Y> no
12. N> M and 13 is None, M!=None
SWAP [ 4 5 , 10 11 , ]
1. X
2. N
3. N
4. Y
5. N
6. Y
7. M
8. Y
9. N
10. Y
11. N
12. N

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. X> Y and 2 is N, Y!=N
2. N> M and 3 is N, M!=N
3. N> M and 4 is Y, M!=Y
4. Y> no
5. N> M and 6 is Y, M!=Y
6. Y> no
7. M> no
8. Y> no
9. N> M and 10 is Y, M!=Y
10. Y> no
11. N> M and 12 is N, M!=N
12. N> M and 13 is None, M!=None
no remove

Swap: consecutive pairs X M or N Y
1. X> M and 2 is N, M!=N
2. N> Y and 3 is N, Y!=N
3. N> Y and 4 is Y, Y==Y swap 3 4
4. Y> no
5. N> Y and 6 is Y, Y==Y swap 5 6
6. Y> no
7. M> no
8. Y> no
9. N> Y and 10 is Y, Y==Y swap 9 10
10. Y> no
11. N> Y and 12 is N, Y!=N
12. N> M and 13 is None, M!=None
SWAP [ 3 4 , 5 6 , 9 10 , ]
1. X
2. N
3. Y
4. N
5. Y
6. N
7. M
8. Y
9. Y
10. N
11. N
12. N

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. X> Y and 2 is N, Y!=N
2. N> M and 3 is Y, M!=Y
3. Y> no
4. N> M and 5 is Y, M!=Y
5. Y> no
6. N> M and 7 is M, M==M remove 6 7
7. M> no
8. Y> no
9. Y> no
10. N> M and 11 is N, M!=N
11. N> M and 12 is N, M!=N
12. N> M and 13 is None, M!=None
REMOVE [ 6 7 , ]
1. X
2. N
3. Y
4. N
5. Y
6. _
7. _
8. Y
9. Y
10. N
11. N
12. N

Cleanup removed
1. X
2. N
3. Y
4. N
5. Y
6. Y
7. Y
8. N
9. N
10. N

Swap: consecutive pairs X M or N Y
1. X> M and 2 is N, M!=N
2. N> Y and 3 is Y, Y==Y swap 2 3
3. Y> no
4. N> Y and 5 is Y, Y==Y swap 4 5
5. Y> no
6. Y> no
7. Y> no
8. N> Y and 9 is N, Y!=N
9. N> Y and 10 is N, Y!=N
10. N> M and 11 is None, M!=None
SWAP [ 2 3 , 4 5 , ]
1. X
2. Y
3. N
4. Y
5. N
6. Y
7. Y
8. N
9. N
10. N

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. X> Y and 2 is Y, Y==Y remove 1 2
2. Y> no
3. N> M and 4 is Y, M!=Y
4. Y> no
5. N> M and 6 is Y, M!=Y
6. Y> no
7. Y> no
8. N> M and 9 is N, M!=N
9. N> M and 10 is N, M!=N
10. N> M and 11 is None, M!=None
REMOVE [ 1 2 , ]
1. _
2. _
3. N
4. Y
5. N
6. Y
7. Y
8. N
9. N
10. N

Cleanup removed
1. N
2. Y
3. N
4. Y
5. Y
6. N
7. N
8. N

Swap: consecutive pairs X M or N Y
1. N> Y and 2 is Y, Y==Y swap 1 2
2. Y> no
3. N> Y and 4 is Y, Y==Y swap 3 4
4. Y> no
5. Y> no
6. N> Y and 7 is N, Y!=N
7. N> Y and 8 is N, Y!=N
8. N> M and 9 is None, M!=None
SWAP [ 1 2 , 3 4 , ]
1. Y
2. N
3. Y
4. N
5. Y
6. N
7. N
8. N

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. N> M and 3 is Y, M!=Y
3. Y> no
4. N> M and 5 is Y, M!=Y
5. Y> no
6. N> M and 7 is N, M!=N
7. N> M and 8 is N, M!=N
8. N> M and 9 is None, M!=None
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. N> Y and 3 is Y, Y==Y swap 2 3
3. Y> no
4. N> Y and 5 is Y, Y==Y swap 4 5
5. Y> no
6. N> Y and 7 is N, Y!=N
7. N> Y and 8 is N, Y!=N
8. N> M and 9 is None, M!=None
SWAP [ 2 3 , 4 5 , ]
1. Y
2. Y
3. N
4. Y
5. N
6. N
7. N
8. N

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. Y> no
3. N> M and 4 is Y, M!=Y
4. Y> no
5. N> M and 6 is N, M!=N
6. N> M and 7 is N, M!=N
7. N> M and 8 is N, M!=N
8. N> M and 9 is None, M!=None
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. Y> no
3. N> Y and 4 is Y, Y==Y swap 3 4
4. Y> no
5. N> Y and 6 is N, Y!=N
6. N> Y and 7 is N, Y!=N
7. N> Y and 8 is N, Y!=N
8. N> M and 9 is None, M!=None
SWAP [ 3 4 , ]
1. Y
2. Y
3. Y
4. N
5. N
6. N
7. N
8. N

Repeat if did cleanup or did swap: no

Final result
1. Y
2. Y
3. Y
4. N
5. N
6. N
7. N
8. N

Translate the tokens back
1. Y = #A
2. Y = #A
3. Y = #A
4. N = B#
5. N = B#
6. N = B#
7. N = B#
8. N = B#

Output the tokens
<solution>#A #A #A B# B# B# B# B#</solution>

AI-Solution: #A #A #A B# B# B# B# B# 

<<correct>>

## Instance 8:
Term: #A B# B# A# A# #B #B #B #B A# #B #B 
Norm: #A #B #B #B #B A# A# A# 
Rwts: 16
AI-RESPONSE:
Translate the tokens
1. Y
2. N
3. N
4. X
5. X
6. M
7. M
8. M
9. M
10. X
11. M
12. M

Remove: consecutive pairs X Y or N M
1. Y> no
2. N> M and 3 is N, M!=N
3. N> M and 4 is X, M!=X
4. X> Y and 5 is X, Y!=X
5. X> Y and 6 is M, Y!=M
6. M> no
7. M> no
8. M> no
9. M> no
10. X> Y and 11 is M, Y!=M
11. M> no
12. M> no
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. N> Y and 3 is N, Y!=N
3. N> Y and 4 is X, Y!=X
4. X> M and 5 is X, M!=X
5. X> M and 6 is M, M==M swap 5 6
6. M> no
7. M> no
8. M> no
9. M> no
10. X> Y and 11 is M, Y!=M
11. M> no
12. M> no
SWAP [ 5 6 , ]
1. Y
2. N
3. N
4. X
5. M
6. X
7. M
8. M
9. M
10. X
11. M
12. M

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. N> M and 3 is N, M!=N
3. N> M and 4 is X, M!=X
4. X> Y and 5 is M, Y!=M
5. M> no
6. X> Y and 7 is M, Y!=M
7. M> no
8. M> no
9. M> no
10. X> Y and 11 is M, Y!=M
11. M> no
12. M> no
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. N> Y and 3 is N, Y!=N
3. N> Y and 4 is X, Y!=X
4. X> M and 5 is M, M==M swap 4 5
5. M> no
6. X> Y and 7 is M, Y!=M
7. M> no
8. M> no
9. M> no
10. X> Y and 11 is M, Y!=M
11. M> no
12. M> no
SWAP [ 4 5 , ]
1. Y
2. N
3. N
4. M
5. X
6. X
7. M
8. M
9. M
10. X
11. M
12. M

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. N> M and 3 is N, M!=N
3. N> M and 4 is M, M==M remove 3 4
4. M> no
5. X> Y and 6 is X, Y!=X
6. X> Y and 7 is M, Y!=M
7. M> no
8. M> no
9. M> no
10. X> Y and 11 is M, Y!=M
11. M> no
12. M> no
REMOVE [ 3 4 , ]
1. Y
2. N
3. _
4. _
5. X
6. X
7. M
8. M
9. M
10. X
11. M
12. M

Cleanup removed
1. Y
2. N
3. X
4. X
5. M
6. M
7. M
8. X
9. M
10. M

Swap: consecutive pairs X M or N Y
1. Y> no
2. N> Y and 3 is X, Y!=X
3. X> M and 4 is X, M!=X
4. X> M and 5 is M, M==M swap 4 5
5. M> no
6. M> no
7. M> no
8. X> Y and 9 is M, Y!=M
9. M> no
10. M> no
SWAP [ 4 5 , ]
1. Y
2. N
3. X
4. M
5. X
6. M
7. M
8. X
9. M
10. M

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. N> M and 3 is X, M!=X
3. X> Y and 4 is M, Y!=M
4. M> no
5. X> Y and 6 is M, Y!=M
6. M> no
7. M> no
8. X> Y and 9 is M, Y!=M
9. M> no
10. M> no
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. N> Y and 3 is X, Y!=X
3. X> M and 4 is M, M==M swap 3 4
4. M> no
5. X> Y and 6 is M, Y!=M
6. M> no
7. M> no
8. X> Y and 9 is M, Y!=M
9. M> no
10. M> no
SWAP [ 3 4 , ]
1. Y
2. N
3. M
4. X
5. X
6. M
7. M
8. X
9. M
10. M

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. N> M and 3 is M, M==M remove 2 3
3. M> no
4. X> Y and 5 is X, Y!=X
5. X> Y and 6 is M, Y!=M
6. M> no
7. M> no
8. X> Y and 9 is M, Y!=M
9. M> no
10. M> no
REMOVE [ 2 3 , ]
1. Y
2. _
3. _
4. X
5. X
6. M
7. M
8. X
9. M
10. M

Cleanup removed
1. Y
2. X
3. X
4. M
5. M
6. X
7. M
8. M

Swap: consecutive pairs X M or N Y
1. Y> no
2. X> M and 3 is X, M!=X
3. X> M and 4 is M, M==M swap 3 4
4. M> no
5. M> no
6. X> Y and 7 is M, Y!=M
7. M> no
8. M> no
SWAP [ 3 4 , ]
1. Y
2. X
3. M
4. X
5. M
6. X
7. M
8. M

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. X> Y and 3 is M, Y!=M
3. M> no
4. X> Y and 5 is M, Y!=M
5. M> no
6. X> Y and 7 is M, Y!=M
7. M> no
8. M> no
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. X> M and 3 is M, M==M swap 2 3
3. M> no
4. X> Y and 5 is M, Y!=M
5. M> no
6. X> Y and 7 is M, Y!=M
7. M> no
8. M> no
SWAP [ 2 3 , ]
1. Y
2. M
3. X
4. X
5. M
6. X
7. M
8. M

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. M> no
3. X> Y and 4 is X, Y!=X
4. X> Y and 5 is M, Y!=M
5. M> no
6. X> Y and 7 is M, Y!=M
7. M> no
8. M> no
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. M> no
3. X> M and 4 is X, M!=X
4. X> M and 5 is M, M==M swap 4 5
5. M> no
6. X> Y and 7 is M, Y!=M
7. M> no
8. M> no
SWAP [ 4 5 , ]
1. Y
2. M
3. X
4. M
5. X
6. X
7. M
8. M

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. M> no
3. X> Y and 4 is M, Y!=M
4. M> no
5. X> Y and 6 is X, Y!=X
6. X> Y and 7 is M, Y!=M
7. M> no
8. M> no
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. M> no
3. X> M and 4 is M, M==M swap 3 4
4. M> no
5. X> Y and 6 is X, Y!=X
6. X> Y and 7 is M, Y!=M
7. M> no
8. M> no
SWAP [ 3 4 , ]
1. Y
2. M
3. M
4. X
5. X
6. X
7. M
8. M

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. M> no
3. M> no
4. X> Y and 5 is X, Y!=X
5. X> Y and 6 is X, Y!=X
6. X> Y and 7 is M, Y!=M
7. M> no
8. M> no
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. M> no
3. M> no
4. X> M and 5 is X, M!=X
5. X> M and 6 is X, M!=X
6. X> M and 7 is M, M==M swap 6 7
7. M> no
8. M> no
SWAP [ 6 7 , ]
1. Y
2. M
3. M
4. X
5. X
6. M
7. X
8. M

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. M> no
3. M> no
4. X> Y and 5 is X, Y!=X
5. X> Y and 6 is M, Y!=M
6. M> no
7. X> Y and 8 is M, Y!=M
8. M> no
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. M> no
3. M> no
4. X> M and 5 is X, M!=X
5. X> M and 6 is M, M==M swap 5 6
6. M> no
7. X> Y and 8 is M, Y!=M
8. M> no
SWAP [ 5 6 , ]
1. Y
2. M
3. M
4. X
5. M
6. X
7. X
8. M

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. M> no
3. M> no
4. X> Y and 5 is M, Y!=M
5. M> no
6. X> Y and 7 is X, Y!=X
7. X> Y and 8 is M, Y!=M
8. M> no
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. M> no
3. M> no
4. X> M and 5 is M, M==M swap 4 5
5. M> no
6. X> Y and 7 is X, Y!=X
7. X> Y and 8 is M, Y!=M
8. M> no
SWAP [ 4 5 , ]
1. Y
2. M
3. M
4. M
5. X
6. X
7. X
8. M

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. M> no
3. M> no
4. M> no
5. X> Y and 6 is X, Y!=X
6. X> Y and 7 is X, Y!=X
7. X> Y and 8 is M, Y!=M
8. M> no
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. M> no
3. M> no
4. M> no
5. X> M and 6 is X, M!=X
6. X> M and 7 is X, M!=X
7. X> M and 8 is M, M==M swap 7 8
8. M> no
SWAP [ 7 8 , ]
1. Y
2. M
3. M
4. M
5. X
6. X
7. M
8. X

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. M> no
3. M> no
4. M> no
5. X> Y and 6 is X, Y!=X
6. X> Y and 7 is M, Y!=M
7. M> no
8. X> Y and 9 is None, Y!=None
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. M> no
3. M> no
4. M> no
5. X> M and 6 is X, M!=X
6. X> M and 7 is M, M==M swap 6 7
7. M> no
8. X> Y and 9 is None, Y!=None
SWAP [ 6 7 , ]
1. Y
2. M
3. M
4. M
5. X
6. M
7. X
8. X

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. M> no
3. M> no
4. M> no
5. X> Y and 6 is M, Y!=M
6. M> no
7. X> Y and 8 is X, Y!=X
8. X> Y and 9 is None, Y!=None
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. M> no
3. M> no
4. M> no
5. X> M and 6 is M, M==M swap 5 6
6. M> no
7. X> Y and 8 is X, Y!=X
8. X> Y and 9 is None, Y!=None
SWAP [ 5 6 , ]
1. Y
2. M
3. M
4. M
5. M
6. X
7. X
8. X

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. M> no
3. M> no
4. M> no
5. M> no
6. X> Y and 7 is X, Y!=X
7. X> Y and 8 is X, Y!=X
8. X> Y and 9 is None, Y!=None
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. M> no
3. M> no
4. M> no
5. M> no
6. X> M and 7 is X, M!=X
7. X> M and 8 is X, M!=X
8. X> M and 9 is None, M!=None
no swap

Repeat if did cleanup or did swap: no

Final result
1. Y
2. M
3. M
4. M
5. M
6. X
7. X
8. X

Translate the tokens back
1. Y = #A
2. M = #B
3. M = #B
4. M = #B
5. M = #B
6. X = A#
7. X = A#
8. X = A#

Output the tokens
<solution>#A #B #B #B #B A# A# A#</solution>

AI-Solution: #A #B #B #B #B A# A# A# 

<<correct>>

## Instance 9:
Term: A# A# #B #B A# A# #B #B #B B# #A B# 
Norm: #B #B #B #B #B A# A# A# B# B# 
Rwts: 18
AI-RESPONSE:
Translate the tokens
1. X
2. X
3. M
4. M
5. X
6. X
7. M
8. M
9. M
10. N
11. Y
12. N

Remove: consecutive pairs X Y or N M
1. X> Y and 2 is X, Y!=X
2. X> Y and 3 is M, Y!=M
3. M> no
4. M> no
5. X> Y and 6 is X, Y!=X
6. X> Y and 7 is M, Y!=M
7. M> no
8. M> no
9. M> no
10. N> M and 11 is Y, M!=Y
11. Y> no
12. N> M and 13 is None, M!=None
no remove

Swap: consecutive pairs X M or N Y
1. X> M and 2 is X, M!=X
2. X> M and 3 is M, M==M swap 2 3
3. M> no
4. M> no
5. X> M and 6 is X, M!=X
6. X> M and 7 is M, M==M swap 6 7
7. M> no
8. M> no
9. M> no
10. N> Y and 11 is Y, Y==Y swap 10 11
11. Y> no
12. N> M and 13 is None, M!=None
SWAP [ 2 3 , 6 7 , 10 11 , ]
1. X
2. M
3. X
4. M
5. X
6. M
7. X
8. M
9. M
10. Y
11. N
12. N

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. X> Y and 2 is M, Y!=M
2. M> no
3. X> Y and 4 is M, Y!=M
4. M> no
5. X> Y and 6 is M, Y!=M
6. M> no
7. X> Y and 8 is M, Y!=M
8. M> no
9. M> no
10. Y> no
11. N> M and 12 is N, M!=N
12. N> M and 13 is None, M!=None
no remove

Swap: consecutive pairs X M or N Y
1. X> M and 2 is M, M==M swap 1 2
2. M> no
3. X> M and 4 is M, M==M swap 3 4
4. M> no
5. X> M and 6 is M, M==M swap 5 6
6. M> no
7. X> M and 8 is M, M==M swap 7 8
8. M> no
9. M> no
10. Y> no
11. N> Y and 12 is N, Y!=N
12. N> Y and 13 is None, Y!=None
SWAP [ 1 2 , 3 4 , 5 6 , 7 8 , ]
1. M
2. X
3. M
4. X
5. M
6. X
7. M
8. X
9. M
10. Y
11. N
12. N

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. M> no
2. X> Y and 3 is M, Y!=M
3. M> no
4. X> Y and 5 is M, Y!=M
5. M> no
6. X> Y and 7 is M, Y!=M
7. M> no
8. X> Y and 9 is M, Y!=M
9. M> no
10. Y> no
11. N> M and 12 is N, M!=N
12. N> M and 13 is None, M!=None
no remove

Swap: consecutive pairs X M or N Y
1. M> no
2. X> M and 3 is M, M==M swap 2 3
3. M> no
4. X> M and 5 is M, M==M swap 4 5
5. M> no
6. X> M and 7 is M, M==M swap 6 7
7. M> no
8. X> M and 9 is M, M==M swap 8 9
9. M> no
10. Y> no
11. N> Y and 12 is N, Y!=N
12. N> Y and 13 is None, Y!=None
SWAP [ 2 3 , 4 5 , 6 7 , 8 9 , ]
1. M
2. M
3. X
4. M
5. X
6. M
7. X
8. M
9. X
10. Y
11. N
12. N

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. M> no
2. M> no
3. X> Y and 4 is M, Y!=M
4. M> no
5. X> Y and 6 is M, Y!=M
6. M> no
7. X> Y and 8 is M, Y!=M
8. M> no
9. X> Y and 10 is Y, Y==Y remove 9 10
10. Y> no
11. N> M and 12 is N, M!=N
12. N> M and 13 is None, M!=None
REMOVE [ 9 10 , ]
1. M
2. M
3. X
4. M
5. X
6. M
7. X
8. M
9. _
10. _
11. N
12. N

Cleanup removed
1. M
2. M
3. X
4. M
5. X
6. M
7. X
8. M
9. N
10. N

Swap: consecutive pairs X M or N Y
1. M> no
2. M> no
3. X> M and 4 is M, M==M swap 3 4
4. M> no
5. X> M and 6 is M, M==M swap 5 6
6. M> no
7. X> M and 8 is M, M==M swap 7 8
8. M> no
9. N> Y and 10 is N, Y!=N
10. N> Y and 11 is None, Y!=None
SWAP [ 3 4 , 5 6 , 7 8 , ]
1. M
2. M
3. M
4. X
5. M
6. X
7. M
8. X
9. N
10. N

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. M> no
2. M> no
3. M> no
4. X> Y and 5 is M, Y!=M
5. M> no
6. X> Y and 7 is M, Y!=M
7. M> no
8. X> Y and 9 is N, Y!=N
9. N> M and 10 is N, M!=N
10. N> M and 11 is None, M!=None
no remove

Swap: consecutive pairs X M or N Y
1. M> no
2. M> no
3. M> no
4. X> M and 5 is M, M==M swap 4 5
5. M> no
6. X> M and 7 is M, M==M swap 6 7
7. M> no
8. X> M and 9 is N, M!=N
9. N> Y and 10 is N, Y!=N
10. N> Y and 11 is None, Y!=None
SWAP [ 4 5 , 6 7 , ]
1. M
2. M
3. M
4. M
5. X
6. M
7. X
8. X
9. N
10. N

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. M> no
2. M> no
3. M> no
4. M> no
5. X> Y and 6 is M, Y!=M
6. M> no
7. X> Y and 8 is X, Y!=X
8. X> Y and 9 is N, Y!=N
9. N> M and 10 is N, M!=N
10. N> M and 11 is None, M!=None
no remove

Swap: consecutive pairs X M or N Y
1. M> no
2. M> no
3. M> no
4. M> no
5. X> M and 6 is M, M==M swap 5 6
6. M> no
7. X> M and 8 is X, M!=X
8. X> M and 9 is N, M!=N
9. N> Y and 10 is N, Y!=N
10. N> Y and 11 is None, Y!=None
SWAP [ 5 6 , ]
1. M
2. M
3. M
4. M
5. M
6. X
7. X
8. X
9. N
10. N

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. M> no
2. M> no
3. M> no
4. M> no
5. M> no
6. X> Y and 7 is X, Y!=X
7. X> Y and 8 is X, Y!=X
8. X> Y and 9 is N, Y!=N
9. N> M and 10 is N, M!=N
10. N> M and 11 is None, M!=None
no remove

Swap: consecutive pairs X M or N Y
1. M> no
2. M> no
3. M> no
4. M> no
5. M> no
6. X> M and 7 is X, M!=X
7. X> M and 8 is X, M!=X
8. X> M and 9 is N, M!=N
9. N> Y and 10 is N, Y!=N
10. N> Y and 11 is None, Y!=None
no swap

Repeat if did cleanup or did swap: no

Final result
1. M
2. M
3. M
4. M
5. M
6. X
7. X
8. X
9. N
10. N

Translate the tokens back
1. M = #B
2. M = #B
3. M = #B
4. M = #B
5. M = #B
6. X = A#
7. X = A#
8. X = A#
9. N = B#
10. N = B#

Output the tokens
<solution>#B #B #B #B #B A# A# A# B# B#</solution>

AI-Solution: #B #B #B #B #B A# A# A# B# B# 

<<correct>>

## Instance 10:
Term: B# B# B# B# #A B# #A A# #A #A #B #A 
Norm: #A #A #A #A B# B# B# B# 
Rwts: 20
AI-RESPONSE:
Translate the tokens
1. N
2. N
3. N
4. N
5. Y
6. N
7. Y
8. X
9. Y
10. Y
11. M
12. Y

Remove: consecutive pairs X Y or N M
1. N> M and 2 is N, M!=N
2. N> M and 3 is N, M!=N
3. N> M and 4 is N, M!=N
4. N> M and 5 is Y, M!=Y
5. Y> no
6. N> M and 7 is Y, M!=Y
7. Y> no
8. X> Y and 9 is Y, Y==Y remove 8 9
9. Y> no
10. Y> no
11. M> no
12. Y> no
REMOVE [ 8 9 , ]
1. N
2. N
3. N
4. N
5. Y
6. N
7. Y
8. _
9. _
10. Y
11. M
12. Y

Cleanup removed
1. N
2. N
3. N
4. N
5. Y
6. N
7. Y
8. Y
9. M
10. Y

Swap: consecutive pairs X M or N Y
1. N> Y and 2 is N, Y!=N
2. N> Y and 3 is N, Y!=N
3. N> Y and 4 is N, Y!=N
4. N> Y and 5 is Y, Y==Y swap 4 5
5. Y> no
6. N> M and 7 is Y, M!=Y
7. Y> no
8. Y> no
9. M> no
10. Y> no
SWAP [ 4 5 , ]
1. N
2. N
3. N
4. Y
5. N
6. N
7. Y
8. Y
9. M
10. Y

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. N> M and 2 is N, M!=N
2. N> M and 3 is N, M!=N
3. N> M and 4 is Y, M!=Y
4. Y> no
5. N> M and 6 is N, M!=N
6. N> M and 7 is Y, M!=Y
7. Y> no
8. Y> no
9. M> no
10. Y> no
no remove

Swap: consecutive pairs X M or N Y
1. N> Y and 2 is N, Y!=N
2. N> Y and 3 is N, Y!=N
3. N> Y and 4 is Y, Y==Y swap 3 4
4. Y> no
5. N> M and 6 is N, M!=N
6. N> M and 7 is Y, M!=Y
7. Y> no
8. Y> no
9. M> no
10. Y> no
SWAP [ 3 4 , ]
1. N
2. N
3. Y
4. N
5. N
6. N
7. Y
8. Y
9. M
10. Y

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. N> M and 2 is N, M!=N
2. N> M and 3 is Y, M!=Y
3. Y> no
4. N> M and 5 is N, M!=N
5. N> M and 6 is N, M!=N
6. N> M and 7 is Y, M!=Y
7. Y> no
8. Y> no
9. M> no
10. Y> no
no remove

Swap: consecutive pairs X M or N Y
1. N> Y and 2 is N, Y!=N
2. N> Y and 3 is Y, Y==Y swap 2 3
3. Y> no
4. N> M and 5 is N, M!=N
5. N> M and 6 is N, M!=N
6. N> M and 7 is Y, M!=Y
7. Y> no
8. Y> no
9. M> no
10. Y> no
SWAP [ 2 3 , ]
1. N
2. Y
3. N
4. N
5. N
6. N
7. Y
8. Y
9. M
10. Y

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. N> M and 2 is Y, M!=Y
2. Y> no
3. N> M and 4 is N, M!=N
4. N> M and 5 is N, M!=N
5. N> M and 6 is N, M!=N
6. N> M and 7 is Y, M!=Y
7. Y> no
8. Y> no
9. M> no
10. Y> no
no remove

Swap: consecutive pairs X M or N Y
1. N> Y and 2 is Y, Y==Y swap 1 2
2. Y> no
3. N> M and 4 is N, M!=N
4. N> M and 5 is N, M!=N
5. N> M and 6 is N, M!=N
6. N> M and 7 is Y, M!=Y
7. Y> no
8. Y> no
9. M> no
10. Y> no
SWAP [ 1 2 , ]
1. Y
2. N
3. N
4. N
5. N
6. N
7. Y
8. Y
9. M
10. Y

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. N> M and 3 is N, M!=N
3. N> M and 4 is N, M!=N
4. N> M and 5 is N, M!=N
5. N> M and 6 is N, M!=N
6. N> M and 7 is Y, M!=Y
7. Y> no
8. Y> no
9. M> no
10. Y> no
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. N> Y and 3 is N, Y!=N
3. N> Y and 4 is N, Y!=N
4. N> Y and 5 is N, Y!=N
5. N> Y and 6 is N, Y!=N
6. N> Y and 7 is Y, Y==Y swap 6 7
7. Y> no
8. Y> no
9. M> no
10. Y> no
SWAP [ 6 7 , ]
1. Y
2. N
3. N
4. N
5. N
6. Y
7. N
8. Y
9. M
10. Y

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. N> M and 3 is N, M!=N
3. N> M and 4 is N, M!=N
4. N> M and 5 is N, M!=N
5. N> M and 6 is Y, M!=Y
6. Y> no
7. N> M and 8 is Y, M!=Y
8. Y> no
9. M> no
10. Y> no
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. N> Y and 3 is N, Y!=N
3. N> Y and 4 is N, Y!=N
4. N> Y and 5 is N, Y!=N
5. N> Y and 6 is Y, Y==Y swap 5 6
6. Y> no
7. N> M and 8 is Y, M!=Y
8. Y> no
9. M> no
10. Y> no
SWAP [ 5 6 , ]
1. Y
2. N
3. N
4. N
5. Y
6. N
7. N
8. Y
9. M
10. Y

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. N> M and 3 is N, M!=N
3. N> M and 4 is N, M!=N
4. N> M and 5 is Y, M!=Y
5. Y> no
6. N> M and 7 is N, M!=N
7. N> M and 8 is Y, M!=Y
8. Y> no
9. M> no
10. Y> no
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. N> Y and 3 is N, Y!=N
3. N> Y and 4 is N, Y!=N
4. N> Y and 5 is Y, Y==Y swap 4 5
5. Y> no
6. N> M and 7 is N, M!=N
7. N> Y and 8 is Y, Y==Y swap 7 8
8. Y> no
9. M> no
10. Y> no
SWAP [ 4 5 , 7 8 , ]
1. Y
2. N
3. N
4. Y
5. N
6. N
7. Y
8. N
9. M
10. Y

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. N> M and 3 is N, M!=N
3. N> M and 4 is Y, M!=Y
4. Y> no
5. N> M and 6 is N, M!=N
6. N> M and 7 is Y, M!=Y
7. Y> no
8. N> M and 9 is M, M==M remove 8 9
9. M> no
10. Y> no
REMOVE [ 8 9 , ]
1. Y
2. N
3. N
4. Y
5. N
6. N
7. Y
8. _
9. _
10. Y

Cleanup removed
1. Y
2. N
3. N
4. Y
5. N
6. N
7. Y
8. Y

Swap: consecutive pairs X M or N Y
1. Y> no
2. N> Y and 3 is N, Y!=N
3. N> Y and 4 is Y, Y==Y swap 3 4
4. Y> no
5. N> M and 6 is N, M!=N
6. N> Y and 7 is Y, Y==Y swap 6 7
7. Y> no
8. Y> no
SWAP [ 3 4 , 6 7 , ]
1. Y
2. N
3. Y
4. N
5. N
6. Y
7. N
8. Y

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. N> M and 3 is Y, M!=Y
3. Y> no
4. N> M and 5 is N, M!=N
5. N> M and 6 is Y, M!=Y
6. Y> no
7. N> M and 8 is Y, M!=Y
8. Y> no
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. N> Y and 3 is Y, Y==Y swap 2 3
3. Y> no
4. N> M and 5 is N, M!=N
5. N> Y and 6 is Y, Y==Y swap 5 6
6. Y> no
7. N> Y and 8 is Y, Y==Y swap 7 8
8. Y> no
SWAP [ 2 3 , 5 6 , 7 8 , ]
1. Y
2. Y
3. N
4. N
5. Y
6. N
7. Y
8. N

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. Y> no
3. N> M and 4 is N, M!=N
4. N> M and 5 is Y, M!=Y
5. Y> no
6. N> M and 7 is Y, M!=Y
7. Y> no
8. N> M and 9 is None, M!=None
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. Y> no
3. N> Y and 4 is N, Y!=N
4. N> Y and 5 is Y, Y==Y swap 4 5
5. Y> no
6. N> Y and 7 is Y, Y==Y swap 6 7
7. Y> no
8. N> Y and 9 is None, Y!=None
SWAP [ 4 5 , 6 7 , ]
1. Y
2. Y
3. N
4. Y
5. N
6. Y
7. N
8. N

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. Y> no
3. N> M and 4 is Y, M!=Y
4. Y> no
5. N> M and 6 is Y, M!=Y
6. Y> no
7. N> M and 8 is N, M!=N
8. N> M and 9 is None, M!=None
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. Y> no
3. N> Y and 4 is Y, Y==Y swap 3 4
4. Y> no
5. N> Y and 6 is Y, Y==Y swap 5 6
6. Y> no
7. N> Y and 8 is N, Y!=N
8. N> Y and 9 is None, Y!=None
SWAP [ 3 4 , 5 6 , ]
1. Y
2. Y
3. Y
4. N
5. Y
6. N
7. N
8. N

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. Y> no
3. Y> no
4. N> M and 5 is Y, M!=Y
5. Y> no
6. N> M and 7 is N, M!=N
7. N> M and 8 is N, M!=N
8. N> M and 9 is None, M!=None
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. Y> no
3. Y> no
4. N> Y and 5 is Y, Y==Y swap 4 5
5. Y> no
6. N> Y and 7 is N, Y!=N
7. N> Y and 8 is N, Y!=N
8. N> Y and 9 is None, Y!=None
SWAP [ 4 5 , ]
1. Y
2. Y
3. Y
4. Y
5. N
6. N
7. N
8. N

Final result
1. Y
2. Y
3. Y
4. Y
5. N
6. N
7. N
8. N

Translate the tokens back
1. Y = #A
2. Y = #A
3. Y = #A
4. Y = #A
5. N = B#
6. N = B#
7. N = B#
8. N = B#

Output the tokens
<solution>#A #A #A #A B# B# B# B#</solution>

AI-Solution: #A #A #A #A B# B# B# B# 

<<correct>>

## Instance 11:
Term: B# B# #A B# B# B# B# #A #A B# #A #B 
Norm: #A #A #A #A B# B# B# B# B# B# 
Rwts: 22
AI-RESPONSE:
Translate the tokens
1. N
2. N
3. Y
4. N
5. N
6. N
7. N
8. Y
9. Y
10. N
11. Y
12. M

Remove: consecutive pairs X Y or N M
1. N> M and 2 is N, M!=N
2. N> M and 3 is Y, M!=Y
3. Y> no
4. N> M and 5 is N, M!=N
5. N> M and 6 is N, M!=N
6. N> M and 7 is N, M!=N
7. N> M and 8 is Y, M!=Y
8. Y> no
9. Y> no
10. N> M and 11 is Y, M!=Y
11. Y> no
12. M> no
no remove

Swap: consecutive pairs X M or N Y
1. N> Y and 2 is N, Y!=N
2. N> Y and 3 is Y, Y==Y swap 2 3
3. Y> no
4. N> Y and 5 is N, Y!=N
5. N> Y and 6 is N, Y!=N
6. N> Y and 7 is N, Y!=N
7. N> Y and 8 is Y, Y==Y swap 7 8
8. Y> no
9. Y> no
10. N> Y and 11 is Y, Y==Y swap 10 11
11. Y> no
12. M> no
SWAP [ 2 3 , 7 8 , 10 11 , ]
1. N
2. Y
3. N
4. N
5. N
6. N
7. Y
8. N
9. Y
10. Y
11. N
12. M

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. N> M and 2 is Y, M!=Y
2. Y> no
3. N> M and 4 is N, M!=N
4. N> M and 5 is N, M!=N
5. N> M and 6 is N, M!=N
6. N> M and 7 is Y, M!=Y
7. Y> no
8. N> M and 9 is Y, M!=Y
9. Y> no
10. Y> no
11. N> M and 12 is M, M==M remove 11 12
REMOVE [ 11 12 , ]
1. N
2. Y
3. N
4. N
5. N
6. N
7. Y
8. N
9. Y
10. Y

Cleanup removed
1. N
2. Y
3. N
4. N
5. N
6. N
7. Y
8. N
9. Y

Swap: consecutive pairs X M or N Y
1. N> Y and 2 is Y, Y==Y swap 1 2
2. Y> no
3. N> Y and 4 is N, Y!=N
4. N> Y and 5 is N, Y!=N
5. N> Y and 6 is N, Y!=N
6. N> Y and 7 is Y, Y==Y swap 6 7
7. Y> no
8. N> Y and 9 is Y, Y==Y swap 8 9
9. Y> no
SWAP [ 1 2 , 6 7 , 8 9 , ]
1. Y
2. N
3. N
4. N
5. N
6. Y
7. N
8. Y
9. N

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. N> M and 3 is N, M!=N
3. N> M and 4 is N, M!=N
4. N> M and 5 is N, M!=N
5. N> M and 6 is Y, M!=Y
6. Y> no
7. N> M and 8 is Y, M!=Y
8. Y> no
9. N> M and 10 is None, M!=None
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. N> Y and 3 is N, Y!=N
3. N> Y and 4 is N, Y!=N
4. N> Y and 5 is N, Y!=N
5. N> Y and 6 is Y, Y==Y swap 5 6
6. Y> no
7. N> Y and 8 is Y, Y==Y swap 7 8
8. Y> no
9. N> Y and 10 is None, Y!=None
SWAP [ 5 6 , 7 8 , ]
1. Y
2. N
3. N
4. N
5. Y
6. N
7. Y
8. N

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. N> M and 3 is N, M!=N
3. N> M and 4 is N, M!=N
4. N> M and 5 is Y, M!=Y
5. Y> no
6. N> M and 7 is Y, M!=Y
7. Y> no
8. N> M and 9 is None, M!=None
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. N> Y and 3 is N, Y!=N
3. N> Y and 4 is N, Y!=N
4. N> Y and 5 is Y, Y==Y swap 4 5
5. Y> no
6. N> Y and 7 is Y, Y==Y swap 6 7
7. Y> no
8. N> Y and 9 is None, Y!=None
SWAP [ 4 5 , 6 7 , ]
1. Y
2. N
3. N
4. Y
5. N
6. Y
7. N

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. N> M and 3 is N, M!=N
3. N> M and 4 is Y, M!=Y
4. Y> no
5. N> M and 6 is Y, M!=Y
6. Y> no
7. N> M and 8 is None, M!=None
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. N> Y and 3 is N, Y!=N
3. N> Y and 4 is Y, Y==Y swap 3 4
4. Y> no
5. N> Y and 6 is Y, Y==Y swap 5 6
6. Y> no
7. N> Y and 8 is None, Y!=None
SWAP [ 3 4 , 5 6 , ]
1. Y
2. N
3. Y
4. N
5. Y
6. N

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. N> M and 3 is Y, M!=Y
3. Y> no
4. N> M and 5 is Y, M!=Y
5. Y> no
6. N> M and 7 is None, M!=None
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. N> Y and 3 is Y, Y==Y swap 2 3
3. Y> no
4. N> Y and 5 is Y, Y==Y swap 4 5
5. Y> no
6. N> Y and 7 is None, Y!=None
SWAP [ 2 3 , 4 5 , ]
1. Y
2. Y
3. N
4. Y
5. N

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. Y> no
3. N> M and 4 is Y, M!=Y
4. Y> no
5. N> M and 6 is None, M!=None
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. Y> no
3. N> Y and 4 is Y, Y==Y swap 3 4
4. Y> no
5. N> Y and 6 is None, Y!=None
SWAP [ 3 4 , ]
1. Y
2. Y
3. Y
4. N
5. N

Repeat if did cleanup or did swap: yes

Remove: consecutive pairs X Y or N M
1. Y> no
2. Y> no
3. Y> no
4. N> M and 5 is N, M!=N
5. N> M and 6 is None, M!=None
no remove

Swap: consecutive pairs X M or N Y
1. Y> no
2. Y> no
3. Y> no
4. N> Y and 5 is N, Y!=N
5. N> Y and 6 is None, Y!=None
no swap

Repeat if did cleanup or did swap: no

Final result
1. Y
2. Y
3. Y
4. N
5. N

Translate the tokens back
1. Y = #A
2. Y = #A
3. Y = #A
4. N = B#
5. N = B#

Output the tokens
<solution>#A #A #A B# B#</solution>

AI-Solution: #A #A #A B# B# 

<<incorrect>>


Final score: 11 / 12