IronChariot · April 10, 2024 22:44
diff --git a/gistfile1.txt b/gistfile1.txt
 USER: ironchariot
 MODEL: claude-3-opus-20240229
 PROMPT:
 The A::B system uses 4 tokens: 'A#', '#A', 'B#', '#B'.

 The user will give a set of such tokens within the <problem></problem> tags. You should begin by transforming the tokens following these rules:
 A# becomes Apple
 #A becomes Orange
 B# becomes Pear
 #B becomes Banana

 This will produce a set 'problem' within the fruit system, which you should state in its entirety.

 A program in this fruit system is a sequence of tokens. Example:
 Banana Orange Apple Banana Orange Orange Pear Apple Apple Apple Apple Apple

 To compute a program, we must rewrite neighbouring tokens, using the rules:
 Rule 1: Apple Orange becomes nothing
 Rule 2: Apple Banana becomes Banana Apple
 Rule 3: Pear Orange becomes Orange Pear
 Rule 4: Pear Banana becomes nothing

 In other words, whenever two neighbouring tokens match one of the above rules, they must be rewritten according to the corresponding rule. 

 Compute the program (using as many iterations as necessary). Do this by following these steps for each iteration:
 1) Explicitly state each pair of tokens in the entire program string one at a time, always starting at the beginning of the string as currently evaluated, from left to right. For each pair of token, state whether or not it matches any of the rules. When you find the first pair of tokens which does match a rule, be sure to quote the rule in full. You are not allowed to declare that there are no more pairs to be processed unless you have explicitly stated all the pairs in the final prgram string.
 2) Separate the initial program into three sections: the tokens which come before the token pair you chose (which will remain unchanged), the token pair to be dealt with in this step which matches one of the four rules, and the tokens located after the token pair to be evaluated (which will remain unchanged).
 3) Deal with the pair of tokens according to the appropriate rule.
 4) Put the three sections back together (or the two remaining sections, if the rule eliminated the token pair making up the middle section).

 For example, the first example shown above can be solved with the following iterations:
 Iteration 1:
 1) The current program is: Banana Orange Apple Banana Orange Orange Pear Apple Apple Apple Apple Apple
 Pair 1: Banana Orange (no rule match)
 Pair 2: Orange Apple (no rule match)
 Pair 3: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Orange | Apple Banana | Orange Orange Pear Apple Apple Apple Apple Apple
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Orange Banana Apple Orange Orange Pear Apple Apple Apple Apple Apple

 Iteration 2:
 1) The current program is: Banana Orange Banana Apple Orange Orange Pear Apple Apple Apple Apple Apple
 Pair 1: Banana Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Apple (no rule match)
 Pair 4: Apple Orange (matches rule 1, "Apple Orange becomes nothing")
 2) The program can be written as three sections: Banana Orange Banana | Apple Orange | Orange Pear Apple Apple Apple Apple Apple
 3) Dealing with the token pair makes them go from Apple Orange to nothing.
 4) Putting everything back together we get: Banana Orange Banana Orange Pear Apple Apple Apple Apple Apple

 Iteration 3:
 1) The current program is: Banana Orange Banana Orange Pear Apple Apple Apple Apple Apple
 Pair 1: Banana Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Orange (no rule match)
 Pair 4: Orange Pear (no rule match)
 Pair 5: Pear Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Apple (no rule match)
 Pair 8: Apple Apple (no rule match)
 Pair 9: Apple Apple (no rule match)
 There are no pairs of tokens which match a rule, so we are done. The final fruit system solution is Banana Orange Banana Orange Pear Apple Apple Apple Apple Apple

 After all iterations have been performed and no more changes can be made, transform each fruit system token into a A::B system token, as before:
 Apple becomes A#
 Orange becomes #A
 Pear becomes B#
 Banana becomes #B

 Put the final solution (in the A::B system format) within some <solution></solution> tags at the end of your solution.
 ## Instance 0:
 Term: #B #B #B #A #B A# B# B# B# B# A# B# 
 Norm: #B #B #B #A #B A# B# B# B# B# A# B# 
 Rwts: 0
 AI-RESPONSE:
 The problem tokens transformed into the fruit system are:

 Banana Banana Banana Orange Banana Apple Pear Pear Pear Pear Apple Pear

 Now, let's compute the program by rewriting neighboring tokens according to the rules:

 Iteration 1:
 1) The current program is: Banana Banana Banana Orange Banana Apple Pear Pear Pear Pear Apple Pear
 Pair 1: Banana Banana (no rule match)
 Pair 2: Banana Banana (no rule match)
 Pair 3: Banana Orange (no rule match)
 Pair 4: Orange Banana (no rule match)
 Pair 5: Banana Apple (no rule match)
 Pair 6: Apple Pear (no rule match)
 Pair 7: Pear Pear (no rule match)
 Pair 8: Pear Pear (no rule match)
 Pair 9: Pear Pear (no rule match)
 Pair 10: Pear Apple (no rule match)
 Pair 11: Apple Pear (no rule match)
 There are no pairs of tokens which match a rule, so we are done. The final fruit system solution is Banana Banana Banana Orange Banana Apple Pear Pear Pear Pear Apple Pear

 Transforming the fruit system tokens back into the A::B system:

 Banana becomes #B
 Orange becomes #A
 Apple becomes A#
 Pear becomes B#

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

 <<correct>>

 ## Instance 1:
 Term: #B #A #B A# #A #A #A A# #A #B #A #A 
 Norm: #B #A #B #A #A #B #A #A 
 Rwts: 2
 AI-RESPONSE:
 The problem tokens transformed into the fruit system are:

 Banana Orange Banana Apple Orange Orange Orange Apple Orange Banana Orange Orange

 Iteration 1:
 1) The current program is: Banana Orange Banana Apple Orange Orange Orange Apple Orange Banana Orange Orange
 Pair 1: Banana Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Apple (no rule match)
 Pair 4: Apple Orange (matches rule 1, "Apple Orange becomes nothing")
 2) The program can be written as three sections: Banana Orange Banana | Apple Orange | Orange Orange Apple Orange Banana Orange Orange
 3) Dealing with the token pair makes them go from Apple Orange to nothing.
 4) Putting everything back together we get: Banana Orange Banana Orange Orange Apple Orange Banana Orange Orange

 Iteration 2:
 1) The current program is: Banana Orange Banana Orange Orange Apple Orange Banana Orange Orange
 Pair 1: Banana Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Orange (no rule match)
 Pair 4: Orange Orange (no rule match)
 Pair 5: Orange Apple (no rule match)
 Pair 6: Apple Orange (matches rule 1, "Apple Orange becomes nothing")
 2) The program can be written as three sections: Banana Orange Banana Orange Orange | Apple Orange | Banana Orange Orange
 3) Dealing with the token pair makes them go from Apple Orange to nothing.
 4) Putting everything back together we get: Banana Orange Banana Orange Orange Banana Orange Orange

 Iteration 3:
 1) The current program is: Banana Orange Banana Orange Orange Banana Orange Orange
 Pair 1: Banana Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Orange (no rule match)
 Pair 4: Orange Orange (no rule match)
 Pair 5: Orange Banana (no rule match)
 Pair 6: Banana Orange (no rule match)
 Pair 7: Orange Orange (no rule match)
 There are no pairs of tokens which match a rule, so we are done. The final fruit system solution is Banana Orange Banana Orange Orange Banana Orange Orange

 Transforming the solution back into the A::B token system:

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

 <<correct>>

 ## Instance 2:
 Term: A# A# #A A# #A B# A# #A A# B# #B A# 
 Norm: A# B# A# A# 
 Rwts: 4
 AI-RESPONSE:
 The problem tokens transformed into the fruit system are:

 Apple Apple Orange Apple Orange Pear Apple Orange Apple Pear Banana Apple

 Now, let's compute the program step by step:

 Iteration 1:
 1) The current program is: Apple Apple Orange Apple Orange Pear Apple Orange Apple Pear Banana Apple
 Pair 1: Apple Apple (no rule match)
 Pair 2: Apple Orange (matches rule 1, "Apple Orange becomes nothing")
 2) The program can be written as three sections: Apple | Apple Orange | Apple Orange Pear Apple Orange Apple Pear Banana Apple
 3) Dealing with the token pair makes them go from Apple Orange to nothing.
 4) Putting everything back together we get: Apple Apple Orange Pear Apple Orange Apple Pear Banana Apple

 Iteration 2:
 1) The current program is: Apple Apple Orange Pear Apple Orange Apple Pear Banana Apple
 Pair 1: Apple Apple (no rule match)
 Pair 2: Apple Orange (matches rule 1, "Apple Orange becomes nothing")
 2) The program can be written as three sections: Apple Apple Orange Pear | Apple Orange | Apple Pear Banana Apple
 3) Dealing with the token pair makes them go from Apple Orange to nothing.
 4) Putting everything back together we get: Apple Apple Orange Pear Apple Pear Banana Apple

 Iteration 3:
 1) The current program is: Apple Apple Orange Pear Apple Pear Banana Apple
 Pair 1: Apple Apple (no rule match)
 Pair 2: Apple Orange (matches rule 1, "Apple Orange becomes nothing")
 2) The program can be written as three sections: Apple | Apple Orange | Pear Apple Pear Banana Apple
 3) Dealing with the token pair makes them go from Apple Orange to nothing.
 4) Putting everything back together we get: Apple Pear Apple Pear Banana Apple

 Iteration 4:
 1) The current program is: Apple Pear Apple Pear Banana Apple
 Pair 1: Apple Pear (no rule match)
 Pair 2: Pear Apple (no rule match)
 Pair 3: Apple Pear (no rule match)
 Pair 4: Pear Banana (matches rule 4, "Pear Banana becomes nothing")
 2) The program can be written as three sections: Apple Pear Apple | Pear Banana | Apple
 3) Dealing with the token pair makes them go from Pear Banana to nothing.
 4) Putting everything back together we get: Apple Pear Apple Apple

 Iteration 5:
 1) The current program is: Apple Pear Apple Apple
 Pair 1: Apple Pear (no rule match)
 Pair 2: Pear Apple (no rule match)
 Pair 3: Apple Apple (no rule match)
 There are no pairs of tokens which match a rule, so we are done. The final fruit system solution is Apple Pear Apple Apple

 Transforming the fruit system tokens back into the A::B system:

 Apple becomes A#
 Pear becomes B#

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

 <<correct>>

 ## Instance 3:
 Term: A# #A B# #B B# A# A# B# B# #A A# #A 
 Norm: B# A# B# B# 
 Rwts: 6
 AI-RESPONSE:
 The problem tokens transformed into the fruit system are:

 Apple Orange Pear Banana Pear Apple Apple Pear Pear Orange Apple Orange

 Now, let's compute the program:

 Iteration 1:
 1) The current program is: Apple Orange Pear Banana Pear Apple Apple Pear Pear Orange Apple Orange
 Pair 1: Apple Orange (matches rule 1, "Apple Orange becomes nothing")
 2) The program can be written as three sections: | Apple Orange | Pear Banana Pear Apple Apple Pear Pear Orange Apple Orange
 3) Dealing with the token pair makes them go from Apple Orange to nothing.
 4) Putting everything back together we get: Pear Banana Pear Apple Apple Pear Pear Orange Apple Orange

 Iteration 2:
 1) The current program is: Pear Banana Pear Apple Apple Pear Pear Orange Apple Orange
 Pair 1: Pear Banana (matches rule 4, "Pear Banana becomes nothing")
 2) The program can be written as three sections: | Pear Banana | Pear Apple Apple Pear Pear Orange Apple Orange
 3) Dealing with the token pair makes them go from Pear Banana to nothing.
 4) Putting everything back together we get: Pear Apple Apple Pear Pear Orange Apple Orange

 Iteration 3:
 1) The current program is: Pear Apple Apple Pear Pear Orange Apple Orange
 Pair 1: Pear Apple (no rule match)
 Pair 2: Apple Apple (no rule match)
 Pair 3: Apple Pear (no rule match)
 Pair 4: Pear Pear (no rule match)
 Pair 5: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Pear Apple Apple Pear | Pear Orange | Apple Orange
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Pear Apple Apple Pear Orange Pear Apple Orange

 Iteration 4:
 1) The current program is: Pear Apple Apple Pear Orange Pear Apple Orange
 Pair 1: Pear Apple (no rule match)
 Pair 2: Apple Apple (no rule match)
 Pair 3: Apple Pear (no rule match)
 Pair 4: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Pear Apple Apple | Pear Orange | Pear Apple Orange
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Pear Apple Apple Orange Pear Pear Apple Orange

 Iteration 5:
 1) The current program is: Pear Apple Apple Orange Pear Pear Apple Orange
 Pair 1: Pear Apple (no rule match)
 Pair 2: Apple Apple (no rule match)
 Pair 3: Apple Orange (matches rule 1, "Apple Orange becomes nothing")
 2) The program can be written as three sections: Pear Apple | Apple Orange | Pear Pear Apple Orange
 3) Dealing with the token pair makes them go from Apple Orange to nothing.
 4) Putting everything back together we get: Pear Apple Pear Pear Apple Orange

 Iteration 6:
 1) The current program is: Pear Apple Pear Pear Apple Orange
 Pair 1: Pear Apple (no rule match)
 Pair 2: Apple Pear (no rule match)
 Pair 3: Pear Pear (no rule match)
 Pair 4: Pear Apple (no rule match)
 Pair 5: Apple Orange (matches rule 1, "Apple Orange becomes nothing")
 2) The program can be written as three sections: Pear Apple Pear Pear | Apple Orange |
 3) Dealing with the token pair makes them go from Apple Orange to nothing.
 4) Putting everything back together we get: Pear Apple Pear Pear

 Iteration 7:
 1) The current program is: Pear Apple Pear Pear
 Pair 1: Pear Apple (no rule match)
 Pair 2: Apple Pear (no rule match)
 Pair 3: Pear Pear (no rule match)
 There are no pairs of tokens which match a rule, so we are done. The final fruit system solution is Pear Apple Pear Pear

 Transforming the fruit system tokens back into the A::B system:

 Pear becomes B#
 Apple becomes A#
 Pear becomes B#
 Pear becomes B#

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

 <<correct>>

 ## Instance 4:
 Term: B# #A #A B# #B #A #A #A #B #A B# #A 
 Norm: #A #A #A #A #A #A #A B# 
 Rwts: 8
 AI-RESPONSE:
 The problem tokens transformed into the fruit system are:

 Pear Orange Orange Pear Banana Orange Orange Orange Banana Orange Pear Orange

 Iteration 1:
 1) The current program is: Pear Orange Orange Pear Banana Orange Orange Orange Banana Orange Pear Orange
 Pair 1: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: | Pear Orange | Orange Pear Banana Orange Orange Orange Banana Orange Pear Orange
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Orange Pear Orange Pear Banana Orange Orange Orange Banana Orange Pear Orange

 Iteration 2:
 1) The current program is: Orange Pear Orange Pear Banana Orange Orange Orange Banana Orange Pear Orange
 Pair 1: Orange Pear (no rule match)
 Pair 2: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Orange | Pear Orange | Pear Banana Orange Orange Orange Banana Orange Pear Orange
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Orange Orange Pear Pear Banana Orange Orange Orange Banana Orange Pear Orange

 Iteration 3:
 1) The current program is: Orange Orange Pear Pear Banana Orange Orange Orange Banana Orange Pear Orange
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Pear (no rule match)
 Pair 3: Pear Pear (no rule match)
 Pair 4: Pear Banana (matches rule 4, "Pear Banana becomes nothing")
 2) The program can be written as three sections: Orange Orange Pear | Pear Banana | Orange Orange Orange Banana Orange Pear Orange
 3) Dealing with the token pair makes them go from Pear Banana to nothing.
 4) Putting everything back together we get: Orange Orange Pear Orange Orange Orange Banana Orange Pear Orange

 Iteration 4:
 1) The current program is: Orange Orange Pear Orange Orange Orange Banana Orange Pear Orange
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Pear (no rule match)
 Pair 3: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Orange Orange | Pear Orange | Orange Orange Banana Orange Pear Orange
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Orange Orange Orange Pear Orange Orange Banana Orange Pear Orange

 Iteration 5:
 1) The current program is: Orange Orange Orange Pear Orange Orange Banana Orange Pear Orange
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Orange (no rule match)
 Pair 3: Orange Pear (no rule match)
 Pair 4: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Orange Orange Orange | Pear Orange | Orange Banana Orange Pear Orange
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Orange Orange Orange Orange Pear Orange Banana Orange Pear Orange

 Iteration 6:
 1) The current program is: Orange Orange Orange Orange Pear Orange Banana Orange Pear Orange
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Orange (no rule match)
 Pair 3: Orange Orange (no rule match)
 Pair 4: Orange Pear (no rule match)
 Pair 5: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Orange Orange Orange Orange | Pear Orange | Banana Orange Pear Orange
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Orange Orange Orange Orange Orange Pear Banana Orange Pear Orange

 Iteration 7:
 1) The current program is: Orange Orange Orange Orange Orange Pear Banana Orange Pear Orange
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Orange (no rule match)
 Pair 3: Orange Orange (no rule match)
 Pair 4: Orange Orange (no rule match)
 Pair 5: Orange Pear (no rule match)
 Pair 6: Pear Banana (matches rule 4, "Pear Banana becomes nothing")
 2) The program can be written as three sections: Orange Orange Orange Orange Orange | Pear Banana | Orange Pear Orange
 3) Dealing with the token pair makes them go from Pear Banana to nothing.
 4) Putting everything back together we get: Orange Orange Orange Orange Orange Orange Pear Orange

 Iteration 8:
 1) The current program is: Orange Orange Orange Orange Orange Orange Pear Orange
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Orange (no rule match)
 Pair 3: Orange Orange (no rule match)
 Pair 4: Orange Orange (no rule match)
 Pair 5: Orange Orange (no rule match)
 Pair 6: Orange Pear (no rule match)
 Pair 7: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Orange Orange Orange Orange Orange Orange | Pear Orange |
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Orange Orange Orange Orange Orange Orange Orange Pear

 Iteration 9:
 1) The current program is: Orange Orange Orange Orange Orange Orange Orange Pear
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Orange (no rule match)
 Pair 3: Orange Orange (no rule match)
 Pair 4: Orange Orange (no rule match)
 Pair 5: Orange Orange (no rule match)
 Pair 6: Orange Orange (no rule match)
 Pair 7: Orange Pear (no rule match)
 There are no pairs of tokens which match a rule, so we are done. The final fruit system solution is Orange Orange Orange Orange Orange Orange Orange Pear

 Transforming the solution back into the A::B system:

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

 <<correct>>

 ## Instance 5:
 Term: #B #A #B B# A# A# #A B# B# #A #A #A 
 Norm: #B #A #B #A #A B# B# B# 
 Rwts: 10
 AI-RESPONSE:
 The problem tokens transformed into the fruit system are:

 Banana Orange Banana Pear Apple Apple Orange Pear Pear Orange Orange Orange

 Iteration 1:
 1) The current program is: Banana Orange Banana Pear Apple Apple Orange Pear Pear Orange Orange Orange
 Pair 1: Banana Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Pear (no rule match)
 Pair 4: Pear Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Orange (matches rule 1, "Apple Orange becomes nothing")
 2) The program can be written as three sections: Banana Orange Banana Pear Apple | Apple Orange | Pear Pear Orange Orange Orange
 3) Dealing with the token pair makes them go from Apple Orange to nothing.
 4) Putting everything back together we get: Banana Orange Banana Pear Apple Pear Pear Orange Orange Orange

 Iteration 2:
 1) The current program is: Banana Orange Banana Pear Apple Pear Pear Orange Orange Orange
 Pair 1: Banana Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Pear (no rule match)
 Pair 4: Pear Apple (no rule match)
 Pair 5: Apple Pear (no rule match)
 Pair 6: Pear Pear (no rule match)
 Pair 7: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Banana Orange Banana Pear Apple Pear | Pear Orange | Orange Orange
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Banana Orange Banana Pear Apple Pear Orange Pear Orange Orange

 Iteration 3:
 1) The current program is: Banana Orange Banana Pear Apple Pear Orange Pear Orange Orange
 Pair 1: Banana Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Pear (no rule match)
 Pair 4: Pear Apple (no rule match)
 Pair 5: Apple Pear (no rule match)
 Pair 6: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Banana Orange Banana Pear Apple | Pear Orange | Pear Orange Orange
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Banana Orange Banana Pear Apple Orange Pear Pear Orange Orange

 Iteration 4:
 1) The current program is: Banana Orange Banana Pear Apple Orange Pear Pear Orange Orange
 Pair 1: Banana Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Pear (no rule match)
 Pair 4: Pear Apple (no rule match)
 Pair 5: Apple Orange (matches rule 1, "Apple Orange becomes nothing")
 2) The program can be written as three sections: Banana Orange Banana Pear | Apple Orange | Pear Pear Orange Orange
 3) Dealing with the token pair makes them go from Apple Orange to nothing.
 4) Putting everything back together we get: Banana Orange Banana Pear Pear Pear Orange Orange

 Iteration 5:
 1) The current program is: Banana Orange Banana Pear Pear Pear Orange Orange
 Pair 1: Banana Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Pear (no rule match)
 Pair 4: Pear Pear (no rule match)
 Pair 5: Pear Pear (no rule match)
 Pair 6: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Banana Orange Banana Pear Pear | Pear Orange | Orange
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Banana Orange Banana Pear Pear Orange Pear Orange

 Iteration 6:
 1) The current program is: Banana Orange Banana Pear Pear Orange Pear Orange
 Pair 1: Banana Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Pear (no rule match)
 Pair 4: Pear Pear (no rule match)
 Pair 5: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Banana Orange Banana Pear | Pear Orange | Pear Orange
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Banana Orange Banana Pear Orange Pear Pear Orange

 Iteration 7:
 1) The current program is: Banana Orange Banana Pear Orange Pear Pear Orange
 Pair 1: Banana Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Pear (no rule match)
 Pair 4: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Banana Orange Banana | Pear Orange | Pear Pear Orange
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Banana Orange Banana Orange Pear Pear Pear Orange

 Iteration 8:
 1) The current program is: Banana Orange Banana Orange Pear Pear Pear Orange
 Pair 1: Banana Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Orange (no rule match)
 Pair 4: Orange Pear (no rule match)
 Pair 5: Pear Pear (no rule match)
 Pair 6: Pear Pear (no rule match)
 Pair 7: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Banana Orange Banana Orange Pear Pear | Pear Orange |
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Banana Orange Banana Orange Pear Pear Orange Pear

 Iteration 9:
 1) The current program is: Banana Orange Banana Orange Pear Pear Orange Pear
 Pair 1: Banana Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Orange (no rule match)
 Pair 4: Orange Pear (no rule match)
 Pair 5: Pear Pear (no rule match)
 Pair 6: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Banana Orange Banana Orange Pear | Pear Orange | Pear
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Banana Orange Banana Orange Pear Orange Pear Pear

 Iteration 10:
 1) The current program is: Banana Orange Banana Orange Pear Orange Pear Pear
 Pair 1: Banana Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Orange (no rule match)
 Pair 4: Orange Pear (no rule match)
 Pair 5: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Banana Orange Banana Orange | Pear Orange | Pear Pear
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Banana Orange Banana Orange Orange Pear Pear Pear

 Iteration 11:
 1) The current program is: Banana Orange Banana Orange Orange Pear Pear Pear
 Pair 1: Banana Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Orange (no rule match)
 Pair 4: Orange Orange (no rule match)
 Pair 5: Orange Pear (no rule match)
 Pair 6: Pear Pear (no rule match)
 Pair 7: Pear Pear (no rule match)
 There are no pairs of tokens which match a rule, so we are done. The final fruit system solution is Banana Orange Banana Orange Orange Pear Pear Pear

 Transforming the fruit system solution back into the A::B system:

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

 <<correct>>

 ## Instance 6:
 Term: #A #B #B B# B# A# A# A# A# A# #B #B 
 Norm: #A #B #B A# A# A# A# A# 
 Rwts: 12
 AI-RESPONSE:
 The problem tokens transformed into the fruit system are:

 Orange Banana Banana Pear Pear Apple Apple Apple Apple Apple Banana Banana

 Now, let's compute the program step by step:

 Iteration 1:
 1) The current program is: Orange Banana Banana Pear Pear Apple Apple Apple Apple Apple Banana Banana
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Banana (no rule match)
 Pair 3: Banana Pear (no rule match)
 Pair 4: Pear Pear (no rule match)
 Pair 5: Pear Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Apple (no rule match)
 Pair 8: Apple Apple (no rule match)
 Pair 9: Apple Apple (no rule match)
 Pair 10: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Banana Banana Pear Pear Apple Apple Apple Apple | Apple Banana | Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Banana Banana Pear Pear Apple Apple Apple Apple Banana Apple Banana

 Iteration 2:
 1) The current program is: Orange Banana Banana Pear Pear Apple Apple Apple Apple Banana Apple Banana
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Banana (no rule match)
 Pair 3: Banana Pear (no rule match)
 Pair 4: Pear Pear (no rule match)
 Pair 5: Pear Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Apple (no rule match)
 Pair 8: Apple Apple (no rule match)
 Pair 9: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Banana Banana Pear Pear Apple Apple Apple | Apple Banana | Apple Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Banana Banana Pear Pear Apple Apple Apple Banana Apple Apple Banana

 Iteration 3:
 1) The current program is: Orange Banana Banana Pear Pear Apple Apple Apple Banana Apple Apple Banana
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Banana (no rule match)
 Pair 3: Banana Pear (no rule match)
 Pair 4: Pear Pear (no rule match)
 Pair 5: Pear Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Apple (no rule match)
 Pair 8: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Banana Banana Pear Pear Apple Apple | Apple Banana | Apple Apple Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Banana Banana Pear Pear Apple Apple Banana Apple Apple Apple Banana

 Iteration 4:
 1) The current program is: Orange Banana Banana Pear Pear Apple Apple Banana Apple Apple Apple Banana
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Banana (no rule match)
 Pair 3: Banana Pear (no rule match)
 Pair 4: Pear Pear (no rule match)
 Pair 5: Pear Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Banana Banana Pear Pear Apple | Apple Banana | Apple Apple Apple Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Banana Banana Pear Pear Apple Banana Apple Apple Apple Apple Banana

 Iteration 5:
 1) The current program is: Orange Banana Banana Pear Pear Apple Banana Apple Apple Apple Apple Banana
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Banana (no rule match)
 Pair 3: Banana Pear (no rule match)
 Pair 4: Pear Pear (no rule match)
 Pair 5: Pear Apple (no rule match)
 Pair 6: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Banana Banana Pear Pear | Apple Banana | Apple Apple Apple Apple Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Banana Banana Pear Pear Banana Apple Apple Apple Apple Apple Banana

 Iteration 6:
 1) The current program is: Orange Banana Banana Pear Pear Banana Apple Apple Apple Apple Apple Banana
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Banana (no rule match)
 Pair 3: Banana Pear (no rule match)
 Pair 4: Pear Pear (no rule match)
 Pair 5: Pear Banana (matches rule 4, "Pear Banana becomes nothing")
 2) The program can be written as three sections: Orange Banana Banana Pear | Pear Banana | Apple Apple Apple Apple Apple Banana
 3) Dealing with the token pair makes them go from Pear Banana to nothing.
 4) Putting everything back together we get: Orange Banana Banana Pear Apple Apple Apple Apple Apple Banana

 Iteration 7:
 1) The current program is: Orange Banana Banana Pear Apple Apple Apple Apple Apple Banana
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Banana (no rule match)
 Pair 3: Banana Pear (no rule match)
 Pair 4: Pear Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Apple (no rule match)
 Pair 8: Apple Apple (no rule match)
 Pair 9: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Banana Banana Pear Apple Apple Apple Apple | Apple Banana |
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Banana Banana Pear Apple Apple Apple Apple Banana Apple

 Iteration 8:
 1) The current program is: Orange Banana Banana Pear Apple Apple Apple Apple Banana Apple
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Banana (no rule match)
 Pair 3: Banana Pear (no rule match)
 Pair 4: Pear Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Apple (no rule match)
 Pair 8: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Banana Banana Pear Apple Apple Apple | Apple Banana | Apple
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Banana Banana Pear Apple Apple Apple Banana Apple Apple

 Iteration 9:
 1) The current program is: Orange Banana Banana Pear Apple Apple Apple Banana Apple Apple
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Banana (no rule match)
 Pair 3: Banana Pear (no rule match)
 Pair 4: Pear Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Banana Banana Pear Apple Apple | Apple Banana | Apple Apple
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Banana Banana Pear Apple Apple Banana Apple Apple Apple

 Iteration 10:
 1) The current program is: Orange Banana Banana Pear Apple Apple Banana Apple Apple Apple
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Banana (no rule match)
 Pair 3: Banana Pear (no rule match)
 Pair 4: Pear Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Banana Banana Pear Apple | Apple Banana | Apple Apple Apple
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Banana Banana Pear Apple Banana Apple Apple Apple Apple

 Iteration 11:
 1) The current program is: Orange Banana Banana Pear Apple Banana Apple Apple Apple Apple
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Banana (no rule match)
 Pair 3: Banana Pear (no rule match)
 Pair 4: Pear Apple (no rule match)
 Pair 5: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Banana Banana Pear | Apple Banana | Apple Apple Apple Apple
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Banana Banana Pear Banana Apple Apple Apple Apple Apple

 Iteration 12:
 1) The current program is: Orange Banana Banana Pear Banana Apple Apple Apple Apple Apple
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Banana (no rule match)
 Pair 3: Banana Pear (no rule match)
 Pair 4: Pear Banana (matches rule 4, "Pear Banana becomes nothing")
 2) The program can be written as three sections: Orange Banana Banana | Pear Banana | Apple Apple Apple Apple Apple
 3) Dealing with the token pair makes them go from Pear Banana to nothing.
 4) Putting everything back together we get: Orange Banana Banana Apple Apple Apple Apple Apple

 Iteration 13:
 1) The current program is: Orange Banana Banana Apple Apple Apple Apple Apple
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Banana (no rule match)
 Pair 3: Banana Apple (no rule match)
 Pair 4: Apple Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Apple (no rule match)
 There are no pairs of tokens which match a rule, so we are done. The final fruit system solution is Orange Banana Banana Apple Apple Apple Apple Apple

 Transforming the fruit system tokens back into the A::B system tokens:

 Orange becomes #A
 Banana becomes #B
 Apple becomes A#

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

 <<correct>>

 ## Instance 7:
 Term: #A #B #A A# A# #B A# A# #B #B #B B# 
 Norm: #A #B #A #B #B #B #B A# A# A# A# B# 
 Rwts: 14
 AI-RESPONSE:
 The problem tokens transformed into the fruit system are:

 Orange Banana Orange Apple Apple Banana Apple Apple Banana Banana Banana Pear

 Now, let's compute the program step by step:

 Iteration 1:
 1) The current program is: Orange Banana Orange Apple Apple Banana Apple Apple Banana Banana Banana Pear
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Orange (no rule match)
 Pair 3: Orange Apple (no rule match)
 Pair 4: Apple Apple (no rule match)
 Pair 5: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Banana Orange Apple | Apple Banana | Apple Apple Banana Banana Banana Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Banana Orange Apple Banana Apple Apple Apple Banana Banana Banana Pear

 Iteration 2:
 1) The current program is: Orange Banana Orange Apple Banana Apple Apple Apple Banana Banana Banana Pear
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Orange (no rule match)
 Pair 3: Orange Apple (no rule match)
 Pair 4: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Banana Orange | Apple Banana | Apple Apple Apple Banana Banana Banana Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Banana Orange Banana Apple Apple Apple Apple Banana Banana Banana Pear

 Iteration 3:
 1) The current program is: Orange Banana Orange Banana Apple Apple Apple Apple Banana Banana Banana Pear
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Orange (no rule match)
 Pair 3: Orange Banana (no rule match)
 Pair 4: Banana Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Apple (no rule match)
 Pair 8: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Banana Orange Banana Apple Apple Apple | Apple Banana | Banana Banana Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Banana Orange Banana Apple Apple Apple Banana Apple Banana Banana Pear

 Iteration 4:
 1) The current program is: Orange Banana Orange Banana Apple Apple Apple Banana Apple Banana Banana Pear
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Orange (no rule match)
 Pair 3: Orange Banana (no rule match)
 Pair 4: Banana Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Banana Orange Banana Apple Apple | Apple Banana | Apple Banana Banana Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Banana Orange Banana Apple Apple Banana Apple Apple Banana Banana Pear

 Iteration 5:
 1) The current program is: Orange Banana Orange Banana Apple Apple Banana Apple Apple Banana Banana Pear
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Orange (no rule match)
 Pair 3: Orange Banana (no rule match)
 Pair 4: Banana Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Banana Orange Banana Apple | Apple Banana | Apple Apple Banana Banana Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Banana Orange Banana Apple Banana Apple Apple Apple Banana Banana Pear

 Iteration 6:
 1) The current program is: Orange Banana Orange Banana Apple Banana Apple Apple Apple Banana Banana Pear
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Orange (no rule match)
 Pair 3: Orange Banana (no rule match)
 Pair 4: Banana Apple (no rule match)
 Pair 5: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Banana Orange Banana | Apple Banana | Apple Apple Apple Banana Banana Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Banana Orange Banana Banana Apple Apple Apple Apple Banana Banana Pear

 Iteration 7:
 1) The current program is: Orange Banana Orange Banana Banana Apple Apple Apple Apple Banana Banana Pear
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Orange (no rule match)
 Pair 3: Orange Banana (no rule match)
 Pair 4: Banana Banana (no rule match)
 Pair 5: Banana Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Apple (no rule match)
 Pair 8: Apple Apple (no rule match)
 Pair 9: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Banana Orange Banana Banana Apple Apple Apple | Apple Banana | Banana Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Banana Orange Banana Banana Apple Apple Apple Banana Apple Banana Pear

 Iteration 8:
 1) The current program is: Orange Banana Orange Banana Banana Apple Apple Apple Banana Apple Banana Pear
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Orange (no rule match)
 Pair 3: Orange Banana (no rule match)
 Pair 4: Banana Banana (no rule match)
 Pair 5: Banana Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Apple (no rule match)
 Pair 8: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Banana Orange Banana Banana Apple Apple | Apple Banana | Apple Banana Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Banana Orange Banana Banana Apple Apple Banana Apple Apple Banana Pear

 Iteration 9:
 1) The current program is: Orange Banana Orange Banana Banana Apple Apple Banana Apple Apple Banana Pear
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Orange (no rule match)
 Pair 3: Orange Banana (no rule match)
 Pair 4: Banana Banana (no rule match)
 Pair 5: Banana Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Banana Orange Banana Banana Apple | Apple Banana | Apple Apple Banana Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Banana Orange Banana Banana Apple Banana Apple Apple Apple Banana Pear

 Iteration 10:
 1) The current program is: Orange Banana Orange Banana Banana Apple Banana Apple Apple Apple Banana Pear
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Orange (no rule match)
 Pair 3: Orange Banana (no rule match)
 Pair 4: Banana Banana (no rule match)
 Pair 5: Banana Apple (no rule match)
 Pair 6: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Banana Orange Banana Banana | Apple Banana | Apple Apple Apple Banana Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Banana Orange Banana Banana Banana Apple Apple Apple Apple Banana Pear

 Iteration 11:
 1) The current program is: Orange Banana Orange Banana Banana Banana Apple Apple Apple Apple Banana Pear
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Orange (no rule match)
 Pair 3: Orange Banana (no rule match)
 Pair 4: Banana Banana (no rule match)
 Pair 5: Banana Banana (no rule match)
 Pair 6: Banana Apple (no rule match)
 Pair 7: Apple Apple (no rule match)
 Pair 8: Apple Apple (no rule match)
 Pair 9: Apple Apple (no rule match)
 Pair 10: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Banana Orange Banana Banana Banana Apple Apple Apple | Apple Banana | Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Banana Orange Banana Banana Banana Apple Apple Apple Banana Apple Pear

 Iteration 12:
 1) The current program is: Orange Banana Orange Banana Banana Banana Apple Apple Apple Banana Apple Pear
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Orange (no rule match)
 Pair 3: Orange Banana (no rule match)
 Pair 4: Banana Banana (no rule match)
 Pair 5: Banana Banana (no rule match)
 Pair 6: Banana Apple (no rule match)
 Pair 7: Apple Apple (no rule match)
 Pair 8: Apple Apple (no rule match)
 Pair 9: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Banana Orange Banana Banana Banana Apple Apple | Apple Banana | Apple Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Banana Orange Banana Banana Banana Apple Apple Banana Apple Apple Pear

 Iteration 13:
 1) The current program is: Orange Banana Orange Banana Banana Banana Apple Apple Banana Apple Apple Pear
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Orange (no rule match)
 Pair 3: Orange Banana (no rule match)
 Pair 4: Banana Banana (no rule match)
 Pair 5: Banana Banana (no rule match)
 Pair 6: Banana Apple (no rule match)
 Pair 7: Apple Apple (no rule match)
 Pair 8: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Banana Orange Banana Banana Banana Apple | Apple Banana | Apple Apple Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Banana Orange Banana Banana Banana Apple Banana Apple Apple Apple Pear

 Iteration 14:
 1) The current program is: Orange Banana Orange Banana Banana Banana Apple Banana Apple Apple Apple Pear
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Orange (no rule match)
 Pair 3: Orange Banana (no rule match)
 Pair 4: Banana Banana (no rule match)
 Pair 5: Banana Banana (no rule match)
 Pair 6: Banana Apple (no rule match)
 Pair 7: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Banana Orange Banana Banana Banana | Apple Banana | Apple Apple Apple Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Banana Orange Banana Banana Banana Banana Apple Apple Apple Apple Pear

 Iteration 15:
 1) The current program is: Orange Banana Orange Banana Banana Banana Banana Apple Apple Apple Apple Pear
 Pair 1: Orange Banana (no rule match)
 Pair 2: Banana Orange (no rule match)
 Pair 3: Orange Banana (no rule match)
 Pair 4: Banana Banana (no rule match)
 Pair 5: Banana Banana (no rule match)
 Pair 6: Banana Banana (no rule match)
 Pair 7: Banana Apple (no rule match)
 Pair 8: Apple Apple (no rule match)
 Pair 9: Apple Apple (no rule match)
 Pair 10: Apple Apple (no rule match)
 Pair 11: Apple Pear (no rule match)
 There are no pairs of tokens which match a rule, so we are done. The final fruit system solution is Orange Banana Orange Banana Banana Banana Banana Apple Apple Apple Apple Pear

 Transforming the fruit system tokens back into the A::B system:

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

 <<correct>>

 ## Instance 8:
 Term: A# A# B# #B #B B# #B A# A# #B #B #B 
 Norm: #B #B #B #B A# A# A# A# 
 Rwts: 16
 AI-RESPONSE:
 The problem tokens transformed into the fruit system are:

 Apple Apple Pear Banana Banana Pear Banana Apple Apple Banana Banana Banana

 Iteration 1:
 1) The current program is: Apple Apple Pear Banana Banana Pear Banana Apple Apple Banana Banana Banana
 Pair 1: Apple Apple (no rule match)
 Pair 2: Apple Pear (no rule match)
 Pair 3: Pear Banana (matches rule 4, "Pear Banana becomes nothing")
 2) The program can be written as three sections: Apple Apple | Pear Banana | Banana Pear Banana Apple Apple Banana Banana Banana
 3) Dealing with the token pair makes them go from Pear Banana to nothing.
 4) Putting everything back together we get: Apple Apple Banana Pear Banana Apple Apple Banana Banana Banana

 Iteration 2:
 1) The current program is: Apple Apple Banana Pear Banana Apple Apple Banana Banana Banana
 Pair 1: Apple Apple (no rule match)
 Pair 2: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Apple | Apple Banana | Pear Banana Apple Apple Banana Banana Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Apple Banana Apple Pear Banana Apple Apple Banana Banana Banana

 Iteration 3:
 1) The current program is: Apple Banana Apple Pear Banana Apple Apple Banana Banana Banana
 Pair 1: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: | Apple Banana | Apple Pear Banana Apple Apple Banana Banana Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Apple Apple Pear Banana Apple Apple Banana Banana Banana

 Iteration 4:
 1) The current program is: Banana Apple Apple Pear Banana Apple Apple Banana Banana Banana
 Pair 1: Banana Apple (no rule match)
 Pair 2: Apple Apple (no rule match)
 Pair 3: Apple Pear (no rule match)
 Pair 4: Pear Banana (matches rule 4, "Pear Banana becomes nothing")
 2) The program can be written as three sections: Banana Apple Apple | Pear Banana | Apple Apple Banana Banana Banana
 3) Dealing with the token pair makes them go from Pear Banana to nothing.
 4) Putting everything back together we get: Banana Apple Apple Apple Apple Banana Banana Banana

 Iteration 5:
 1) The current program is: Banana Apple Apple Apple Apple Banana Banana Banana
 Pair 1: Banana Apple (no rule match)
 Pair 2: Apple Apple (no rule match)
 Pair 3: Apple Apple (no rule match)
 Pair 4: Apple Apple (no rule match)
 Pair 5: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Apple Apple Apple | Apple Banana | Banana Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Apple Apple Apple Banana Apple Banana Banana

 Iteration 6:
 1) The current program is: Banana Apple Apple Apple Banana Apple Banana Banana
 Pair 1: Banana Apple (no rule match)
 Pair 2: Apple Apple (no rule match)
 Pair 3: Apple Apple (no rule match)
 Pair 4: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Apple Apple | Apple Banana | Apple Banana Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Apple Apple Banana Apple Apple Banana Banana

 Iteration 7:
 1) The current program is: Banana Apple Apple Banana Apple Apple Banana Banana
 Pair 1: Banana Apple (no rule match)
 Pair 2: Apple Apple (no rule match)
 Pair 3: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Apple | Apple Banana | Apple Apple Banana Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Apple Banana Apple Apple Apple Banana Banana

 Iteration 8:
 1) The current program is: Banana Apple Banana Apple Apple Apple Banana Banana
 Pair 1: Banana Apple (no rule match)
 Pair 2: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana | Apple Banana | Apple Apple Apple Banana Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Banana Apple Apple Apple Apple Banana Banana

 Iteration 9:
 1) The current program is: Banana Banana Apple Apple Apple Apple Banana Banana
 Pair 1: Banana Banana (no rule match)
 Pair 2: Banana Apple (no rule match)
 Pair 3: Apple Apple (no rule match)
 Pair 4: Apple Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Banana Apple Apple Apple | Apple Banana | Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Banana Apple Apple Apple Banana Apple Banana

 Iteration 10:
 1) The current program is: Banana Banana Apple Apple Apple Banana Apple Banana
 Pair 1: Banana Banana (no rule match)
 Pair 2: Banana Apple (no rule match)
 Pair 3: Apple Apple (no rule match)
 Pair 4: Apple Apple (no rule match)
 Pair 5: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Banana Apple Apple | Apple Banana | Apple Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Banana Apple Apple Banana Apple Apple Banana

 Iteration 11:
 1) The current program is: Banana Banana Apple Apple Banana Apple Apple Banana
 Pair 1: Banana Banana (no rule match)
 Pair 2: Banana Apple (no rule match)
 Pair 3: Apple Apple (no rule match)
 Pair 4: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Banana Apple | Apple Banana | Apple Apple Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Banana Apple Banana Apple Apple Apple Banana

 Iteration 12:
 1) The current program is: Banana Banana Apple Banana Apple Apple Apple Banana
 Pair 1: Banana Banana (no rule match)
 Pair 2: Banana Apple (no rule match)
 Pair 3: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Banana | Apple Banana | Apple Apple Apple Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Banana Banana Apple Apple Apple Apple Banana

 Iteration 13:
 1) The current program is: Banana Banana Banana Apple Apple Apple Apple Banana
 Pair 1: Banana Banana (no rule match)
 Pair 2: Banana Banana (no rule match)
 Pair 3: Banana Apple (no rule match)
 Pair 4: Apple Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Banana Banana Apple Apple Apple | Apple Banana |
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Banana Banana Apple Apple Apple Banana Apple

 Iteration 14:
 1) The current program is: Banana Banana Banana Apple Apple Apple Banana Apple
 Pair 1: Banana Banana (no rule match)
 Pair 2: Banana Banana (no rule match)
 Pair 3: Banana Apple (no rule match)
 Pair 4: Apple Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Banana Banana Apple Apple | Apple Banana | Apple
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Banana Banana Apple Apple Banana Apple Apple

 Iteration 15:
 1) The current program is: Banana Banana Banana Apple Apple Banana Apple Apple
 Pair 1: Banana Banana (no rule match)
 Pair 2: Banana Banana (no rule match)
 Pair 3: Banana Apple (no rule match)
 Pair 4: Apple Apple (no rule match)
 Pair 5: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Banana Banana Apple | Apple Banana | Apple Apple
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Banana Banana Apple Banana Apple Apple Apple

 Iteration 16:
 1) The current program is: Banana Banana Banana Apple Banana Apple Apple Apple
 Pair 1: Banana Banana (no rule match)
 Pair 2: Banana Banana (no rule match)
 Pair 3: Banana Apple (no rule match)
 Pair 4: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Banana Banana | Apple Banana | Apple Apple Apple
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Banana Banana Banana Apple Apple Apple Apple

 Iteration 17:
 1) The current program is: Banana Banana Banana Banana Apple Apple Apple Apple
 Pair 1: Banana Banana (no rule match)
 Pair 2: Banana Banana (no rule match)
 Pair 3: Banana Banana (no rule match)
 Pair 4: Banana Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Apple (no rule match)
 There are no pairs of tokens which match a rule, so we are done. The final fruit system solution is Banana Banana Banana Banana Apple Apple Apple Apple

 Transforming the fruit system solution back into the A::B system:

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

 <<correct>>

 ## Instance 9:
 Term: #A #A A# A# A# #B #B A# #B #B #B B# 
 Norm: #A #A #B #B #B #B #B A# A# A# A# B# 
 Rwts: 18
 AI-RESPONSE:
 The problem tokens transformed into the fruit system are:

 Orange Orange Apple Apple Apple Banana Banana Apple Banana Banana Banana Pear

 Iteration 1:
 1) The current program is: Orange Orange Apple Apple Apple Banana Banana Apple Banana Banana Banana Pear
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Apple (no rule match)
 Pair 3: Apple Apple (no rule match)
 Pair 4: Apple Apple (no rule match)
 Pair 5: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Orange Apple Apple | Apple Banana | Banana Apple Banana Banana Banana Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Orange Apple Apple Banana Apple Banana Apple Banana Banana Banana Pear

 Iteration 2:
 1) The current program is: Orange Orange Apple Apple Banana Apple Banana Apple Banana Banana Banana Pear
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Apple (no rule match)
 Pair 3: Apple Apple (no rule match)
 Pair 4: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Orange Apple | Apple Banana | Apple Banana Apple Banana Banana Banana Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Orange Apple Banana Apple Apple Banana Apple Banana Banana Banana Pear

 Iteration 3:
 1) The current program is: Orange Orange Apple Banana Apple Apple Banana Apple Banana Banana Banana Pear
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Apple (no rule match)
 Pair 3: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Orange | Apple Banana | Apple Apple Banana Apple Banana Banana Banana Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Orange Banana Apple Apple Apple Banana Apple Banana Banana Banana Pear

 Iteration 4:
 1) The current program is: Orange Orange Banana Apple Apple Apple Banana Apple Banana Banana Banana Pear
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Apple (no rule match)
 Pair 4: Apple Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Orange Banana Apple Apple | Apple Banana | Apple Banana Banana Banana Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Orange Banana Apple Apple Banana Apple Apple Banana Banana Banana Pear

 Iteration 5:
 1) The current program is: Orange Orange Banana Apple Apple Banana Apple Apple Banana Banana Banana Pear
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Apple (no rule match)
 Pair 4: Apple Apple (no rule match)
 Pair 5: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Orange Banana Apple | Apple Banana | Apple Apple Banana Banana Banana Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Orange Banana Apple Banana Apple Apple Apple Banana Banana Banana Pear

 Iteration 6:
 1) The current program is: Orange Orange Banana Apple Banana Apple Apple Apple Banana Banana Banana Pear
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Apple (no rule match)
 Pair 4: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Orange Banana | Apple Banana | Apple Apple Apple Banana Banana Banana Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Orange Banana Banana Apple Apple Apple Apple Banana Banana Banana Pear

 Iteration 7:
 1) The current program is: Orange Orange Banana Banana Apple Apple Apple Apple Banana Banana Banana Pear
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Banana (no rule match)
 Pair 4: Banana Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Apple (no rule match)
 Pair 8: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Orange Banana Banana Apple Apple Apple | Apple Banana | Banana Banana Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Orange Banana Banana Apple Apple Apple Banana Apple Banana Banana Pear

 Iteration 8:
 1) The current program is: Orange Orange Banana Banana Apple Apple Apple Banana Apple Banana Banana Pear
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Banana (no rule match)
 Pair 4: Banana Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Orange Banana Banana Apple Apple | Apple Banana | Apple Banana Banana Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Orange Banana Banana Apple Apple Banana Apple Apple Banana Banana Pear

 Iteration 9:
 1) The current program is: Orange Orange Banana Banana Apple Apple Banana Apple Apple Banana Banana Pear
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Banana (no rule match)
 Pair 4: Banana Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Orange Banana Banana Apple | Apple Banana | Apple Apple Banana Banana Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Orange Banana Banana Apple Banana Apple Apple Apple Banana Banana Pear

 Iteration 10:
 1) The current program is: Orange Orange Banana Banana Apple Banana Apple Apple Apple Banana Banana Pear
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Banana (no rule match)
 Pair 4: Banana Apple (no rule match)
 Pair 5: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Orange Banana Banana | Apple Banana | Apple Apple Apple Banana Banana Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Orange Banana Banana Banana Apple Apple Apple Apple Banana Banana Pear

 Iteration 11:
 1) The current program is: Orange Orange Banana Banana Banana Apple Apple Apple Apple Banana Banana Pear
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Banana (no rule match)
 Pair 4: Banana Banana (no rule match)
 Pair 5: Banana Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Apple (no rule match)
 Pair 8: Apple Apple (no rule match)
 Pair 9: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Orange Banana Banana Banana Apple Apple Apple | Apple Banana | Banana Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Orange Banana Banana Banana Apple Apple Apple Banana Apple Banana Pear

 Iteration 12:
 1) The current program is: Orange Orange Banana Banana Banana Apple Apple Apple Banana Apple Banana Pear
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Banana (no rule match)
 Pair 4: Banana Banana (no rule match)
 Pair 5: Banana Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Apple (no rule match)
 Pair 8: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Orange Banana Banana Banana Apple Apple | Apple Banana | Apple Banana Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Orange Banana Banana Banana Apple Apple Banana Apple Apple Banana Pear

 Iteration 13:
 1) The current program is: Orange Orange Banana Banana Banana Apple Apple Banana Apple Apple Banana Pear
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Banana (no rule match)
 Pair 4: Banana Banana (no rule match)
 Pair 5: Banana Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Orange Banana Banana Banana Apple | Apple Banana | Apple Apple Banana Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Orange Banana Banana Banana Apple Banana Apple Apple Apple Banana Pear

 Iteration 14:
 1) The current program is: Orange Orange Banana Banana Banana Apple Banana Apple Apple Apple Banana Pear
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Banana (no rule match)
 Pair 4: Banana Banana (no rule match)
 Pair 5: Banana Apple (no rule match)
 Pair 6: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Orange Banana Banana Banana | Apple Banana | Apple Apple Apple Banana Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Orange Banana Banana Banana Banana Apple Apple Apple Apple Banana Pear

 Iteration 15:
 1) The current program is: Orange Orange Banana Banana Banana Banana Apple Apple Apple Apple Banana Pear
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Banana (no rule match)
 Pair 4: Banana Banana (no rule match)
 Pair 5: Banana Banana (no rule match)
 Pair 6: Banana Apple (no rule match)
 Pair 7: Apple Apple (no rule match)
 Pair 8: Apple Apple (no rule match)
 Pair 9: Apple Apple (no rule match)
 Pair 10: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Orange Banana Banana Banana Banana Apple Apple Apple | Apple Banana | Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Orange Banana Banana Banana Banana Apple Apple Apple Banana Apple Pear

 Iteration 16:
 1) The current program is: Orange Orange Banana Banana Banana Banana Apple Apple Apple Banana Apple Pear
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Banana (no rule match)
 Pair 4: Banana Banana (no rule match)
 Pair 5: Banana Banana (no rule match)
 Pair 6: Banana Apple (no rule match)
 Pair 7: Apple Apple (no rule match)
 Pair 8: Apple Apple (no rule match)
 Pair 9: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Orange Banana Banana Banana Banana Apple Apple | Apple Banana | Apple Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Orange Banana Banana Banana Banana Apple Apple Banana Apple Apple Pear

 Iteration 17:
 1) The current program is: Orange Orange Banana Banana Banana Banana Apple Apple Banana Apple Apple Pear
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Banana (no rule match)
 Pair 4: Banana Banana (no rule match)
 Pair 5: Banana Banana (no rule match)
 Pair 6: Banana Apple (no rule match)
 Pair 7: Apple Apple (no rule match)
 Pair 8: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Orange Banana Banana Banana Banana Apple | Apple Banana | Apple Apple Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Orange Banana Banana Banana Banana Apple Banana Apple Apple Apple Pear

 Iteration 18:
 1) The current program is: Orange Orange Banana Banana Banana Banana Apple Banana Apple Apple Apple Pear
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Banana (no rule match)
 Pair 4: Banana Banana (no rule match)
 Pair 5: Banana Banana (no rule match)
 Pair 6: Banana Apple (no rule match)
 Pair 7: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Orange Orange Banana Banana Banana Banana | Apple Banana | Apple Apple Apple Pear
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Orange Orange Banana Banana Banana Banana Banana Apple Apple Apple Apple Pear

 Iteration 19:
 1) The current program is: Orange Orange Banana Banana Banana Banana Banana Apple Apple Apple Apple Pear
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Banana (no rule match)
 Pair 3: Banana Banana (no rule match)
 Pair 4: Banana Banana (no rule match)
 Pair 5: Banana Banana (no rule match)
 Pair 6: Banana Banana (no rule match)
 Pair 7: Banana Apple (no rule match)
 Pair 8: Apple Apple (no rule match)
 Pair 9: Apple Apple (no rule match)
 Pair<<not-found>>

 ## Instance 10:
 Term: A# B# B# #A B# A# B# #A B# #A #A #A 
 Norm: #A #A #A B# B# B# B# B# 
 Rwts: 20
 AI-RESPONSE:
 The problem tokens transformed into the fruit system are:

 Apple Pear Pear Orange Pear Apple Pear Orange Pear Orange Orange Orange

 Iteration 1:
 1) The current program is: Apple Pear Pear Orange Pear Apple Pear Orange Pear Orange Orange Orange
 Pair 1: Apple Pear (no rule match)
 Pair 2: Pear Pear (no rule match)
 Pair 3: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Apple Pear | Pear Orange | Pear Apple Pear Orange Pear Orange Orange Orange
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Apple Pear Orange Pear Pear Apple Pear Orange Pear Orange Orange Orange

 Iteration 2:
 1) The current program is: Apple Pear Orange Pear Pear Apple Pear Orange Pear Orange Orange Orange
 Pair 1: Apple Pear (no rule match)
 Pair 2: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Apple | Pear Orange | Pear Pear Apple Pear Orange Pear Orange Orange Orange
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Apple Orange Pear Pear Pear Apple Pear Orange Pear Orange Orange Orange

 Iteration 3:
 1) The current program is: Apple Orange Pear Pear Pear Apple Pear Orange Pear Orange Orange Orange
 Pair 1: Apple Orange (matches rule 1, "Apple Orange becomes nothing")
 2) The program can be written as three sections: | Apple Orange | Pear Pear Pear Apple Pear Orange Pear Orange Orange Orange
 3) Dealing with the token pair makes them go from Apple Orange to nothing.
 4) Putting everything back together we get: Pear Pear Pear Apple Pear Orange Pear Orange Orange Orange

 Iteration 4:
 1) The current program is: Pear Pear Pear Apple Pear Orange Pear Orange Orange Orange
 Pair 1: Pear Pear (no rule match)
 Pair 2: Pear Pear (no rule match)
 Pair 3: Pear Apple (no rule match)
 Pair 4: Apple Pear (no rule match)
 Pair 5: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Pear Pear Pear Apple | Pear Orange | Pear Orange Orange Orange
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Pear Pear Pear Apple Orange Pear Pear Orange Orange Orange

 Iteration 5:
 1) The current program is: Pear Pear Pear Apple Orange Pear Pear Orange Orange Orange
 Pair 1: Pear Pear (no rule match)
 Pair 2: Pear Pear (no rule match)
 Pair 3: Pear Apple (no rule match)
 Pair 4: Apple Orange (matches rule 1, "Apple Orange becomes nothing")
 2) The program can be written as three sections: Pear Pear Pear | Apple Orange | Pear Pear Orange Orange Orange
 3) Dealing with the token pair makes them go from Apple Orange to nothing.
 4) Putting everything back together we get: Pear Pear Pear Pear Pear Orange Orange Orange

 Iteration 6:
 1) The current program is: Pear Pear Pear Pear Pear Orange Orange Orange
 Pair 1: Pear Pear (no rule match)
 Pair 2: Pear Pear (no rule match)
 Pair 3: Pear Pear (no rule match)
 Pair 4: Pear Pear (no rule match)
 Pair 5: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Pear Pear Pear Pear | Pear Orange | Orange Orange
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Pear Pear Pear Pear Orange Pear Orange Orange

 Iteration 7:
 1) The current program is: Pear Pear Pear Pear Orange Pear Orange Orange
 Pair 1: Pear Pear (no rule match)
 Pair 2: Pear Pear (no rule match)
 Pair 3: Pear Pear (no rule match)
 Pair 4: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Pear Pear Pear | Pear Orange | Pear Orange Orange
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Pear Pear Pear Orange Pear Pear Orange Orange

 Iteration 8:
 1) The current program is: Pear Pear Pear Orange Pear Pear Orange Orange
 Pair 1: Pear Pear (no rule match)
 Pair 2: Pear Pear (no rule match)
 Pair 3: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Pear Pear | Pear Orange | Pear Pear Orange Orange
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Pear Pear Orange Pear Pear Pear Orange Orange

 Iteration 9:
 1) The current program is: Pear Pear Orange Pear Pear Pear Orange Orange
 Pair 1: Pear Pear (no rule match)
 Pair 2: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Pear | Pear Orange | Pear Pear Pear Orange Orange
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Pear Orange Pear Pear Pear Pear Orange Orange

 Iteration 10:
 1) The current program is: Pear Orange Pear Pear Pear Pear Orange Orange
 Pair 1: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: | Pear Orange | Pear Pear Pear Pear Orange Orange
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Orange Pear Pear Pear Pear Pear Orange Orange

 Iteration 11:
 1) The current program is: Orange Pear Pear Pear Pear Pear Orange Orange
 Pair 1: Orange Pear (no rule match)
 Pair 2: Pear Pear (no rule match)
 Pair 3: Pear Pear (no rule match)
 Pair 4: Pear Pear (no rule match)
 Pair 5: Pear Pear (no rule match)
 Pair 6: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Orange Pear Pear Pear Pear | Pear Orange | Orange
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Orange Pear Pear Pear Pear Orange Pear Orange

 Iteration 12:
 1) The current program is: Orange Pear Pear Pear Pear Orange Pear Orange
 Pair 1: Orange Pear (no rule match)
 Pair 2: Pear Pear (no rule match)
 Pair 3: Pear Pear (no rule match)
 Pair 4: Pear Pear (no rule match)
 Pair 5: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Orange Pear Pear Pear | Pear Orange | Pear Orange
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Orange Pear Pear Pear Orange Pear Pear Orange

 Iteration 13:
 1) The current program is: Orange Pear Pear Pear Orange Pear Pear Orange
 Pair 1: Orange Pear (no rule match)
 Pair 2: Pear Pear (no rule match)
 Pair 3: Pear Pear (no rule match)
 Pair 4: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Orange Pear Pear | Pear Orange | Pear Pear Orange
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Orange Pear Pear Orange Pear Pear Pear Orange

 Iteration 14:
 1) The current program is: Orange Pear Pear Orange Pear Pear Pear Orange
 Pair 1: Orange Pear (no rule match)
 Pair 2: Pear Pear (no rule match)
 Pair 3: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Orange Pear | Pear Orange | Pear Pear Pear Orange
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Orange Pear Orange Pear Pear Pear Pear Orange

 Iteration 15:
 1) The current program is: Orange Pear Orange Pear Pear Pear Pear Orange
 Pair 1: Orange Pear (no rule match)
 Pair 2: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Orange | Pear Orange | Pear Pear Pear Pear Orange
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Orange Orange Pear Pear Pear Pear Pear Orange

 Iteration 16:
 1) The current program is: Orange Orange Pear Pear Pear Pear Pear Orange
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Pear (no rule match)
 Pair 3: Pear Pear (no rule match)
 Pair 4: Pear Pear (no rule match)
 Pair 5: Pear Pear (no rule match)
 Pair 6: Pear Pear (no rule match)
 Pair 7: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Orange Orange Pear Pear Pear Pear | Pear Orange |
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Orange Orange Pear Pear Pear Pear Orange Pear

 Iteration 17:
 1) The current program is: Orange Orange Pear Pear Pear Pear Orange Pear
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Pear (no rule match)
 Pair 3: Pear Pear (no rule match)
 Pair 4: Pear Pear (no rule match)
 Pair 5: Pear Pear (no rule match)
 Pair 6: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Orange Orange Pear Pear Pear | Pear Orange | Pear
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Orange Orange Pear Pear Pear Orange Pear Pear

 Iteration 18:
 1) The current program is: Orange Orange Pear Pear Pear Orange Pear Pear
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Pear (no rule match)
 Pair 3: Pear Pear (no rule match)
 Pair 4: Pear Pear (no rule match)
 Pair 5: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Orange Orange Pear Pear | Pear Orange | Pear Pear
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Orange Orange Pear Pear Orange Pear Pear Pear

 Iteration 19:
 1) The current program is: Orange Orange Pear Pear Orange Pear Pear Pear
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Pear (no rule match)
 Pair 3: Pear Pear (no rule match)
 Pair 4: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Orange Orange Pear | Pear Orange | Pear Pear Pear
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Orange Orange Pear Orange Pear Pear Pear Pear

 Iteration 20:
 1) The current program is: Orange Orange Pear Orange Pear Pear Pear Pear
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Pear (no rule match)
 Pair 3: Pear Orange (matches rule 3, "Pear Orange becomes Orange Pear")
 2) The program can be written as three sections: Orange Orange | Pear Orange | Pear Pear Pear Pear
 3) Dealing with the token pair makes them go from Pear Orange to Orange Pear.
 4) Putting everything back together we get: Orange Orange Orange Pear Pear Pear Pear Pear

 Iteration 21:
 1) The current program is: Orange Orange Orange Pear Pear Pear Pear Pear
 Pair 1: Orange Orange (no rule match)
 Pair 2: Orange Orange (no rule match)
 Pair 3: Orange Pear (no rule match)
 Pair 4: Pear Pear (no rule match)
 Pair 5: Pear Pear (no rule match)
 Pair 6: Pear Pear (no rule match)
 Pair 7: Pear Pear (no rule match)
 There are no pairs of tokens which match a rule, so we are done. The final fruit system solution is Orange Orange Orange Pear Pear Pear Pear Pear

 Transforming the fruit system solution back into the A::B system:

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

 <<correct>>

 ## Instance 11:
 Term: A# A# A# A# #B A# #B A# #B B# #B #B 
 Norm: #B #B #B #B A# A# A# A# A# A# 
 Rwts: 22
 AI-RESPONSE:
 The problem tokens transformed into the fruit system are:

 Apple Apple Apple Apple Banana Apple Banana Apple Banana Pear Banana Banana

 Iteration 1:
 1) The current program is: Apple Apple Apple Apple Banana Apple Banana Apple Banana Pear Banana Banana
 Pair 1: Apple Apple (no rule match)
 Pair 2: Apple Apple (no rule match)
 Pair 3: Apple Apple (no rule match)
 Pair 4: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Apple Apple Apple | Apple Banana | Apple Banana Apple Banana Pear Banana Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Apple Apple Apple Banana Apple Apple Banana Apple Banana Pear Banana Banana

 Iteration 2:
 1) The current program is: Apple Apple Apple Banana Apple Apple Banana Apple Banana Pear Banana Banana
 Pair 1: Apple Apple (no rule match)
 Pair 2: Apple Apple (no rule match)
 Pair 3: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Apple Apple | Apple Banana | Apple Apple Banana Apple Banana Pear Banana Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Apple Apple Banana Apple Apple Apple Banana Apple Banana Pear Banana Banana

 Iteration 3:
 1) The current program is: Apple Apple Banana Apple Apple Apple Banana Apple Banana Pear Banana Banana
 Pair 1: Apple Apple (no rule match)
 Pair 2: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Apple | Apple Banana | Apple Apple Apple Banana Apple Banana Pear Banana Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Apple Banana Apple Apple Apple Apple Banana Apple Banana Pear Banana Banana

 Iteration 4:
 1) The current program is: Apple Banana Apple Apple Apple Apple Banana Apple Banana Pear Banana Banana
 Pair 1: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: | Apple Banana | Apple Apple Apple Apple Banana Apple Banana Pear Banana Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Apple Apple Apple Apple Apple Banana Apple Banana Pear Banana Banana

 Iteration 5:
 1) The current program is: Banana Apple Apple Apple Apple Apple Banana Apple Banana Pear Banana Banana
 Pair 1: Banana Apple (no rule match)
 Pair 2: Apple Apple (no rule match)
 Pair 3: Apple Apple (no rule match)
 Pair 4: Apple Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Apple Apple Apple Apple | Apple Banana | Apple Banana Pear Banana Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Apple Apple Apple Apple Banana Apple Apple Banana Pear Banana Banana

 Iteration 6:
 1) The current program is: Banana Apple Apple Apple Apple Banana Apple Apple Banana Pear Banana Banana
 Pair 1: Banana Apple (no rule match)
 Pair 2: Apple Apple (no rule match)
 Pair 3: Apple Apple (no rule match)
 Pair 4: Apple Apple (no rule match)
 Pair 5: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Apple Apple Apple | Apple Banana | Apple Apple Banana Pear Banana Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Apple Apple Apple Banana Apple Apple Apple Banana Pear Banana Banana

 Iteration 7:
 1) The current program is: Banana Apple Apple Apple Banana Apple Apple Apple Banana Pear Banana Banana
 Pair 1: Banana Apple (no rule match)
 Pair 2: Apple Apple (no rule match)
 Pair 3: Apple Apple (no rule match)
 Pair 4: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Apple Apple | Apple Banana | Apple Apple Apple Banana Pear Banana Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Apple Apple Banana Apple Apple Apple Apple Banana Pear Banana Banana

 Iteration 8:
 1) The current program is: Banana Apple Apple Banana Apple Apple Apple Apple Banana Pear Banana Banana
 Pair 1: Banana Apple (no rule match)
 Pair 2: Apple Apple (no rule match)
 Pair 3: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Apple | Apple Banana | Apple Apple Apple Apple Banana Pear Banana Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Apple Banana Apple Apple Apple Apple Apple Banana Pear Banana Banana

 Iteration 9:
 1) The current program is: Banana Apple Banana Apple Apple Apple Apple Apple Banana Pear Banana Banana
 Pair 1: Banana Apple (no rule match)
 Pair 2: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana | Apple Banana | Apple Apple Apple Apple Apple Banana Pear Banana Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Banana Apple Apple Apple Apple Apple Apple Banana Pear Banana Banana

 Iteration 10:
 1) The current program is: Banana Banana Apple Apple Apple Apple Apple Apple Banana Pear Banana Banana
 Pair 1: Banana Banana (no rule match)
 Pair 2: Banana Apple (no rule match)
 Pair 3: Apple Apple (no rule match)
 Pair 4: Apple Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Apple (no rule match)
 Pair 8: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Banana Apple Apple Apple Apple Apple | Apple Banana | Pear Banana Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Banana Apple Apple Apple Apple Apple Banana Apple Pear Banana Banana

 Iteration 11:
 1) The current program is: Banana Banana Apple Apple Apple Apple Apple Banana Apple Pear Banana Banana
 Pair 1: Banana Banana (no rule match)
 Pair 2: Banana Apple (no rule match)
 Pair 3: Apple Apple (no rule match)
 Pair 4: Apple Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Banana Apple Apple Apple Apple | Apple Banana | Apple Pear Banana Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Banana Apple Apple Apple Apple Banana Apple Apple Pear Banana Banana

 Iteration 12:
 1) The current program is: Banana Banana Apple Apple Apple Apple Banana Apple Apple Pear Banana Banana
 Pair 1: Banana Banana (no rule match)
 Pair 2: Banana Apple (no rule match)
 Pair 3: Apple Apple (no rule match)
 Pair 4: Apple Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Banana Apple Apple Apple | Apple Banana | Apple Apple Pear Banana Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Banana Apple Apple Apple Banana Apple Apple Apple Pear Banana Banana

 Iteration 13:
 1) The current program is: Banana Banana Apple Apple Apple Banana Apple Apple Apple Pear Banana Banana
 Pair 1: Banana Banana (no rule match)
 Pair 2: Banana Apple (no rule match)
 Pair 3: Apple Apple (no rule match)
 Pair 4: Apple Apple (no rule match)
 Pair 5: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Banana Apple Apple | Apple Banana | Apple Apple Apple Pear Banana Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Banana Apple Apple Banana Apple Apple Apple Apple Pear Banana Banana

 Iteration 14:
 1) The current program is: Banana Banana Apple Apple Banana Apple Apple Apple Apple Pear Banana Banana
 Pair 1: Banana Banana (no rule match)
 Pair 2: Banana Apple (no rule match)
 Pair 3: Apple Apple (no rule match)
 Pair 4: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Banana Apple | Apple Banana | Apple Apple Apple Apple Pear Banana Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Banana Apple Banana Apple Apple Apple Apple Apple Pear Banana Banana

 Iteration 15:
 1) The current program is: Banana Banana Apple Banana Apple Apple Apple Apple Apple Pear Banana Banana
 Pair 1: Banana Banana (no rule match)
 Pair 2: Banana Apple (no rule match)
 Pair 3: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Banana | Apple Banana | Apple Apple Apple Apple Apple Pear Banana Banana
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Banana Banana Apple Apple Apple Apple Apple Apple Pear Banana Banana

 Iteration 16:
 1) The current program is: Banana Banana Banana Apple Apple Apple Apple Apple Apple Pear Banana Banana
 Pair 1: Banana Banana (no rule match)
 Pair 2: Banana Banana (no rule match)
 Pair 3: Banana Apple (no rule match)
 Pair 4: Apple Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Apple (no rule match)
 Pair 8: Apple Apple (no rule match)
 Pair 9: Apple Pear (no rule match)
 Pair 10: Pear Banana (matches rule 4, "Pear Banana becomes nothing")
 2) The program can be written as three sections: Banana Banana Banana Apple Apple Apple Apple Apple Apple | Pear Banana | Banana
 3) Dealing with the token pair makes them go from Pear Banana to nothing.
 4) Putting everything back together we get: Banana Banana Banana Apple Apple Apple Apple Apple Apple Banana

 Iteration 17:
 1) The current program is: Banana Banana Banana Apple Apple Apple Apple Apple Apple Banana
 Pair 1: Banana Banana (no rule match)
 Pair 2: Banana Banana (no rule match)
 Pair 3: Banana Apple (no rule match)
 Pair 4: Apple Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Apple (no rule match)
 Pair 8: Apple Apple (no rule match)
 Pair 9: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Banana Banana Apple Apple Apple Apple Apple | Apple Banana |
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Banana Banana Apple Apple Apple Apple Apple Banana Apple

 Iteration 18:
 1) The current program is: Banana Banana Banana Apple Apple Apple Apple Apple Banana Apple
 Pair 1: Banana Banana (no rule match)
 Pair 2: Banana Banana (no rule match)
 Pair 3: Banana Apple (no rule match)
 Pair 4: Apple Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Apple (no rule match)
 Pair 8: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Banana Banana Apple Apple Apple Apple | Apple Banana | Apple
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Banana Banana Apple Apple Apple Apple Banana Apple Apple

 Iteration 19:
 1) The current program is: Banana Banana Banana Apple Apple Apple Apple Banana Apple Apple
 Pair 1: Banana Banana (no rule match)
 Pair 2: Banana Banana (no rule match)
 Pair 3: Banana Apple (no rule match)
 Pair 4: Apple Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Apple (no rule match)
 Pair 7: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Banana Banana Apple Apple Apple | Apple Banana | Apple Apple
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Banana Banana Apple Apple Apple Banana Apple Apple Apple

 Iteration 20:
 1) The current program is: Banana Banana Banana Apple Apple Apple Banana Apple Apple Apple
 Pair 1: Banana Banana (no rule match)
 Pair 2: Banana Banana (no rule match)
 Pair 3: Banana Apple (no rule match)
 Pair 4: Apple Apple (no rule match)
 Pair 5: Apple Apple (no rule match)
 Pair 6: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Banana Banana Apple Apple | Apple Banana | Apple Apple Apple
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Banana Banana Apple Apple Banana Apple Apple Apple Apple

 Iteration 21:
 1) The current program is: Banana Banana Banana Apple Apple Banana Apple Apple Apple Apple
 Pair 1: Banana Banana (no rule match)
 Pair 2: Banana Banana (no rule match)
 Pair 3: Banana Apple (no rule match)
 Pair 4: Apple Apple (no rule match)
 Pair 5: Apple Banana (matches rule 2, "Apple Banana becomes Banana Apple")
 2) The program can be written as three sections: Banana Banana Banana Apple | Apple Banana | Apple Apple Apple Apple
 3) Dealing with the token pair makes them go from Apple Banana to Banana Apple.
 4) Putting everything back together we get: Banana Banana Banana Apple Banana Apple Apple<<not-found>>


 Final score: 10 / 12