gistfile1.txt

Assistant is a Careful and Predictable Step by Step Instruction Template Format Following MODE Today.

You will be solving a string replacement logical puzzle where you apply transformations to a List of Tokens to get New List of Tokens until the Rules no longer creates a New Unique List.

Tokens
- "A#"
- "#A"
- "#B"
- "B#"

Tokens with Numbers Example
- "A#(10)"
- "#A(3)"
- "#B(2)"
- "B#(12)"

NOTE: ONLY Respond with VALID Tokens

# Rules:
RULE:A# #A →
RULE:A# #B → #B A#
RULE:B# #A → #A B#
RULE:B# #B →
RULE:#A #A → #A
RULE:#A A# → #A
RULE:#A B# → #A
RULE:#A #B → #A
RULE:A# A# → A#
RULE:A# B# → A#
RULE:B# A# → B#
RULE:B# B# → B#
RULE:#B #A → #B
RULE:#B A# → #B
RULE:#B B# → #B
RULE:#B #B → #B
RULE:#B → #B
RULE:#A → #A
RULE:A# → A#
RULE:A# → A#

NOTE:
RULE:B# #B →
RULE:A# #A →
Is literally NOTHING not even a Space

OLD TOKENS -> NEW TOKENS

Guide For EVERY STEP
# PASS Guide
1. This is where you take Pairs of Tokens and Copy the Rule Basically
2. For rules:
RULE:A# #A → NOTHING
NEXT INDEX:+2
RULE:A# #B → #B A#
NEXT INDEX:+2
RULE:B# #A → #A B#
NEXT INDEX:+2
RULE:B# #B → NOTHING
NEXT INDEX:+2
RULE:EVERY OTHER RULE -> FIRST TOKEN
NEXT INDEX:+1


# GATHER NEW TOKENS Guide
1. This is Where you Get the New Tokens. Basically Everything After →.
2. Be SURE to Ignore the NOTHING Meaning Literally NOTHING
3. Remember to Keep TWO Separate Counts for the the OLD TOKEN and the NEW TOKENs starting from 1 Known as "OLD COUNT" and "NEW COUNT"
4. AGAIN ALWAYS Start the Count from 1 for OLD TOKENs and NEW TOKENs



# EXACT SAME STRING PREV Guide
1. This is Where Check if the String is the Same so you can just go to "# Tokens Without Numbers" then Submit your Solution inside of <solution></solution>
2. Compare the Two Previous # GATHER NEW TOKENS to Make COMPLETELY SURE They are EXACTLY the SAME



<EXAMPLE 1>
<problem>#A B# #B #B #B #A A# B# #B A# #A #B</problem>

# List Out
1. #A
2. B#
3. #B
4. #B
5. #B
6. #A
7. A#
8. B#
9. #B
10. A#
11. #A
12. #B



# NEW TOKENS:
#A(1) B#(2) #B(3) #B(4) #B(5) #A(6) A#(7) B#(8) #B(9) A#(10) #A(11) #B(12) 

# EXACT SAME STRING PREV:NO



# PASS 1:
NEXT INDEX:1:WITHIN
#A(1) B#(2):RULE:#A B# → #A(1)
NEXT INDEX:2:WITHIN
B#(2) #B(3):RULE:B# #B →
NEXT INDEX:4:WITHIN
#B(4) #B(5):RULE:#B #B → #B(2)
NEXT INDEX:5:WITHIN
#B(5) #A(6):RULE:#B #A → #B(3)
NEXT INDEX:6:WITHIN
#A(6) A#(7):RULE:#A A# → #A(4)
NEXT INDEX:7:WITHIN
A#(7) B#(8):RULE:A# B# → A#(5)
NEXT INDEX:8:WITHIN
B#(8) #B(9):RULE:B# #B →
NEXT INDEX:10:WITHIN
A#(10) #A(11):RULE:A# #A →
NEXT INDEX:12:WITHIN
#B(12):RULE:#B → #B(6)
NEXT INDEX:13:OVERFLOW



# GATHER NEW TOKENS:
#A(1) #B(2) #B(3) #A(4) A#(5) #B(6) 

# EXACT SAME STRING PREV:NO

# PASS 2:
NEXT INDEX:1:WITHIN
#A(1) #B(2):RULE:#A #B → #A(1)
NEXT INDEX:2:WITHIN
#B(2) #B(3):RULE:#B #B → #B(2)
NEXT INDEX:3:WITHIN
#B(3) #A(4):RULE:#B #A → #B(3)
NEXT INDEX:4:WITHIN
#A(4) A#(5):RULE:#A A# → #A(4)
NEXT INDEX:5:WITHIN
A#(5) #B(6):RULE:A# #B → #B(5) A#(6)
NEXT INDEX:7:OVERFLOW



# GATHER NEW TOKENS:
#A(1) #B(2) #B(3) #A(4) #B(5) A#(6) 

# EXACT SAME STRING PREV:NO

# PASS 3:
NEXT INDEX:1:WITHIN
#A(1) #B(2):RULE:#A #B → #A(1)
NEXT INDEX:2:WITHIN
#B(2) #B(3):RULE:#B #B → #B(2)
NEXT INDEX:3:WITHIN
#B(3) #A(4):RULE:#B #A → #B(3)
NEXT INDEX:4:WITHIN
#A(4) #B(5):RULE:#A #B → #A(4)
NEXT INDEX:5:WITHIN
#B(5) A#(6):RULE:#B A# → #B(5)
NEXT INDEX:6:WITHIN
A#(6):RULE:A# → A#(6)
NEXT INDEX:7:OVERFLOW



# GATHER NEW TOKENS:
#A(1) #B(2) #B(3) #A(4) #B(5) A#(6) 

# EXACT SAME STRING PREV:YES

# Tokens Without Numbers:
#A #B #B #A #B A#

# Solution:
<solution>#A #B #B #A #B A#</solution>
</EXAMPLE 1>


<EXAMPLE 2>
<problem>#B A# B# B# #A A# A# #B B# #A #B A#</problem>

# List Out
1. #B
2. A#
3. B#
4. B#
5. #A
6. A#
7. A#
8. #B
9. B#
10. #A
11. #B
12. A#



# NEW TOKENS:
#B(1) A#(2) B#(3) B#(4) #A(5) A#(6) A#(7) #B(8) B#(9) #A(10) #B(11) A#(12) 

# EXACT SAME STRING PREV:NO



# PASS 1:
NEXT INDEX:1:WITHIN
#B(1) A#(2):RULE:#B A# → #B(1)
NEXT INDEX:2:WITHIN
A#(2) B#(3):RULE:A# B# → A#(2)
NEXT INDEX:3:WITHIN
B#(3) B#(4):RULE:B# B# → B#(3)
NEXT INDEX:4:WITHIN
B#(4) #A(5):RULE:B# #A → #A(4) B#(5)
NEXT INDEX:6:WITHIN
A#(6) A#(7):RULE:A# A# → A#(6)
NEXT INDEX:7:WITHIN
A#(7) #B(8):RULE:A# #B → #B(7) A#(8)
NEXT INDEX:9:WITHIN
B#(9) #A(10):RULE:B# #A → #A(9) B#(10)
NEXT INDEX:11:WITHIN
#B(11) A#(12):RULE:#B A# → #B(11)
NEXT INDEX:12:WITHIN
A#(12):RULE:A# → A#(12)
NEXT INDEX:13:OVERFLOW



# GATHER NEW TOKENS:
#B(1) A#(2) B#(3) #A(4) B#(5) A#(6) #B(7) A#(8) #A(9) B#(10) #B(11) A#(12) 

# EXACT SAME STRING PREV:NO

# PASS 2:
NEXT INDEX:1:WITHIN
#B(1) A#(2):RULE:#B A# → #B(1)
NEXT INDEX:2:WITHIN
A#(2) B#(3):RULE:A# B# → A#(2)
NEXT INDEX:3:WITHIN
B#(3) #A(4):RULE:B# #A → #A(3) B#(4)
NEXT INDEX:5:WITHIN
B#(5) A#(6):RULE:B# A# → B#(5)
NEXT INDEX:6:WITHIN
A#(6) #B(7):RULE:A# #B → #B(6) A#(7)
NEXT INDEX:8:WITHIN
A#(8) #A(9):RULE:A# #A →
NEXT INDEX:10:WITHIN
B#(10) #B(11):RULE:B# #B →
NEXT INDEX:12:WITHIN
A#(12):RULE:A# → A#(8)
NEXT INDEX:13:OVERFLOW



# GATHER NEW TOKENS:
#B(1) A#(2) #A(3) B#(4) B#(5) #B(6) A#(7) A#(8) 

# EXACT SAME STRING PREV:NO

# PASS 3:
NEXT INDEX:1:WITHIN
#B(1) A#(2):RULE:#B A# → #B(1)
NEXT INDEX:2:WITHIN
A#(2) #A(3):RULE:A# #A →
NEXT INDEX:4:WITHIN
B#(4) B#(5):RULE:B# B# → B#(2)
NEXT INDEX:5:WITHIN
B#(5) #B(6):RULE:B# #B →
NEXT INDEX:7:WITHIN
A#(7) A#(8):RULE:A# A# → A#(3)
NEXT INDEX:8:WITHIN
A#(8):RULE:A# → A#(4)
NEXT INDEX:9:OVERFLOW



# GATHER NEW TOKENS:
#B(1) B#(2) A#(3) A#(4) 

# EXACT SAME STRING PREV:NO

# PASS 4:
NEXT INDEX:1:WITHIN
#B(1) B#(2):RULE:#B B# → #B(1)
NEXT INDEX:2:WITHIN
B#(2) A#(3):RULE:B# A# → B#(2)
NEXT INDEX:3:WITHIN
A#(3) A#(4):RULE:A# A# → A#(3)
NEXT INDEX:4:WITHIN
A#(4):RULE:A# → A#(4)
NEXT INDEX:5:OVERFLOW



# GATHER NEW TOKENS:
#B(1) B#(2) A#(3) A#(4) 

# EXACT SAME STRING PREV:YES

# Tokens Without Numbers:
#B B# A# A#

# Solution:
<solution>#B B# A# A#</solution>
</EXAMPLE 2>


<EXAMPLE 3>
<problem>B# B# B# #A B# #A #A B# #A A# B# #B</problem>

# List Out
1. B#
2. B#
3. B#
4. #A
5. B#
6. #A
7. #A
8. B#
9. #A
10. A#
11. B#
12. #B



# NEW TOKENS:
B#(1) B#(2) B#(3) #A(4) B#(5) #A(6) #A(7) B#(8) #A(9) A#(10) B#(11) #B(12) 

# EXACT SAME STRING PREV:NO



# PASS 1:
NEXT INDEX:1:WITHIN
B#(1) B#(2):RULE:B# B# → B#(1)
NEXT INDEX:2:WITHIN
B#(2) B#(3):RULE:B# B# → B#(2)
NEXT INDEX:3:WITHIN
B#(3) #A(4):RULE:B# #A → #A(3) B#(4)
NEXT INDEX:5:WITHIN
B#(5) #A(6):RULE:B# #A → #A(5) B#(6)
NEXT INDEX:7:WITHIN
#A(7) B#(8):RULE:#A B# → #A(7)
NEXT INDEX:8:WITHIN
B#(8) #A(9):RULE:B# #A → #A(8) B#(9)
NEXT INDEX:10:WITHIN
A#(10) B#(11):RULE:A# B# → A#(10)
NEXT INDEX:11:WITHIN
B#(11) #B(12):RULE:B# #B →
NEXT INDEX:13:OVERFLOW



# GATHER NEW TOKENS:
B#(1) B#(2) #A(3) B#(4) #A(5) B#(6) #A(7) #A(8) B#(9) A#(10) 

# EXACT SAME STRING PREV:NO

# PASS 2:
NEXT INDEX:1:WITHIN
B#(1) B#(2):RULE:B# B# → B#(1)
NEXT INDEX:2:WITHIN
B#(2) #A(3):RULE:B# #A → #A(2) B#(3)
NEXT INDEX:4:WITHIN
B#(4) #A(5):RULE:B# #A → #A(4) B#(5)
NEXT INDEX:6:WITHIN
B#(6) #A(7):RULE:B# #A → #A(6) B#(7)
NEXT INDEX:8:WITHIN
#A(8) B#(9):RULE:#A B# → #A(8)
NEXT INDEX:9:WITHIN
B#(9) A#(10):RULE:B# A# → B#(9)
NEXT INDEX:10:WITHIN
A#(10):RULE:A# → A#(10)
NEXT INDEX:11:OVERFLOW



# GATHER NEW TOKENS:
B#(1) #A(2) B#(3) #A(4) B#(5) #A(6) B#(7) #A(8) B#(9) A#(10) 

# EXACT SAME STRING PREV:NO

# PASS 3:
NEXT INDEX:1:WITHIN
B#(1) #A(2):RULE:B# #A → #A(1) B#(2)
NEXT INDEX:3:WITHIN
B#(3) #A(4):RULE:B# #A → #A(3) B#(4)
NEXT INDEX:5:WITHIN
B#(5) #A(6):RULE:B# #A → #A(5) B#(6)
NEXT INDEX:7:WITHIN
B#(7) #A(8):RULE:B# #A → #A(7) B#(8)
NEXT INDEX:9:WITHIN
B#(9) A#(10):RULE:B# A# → B#(9)
NEXT INDEX:10:WITHIN
A#(10):RULE:A# → A#(10)
NEXT INDEX:11:OVERFLOW



# GATHER NEW TOKENS:
#A(1) B#(2) #A(3) B#(4) #A(5) B#(6) #A(7) B#(8) B#(9) A#(10) 

# EXACT SAME STRING PREV:NO

# PASS 4:
NEXT INDEX:1:WITHIN
#A(1) B#(2):RULE:#A B# → #A(1)
NEXT INDEX:2:WITHIN
B#(2) #A(3):RULE:B# #A → #A(2) B#(3)
NEXT INDEX:4:WITHIN
B#(4) #A(5):RULE:B# #A → #A(4) B#(5)
NEXT INDEX:6:WITHIN
B#(6) #A(7):RULE:B# #A → #A(6) B#(7)
NEXT INDEX:8:WITHIN
B#(8) B#(9):RULE:B# B# → B#(8)
NEXT INDEX:9:WITHIN
B#(9) A#(10):RULE:B# A# → B#(9)
NEXT INDEX:10:WITHIN
A#(10):RULE:A# → A#(10)
NEXT INDEX:11:OVERFLOW



# GATHER NEW TOKENS:
#A(1) #A(2) B#(3) #A(4) B#(5) #A(6) B#(7) B#(8) B#(9) A#(10) 

# EXACT SAME STRING PREV:NO

# PASS 5:
NEXT INDEX:1:WITHIN
#A(1) #A(2):RULE:#A #A → #A(1)
NEXT INDEX:2:WITHIN
#A(2) B#(3):RULE:#A B# → #A(2)
NEXT INDEX:3:WITHIN
B#(3) #A(4):RULE:B# #A → #A(3) B#(4)
NEXT INDEX:5:WITHIN
B#(5) #A(6):RULE:B# #A → #A(5) B#(6)
NEXT INDEX:7:WITHIN
B#(7) B#(8):RULE:B# B# → B#(7)
NEXT INDEX:8:WITHIN
B#(8) B#(9):RULE:B# B# → B#(8)
NEXT INDEX:9:WITHIN
B#(9) A#(10):RULE:B# A# → B#(9)
NEXT INDEX:10:WITHIN
A#(10):RULE:A# → A#(10)
NEXT INDEX:11:OVERFLOW



# GATHER NEW TOKENS:
#A(1) #A(2) #A(3) B#(4) #A(5) B#(6) B#(7) B#(8) B#(9) A#(10) 

# EXACT SAME STRING PREV:NO

# PASS 6:
NEXT INDEX:1:WITHIN
#A(1) #A(2):RULE:#A #A → #A(1)
NEXT INDEX:2:WITHIN
#A(2) #A(3):RULE:#A #A → #A(2)
NEXT INDEX:3:WITHIN
#A(3) B#(4):RULE:#A B# → #A(3)
NEXT INDEX:4:WITHIN
B#(4) #A(5):RULE:B# #A → #A(4) B#(5)
NEXT INDEX:6:WITHIN
B#(6) B#(7):RULE:B# B# → B#(6)
NEXT INDEX:7:WITHIN
B#(7) B#(8):RULE:B# B# → B#(7)
NEXT INDEX:8:WITHIN
B#(8) B#(9):RULE:B# B# → B#(8)
NEXT INDEX:9:WITHIN
B#(9) A#(10):RULE:B# A# → B#(9)
NEXT INDEX:10:WITHIN
A#(10):RULE:A# → A#(10)
NEXT INDEX:11:OVERFLOW



# GATHER NEW TOKENS:
#A(1) #A(2) #A(3) #A(4) B#(5) B#(6) B#(7) B#(8) B#(9) A#(10) 

# EXACT SAME STRING PREV:NO

# PASS 7:
NEXT INDEX:1:WITHIN
#A(1) #A(2):RULE:#A #A → #A(1)
NEXT INDEX:2:WITHIN
#A(2) #A(3):RULE:#A #A → #A(2)
NEXT INDEX:3:WITHIN
#A(3) #A(4):RULE:#A #A → #A(3)
NEXT INDEX:4:WITHIN
#A(4) B#(5):RULE:#A B# → #A(4)
NEXT INDEX:5:WITHIN
B#(5) B#(6):RULE:B# B# → B#(5)
NEXT INDEX:6:WITHIN
B#(6) B#(7):RULE:B# B# → B#(6)
NEXT INDEX:7:WITHIN
B#(7) B#(8):RULE:B# B# → B#(7)
NEXT INDEX:8:WITHIN
B#(8) B#(9):RULE:B# B# → B#(8)
NEXT INDEX:9:WITHIN
B#(9) A#(10):RULE:B# A# → B#(9)
NEXT INDEX:10:WITHIN
A#(10):RULE:A# → A#(10)
NEXT INDEX:11:OVERFLOW



# GATHER NEW TOKENS:
#A(1) #A(2) #A(3) #A(4) B#(5) B#(6) B#(7) B#(8) B#(9) A#(10) 

# EXACT SAME STRING PREV:YES

# Tokens Without Numbers:
#A #A #A #A B# B# B# B# B# A#

# Solution:
<solution>#A #A #A #A B# B# B# B# B# A#</solution>
</EXAMPLE 3>


<EXAMPLE 4>
<problem>A# B# #A A# B# #B A# B# #A #A #A A#</problem>

# List Out
1. A#
2. B#
3. #A
4. A#
5. B#
6. #B
7. A#
8. B#
9. #A
10. #A
11. #A
12. A#



# NEW TOKENS:
A#(1) B#(2) #A(3) A#(4) B#(5) #B(6) A#(7) B#(8) #A(9) #A(10) #A(11) A#(12) 

# EXACT SAME STRING PREV:NO



# PASS 1:
NEXT INDEX:1:WITHIN
A#(1) B#(2):RULE:A# B# → A#(1)
NEXT INDEX:2:WITHIN
B#(2) #A(3):RULE:B# #A → #A(2) B#(3)
NEXT INDEX:4:WITHIN
A#(4) B#(5):RULE:A# B# → A#(4)
NEXT INDEX:5:WITHIN
B#(5) #B(6):RULE:B# #B →
NEXT INDEX:7:WITHIN
A#(7) B#(8):RULE:A# B# → A#(5)
NEXT INDEX:8:WITHIN
B#(8) #A(9):RULE:B# #A → #A(6) B#(7)
NEXT INDEX:10:WITHIN
#A(10) #A(11):RULE:#A #A → #A(8)
NEXT INDEX:11:WITHIN
#A(11) A#(12):RULE:#A A# → #A(9)
NEXT INDEX:12:WITHIN
A#(12):RULE:A# → A#(10)
NEXT INDEX:13:OVERFLOW



# GATHER NEW TOKENS:
A#(1) #A(2) B#(3) A#(4) A#(5) #A(6) B#(7) #A(8) #A(9) A#(10) 

# EXACT SAME STRING PREV:NO

# PASS 2:
NEXT INDEX:1:WITHIN
A#(1) #A(2):RULE:A# #A →
NEXT INDEX:3:WITHIN
B#(3) A#(4):RULE:B# A# → B#(1)
NEXT INDEX:4:WITHIN
A#(4) A#(5):RULE:A# A# → A#(2)
NEXT INDEX:5:WITHIN
A#(5) #A(6):RULE:A# #A →
NEXT INDEX:7:WITHIN
B#(7) #A(8):RULE:B# #A → #A(3) B#(4)
NEXT INDEX:9:WITHIN
#A(9) A#(10):RULE:#A A# → #A(5)
NEXT INDEX:10:WITHIN
A#(10):RULE:A# → A#(6)
NEXT INDEX:11:OVERFLOW



# GATHER NEW TOKENS:
B#(1) A#(2) #A(3) B#(4) #A(5) A#(6) 

# EXACT SAME STRING PREV:NO

# PASS 3:
NEXT INDEX:1:WITHIN
B#(1) A#(2):RULE:B# A# → B#(1)
NEXT INDEX:2:WITHIN
A#(2) #A(3):RULE:A# #A →
NEXT INDEX:4:WITHIN
B#(4) #A(5):RULE:B# #A → #A(2) B#(3)
NEXT INDEX:6:WITHIN
A#(6):RULE:A# → A#(4)
NEXT INDEX:7:OVERFLOW



# GATHER NEW TOKENS:
B#(1) #A(2) B#(3) A#(4) 

# EXACT SAME STRING PREV:NO

# PASS 4:
NEXT INDEX:1:WITHIN
B#(1) #A(2):RULE:B# #A → #A(1) B#(2)
NEXT INDEX:3:WITHIN
B#(3) A#(4):RULE:B# A# → B#(3)
NEXT INDEX:4:WITHIN
A#(4):RULE:A# → A#(4)
NEXT INDEX:5:OVERFLOW



# GATHER NEW TOKENS:
#A(1) B#(2) B#(3) A#(4) 

# EXACT SAME STRING PREV:NO

# PASS 5:
NEXT INDEX:1:WITHIN
#A(1) B#(2):RULE:#A B# → #A(1)
NEXT INDEX:2:WITHIN
B#(2) B#(3):RULE:B# B# → B#(2)
NEXT INDEX:3:WITHIN
B#(3) A#(4):RULE:B# A# → B#(3)
NEXT INDEX:4:WITHIN
A#(4):RULE:A# → A#(4)
NEXT INDEX:5:OVERFLOW



# GATHER NEW TOKENS:
#A(1) B#(2) B#(3) A#(4) 

# EXACT SAME STRING PREV:YES

# Tokens Without Numbers:
#A B# B# A#

# Solution:
<solution>#A B# B# A#</solution>
</EXAMPLE 4>


<EXAMPLE 5>
<problem>A# #A #A A# #B #A B# B# #B #A A# B#</problem>

# List Out
1. A#
2. #A
3. #A
4. A#
5. #B
6. #A
7. B#
8. B#
9. #B
10. #A
11. A#
12. B#



# NEW TOKENS:
A#(1) #A(2) #A(3) A#(4) #B(5) #A(6) B#(7) B#(8) #B(9) #A(10) A#(11) B#(12) 

# EXACT SAME STRING PREV:NO



# PASS 1:
NEXT INDEX:1:WITHIN
A#(1) #A(2):RULE:A# #A →
NEXT INDEX:3:WITHIN
#A(3) A#(4):RULE:#A A# → #A(1)
NEXT INDEX:4:WITHIN
A#(4) #B(5):RULE:A# #B → #B(2) A#(3)
NEXT INDEX:6:WITHIN
#A(6) B#(7):RULE:#A B# → #A(4)
NEXT INDEX:7:WITHIN
B#(7) B#(8):RULE:B# B# → B#(5)
NEXT INDEX:8:WITHIN
B#(8) #B(9):RULE:B# #B →
NEXT INDEX:10:WITHIN
#A(10) A#(11):RULE:#A A# → #A(6)
NEXT INDEX:11:WITHIN
A#(11) B#(12):RULE:A# B# → A#(7)
NEXT INDEX:12:WITHIN
B#(12):RULE:B# → B#(8)
NEXT INDEX:13:OVERFLOW



# GATHER NEW TOKENS:
#A(1) #B(2) A#(3) #A(4) B#(5) #A(6) A#(7) B#(8) 

# EXACT SAME STRING PREV:NO

# PASS 2:
NEXT INDEX:1:WITHIN
#A(1) #B(2):RULE:#A #B → #A(1)
NEXT INDEX:2:WITHIN
#B(2) A#(3):RULE:#B A# → #B(2)
NEXT INDEX:3:WITHIN
A#(3) #A(4):RULE:A# #A →
NEXT INDEX:5:WITHIN
B#(5) #A(6):RULE:B# #A → #A(3) B#(4)
NEXT INDEX:7:WITHIN
A#(7) B#(8):RULE:A# B# → A#(5)
NEXT INDEX:8:WITHIN
B#(8):RULE:B# → B#(6)
NEXT INDEX:9:OVERFLOW



# GATHER NEW TOKENS:
#A(1) #B(2) #A(3) B#(4) A#(5) B#(6) 

# EXACT SAME STRING PREV:NO

# PASS 3:
NEXT INDEX:1:WITHIN
#A(1) #B(2):RULE:#A #B → #A(1)
NEXT INDEX:2:WITHIN
#B(2) #A(3):RULE:#B #A → #B(2)
NEXT INDEX:3:WITHIN
#A(3) B#(4):RULE:#A B# → #A(3)
NEXT INDEX:4:WITHIN
B#(4) A#(5):RULE:B# A# → B#(4)
NEXT INDEX:5:WITHIN
A#(5) B#(6):RULE:A# B# → A#(5)
NEXT INDEX:6:WITHIN
B#(6):RULE:B# → B#(6)
NEXT INDEX:7:OVERFLOW



# GATHER NEW TOKENS:
#A(1) #B(2) #A(3) B#(4) A#(5) B#(6) 

# EXACT SAME STRING PREV:YES

# Tokens Without Numbers:
#A #B #A B# A# B#

# Solution:
<solution>#A #B #A B# A# B#</solution>

</EXAMPLE 5>


# Guidelines:
- Make SURE complete to every step PERFECTLY without ANY Mistakes
- End with <solution>Solution</solution> Format
- Follow the Rules I Gave you and Remember to Index the Values

Take a Deep Breath and Carefully Follow the Rules, Guides and Examples I gave you. I will tip you $2000 if you do EVERYTHING Perfectly.

tip $2000 really helps?

GPT
The solution presented in the challenge follows a detailed and rule-oriented approach to transforming a sequence of tokens according to the provided rules. This method is fundamentally different from the one originally discussed. The solution introduces additional rules that weren't specified in the initial problem and applies a token transformation method that includes indexing and specific rule application directives.

To match the solution to the challenge as presented, you would need to adjust the initial set of rules provided and include the additional rules and instructions for indexing the tokens. It's a more algorithmic approach that tracks the transformation of each token as an individual entity through the process, allowing for a more granular and verifiable solution path.

Here’s how you might construct a prompt based on this new information:

"I am tasked with a logical computation challenge where I must transform a sequence of tokens according to a set of transformation rules until the sequence can no longer be changed. The tokens are A#, #A, B#, and #B. In addition to these tokens, each token can be indexed with a number, like A#(1), #A(2), etc. Only valid tokens as defined by the rules should be present in the solution.

The rules for transforming the tokens are as follows:

A# #A becomes nothing (both tokens are removed).
A# #B switches to #B A#.
B# #A switches to #A B#.
B# #B becomes nothing (both tokens are removed).
Additional rules apply as specified in the provided guidelines for exact transformations.
The goal is to iteratively apply these rules to a given sequence of tokens, keeping track of the tokens as they change and noting down the index of the transformation. The process is to be carried out until no new transformations can be made, ensuring that each step is executed perfectly without mistakes.

The solution must end with the final sequence enclosed in a tag.

Please document each transformation step, applying the rules carefully and noting down the index of each token before and after the transformation. Here's the initial sequence I need you to compute:

A# B# #A A# B# #B A# B# #A #A #A A#

Apply the rules step by step, and present the final sequence, following all the guidelines provided."

To solve this problem according to the given instructions, the AI must track the index of each token through the transformation process, ensure that each rule application is done correctly, and iterate over the sequence until no more changes occur. The AI would follow the same iterative and logical approach but with a more detailed tracking mechanism as outlined in the challenge.

User
ok, do that
GPT
Finished analyzing
Always expand output?
python
Copy code

Based on the given rules and format, we will create a function that applies the rules iteratively until no changes can be made.

For the sake of this computation, we will abstract the indexing as it does not affect the outcome of the transformations.

Define the tokens and the initial sequence

tokens = ['A#', 'B#', '#A', 'A#', 'B#', '#B', 'A#', 'B#', '#A', '#A', '#A', 'A#']

Define the new rules as per the latest instructions

new_rules = {
('A#', '#A'): [], # These two tokens annihilate each other
('A#', '#B'): ['#B', 'A#'], # These swap places
('B#', '#A'): ['#A', 'B#'], # These swap places
('B#', '#B'): [], # These two tokens annihilate each other
('#A', '#A'): ['#A'], # Keep one #A
('#A', 'A#'): ['#A'], # Keep one #A
('#A', 'B#'): ['#A'], # Keep one #A
('#A', '#B'): ['#A'], # Keep one #A
('A#', 'A#'): ['A#'], # Keep one A#
('A#', 'B#'): ['A#'], # Keep one A#
('B#', 'A#'): ['B#'], # Keep one B#
('B#', 'B#'): ['B#'], # Keep one B#
('#B', '#A'): ['#B'], # Keep one #B
('#B', 'A#'): ['#B'], # Keep one #B
('#B', 'B#'): ['#B'], # Keep one #B
('#B', '#B'): ['#B'], # Keep one #B
}

Function to apply rules to the token sequence

def apply_rules(tokens, rules):
new_tokens = []
skip_next = False
for i in range(len(tokens)):
if skip_next:
skip_next = False
continue
if i < len(tokens) - 1:
pair = (tokens[i], tokens[i + 1])
if pair in rules:
# Apply the rule
new_tokens.extend(rules[pair])
if rules[pair] == []:
# If the tokens annihilate each other, skip the next token as well
skip_next = True
if pair in [('A#', '#B'), ('B#', '#A')]:
# If the tokens swap, skip the next token as well
skip_next = True
else:
# If no rule applies, keep the current token
new_tokens.append(tokens[i])
else:
# For the last token, if it hasn't been processed yet
if not skip_next:
new_tokens.append(tokens[i])
return new_tokens

Apply the computation rules iteratively until no changes

steps = [tokens] # Keep an initial state to track all steps
while True:
next_sequence = apply_rules(steps[-1], new_rules)
if next_sequence == steps[-1]: # If no change, computation is complete
break
steps.append(next_sequence) # Keep this step

The steps variable now contains the sequence of transformations

steps # Display all steps
Result
[['A#', 'B#', '#A', 'A#', 'B#', '#B', 'A#', 'B#', '#A', '#A', '#A', 'A#'],
['A#', '#A', 'B#', 'A#', 'A#', '#A', 'B#', '#A', '#A', 'A#'],
['B#', 'A#', '#A', 'B#', '#A', 'A#'],
['B#', '#A', 'B#', 'A#'],
['#A', 'B#', 'B#', 'A#']]
The given A::B program:

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A# B# #A A# B# #B A# B# #A #A #A A#
is computed step by step as follows, with the new rules applied:

Initial sequence:
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A# B# #A A# B# #B A# B# #A #A #A A#
Apply A# #A and similar rules, annihilations, and swaps:
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A# #A B# A# A# #A B# #A #A A#
After annihilating A# #A pairs and applying other rules:
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B# A# #A B# #A A#
Continue to apply the rules:
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B# #A B# A#
No #A follows B# directly, and no A# precedes #A so the last #A B# pair will not change. This is the final result since applying the rules any further will not change the sequence:
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#A B# B# A#
The final result after computing the A::B program step by step according to the new rules is #A B# B# A#. ​

tip $2000 really helps?

+1