Created
April 11, 2024 08:35
-
-
Save abrasumente233/38af2cf0f68354e91f8f73de0097eccd to your computer and use it in GitHub Desktop.
mixtral-8x22b-log.txt
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| ## Instance 0: | |
| Term: #A #A #B #B #B #B #B A# A# A# A# B# | |
| Norm: #A #A #B #B #B #B #B A# A# A# A# B# | |
| Rwt: 0 | |
| AI-RESPONSE: | |
| - #A -> J | |
| - #A -> J | |
| - #B -> L | |
| - #B -> L | |
| - #B -> L | |
| - #B -> L | |
| - #B -> L | |
| - A# -> H | |
| - A# -> H | |
| - A# -> H | |
| - A# -> H | |
| - B# -> K | |
| P2: Compute the program | |
| Initial program in the internal format: [0:J, 1:J, 2:L, 3:L, 4:L, 5:L, 6:L, 7:H, 8:H, 9:H, 10:H, 11:K] | |
| pos (0, 1): «0:J, 1:J». Checking whether «JJ» is among the four rules: «HJ» == «JJ»? No. «HL» == «JJ»? No. «KJ» == «JJ»? No. «KL» == «JJ»? No. Did not find a matching rule | |
| pos (1, 2): «1:J, 2:L». Checking whether «JL» is among the four rules: «HJ» == «JL»? No. «HL» == «JL»? No. «KJ» == «JL»? No. «KL» == «JL»? No. Did not find a matching rule | |
| pos (2, 3): «2:L, 3:L». Checking whether «LL» is among the four rules: «HJ» == «LL»? No. «HL» == «LL»? No. «KJ» == «LL»? No. «KL» == «LL»? No. Did not find a matching rule | |
| pos (3, 4): «3:L, 4:L». Checking whether «LL» is among the four rules: «HJ» == «LL»? No. «HL» == «LL»? No. «KJ» == «LL»? No. «KL» == «LL»? No. Did not find a matching rule | |
| pos (4, 5): «4:L, 5:L». Checking whether «LL» is among the four rules: «HJ» == «LL»? No. «HL» == «LL»? No. «KJ» == «LL»? No. «KL» == «LL»? No. Did not find a matching rule | |
| pos (5, 6): «5:L, 6:L». Checking whether «LL» is among the four rules: «HJ» == «LL»? No. «HL» == «LL»? No. «KJ» == «LL»? No. «KL» == «LL»? No. Did not find a matching rule | |
| pos (6, 7): «6:L, 7:H». Checking whether «LH» is among the four rules: «HJ» == «LH»? No. «HL» == «LH»? No. «KJ» == «LH»? No. «KL» == «LH»? No. Did not find a matching rule | |
| pos (7, 8): «7:H, 8:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (8, 9): «8:H, 9:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (9, 10): «9:H, 10:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (10, 11): «10:H, 11:K». Checking whether «HK» is among the four rules: «HJ» == «HK»? No. «HL» == «HK»? No. «KJ» == «HK»? No. «KL» == «HK»? No. Did not find a matching rule | |
| In this step, we did not perform any rewrite or removal, thus stopping | |
| Final result in the internal format: [0:J, 1:J, 2:L, 3:L, 4:L, 5:L, 6:L, 7:H, 8:H, 9:H, 10:H, 11:K] | |
| P3. Translating from the internal format to original format, step by step: | |
| P3.1. As a reminder, list the translation rules from internal to original: | |
| - H -> A# | |
| - J -> #A | |
| - K -> B# | |
| - L -> #B | |
| P3.2. Translate the program back to the original format: | |
| - J -> #A | |
| - J -> #A | |
| - L -> #B | |
| - L -> #B | |
| - L -> #B | |
| - L -> #B | |
| - L -> #B | |
| - H -> A# | |
| - H -> A# | |
| - H -> A# | |
| - H -> A# | |
| - K -> B# | |
| Final result in the original format: #A #A #B #B #B #B #B A# A# A# A# B# | |
| <solution>#A #A #B #B #B #B #B A# A# A# A# B# | |
| AI-Solution: #A #A #B #B #B #B #B A# A# A# A# B# | |
| <<correct>> | |
| ## Instance 1: | |
| Term: #B B# A# B# #B B# A# B# #B A# B# B# | |
| Norm: #B B# A# B# #B B# A# B# #B A# B# B# | |
| Rwt: 2 | |
| AI-RESPONSE: | |
| - #B -> L | |
| - B# -> K | |
| - A# -> H | |
| - B# -> K | |
| - #B -> L | |
| - B# -> K | |
| - A# -> H | |
| - B# -> K | |
| - #B -> L | |
| - A# -> H | |
| - B# -> K | |
| - B# -> K | |
| Initial program in the internal format: [0:L, 1:K, 2:H, 3:K, 4:L, 5:K, 6:H, 7:K, 8:L, 9:H, 10:K, 11:K] | |
| P2: Compute the program | |
| Step 0: [0:L, 1:K, 2:H, 3:K, 4:L, 5:K, 6:H, 7:K, 8:L, 9:H, 10:K, 11:K] | |
| pos (0, 1): «0:L, 1:K». Checking whether «LK» is among the four rules: «HJ» == «LK»? No. «HL» == «LK»? No. «KJ» == «LK»? No. «KL» == «LK»? No. Did not find a matching rule | |
| pos (1, 2): «1:K, 2:H». Checking whether «KH» is among the four rules: «HJ» == «KH»? No. «HL» == «KH»? No. «KJ» == «KH»? No. «KL» == «KH»? No. Did not find a matching rule | |
| pos (2, 3): «2:H, 3:K». Checking whether «HK» is among the four rules: «HJ» == «HK»? No. «HL» == «HK»? No. «KJ» == «HK»? No. «KL» == «HK»? No. Did not find a matching rule | |
| pos (3, 4): «3:K, 4:L». Checking whether «KL» is among the four rules: «HJ» == «KL»? No. «HL» == «KL»? No. «KJ» == «KL»? No. «KL» == «KL»? Yes. Found a matching rule | |
| Removing the pair «3:K, 4:L». Old index = old_i = 3 | |
| Before removing: [0:L, 1:K, 2:H, 3:K, 4:L, 5:K, 6:H, 7:K, 8:L, 9:H, 10:K, 11:K] | |
| Labelling the TWO elements «3:K, 4:L» to be removed: [0:L, 1:K, 2:H, 3:removed, 4:removed, 5:K, 6:H, 7:K, 8:L, 9:H, 10:K, 11:K] | |
| After removing the labelled TWO elements «3:K, 4:L» to be removed, without renumbering: [0:L, 1:K, 2:H, 5:K, 6:H, 7:K, 8:L, 9:H, 10:K, 11:K] | |
| Renumbering: [0:L, 1:K, 2:H, 3:K, 4:H, 5:K, 6:L, 7:H, 8:K, 9:K]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=3+0=3. max_i:=9 Reached end of the step = (i >= max_i) = (3 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (3, 4): «3:K, 4:H». Checking whether «KH» is among the four rules: «HJ» == «KH»? No. «HL» == «KH»? No. «KJ» == «KH»? No. «KL» == «KH»? No. Did not find a matching rule | |
| pos (4, 5): «4:H, 5:K». Checking whether «HK» is among the four rules: «HJ» == «HK»? No. «HL» == «HK»? No. «KJ» == «HK»? No. «KL» == «HK»? No. Did not find a matching rule | |
| pos (5, 6): «5:K, 6:L». Checking whether «KL» is among the four rules: «HJ» == «KL»? No. «HL» == «KL»? No. «KJ» == «KL»? No. «KL» == «KL»? Yes. Found a matching rule | |
| Removing the pair «5:K, 6:L». Old index = old_i = 5 | |
| Before removing: [0:L, 1:K, 2:H, 3:K, 4:H, 5:K, 6:L, 7:H, 8:K, 9:K] | |
| Labelling the TWO elements «5:K, 6:L» to be removed: [0:L, 1:K, 2:H, 3:K, 4:H, 5:removed, 6:removed, 7:H, 8:K, 9:K] | |
| After removing the labelled TWO elements «5:K, 6:L» to be removed, without renumbering: [0:L, 1:K, 2:H, 3:K, 4:H, 7:H, 8:K, 9:K] | |
| Renumbering: [0:L, 1:K, 2:H, 3:K, 4:H, 5:H, 6:K, 7:K]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=5+0=5. max_i:=7 Reached end of the step = (i >= max_i) = (5 >= 7) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (5, 6): «5:H, 6:K». Checking whether «HK» is among the four rules: «HJ» == «HK»? No. «HL» == «HK»? No. «KJ» == «HK»? No. «KL» == «HK»? No. Did not find a matching rule | |
| pos (6, 7): «6:K, 7:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 1: [0:L, 1:K, 2:H, 3:K, 4:H, 5:H, 6:K, 7:K] | |
| pos (0, 1): «0:L, 1:K». Checking whether «LK» is among the four rules: «HJ» == «LK»? No. «HL» == «LK»? No. «KJ» == «LK»? No. «KL» == «LK»? No. Did not find a matching rule | |
| pos (1, 2): «1:K, 2:H». Checking whether «KH» is among the four rules: «HJ» == «KH»? No. «HL» == «KH»? No. «KJ» == «KH»? No. «KL» == «KH»? No. Did not find a matching rule | |
| pos (2, 3): «2:H, 3:K». Checking whether «HK» is among the four rules: «HJ» == «HK»? No. «HL» == «HK»? No. «KJ» == «HK»? No. «KL» == «HK»? No. Did not find a matching rule | |
| pos (3, 4): «3:K, 4:H». Checking whether «KH» is among the four rules: «HJ» == «KH»? No. «HL» == «KH»? No. «KJ» == «KH»? No. «KL» == «KH»? No. Did not find a matching rule | |
| pos (4, 5): «4:H, 5:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (5, 6): «5:H, 6:K». Checking whether «HK» is among the four rules: «HJ» == «HK»? No. «HL» == «HK»? No. «KJ» == «HK»? No. «KL» == «HK»? No. Did not find a matching rule | |
| pos (6, 7): «6:K, 7:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| In this step, we did not perform any rewrite or removal, thus stopping | |
| Final result in the internal format: [0:L, 1:K, 2:H, 3:K, 4:H, 5:H, 6:K, 7:K] | |
| P3. Translating from the internal format to original format, step by step: | |
| P3.1. As a reminder, list the translation rules from internal to original: | |
| - H -> A# | |
| - J -> #A | |
| - K -> B# | |
| - L -> #B | |
| P3.2. Translate the program back to the original format: | |
| - L -> #B | |
| - K -> B# | |
| - H -> A# | |
| - K -> B# | |
| - H -> A# | |
| - H -> A# | |
| - K -> B# | |
| - K -> B# | |
| Final result in the original format: #B B# A# B# A# A# B# B# | |
| <solution>#B B# A# B# A# A# B# B# | |
| AI-Solution: #B B# A# B# A# A# B# B# | |
| <<correct>> | |
| ## Instance 2: | |
| Term: B# #A #B A# #A #B #B B# #B #A #A A# | |
| Norm: B# #A #B A# #A #B #B B# #B #A #A A# | |
| Rwt: 4 | |
| AI-RESPONSE: | |
| - B# -> K | |
| - #A -> J | |
| - #B -> L | |
| - A# -> H | |
| - #A -> J | |
| - #B -> L | |
| - #B -> L | |
| - B# -> K | |
| - #B -> L | |
| - #A -> J | |
| - #A -> J | |
| - A# -> H | |
| Initial program in the internal format: [0:K, 1:J, 2:L, 3:H, 4:J, 5:L, 6:L, 7:K, 8:L, 9:J, 10:J, 11:H] | |
| P2: Compute the program | |
| Step 0: [0:K, 1:J, 2:L, 3:H, 4:J, 5:L, 6:L, 7:K, 8:L, 9:J, 10:J, 11:H] | |
| pos (0, 1): «0:K, 1:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «0:K, 1:J» to «0:J, 1:K». Old index = old_i = 0 | |
| After rewrite: [0:J, 1:K, 2:L, 3:H, 4:J, 5:L, 6:L, 7:K, 8:L, 9:J, 10:J, 11:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=0+1=1. max_i:=11 Reached end of the step = (i >= max_i) = (1 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (1, 2): «1:K, 2:L». Checking whether «KL» is among the four rules: «HJ» == «KL»? No. «HL» == «KL»? No. «KJ» == «KL»? No. «KL» == «KL»? Yes. Found a matching rule | |
| Removing the pair «1:K, 2:L». Old index = old_i = 1 | |
| Before removing: [0:J, 1:K, 2:L, 3:H, 4:J, 5:L, 6:L, 7:K, 8:L, 9:J, 10:J, 11:H] | |
| Labelling the TWO elements «1:K, 2:L» to be removed: [0:J, 1:removed, 2:removed, 3:H, 4:J, 5:L, 6:L, 7:K, 8:L, 9:J, 10:J, 11:H] | |
| After removing the labelled TWO elements «1:K, 2:L» to be removed, without renumbering: [0:J, 3:H, 4:J, 5:L, 6:L, 7:K, 8:L, 9:J, 10:J, 11:H] | |
| Renumbering: [0:J, 1:H, 2:J, 3:L, 4:L, 5:K, 6:L, 7:J, 8:J, 9:H]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=1+0=1. max_i:=9 Reached end of the step = (i >= max_i) = (1 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (1, 2): «1:H, 2:J». Checking whether «HJ» is among the four rules: «HJ» == «HJ»? Yes. «HL» == «HJ»? No. «KJ» == «HJ»? No. «KL» == «HJ»? No. Found a matching rule | |
| Removing the pair «1:H, 2:J». Old index = old_i = 1 | |
| Before removing: [0:J, 1:H, 2:J, 3:L, 4:L, 5:K, 6:L, 7:J, 8:J, 9:H] | |
| Labelling the TWO elements «1:H, 2:J» to be removed: [0:J, 1:removed, 2:removed, 3:L, 4:L, 5:K, 6:L, 7:J, 8:J, 9:H] | |
| After removing the labelled TWO elements «1:H, 2:J» to be removed, without renumbering: [0:J, 3:L, 4:L, 5:K, 6:L, 7:J, 8:J, 9:H] | |
| Renumbering: [0:J, 1:L, 2:L, 3:K, 4:L, 5:J, 6:J, 7:H]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=1+0=1. max_i:=7 Reached end of the step = (i >= max_i) = (1 >= 7) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (1, 2): «1:L, 2:L». Checking whether «LL» is among the four rules: «HJ» == «LL»? No. «HL» == «LL»? No. «KJ» == «LL»? No. «KL» == «LL»? No. Did not find a matching rule | |
| pos (2, 3): «2:L, 3:K». Checking whether «LK» is among the four rules: «HJ» == «LK»? No. «HL» == «LK»? No. «KJ» == «LK»? No. «KL» == «LK»? No. Did not find a matching rule | |
| pos (3, 4): «3:K, 4:L». Checking whether «KL» is among the four rules: «HJ» == «KL»? No. «HL» == «KL»? No. «KJ» == «KL»? No. «KL» == «KL»? Yes. Found a matching rule | |
| Removing the pair «3:K, 4:L». Old index = old_i = 3 | |
| Before removing: [0:J, 1:L, 2:L, 3:K, 4:L, 5:J, 6:J, 7:H] | |
| Labelling the TWO elements «3:K, 4:L» to be removed: [0:J, 1:L, 2:L, 3:removed, 4:removed, 5:J, 6:J, 7:H] | |
| After removing the labelled TWO elements «3:K, 4:L» to be removed, without renumbering: [0:J, 1:L, 2:L, 5:J, 6:J, 7:H] | |
| Renumbering: [0:J, 1:L, 2:L, 3:J, 4:J, 5:H]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=3+0=3. max_i:=5 Reached end of the step = (i >= max_i) = (3 >= 5) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (3, 4): «3:L, 4:J». Checking whether «LJ» is among the four rules: «HJ» == «LJ»? No. «HL» == «LJ»? No. «KJ» == «LJ»? No. «KL» == «LJ»? No. Did not find a matching rule | |
| pos (4, 5): «4:J, 5:H». Checking whether «JH» is among the four rules: «HJ» == «JH»? No. «HL» == «JH»? No. «KJ» == «JH»? No. «KL» == «JH»? No. Did not find a matching rule | |
| In this step, we did not perform any rewrite or removal, thus stopping | |
| Final result in the internal format: [0:J, 1:L, 2:L, 3:J, 4:J, 5:H] | |
| P3. Translating from the internal format to original format, step by step: | |
| P3.1. As a reminder, list the translation rules from internal to original: | |
| - H -> A# | |
| - J -> #A | |
| - K -> B# | |
| - L -> #B | |
| P3.2. Translate the program back to the original format: | |
| - J -> #A | |
| - L -> #B | |
| - L -> #B | |
| - J -> #A | |
| - J -> #A | |
| - H -> A# | |
| Final result in the original format: #A #B #B #A #A A# | |
| <solution>#A #B #B #A #A A# | |
| AI-Solution: #A #B #B #A #A A# | |
| <<correct>> | |
| ## Instance 3: | |
| Term: B# B# #B #B A# #A #B A# A# A# #B A# | |
| Norm: B# B# #B #B A# #A #B A# A# A# #B A# | |
| Rwt: 6 | |
| AI-RESPONSE: | |
| - B# -> K | |
| - B# -> K | |
| - #B -> L | |
| - #B -> L | |
| - A# -> H | |
| - #A -> J | |
| - #B -> L | |
| - A# -> H | |
| - A# -> H | |
| - A# -> H | |
| - #B -> L | |
| - A# -> H | |
| P2: Compute the program | |
| Initial program in the internal format: [0:K, 1:K, 2:L, 3:L, 4:H, 5:J, 6:L, 7:H, 8:H, 9:H, 10:L, 11:H] | |
| pos (0, 1): «0:K, 1:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| pos (1, 2): «1:K, 2:L». Checking whether «KL» is among the four rules: «HJ» == «KL»? No. «HL» == «KL»? No. «KJ» == «KL»? No. «KL» == «KL»? Yes. Found a matching rule | |
| Removing the pair «1:K, 2:L». Old index = old_i = 1 | |
| Before removing: [0:K, 1:K, 2:L, 3:L, 4:H, 5:J, 6:L, 7:H, 8:H, 9:H, 10:L, 11:H] | |
| Labelling the TWO elements «1:K, 2:L» to be removed: [0:K, 1:removed, 2:removed, 3:L, 4:H, 5:J, 6:L, 7:H, 8:H, 9:H, 10:L, 11:H] | |
| After removing the labelled TWO elements «1:K, 2:L» to be removed, without renumbering: [0:K, 3:L, 4:H, 5:J, 6:L, 7:H, 8:H, 9:H, 10:L, 11:H] | |
| Renumbering: [0:K, 1:L, 2:H, 3:J, 4:L, 5:H, 6:H, 7:H, 8:L, 9:H]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=1+0=1. max_i:=9 Reached end of the step = (i >= max_i) = (1 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (1, 2): «1:L, 2:H». Checking whether «LH» is among the four rules: «HJ» == «LH»? No. «HL» == «LH»? No. «KJ» == «LH»? No. «KL» == «LH»? No. Did not find a matching rule | |
| pos (2, 3): «2:H, 3:J». Checking whether «HJ» is among the four rules: «HJ» == «HJ»? Yes. «HL» == «HJ»? No. «KJ» == «HJ»? No. «KL» == «HJ»? No. Found a matching rule | |
| Removing the pair «2:H, 3:J». Old index = old_i = 2 | |
| Before removing: [0:K, 1:L, 2:H, 3:J, 4:L, 5:H, 6:H, 7:H, 8:L, 9:H] | |
| Labelling the TWO elements «2:H, 3:J» to be removed: [0:K, 1:L, 2:removed, 3:removed, 4:L, 5:H, 6:H, 7:H, 8:L, 9:H] | |
| After removing the labelled TWO elements «2:H, 3:J» to be removed, without renumbering: [0:K, 1:L, 4:L, 5:H, 6:H, 7:H, 8:L, 9:H] | |
| Renumbering: [0:K, 1:L, 2:L, 3:H, 4:H, 5:H, 6:L, 7:H]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=2+0=2. max_i:=7 Reached end of the step = (i >= max_i) = (2 >= 7) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (2, 3): «2:L, 3:H». Checking whether «LH» is among the four rules: «HJ» == «LH»? No. «HL» == «LH»? No. «KJ» == «LH»? No. «KL» == «LH»? No. Did not find a matching rule | |
| pos (3, 4): «3:H, 4:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (4, 5): «4:H, 5:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (5, 6): «5:H, 6:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «5:H, 6:L» to «5:L, 6:H». Old index = old_i = 5 | |
| After rewrite: [0:K, 1:L, 2:L, 3:H, 4:H, 5:L, 6:H, 7:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=5+1=6. max_i:=7 Reached end of the step = (i >= max_i) = (6 >= 7) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (6, 7): «6:H, 7:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 1: [0:K, 1:L, 2:L, 3:H, 4:H, 5:L, 6:H, 7:H] | |
| pos (0, 1): «0:K, 1:L». Checking whether «KL» is among the four rules: «HJ» == «KL»? No. «HL» == «KL»? No. «KJ» == «KL»? No. «KL» == «KL»? Yes. Found a matching rule | |
| Removing the pair «0:K, 1:L». Old index = old_i = 0 | |
| Before removing: [0:K, 1:L, 2:L, 3:H, 4:H, 5:L, 6:H, 7:H] | |
| Labelling the TWO elements «0:K, 1:L» to be removed: [0:removed, 1:removed, 2:L, 3:H, 4:H, 5:L, 6:H, 7:H] | |
| After removing the labelled TWO elements «0:K, 1:L» to be removed, without renumbering: [2:L, 3:H, 4:H, 5:L, 6:H, 7:H] | |
| Renumbering: [0:L, 1:H, 2:H, 3:L, 4:H, 5:H]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=0+0=0. max_i:=5 Reached end of the step = (i >= max_i) = (0 >= 5) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (0, 1): «0:L, 1:H». Checking whether «LH» is among the four rules: «HJ» == «LH»? No. «HL» == «LH»? No. «KJ» == «LH»? No. «KL» == «LH»? No. Did not find a matching rule | |
| pos (1, 2): «1:H, 2:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (2, 3): «2:H, 3:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «2:H, 3:L» to «2:L, 3:H». Old index = old_i = 2 | |
| After rewrite: [0:L, 1:H, 2:L, 3:H, 4:H, 5:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=2+1=3. max_i:=5 Reached end of the step = (i >= max_i) = (3 >= 5) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (3, 4): «3:H, 4:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (4, 5): «4:H, 5:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 2: [0:L, 1:H, 2:L, 3:H, 4:H, 5:H] | |
| pos (0, 1): «0:L, 1:H». Checking whether «LH» is among the four rules: «HJ» == «LH»? No. «HL» == «LH»? No. «KJ» == «LH»? No. «KL» == «LH»? No. Did not find a matching rule | |
| pos (1, 2): «1:H, 2:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «1:H, 2:L» to «1:L, 2:H». Old index = old_i = 1 | |
| After rewrite: [0:L, 1:L, 2:H, 3:H, 4:H, 5:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=1+1=2. max_i:=5 Reached end of the step = (i >= max_i) = (2 >= 5) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (2, 3): «2:H, 3:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (3, 4): «3:H, 4:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (4, 5): «4:H, 5:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 3: [0:L, 1:L, 2:H, 3:H, 4:H, 5:H] | |
| pos (0, 1): «0:L, 1:L». Checking whether «LL» is among the four rules: «HJ» == «LL»? No. «HL» == «LL»? No. «KJ» == «LL»? No. «KL» == «LL»? No. Did not find a matching rule | |
| pos (1, 2): «1:L, 2:H». Checking whether «LH» is among the four rules: «HJ» == «LH»? No. «HL» == «LH»? No. «KJ» == «LH»? No. «KL» == «LH»? No. Did not find a matching rule | |
| pos (2, 3): «2:H, 3:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (3, 4): «3:H, 4:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (4, 5): «4:H, 5:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| In this step, we did not perform any rewrite or removal, thus stopping | |
| Final result in the internal format: [0:L, 1:L, 2:H, 3:H, 4:H, 5:H] | |
| P3. Translating from the internal format to original format, step by step: | |
| P3.1. As a reminder, list the translation rules from internal to original: | |
| - H -> A# | |
| - J -> #A | |
| - K -> B# | |
| - L -> #B | |
| P3.2. Translate the program back to the original format: | |
| - L -> #B | |
| - L -> #B | |
| - H -> A# | |
| - H -> A# | |
| - H -> A# | |
| - H -> A# | |
| Final result in the original format: #B #B A# A# A# A# | |
| <solution>#B #B A# A# A# A# | |
| AI-Solution: #B #B A# A# A# A# | |
| <<correct>> | |
| ## Instance 4: | |
| Term: A# B# B# #A #A B# A# B# #A #B A# B# | |
| Norm: A# B# B# #A #A B# A# B# #A #B A# B# | |
| Rwt: 8 | |
| AI-RESPONSE: | |
| - A# -> H | |
| - B# -> K | |
| - B# -> K | |
| - #A -> J | |
| - #A -> J | |
| - B# -> K | |
| - A# -> H | |
| - B# -> K | |
| - #A -> J | |
| - #B -> L | |
| - A# -> H | |
| - B# -> K | |
| Initial program in the internal format: [0:H, 1:K, 2:K, 3:J, 4:J, 5:K, 6:H, 7:K, 8:J, 9:L, 10:H, 11:K] | |
| P2: Compute the program | |
| Step 0: [0:H, 1:K, 2:K, 3:J, 4:J, 5:K, 6:H, 7:K, 8:J, 9:L, 10:H, 11:K] | |
| pos (0, 1): «0:H, 1:K». Checking whether «HK» is among the four rules: «HJ» == «HK»? No. «HL» == «HK»? No. «KJ» == «HK»? No. «KL» == «HK»? No. Did not find a matching rule | |
| pos (1, 2): «1:K, 2:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| pos (2, 3): «2:K, 3:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «2:K, 3:J» to «2:J, 3:K». Old index = old_i = 2 | |
| After rewrite: [0:H, 1:K, 2:J, 3:K, 4:J, 5:K, 6:H, 7:K, 8:J, 9:L, 10:H, 11:K]. Using this as the new input | |
| rule is not empty, i:=old_i+1=2+1=3. max_i:=11 Reached end of the step = (i >= max_i) = (3 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (3, 4): «3:K, 4:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «3:K, 4:J» to «3:J, 4:K». Old index = old_i = 3 | |
| After rewrite: [0:H, 1:K, 2:J, 3:J, 4:K, 5:K, 6:H, 7:K, 8:J, 9:L, 10:H, 11:K]. Using this as the new input | |
| rule is not empty, i:=old_i+1=3+1=4. max_i:=11 Reached end of the step = (i >= max_i) = (4 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (4, 5): «4:K, 5:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| pos (5, 6): «5:K, 6:H». Checking whether «KH» is among the four rules: «HJ» == «KH»? No. «HL» == «KH»? No. «KJ» == «KH»? No. «KL» == «KH»? No. Did not find a matching rule | |
| pos (6, 7): «6:H, 7:K». Checking whether «HK» is among the four rules: «HJ» == «HK»? No. «HL» == «HK»? No. «KJ» == «HK»? No. «KL» == «HK»? No. Did not find a matching rule | |
| pos (7, 8): «7:K, 8:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «7:K, 8:J» to «7:J, 8:K». Old index = old_i = 7 | |
| After rewrite: [0:H, 1:K, 2:J, 3:J, 4:K, 5:K, 6:H, 7:J, 8:K, 9:L, 10:H, 11:K]. Using this as the new input | |
| rule is not empty, i:=old_i+1=7+1=8. max_i:=11 Reached end of the step = (i >= max_i) = (8 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (8, 9): «8:K, 9:L». Checking whether «KL» is among the four rules: «HJ» == «KL»? No. «HL» == «KL»? No. «KJ» == «KL»? No. «KL» == «KL»? Yes. Found a matching rule | |
| Removing the pair «8:K, 9:L». Old index = old_i = 8 | |
| Before removing: [0:H, 1:K, 2:J, 3:J, 4:K, 5:K, 6:H, 7:J, 8:K, 9:L, 10:H, 11:K] | |
| Labelling the TWO elements «8:K, 9:L» to be removed: [0:H, 1:K, 2:J, 3:J, 4:K, 5:K, 6:H, 7:J, 8:removed, 9:removed, 10:H, 11:K] | |
| After removing the labelled TWO elements «8:K, 9:L» to be removed, without renumbering: [0:H, 1:K, 2:J, 3:J, 4:K, 5:K, 6:H, 7:J, 10:H, 11:K] | |
| Renumbering: [0:H, 1:K, 2:J, 3:J, 4:K, 5:K, 6:H, 7:J, 8:H, 9:K]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=8+0=8. max_i:=9 Reached end of the step = (i >= max_i) = (8 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (8, 9): «8:H, 9:K». Checking whether «HK» is among the four rules: «HJ» == «HK»? No. «HL» == «HK»? No. «KJ» == «HK»? No. «KL» == «HK»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 1: [0:H, 1:K, 2:J, 3:J, 4:K, 5:K, 6:H, 7:J, 8:H, 9:K] | |
| pos (0, 1): «0:H, 1:K». Checking whether «HK» is among the four rules: «HJ» == «HK»? No. «HL» == «HK»? No. «KJ» == «HK»? No. «KL» == «HK»? No. Did not find a matching rule | |
| pos (1, 2): «1:K, 2:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «1:K, 2:J» to «1:J, 2:K». Old index = old_i = 1 | |
| After rewrite: [0:H, 1:J, 2:K, 3:J, 4:K, 5:K, 6:H, 7:J, 8:H, 9:K]. Using this as the new input | |
| rule is not empty, i:=old_i+1=1+1=2. max_i:=9 Reached end of the step = (i >= max_i) = (2 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (2, 3): «2:K, 3:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «2:K, 3:J» to «2:J, 3:K». Old index = old_i = 2 | |
| After rewrite: [0:H, 1:J, 2:J, 3:K, 4:K, 5:K, 6:H, 7:J, 8:H, 9:K]. Using this as the new input | |
| rule is not empty, i:=old_i+1=2+1=3. max_i:=9 Reached end of the step = (i >= max_i) = (3 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (3, 4): «3:K, 4:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| pos (4, 5): «4:K, 5:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| pos (5, 6): «5:K, 6:H». Checking whether «KH» is among the four rules: «HJ» == «KH»? No. «HL» == «KH»? No. «KJ» == «KH»? No. «KL» == «KH»? No. Did not find a matching rule | |
| pos (6, 7): «6:H, 7:J». Checking whether «HJ» is among the four rules: «HJ» == «HJ»? Yes. «HL» == «HJ»? No. «KJ» == «HJ»? No. «KL» == «HJ»? No. Found a matching rule | |
| Removing the pair «6:H, 7:J». Old index = old_i = 6 | |
| Before removing: [0:H, 1:J, 2:J, 3:K, 4:K, 5:K, 6:H, 7:J, 8:H, 9:K] | |
| Labelling the TWO elements «6:H, 7:J» to be removed: [0:H, 1:J, 2:J, 3:K, 4:K, 5:K, 6:removed, 7:removed, 8:H, 9:K] | |
| After removing the labelled TWO elements «6:H, 7:J» to be removed, without renumbering: [0:H, 1:J, 2:J, 3:K, 4:K, 5:K, 8:H, 9:K] | |
| Renumbering: [0:H, 1:J, 2:J, 3:K, 4:K, 5:K, 6:H, 7:K]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=6+0=6. max_i:=7 Reached end of the step = (i >= max_i) = (6 >= 7) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (6, 7): «6:H, 7:K». Checking whether «HK» is among the four rules: «HJ» == «HK»? No. «HL» == «HK»? No. «KJ» == «HK»? No. «KL» == «HK»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 2: [0:H, 1:J, 2:J, 3:K, 4:K, 5:K, 6:H, 7:K] | |
| pos (0, 1): «0:H, 1:J». Checking whether «HJ» is among the four rules: «HJ» == «HJ»? Yes. «HL» == «HJ»? No. «KJ» == «HJ»? No. «KL» == «HJ»? No. Found a matching rule | |
| Removing the pair «0:H, 1:J». Old index = old_i = 0 | |
| Before removing: [0:H, 1:J, 2:J, 3:K, 4:K, 5:K, 6:H, 7:K] | |
| Labelling the TWO elements «0:H, 1:J» to be removed: [0:removed, 1:removed, 2:J, 3:K, 4:K, 5:K, 6:H, 7:K] | |
| After removing the labelled TWO elements «0:H, 1:J» to be removed, without renumbering: [2:J, 3:K, 4:K, 5:K, 6:H, 7:K] | |
| Renumbering: [0:J, 1:K, 2:K, 3:K, 4:H, 5:K]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=0+0=0. max_i:=5 Reached end of the step = (i >= max_i) = (0 >= 5) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (0, 1): «0:J, 1:K». Checking whether «JK» is among the four rules: «HJ» == «JK»? No. «HL» == «JK»? No. «KJ» == «JK»? No. «KL» == «JK»? No. Did not find a matching rule | |
| pos (1, 2): «1:K, 2:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| pos (2, 3): «2:K, 3:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| pos (3, 4): «3:K, 4:H». Checking whether «KH» is among the four rules: «HJ» == «KH»? No. «HL» == «KH»? No. «KJ» == «KH»? No. «KL» == «KH»? No. Did not find a matching rule | |
| pos (4, 5): «4:H, 5:K». Checking whether «HK» is among the four rules: «HJ» == «HK»? No. «HL» == «HK»? No. «KJ» == «HK»? No. «KL» == «HK»? No. Did not find a matching rule | |
| In this step, we did not perform any rewrite or removal, thus stopping | |
| Final result in the internal format: [0:J, 1:K, 2:K, 3:K, 4:H, 5:K] | |
| P3. Translating from the internal format to original format, step by step: | |
| P3.1. As a reminder, list the translation rules from internal to original: | |
| - H -> A# | |
| - J -> #A | |
| - K -> B# | |
| - L -> #B | |
| P3.2. Translate the program back to the original format: | |
| - J -> #A | |
| - K -> B# | |
| - K -> B# | |
| - K -> B# | |
| - H -> A# | |
| - K -> B# | |
| Final result in the original format: #A B# B# B# A# B# | |
| <solution>#A B# B# B# A# B# | |
| AI-Solution: #A B# B# B# A# B# | |
| <<correct>> | |
| ## Instance 5: | |
| Term: B# A# A# #B A# B# #A #A #A #B #A A# | |
| Norm: B# A# A# #B A# B# #A #A #A #B #A A# | |
| Rwt: 10 | |
| AI-RESPONSE: | |
| - B# -> K | |
| - A# -> H | |
| - A# -> H | |
| - #B -> L | |
| - A# -> H | |
| - B# -> K | |
| - #A -> J | |
| - #A -> J | |
| - #A -> J | |
| - #B -> L | |
| - #A -> J | |
| - A# -> H | |
| P2: Compute the program | |
| Initial program in the internal format: [0:K, 1:H, 2:H, 3:L, 4:H, 5:K, 6:J, 7:J, 8:J, 9:L, 10:J, 11:H] | |
| pos (0, 1): «0:K, 1:H». Checking whether «KH» is among the four rules: «HJ» == «KH»? No. «HL» == «KH»? No. «KJ» == «KH»? No. «KL» == «KH»? No. Did not find a matching rule | |
| pos (1, 2): «1:H, 2:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (2, 3): «2:H, 3:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «2:H, 3:L» to «2:L, 3:H». Old index = old_i = 2 | |
| After rewrite: [0:K, 1:H, 2:L, 3:H, 4:H, 5:K, 6:J, 7:J, 8:J, 9:L, 10:J, 11:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=2+1=3. max_i:=11 Reached end of the step = (i >= max_i) = (3 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (3, 4): «3:H, 4:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (4, 5): «4:H, 5:K». Checking whether «HK» is among the four rules: «HJ» == «HK»? No. «HL» == «HK»? No. «KJ» == «HK»? No. «KL» == «HK»? No. Did not find a matching rule | |
| pos (5, 6): «5:K, 6:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «5:K, 6:J» to «5:J, 6:K». Old index = old_i = 5 | |
| After rewrite: [0:K, 1:H, 2:L, 3:H, 4:H, 5:J, 6:K, 7:J, 8:J, 9:L, 10:J, 11:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=5+1=6. max_i:=11 Reached end of the step = (i >= max_i) = (6 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (6, 7): «6:K, 7:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «6:K, 7:J» to «6:J, 7:K». Old index = old_i = 6 | |
| After rewrite: [0:K, 1:H, 2:L, 3:H, 4:H, 5:J, 6:J, 7:K, 8:J, 9:L, 10:J, 11:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=6+1=7. max_i:=11 Reached end of the step = (i >= max_i) = (7 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (7, 8): «7:K, 8:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «7:K, 8:J» to «7:J, 8:K». Old index = old_i = 7 | |
| After rewrite: [0:K, 1:H, 2:L, 3:H, 4:H, 5:J, 6:J, 7:J, 8:K, 9:L, 10:J, 11:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=7+1=8. max_i:=11 Reached end of the step = (i >= max_i) = (8 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (8, 9): «8:K, 9:L». Checking whether «KL» is among the four rules: «HJ» == «KL»? No. «HL» == «KL»? No. «KJ» == «KL»? No. «KL» == «KL»? Yes. Found a matching rule | |
| Removing the pair «8:K, 9:L». Old index = old_i = 8 | |
| Before removing: [0:K, 1:H, 2:L, 3:H, 4:H, 5:J, 6:J, 7:J, 8:K, 9:L, 10:J, 11:H] | |
| Labelling the TWO elements «8:K, 9:L» to be removed: [0:K, 1:H, 2:L, 3:H, 4:H, 5:J, 6:J, 7:J, 8:removed, 9:removed, 10:J, 11:H] | |
| After removing the labelled TWO elements «8:K, 9:L» to be removed, without renumbering: [0:K, 1:H, 2:L, 3:H, 4:H, 5:J, 6:J, 7:J, 10:J, 11:H] | |
| Renumbering: [0:K, 1:H, 2:L, 3:H, 4:H, 5:J, 6:J, 7:J, 8:J, 9:H]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=8+0=8. max_i:=9 Reached end of the step = (i >= max_i) = (8 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (8, 9): «8:J, 9:H». Checking whether «JH» is among the four rules: «HJ» == «JH»? No. «HL» == «JH»? No. «KJ» == «JH»? No. «KL» == «JH»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 1: [0:K, 1:H, 2:L, 3:H, 4:H, 5:J, 6:J, 7:J, 8:J, 9:H] | |
| pos (0, 1): «0:K, 1:H». Checking whether «KH» is among the four rules: «HJ» == «KH»? No. «HL» == «KH»? No. «KJ» == «KH»? No. «KL» == «KH»? No. Did not find a matching rule | |
| pos (1, 2): «1:H, 2:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «1:H, 2:L» to «1:L, 2:H». Old index = old_i = 1 | |
| After rewrite: [0:K, 1:L, 2:H, 3:H, 4:H, 5:J, 6:J, 7:J, 8:J, 9:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=1+1=2. max_i:=9 Reached end of the step = (i >= max_i) = (2 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (2, 3): «2:H, 3:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (3, 4): «3:H, 4:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (4, 5): «4:H, 5:J». Checking whether «HJ» is among the four rules: «HJ» == «HJ»? Yes. «HL» == «HJ»? No. «KJ» == «HJ»? No. «KL» == «HJ»? No. Found a matching rule | |
| Removing the pair «4:H, 5:J». Old index = old_i = 4 | |
| Before removing: [0:K, 1:L, 2:H, 3:H, 4:H, 5:J, 6:J, 7:J, 8:J, 9:H] | |
| Labelling the TWO elements «4:H, 5:J» to be removed: [0:K, 1:L, 2:H, 3:H, 4:removed, 5:removed, 6:J, 7:J, 8:J, 9:H] | |
| After removing the labelled TWO elements «4:H, 5:J» to be removed, without renumbering: [0:K, 1:L, 2:H, 3:H, 6:J, 7:J, 8:J, 9:H] | |
| Renumbering: [0:K, 1:L, 2:H, 3:H, 4:J, 5:J, 6:J, 7:H]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=4+0=4. max_i:=7 Reached end of the step = (i >= max_i) = (4 >= 7) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (4, 5): «4:J, 5:J». Checking whether «JJ» is among the four rules: «HJ» == «JJ»? No. «HL» == «JJ»? No. «KJ» == «JJ»? No. «KL» == «JJ»? No. Did not find a matching rule | |
| pos (5, 6): «5:J, 6:J». Checking whether «JJ» is among the four rules: «HJ» == «JJ»? No. «HL» == «JJ»? No. «KJ» == «JJ»? No. «KL» == «JJ»? No. Did not find a matching rule | |
| pos (6, 7): «6:J, 7:H». Checking whether «JH» is among the four rules: «HJ» == «JH»? No. «HL» == «JH»? No. «KJ» == «JH»? No. «KL» == «JH»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 2: [0:K, 1:L, 2:H, 3:H, 4:J, 5:J, 6:J, 7:H] | |
| pos (0, 1): «0:K, 1:L». Checking whether «KL» is among the four rules: «HJ» == «KL»? No. «HL» == «KL»? No. «KJ» == «KL»? No. «KL» == «KL»? Yes. Found a matching rule | |
| Removing the pair «0:K, 1:L». Old index = old_i = 0 | |
| Before removing: [0:K, 1:L, 2:H, 3:H, 4:J, 5:J, 6:J, 7:H] | |
| Labelling the TWO elements «0:K, 1:L» to be removed: [0:removed, 1:removed, 2:H, 3:H, 4:J, 5:J, 6:J, 7:H] | |
| After removing the labelled TWO elements «0:K, 1:L» to be removed, without renumbering: [2:H, 3:H, 4:J, 5:J, 6:J, 7:H] | |
| Renumbering: [0:H, 1:H, 2:J, 3:J, 4:J, 5:H]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=0+0=0. max_i:=5 Reached end of the step = (i >= max_i) = (0 >= 5) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (0, 1): «0:H, 1:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (1, 2): «1:H, 2:J». Checking whether «HJ» is among the four rules: «HJ» == «HJ»? Yes. «HL» == «HJ»? No. «KJ» == «HJ»? No. «KL» == «HJ»? No. Found a matching rule | |
| Removing the pair «1:H, 2:J». Old index = old_i = 1 | |
| Before removing: [0:H, 1:H, 2:J, 3:J, 4:J, 5:H] | |
| Labelling the TWO elements «1:H, 2:J» to be removed: [0:H, 1:removed, 2:removed, 3:J, 4:J, 5:H] | |
| After removing the labelled TWO elements «1:H, 2:J» to be removed, without renumbering: [0:H, 3:J, 4:J, 5:H] | |
| Renumbering: [0:H, 1:J, 2:J, 3:H]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=1+0=1. max_i:=3 Reached end of the step = (i >= max_i) = (1 >= 3) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (1, 2): «1:J, 2:J». Checking whether «JJ» is among the four rules: «HJ» == «JJ»? No. «HL» == «JJ»? No. «KJ» == «JJ»? No. «KL» == «JJ»? No. Did not find a matching rule | |
| pos (2, 3): «2:J, 3:H». Checking whether «JH» is among the four rules: «HJ» == «JH»? No. «HL» == «JH»? No. «KJ» == «JH»? No. «KL» == «JH»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 3: [0:H, 1:J, 2:J, 3:H] | |
| pos (0, 1): «0:H, 1:J». Checking whether «HJ» is among the four rules: «HJ» == «HJ»? Yes. «HL» == «HJ»? No. «KJ» == «HJ»? No. «KL» == «HJ»? No. Found a matching rule | |
| Removing the pair «0:H, 1:J». Old index = old_i = 0 | |
| Before removing: [0:H, 1:J, 2:J, 3:H] | |
| Labelling the TWO elements «0:H, 1:J» to be removed: [0:removed, 1:removed, 2:J, 3:H] | |
| After removing the labelled TWO elements «0:H, 1:J» to be removed, without renumbering: [2:J, 3:H] | |
| Renumbering: [0:J, 1:H]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=0+0=0. max_i:=1 Reached end of the step = (i >= max_i) = (0 >= 1) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (0, 1): «0:J, 1:H». Checking whether «JH» is among the four rules: «HJ» == «JH»? No. «HL» == «JH»? No. «KJ» == «JH»? No. «KL» == «JH»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 4: [0:J, 1:H] | |
| pos (0, 1): «0:J, 1:H». Checking whether «JH» is among the four rules: «HJ» == «JH»? No. «HL» == «JH»? No. «KJ» == «JH»? No. «KL» == «JH»? No. Did not find a matching rule | |
| In this step, we did not perform any rewrite or removal, thus stopping | |
| Final result in the internal format: [0:J, 1:H] | |
| P3. Translating from the internal format to original format, step by step: | |
| P3.1. As a reminder, list the translation rules from internal to original: | |
| - H -> A# | |
| - J -> #A | |
| - K -> B# | |
| - L -> #B | |
| P3.2. Translate the program back to the original format: | |
| - J -> #A | |
| - H -> A# | |
| Final result in the original format: #A A# | |
| <solution>#A A# | |
| AI-Solution: #A A# | |
| <<correct>> | |
| ## Instance 6: | |
| Term: A# B# A# #B #B #B #B B# #A #B #B A# | |
| Norm: A# B# A# #B #B #B #B B# #A #B #B A# | |
| Rwt: 12 | |
| AI-RESPONSE: | |
| - A# -> H | |
| - B# -> K | |
| - A# -> H | |
| - #B -> L | |
| - #B -> L | |
| - #B -> L | |
| - #B -> L | |
| - B# -> K | |
| - #A -> J | |
| - #B -> L | |
| - #B -> L | |
| - A# -> H | |
| P2: Compute the program | |
| Initial program in the internal format: [0:H, 1:K, 2:H, 3:L, 4:L, 5:L, 6:L, 7:K, 8:J, 9:L, 10:L, 11:H] | |
| pos (0, 1): «0:H, 1:K». Checking whether «HK» is among the four rules: «HJ» == «HK»? No. «HL» == «HK»? No. «KJ» == «HK»? No. «KL» == «HK»? No. Did not find a matching rule | |
| pos (1, 2): «1:K, 2:H». Checking whether «KH» is among the four rules: «HJ» == «KH»? No. «HL» == «KH»? No. «KJ» == «KH»? No. «KL» == «KH»? No. Did not find a matching rule | |
| pos (2, 3): «2:H, 3:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «2:H, 3:L» to «2:L, 3:H». Old index = old_i = 2 | |
| After rewrite: [0:H, 1:K, 2:L, 3:H, 4:L, 5:L, 6:L, 7:K, 8:J, 9:L, 10:L, 11:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=2+1=3. max_i:=11 Reached end of the step = (i >= max_i) = (3 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (3, 4): «3:H, 4:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «3:H, 4:L» to «3:L, 4:H». Old index = old_i = 3 | |
| After rewrite: [0:H, 1:K, 2:L, 3:L, 4:H, 5:L, 6:L, 7:K, 8:J, 9:L, 10:L, 11:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=3+1=4. max_i:=11 Reached end of the step = (i >= max_i) = (4 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (4, 5): «4:H, 5:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «4:H, 5:L» to «4:L, 5:H». Old index = old_i = 4 | |
| After rewrite: [0:H, 1:K, 2:L, 3:L, 4:L, 5:H, 6:L, 7:K, 8:J, 9:L, 10:L, 11:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=4+1=5. max_i:=11 Reached end of the step = (i >= max_i) = (5 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (5, 6): «5:H, 6:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «5:H, 6:L» to «5:L, 6:H». Old index = old_i = 5 | |
| After rewrite: [0:H, 1:K, 2:L, 3:L, 4:L, 5:L, 6:H, 7:K, 8:J, 9:L, 10:L, 11:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=5+1=6. max_i:=11 Reached end of the step = (i >= max_i) = (6 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (6, 7): «6:H, 7:K». Checking whether «HK» is among the four rules: «HJ» == «HK»? No. «HL» == «HK»? No. «KJ» == «HK»? No. «KL» == «HK»? No. Did not find a matching rule | |
| pos (7, 8): «7:K, 8:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «7:K, 8:J» to «7:J, 8:K». Old index = old_i = 7 | |
| After rewrite: [0:H, 1:K, 2:L, 3:L, 4:L, 5:L, 6:H, 7:J, 8:K, 9:L, 10:L, 11:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=7+1=8. max_i:=11 Reached end of the step = (i >= max_i) = (8 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (8, 9): «8:K, 9:L». Checking whether «KL» is among the four rules: «HJ» == «KL»? No. «HL» == «KL»? No. «KJ» == «KL»? No. «KL» == «KL»? Yes. Found a matching rule | |
| Removing the pair «8:K, 9:L». Old index = old_i = 8 | |
| Before removing: [0:H, 1:K, 2:L, 3:L, 4:L, 5:L, 6:H, 7:J, 8:K, 9:L, 10:L, 11:H] | |
| Labelling the TWO elements «8:K, 9:L» to be removed: [0:H, 1:K, 2:L, 3:L, 4:L, 5:L, 6:H, 7:J, 8:removed, 9:removed, 10:L, 11:H] | |
| After removing the labelled TWO elements «8:K, 9:L» to be removed, without renumbering: [0:H, 1:K, 2:L, 3:L, 4:L, 5:L, 6:H, 7:J, 10:L, 11:H] | |
| Renumbering: [0:H, 1:K, 2:L, 3:L, 4:L, 5:L, 6:H, 7:J, 8:L, 9:H]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=8+0=8. max_i:=9 Reached end of the step = (i >= max_i) = (8 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (8, 9): «8:L, 9:H». Checking whether «LH» is among the four rules: «HJ» == «LH»? No. «HL» == «LH»? No. «KJ» == «LH»? No. «KL» == «LH»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 1: [0:H, 1:K, 2:L, 3:L, 4:L, 5:L, 6:H, 7:J, 8:L, 9:H] | |
| pos (0, 1): «0:H, 1:K». Checking whether «HK» is among the four rules: «HJ» == «HK»? No. «HL» == «HK»? No. «KJ» == «HK»? No. «KL» == «HK»? No. Did not find a matching rule | |
| pos (1, 2): «1:K, 2:L». Checking whether «KL» is among the four rules: «HJ» == «KL»? No. «HL» == «KL»? No. «KJ» == «KL»? No. «KL» == «KL»? Yes. Found a matching rule | |
| Removing the pair «1:K, 2:L». Old index = old_i = 1 | |
| Before removing: [0:H, 1:K, 2:L, 3:L, 4:L, 5:L, 6:H, 7:J, 8:L, 9:H] | |
| Labelling the TWO elements «1:K, 2:L» to be removed: [0:H, 1:removed, 2:removed, 3:L, 4:L, 5:L, 6:H, 7:J, 8:L, 9:H] | |
| After removing the labelled TWO elements «1:K, 2:L» to be removed, without renumbering: [0:H, 3:L, 4:L, 5:L, 6:H, 7:J, 8:L, 9:H] | |
| Renumbering: [0:H, 1:L, 2:L, 3:L, 4:H, 5:J, 6:L, 7:H]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=1+0=1. max_i:=7 Reached end of the step = (i >= max_i) = (1 >= 7) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (1, 2): «1:L, 2:L». Checking whether «LL» is among the four rules: «HJ» == «LL»? No. «HL» == «LL»? No. «KJ» == «LL»? No. «KL» == «LL»? No. Did not find a matching rule | |
| pos (2, 3): «2:L, 3:L». Checking whether «LL» is among the four rules: «HJ» == «LL»? No. «HL» == «LL»? No. «KJ» == «LL»? No. «KL» == «LL»? No. Did not find a matching rule | |
| pos (3, 4): «3:L, 4:H». Checking whether «LH» is among the four rules: «HJ» == «LH»? No. «HL» == «LH»? No. «KJ» == «LH»? No. «KL» == «LH»? No. Did not find a matching rule | |
| pos (4, 5): «4:H, 5:J». Checking whether «HJ» is among the four rules: «HJ» == «HJ»? Yes. «HL» == «HJ»? No. «KJ» == «HJ»? No. «KL» == «HJ»? No. Found a matching rule | |
| Removing the pair «4:H, 5:J». Old index = old_i = 4 | |
| Before removing: [0:H, 1:L, 2:L, 3:L, 4:H, 5:J, 6:L, 7:H] | |
| Labelling the TWO elements «4:H, 5:J» to be removed: [0:H, 1:L, 2:L, 3:L, 4:removed, 5:removed, 6:L, 7:H] | |
| After removing the labelled TWO elements «4:H, 5:J» to be removed, without renumbering: [0:H, 1:L, 2:L, 3:L, 6:L, 7:H] | |
| Renumbering: [0:H, 1:L, 2:L, 3:L, 4:L, 5:H]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=4+0=4. max_i:=5 Reached end of the step = (i >= max_i) = (4 >= 5) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (4, 5): «4:L, 5:H». Checking whether «LH» is among the four rules: «HJ» == «LH»? No. «HL» == «LH»? No. «KJ» == «LH»? No. «KL» == «LH»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 2: [0:H, 1:L, 2:L, 3:L, 4:L, 5:H] | |
| pos (0, 1): «0:H, 1:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «0:H, 1:L» to «0:L, 1:H». Old index = old_i = 0 | |
| After rewrite: [0:L, 1:H, 2:L, 3:L, 4:L, 5:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=0+1=1. max_i:=5 Reached end of the step = (i >= max_i) = (1 >= 5) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (1, 2): «1:H, 2:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «1:H, 2:L» to «1:L, 2:H». Old index = old_i = 1 | |
| After rewrite: [0:L, 1:L, 2:H, 3:L, 4:L, 5:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=1+1=2. max_i:=5 Reached end of the step = (i >= max_i) = (2 >= 5) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (2, 3): «2:H, 3:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «2:H, 3:L» to «2:L, 3:H». Old index = old_i = 2 | |
| After rewrite: [0:L, 1:L, 2:L, 3:H, 4:L, 5:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=2+1=3. max_i:=5 Reached end of the step = (i >= max_i) = (3 >= 5) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (3, 4): «3:H, 4:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «3:H, 4:L» to «3:L, 4:H». Old index = old_i = 3 | |
| After rewrite: [0:L, 1:L, 2:L, 3:L, 4:H, 5:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=3+1=4. max_i:=5 Reached end of the step = (i >= max_i) = (4 >= 5) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (4, 5): «4:H, 5:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 3: [0:L, 1:L, 2:L, 3:L, 4:H, 5:H] | |
| pos (0, 1): «0:L, 1:L». Checking whether «LL» is among the four rules: «HJ» == «LL»? No. «HL» == «LL»? No. «KJ» == «LL»? No. «KL» == «LL»? No. Did not find a matching rule | |
| pos (1, 2): «1:L, 2:L». Checking whether «LL» is among the four rules: «HJ» == «LL»? No. «HL» == «LL»? No. «KJ» == «LL»? No. «KL» == «LL»? No. Did not find a matching rule | |
| pos (2, 3): «2:L, 3:L». Checking whether «LL» is among the four rules: «HJ» == «LL»? No. «HL» == «LL»? No. «KJ» == «LL»? No. «KL» == «LL»? No. Did not find a matching rule | |
| pos (3, 4): «3:L, 4:H». Checking whether «LH» is among the four rules: «HJ» == «LH»? No. «HL» == «LH»? No. «KJ» == «LH»? No. «KL» == «LH»? No. Did not find a matching rule | |
| pos (4, 5): «4:H, 5:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| In this step, we did not perform any rewrite or removal, thus stopping | |
| Final result in the internal format: [0:L, 1:L, 2:L, 3:L, 4:H, 5:H] | |
| P3. Translating from the internal format to original format, step by step: | |
| P3.1. As a reminder, list the translation rules from internal to original: | |
| - H -> A# | |
| - J -> #A | |
| - K -> B# | |
| - L -> #B | |
| P3.2. Translate the program back to the original format: | |
| - L -> #B | |
| - L -> #B | |
| - L -> #B | |
| - L -> #B | |
| - H -> A# | |
| - H -> A# | |
| Final result in the original format: #B #B #B #B A# A# | |
| <solution>#B #B #B #B A# A# | |
| AI-Solution: #B #B #B #B A# A# | |
| <<correct>> | |
| ## Instance 7: | |
| Term: B# #A A# #B A# #B A# #B A# A# A# #B | |
| Norm: B# #A A# #B A# #B A# #B A# A# A# #B | |
| Rwt: 14 | |
| AI-RESPONSE: | |
| - B# -> K | |
| - #A -> J | |
| - A# -> H | |
| - #B -> L | |
| - A# -> H | |
| - #B -> L | |
| - A# -> H | |
| - #B -> L | |
| - A# -> H | |
| - A# -> H | |
| - A# -> H | |
| - #B -> L | |
| Initial program in the internal format: [0:K, 1:J, 2:H, 3:L, 4:H, 5:L, 6:H, 7:L, 8:H, 9:H, 10:H, 11:L] | |
| P2: Compute the program | |
| Step 0: [0:K, 1:J, 2:H, 3:L, 4:H, 5:L, 6:H, 7:L, 8:H, 9:H, 10:H, 11:L] | |
| pos (0, 1): «0:K, 1:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «0:K, 1:J» to «0:J, 1:K». Old index = old_i = 0 | |
| After rewrite: [0:J, 1:K, 2:H, 3:L, 4:H, 5:L, 6:H, 7:L, 8:H, 9:H, 10:H, 11:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=0+1=1. max_i:=11 Reached end of the step = (i >= max_i) = (1 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (1, 2): «1:K, 2:H». Checking whether «KH» is among the four rules: «HJ» == «KH»? No. «HL» == «KH»? No. «KJ» == «KH»? No. «KL» == «KH»? No. Did not find a matching rule | |
| pos (2, 3): «2:H, 3:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «2:H, 3:L» to «2:L, 3:H». Old index = old_i = 2 | |
| After rewrite: [0:J, 1:K, 2:L, 3:H, 4:H, 5:L, 6:H, 7:L, 8:H, 9:H, 10:H, 11:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=2+1=3. max_i:=11 Reached end of the step = (i >= max_i) = (3 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (3, 4): «3:H, 4:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (4, 5): «4:H, 5:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «4:H, 5:L» to «4:L, 5:H». Old index = old_i = 4 | |
| After rewrite: [0:J, 1:K, 2:L, 3:H, 4:L, 5:H, 6:H, 7:L, 8:H, 9:H, 10:H, 11:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=4+1=5. max_i:=11 Reached end of the step = (i >= max_i) = (5 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (5, 6): «5:H, 6:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (6, 7): «6:H, 7:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «6:H, 7:L» to «6:L, 7:H». Old index = old_i = 6 | |
| After rewrite: [0:J, 1:K, 2:L, 3:H, 4:L, 5:H, 6:L, 7:H, 8:H, 9:H, 10:H, 11:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=6+1=7. max_i:=11 Reached end of the step = (i >= max_i) = (7 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (7, 8): «7:H, 8:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (8, 9): «8:H, 9:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (9, 10): «9:H, 10:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (10, 11): «10:H, 11:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «10:H, 11:L» to «10:L, 11:H». Old index = old_i = 10 | |
| After rewrite: [0:J, 1:K, 2:L, 3:H, 4:L, 5:H, 6:L, 7:H, 8:H, 9:H, 10:L, 11:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=10+1=11. max_i:=11 Reached end of the step = (i >= max_i) = (11 >= 11) = True. Proceed to next step | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 1: [0:J, 1:K, 2:L, 3:H, 4:L, 5:H, 6:L, 7:H, 8:H, 9:H, 10:L, 11:H] | |
| pos (0, 1): «0:J, 1:K». Checking whether «JK» is among the four rules: «HJ» == «JK»? No. «HL» == «JK»? No. «KJ» == «JK»? No. «KL» == «JK»? No. Did not find a matching rule | |
| pos (1, 2): «1:K, 2:L». Checking whether «KL» is among the four rules: «HJ» == «KL»? No. «HL» == «KL»? No. «KJ» == «KL»? No. «KL» == «KL»? Yes. Found a matching rule | |
| Removing the pair «1:K, 2:L». Old index = old_i = 1 | |
| Before removing: [0:J, 1:K, 2:L, 3:H, 4:L, 5:H, 6:L, 7:H, 8:H, 9:H, 10:L, 11:H] | |
| Labelling the TWO elements «1:K, 2:L» to be removed: [0:J, 1:removed, 2:removed, 3:H, 4:L, 5:H, 6:L, 7:H, 8:H, 9:H, 10:L, 11:H] | |
| After removing the labelled TWO elements «1:K, 2:L» to be removed, without renumbering: [0:J, 3:H, 4:L, 5:H, 6:L, 7:H, 8:H, 9:H, 10:L, 11:H] | |
| Renumbering: [0:J, 1:H, 2:L, 3:H, 4:L, 5:H, 6:H, 7:H, 8:L, 9:H]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=1+0=1. max_i:=9 Reached end of the step = (i >= max_i) = (1 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (1, 2): «1:H, 2:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «1:H, 2:L» to «1:L, 2:H». Old index = old_i = 1 | |
| After rewrite: [0:J, 1:L, 2:H, 3:H, 4:L, 5:H, 6:H, 7:H, 8:L, 9:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=1+1=2. max_i:=9 Reached end of the step = (i >= max_i) = (2 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (2, 3): «2:H, 3:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (3, 4): «3:H, 4:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «3:H, 4:L» to «3:L, 4:H». Old index = old_i = 3 | |
| After rewrite: [0:J, 1:L, 2:H, 3:L, 4:H, 5:H, 6:H, 7:H, 8:L, 9:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=3+1=4. max_i:=9 Reached end of the step = (i >= max_i) = (4 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (4, 5): «4:H, 5:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (5, 6): «5:H, 6:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (6, 7): «6:H, 7:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (7, 8): «7:H, 8:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «7:H, 8:L» to «7:L, 8:H». Old index = old_i = 7 | |
| After rewrite: [0:J, 1:L, 2:H, 3:L, 4:H, 5:H, 6:H, 7:L, 8:H, 9:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=7+1=8. max_i:=9 Reached end of the step = (i >= max_i) = (8 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (8, 9): «8:H, 9:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 2: [0:J, 1:L, 2:H, 3:L, 4:H, 5:H, 6:H, 7:L, 8:H, 9:H] | |
| pos (0, 1): «0:J, 1:L». Checking whether «JL» is among the four rules: «HJ» == «JL»? No. «HL» == «JL»? No. «KJ» == «JL»? No. «KL» == «JL»? No. Did not find a matching rule | |
| pos (1, 2): «1:L, 2:H». Checking whether «LH» is among the four rules: «HJ» == «LH»? No. «HL» == «LH»? No. «KJ» == «LH»? No. «KL» == «LH»? No. Did not find a matching rule | |
| pos (2, 3): «2:H, 3:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «2:H, 3:L» to «2:L, 3:H». Old index = old_i = 2 | |
| After rewrite: [0:J, 1:L, 2:L, 3:H, 4:H, 5:H, 6:H, 7:L, 8:H, 9:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=2+1=3. max_i:=9 Reached end of the step = (i >= max_i) = (3 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (3, 4): «3:H, 4:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (4, 5): «4:H, 5:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (5, 6): «5:H, 6:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (6, 7): «6:H, 7:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «6:H, 7:L» to «6:L, 7:H». Old index = old_i = 6 | |
| After rewrite: [0:J, 1:L, 2:L, 3:H, 4:H, 5:H, 6:L, 7:H, 8:H, 9:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=6+1=7. max_i:=9 Reached end of the step = (i >= max_i) = (7 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (7, 8): «7:H, 8:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (8, 9): «8:H, 9:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 3: [0:J, 1:L, 2:L, 3:H, 4:H, 5:H, 6:L, 7:H, 8:H, 9:H] | |
| pos (0, 1): «0:J, 1:L». Checking whether «JL» is among the four rules: «HJ» == «JL»? No. «HL» == «JL»? No. «KJ» == «JL»? No. «KL» == «JL»? No. Did not find a matching rule | |
| pos (1, 2): «1:L, 2:L». Checking whether «LL» is among the four rules: «HJ» == «LL»? No. «HL» == «LL»? No. «KJ» == «LL»? No. «KL» == «LL»? No. Did not find a matching rule | |
| pos (2, 3): «2:L, 3:H». Checking whether «LH» is among the four rules: «HJ» == «LH»? No. «HL» == «LH»? No. «KJ» == «LH»? No. «KL» == «LH»? No. Did not find a matching rule | |
| pos (3, 4): «3:H, 4:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (4, 5): «4:H, 5:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (5, 6): «5:H, 6:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «5:H, 6:L» to «5:L, 6:H». Old index = old_i = 5 | |
| After rewrite: [0:J, 1:L, 2:L, 3:H, 4:H, 5:L, 6:H, 7:H, 8:H, 9:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=5+1=6. max_i:=9 Reached end of the step = (i >= max_i) = (6 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (6, 7): «6:H, 7:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (7, 8): «7:H, 8:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (8, 9): «8:H, 9:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 4: [0:J, 1:L, 2:L, 3:H, 4:H, 5:L, 6:H, 7:H, 8:H, 9:H] | |
| pos (0, 1): «0:J, 1:L». Checking whether «JL» is among the four rules: «HJ» == «JL»? No. «HL» == «JL»? No. «KJ» == «JL»? No. «KL» == «JL»? No. Did not find a matching rule | |
| pos (1, 2): «1:L, 2:L». Checking whether «LL» is among the four rules: «HJ» == «LL»? No. «HL» == «LL»? No. «KJ» == «LL»? No. «KL» == «LL»? No. Did not find a matching rule | |
| pos (2, 3): «2:L, 3:H». Checking whether «LH» is among the four rules: «HJ» == «LH»? No. «HL» == «LH»? No. «KJ» == «LH»? No. «KL» == «LH»? No. Did not find a matching rule | |
| pos (3, 4): «3:H, 4:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (4, 5): «4:H, 5:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «4:H, 5:L» to «4:L, 5:H». Old index = old_i = 4 | |
| After rewrite: [0:J, 1:L, 2:L, 3:H, 4:L, 5:H, 6:H, 7:H, 8:H, 9:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=4+1=5. max_i:=9 Reached end of the step = (i >= max_i) = (5 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (5, 6): «5:H, 6:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (6, 7): «6:H, 7:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (7, 8): «7:H, 8:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (8, 9): «8:H, 9:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 5: [0:J, 1:L, 2:L, 3:H, 4:L, 5:H, 6:H, 7:H, 8:H, 9:H] | |
| pos (0, 1): «0:J, 1:L». Checking whether «JL» is among the four rules: «HJ» == «JL»? No. «HL» == «JL»? No. «KJ» == «JL»? No. «KL» == «JL»? No. Did not find a matching rule | |
| pos (1, 2): «1:L, 2:L». Checking whether «LL» is among the four rules: «HJ» == «LL»? No. «HL» == «LL»? No. «KJ» == «LL»? No. «KL» == «LL»? No. Did not find a matching rule | |
| pos (2, 3): «2:L, 3:H». Checking whether «LH» is among the four rules: «HJ» == «LH»? No. «HL» == «LH»? No. «KJ» == «LH»? No. «KL» == «LH»? No. Did not find a matching rule | |
| pos (3, 4): «3:H, 4:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «3:H, 4:L» to «3:L, 4:H». Old index = old_i = 3 | |
| After rewrite: [0:J, 1:L, 2:L, 3:L, 4:H, 5:H, 6:H, 7:H, 8:H, 9:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=3+1=4. max_i:=9 Reached end of the step = (i >= max_i) = (4 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (4, 5): «4:H, 5:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (5, 6): «5:H, 6:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (6, 7): «6:H, 7:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (7, 8): «7:H, 8:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (8, 9): «8:H, 9:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 6: [0:J, 1:L, 2:L, 3:L, 4:H, 5:H, 6:H, 7:H, 8:H, 9:H] | |
| pos (0, 1): «0:J, 1:L». Checking whether «JL» is among the four rules: «HJ» == «JL»? No. «HL» == «JL»? No. «KJ» == «JL»? No. «KL» == «JL»? No. Did not find a matching rule | |
| pos (1, 2): «1:L, 2:L». Checking whether «LL» is among the four rules: «HJ» == «LL»? No. «HL» == «LL»? No. «KJ» == «LL»? No. «KL» == «LL»? No. Did not find a matching rule | |
| pos (2, 3): «2:L, 3:L». Checking whether «LL» is among the four rules: «HJ» == «LL»? No. «HL» == «LL»? No. «KJ» == «LL»? No. «KL» == «LL»? No. Did not find a matching rule | |
| pos (3, 4): «3:L, 4:H». Checking whether «LH» is among the four rules: «HJ» == «LH»? No. «HL» == «LH»? No. «KJ» == «LH»? No. «KL» == «LH»? No. Did not find a matching rule | |
| pos (4, 5): «4:H, 5:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (5, 6): «5:H, 6:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (6, 7): «6:H, 7:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (7, 8): «7:H, 8:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (8, 9): «8:H, 9:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| In this step, we did not perform any rewrite or removal, thus stopping | |
| Final result in the internal format: [0:J, 1:L, 2:L, 3:L, 4:H, 5:H, 6:H, 7:H, 8:H, 9:H] | |
| P3. Translating from the internal format to original format, step by step: | |
| P3.1. As a reminder, list the translation rules from internal to original: | |
| - H -> A# | |
| - J -> #A | |
| - K -> B# | |
| - L -> #B | |
| P3.2. Translate the program back to the original format: | |
| - J -> #A | |
| - L -> #B | |
| - L -> #B | |
| - L -> #B | |
| - H -> A# | |
| - H -> A# | |
| - H -> A# | |
| - H -> A# | |
| - H -> A# | |
| - H -> A# | |
| Final result in the original format: #A #B #B #B A# A# A# A# A# A# | |
| <solution>#A #B #B #B A# A# A# A# A# A# | |
| AI-Solution: #A #B #B #B A# A# A# A# A# A# | |
| <<correct>> | |
| ## Instance 8: | |
| Term: B# #A B# #A #A #A #A #A B# #A #B #B | |
| Norm: B# #A B# #A #A #A #A #A B# #A #B #B | |
| Rwt: 16 | |
| AI-RESPONSE: | |
| - B# -> K | |
| - #A -> J | |
| - B# -> K | |
| - #A -> J | |
| - #A -> J | |
| - #A -> J | |
| - #A -> J | |
| - #A -> J | |
| - B# -> K | |
| - #A -> J | |
| - #B -> L | |
| - #B -> L | |
| Initial program in the internal format: [0:K, 1:J, 2:K, 3:J, 4:J, 5:J, 6:J, 7:J, 8:K, 9:J, 10:L, 11:L] | |
| P2: Compute the program | |
| Step 0: [0:K, 1:J, 2:K, 3:J, 4:J, 5:J, 6:J, 7:J, 8:K, 9:J, 10:L, 11:L] | |
| pos (0, 1): «0:K, 1:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «0:K, 1:J» to «0:J, 1:K». Old index = old_i = 0 | |
| After rewrite: [0:J, 1:K, 2:K, 3:J, 4:J, 5:J, 6:J, 7:J, 8:K, 9:J, 10:L, 11:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=0+1=1. max_i:=11 Reached end of the step = (i >= max_i) = (1 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (1, 2): «1:K, 2:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| pos (2, 3): «2:K, 3:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «2:K, 3:J» to «2:J, 3:K». Old index = old_i = 2 | |
| After rewrite: [0:J, 1:K, 2:J, 3:K, 4:J, 5:J, 6:J, 7:J, 8:K, 9:J, 10:L, 11:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=2+1=3. max_i:=11 Reached end of the step = (i >= max_i) = (3 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (3, 4): «3:K, 4:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «3:K, 4:J» to «3:J, 4:K». Old index = old_i = 3 | |
| After rewrite: [0:J, 1:K, 2:J, 3:J, 4:K, 5:J, 6:J, 7:J, 8:K, 9:J, 10:L, 11:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=3+1=4. max_i:=11 Reached end of the step = (i >= max_i) = (4 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (4, 5): «4:K, 5:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «4:K, 5:J» to «4:J, 5:K». Old index = old_i = 4 | |
| After rewrite: [0:J, 1:K, 2:J, 3:J, 4:J, 5:K, 6:J, 7:J, 8:K, 9:J, 10:L, 11:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=4+1=5. max_i:=11 Reached end of the step = (i >= max_i) = (5 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (5, 6): «5:K, 6:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «5:K, 6:J» to «5:J, 6:K». Old index = old_i = 5 | |
| After rewrite: [0:J, 1:K, 2:J, 3:J, 4:J, 5:J, 6:K, 7:J, 8:K, 9:J, 10:L, 11:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=5+1=6. max_i:=11 Reached end of the step = (i >= max_i) = (6 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (6, 7): «6:K, 7:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «6:K, 7:J» to «6:J, 7:K». Old index = old_i = 6 | |
| After rewrite: [0:J, 1:K, 2:J, 3:J, 4:J, 5:J, 6:J, 7:K, 8:K, 9:J, 10:L, 11:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=6+1=7. max_i:=11 Reached end of the step = (i >= max_i) = (7 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (7, 8): «7:K, 8:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| pos (8, 9): «8:K, 9:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «8:K, 9:J» to «8:J, 9:K». Old index = old_i = 8 | |
| After rewrite: [0:J, 1:K, 2:J, 3:J, 4:J, 5:J, 6:J, 7:K, 8:J, 9:K, 10:L, 11:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=8+1=9. max_i:=11 Reached end of the step = (i >= max_i) = (9 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (9, 10): «9:K, 10:L». Checking whether «KL» is among the four rules: «HJ» == «KL»? No. «HL» == «KL»? No. «KJ» == «KL»? No. «KL» == «KL»? Yes. Found a matching rule | |
| Removing the pair «9:K, 10:L». Old index = old_i = 9 | |
| Before removing: [0:J, 1:K, 2:J, 3:J, 4:J, 5:J, 6:J, 7:K, 8:J, 9:K, 10:L, 11:L] | |
| Labelling the TWO elements «9:K, 10:L» to be removed: [0:J, 1:K, 2:J, 3:J, 4:J, 5:J, 6:J, 7:K, 8:J, 9:removed, 10:removed, 11:L] | |
| After removing the labelled TWO elements «9:K, 10:L» to be removed, without renumbering: [0:J, 1:K, 2:J, 3:J, 4:J, 5:J, 6:J, 7:K, 8:J, 11:L] | |
| Renumbering: [0:J, 1:K, 2:J, 3:J, 4:J, 5:J, 6:J, 7:K, 8:J, 9:L]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=9+0=9. max_i:=9 Reached end of the step = (i >= max_i) = (9 >= 9) = True. Proceed to next step | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 1: [0:J, 1:K, 2:J, 3:J, 4:J, 5:J, 6:J, 7:K, 8:J, 9:L] | |
| pos (0, 1): «0:J, 1:K». Checking whether «JK» is among the four rules: «HJ» == «JK»? No. «HL» == «JK»? No. «KJ» == «JK»? No. «KL» == «JK»? No. Did not find a matching rule | |
| pos (1, 2): «1:K, 2:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «1:K, 2:J» to «1:J, 2:K». Old index = old_i = 1 | |
| After rewrite: [0:J, 1:J, 2:K, 3:J, 4:J, 5:J, 6:J, 7:K, 8:J, 9:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=1+1=2. max_i:=9 Reached end of the step = (i >= max_i) = (2 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (2, 3): «2:K, 3:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «2:K, 3:J» to «2:J, 3:K». Old index = old_i = 2 | |
| After rewrite: [0:J, 1:J, 2:J, 3:K, 4:J, 5:J, 6:J, 7:K, 8:J, 9:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=2+1=3. max_i:=9 Reached end of the step = (i >= max_i) = (3 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (3, 4): «3:K, 4:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «3:K, 4:J» to «3:J, 4:K». Old index = old_i = 3 | |
| After rewrite: [0:J, 1:J, 2:J, 3:J, 4:K, 5:J, 6:J, 7:K, 8:J, 9:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=3+1=4. max_i:=9 Reached end of the step = (i >= max_i) = (4 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (4, 5): «4:K, 5:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «4:K, 5:J» to «4:J, 5:K». Old index = old_i = 4 | |
| After rewrite: [0:J, 1:J, 2:J, 3:J, 4:J, 5:K, 6:J, 7:K, 8:J, 9:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=4+1=5. max_i:=9 Reached end of the step = (i >= max_i) = (5 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (5, 6): «5:K, 6:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «5:K, 6:J» to «5:J, 6:K». Old index = old_i = 5 | |
| After rewrite: [0:J, 1:J, 2:J, 3:J, 4:J, 5:J, 6:K, 7:K, 8:J, 9:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=5+1=6. max_i:=9 Reached end of the step = (i >= max_i) = (6 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (6, 7): «6:K, 7:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| pos (7, 8): «7:K, 8:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «7:K, 8:J» to «7:J, 8:K». Old index = old_i = 7 | |
| After rewrite: [0:J, 1:J, 2:J, 3:J, 4:J, 5:J, 6:K, 7:J, 8:K, 9:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=7+1=8. max_i:=9 Reached end of the step = (i >= max_i) = (8 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (8, 9): «8:K, 9:L». Checking whether «KL» is among the four rules: «HJ» == «KL»? No. «HL» == «KL»? No. «KJ» == «KL»? No. «KL» == «KL»? Yes. Found a matching rule | |
| Removing the pair «8:K, 9:L». Old index = old_i = 8 | |
| Before removing: [0:J, 1:J, 2:J, 3:J, 4:J, 5:J, 6:K, 7:J, 8:K, 9:L] | |
| Labelling the TWO elements «8:K, 9:L» to be removed: [0:J, 1:J, 2:J, 3:J, 4:J, 5:J, 6:K, 7:J, 8:removed, 9:removed] | |
| After removing the labelled TWO elements «8:K, 9:L» to be removed, without renumbering: [0:J, 1:J, 2:J, 3:J, 4:J, 5:J, 6:K, 7:J] | |
| Renumbering: [0:J, 1:J, 2:J, 3:J, 4:J, 5:J, 6:K, 7:J]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=8+0=8. max_i:=7 Reached end of the step = (i >= max_i) = (8 >= 7) = True. Proceed to next step | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 2: [0:J, 1:J, 2:J, 3:J, 4:J, 5:J, 6:K, 7:J] | |
| pos (0, 1): «0:J, 1:J». Checking whether «JJ» is among the four rules: «HJ» == «JJ»? No. «HL» == «JJ»? No. «KJ» == «JJ»? No. «KL» == «JJ»? No. Did not find a matching rule | |
| pos (1, 2): «1:J, 2:J». Checking whether «JJ» is among the four rules: «HJ» == «JJ»? No. «HL» == «JJ»? No. «KJ» == «JJ»? No. «KL» == «JJ»? No. Did not find a matching rule | |
| pos (2, 3): «2:J, 3:J». Checking whether «JJ» is among the four rules: «HJ» == «JJ»? No. «HL» == «JJ»? No. «KJ» == «JJ»? No. «KL» == «JJ»? No. Did not find a matching rule | |
| pos (3, 4): «3:J, 4:J». Checking whether «JJ» is among the four rules: «HJ» == «JJ»? No. «HL» == «JJ»? No. «KJ» == «JJ»? No. «KL» == «JJ»? No. Did not find a matching rule | |
| pos (4, 5): «4:J, 5:J». Checking whether «JJ» is among the four rules: «HJ» == «JJ»? No. «HL» == «JJ»? No. «KJ» == «JJ»? No. «KL» == «JJ»? No. Did not find a matching rule | |
| pos (5, 6): «5:J, 6:K». Checking whether «JK» is among the four rules: «HJ» == «JK»? No. «HL» == «JK»? No. «KJ» == «JK»? No. «KL» == «JK»? No. Did not find a matching rule | |
| pos (6, 7): «6:K, 7:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «6:K, 7:J» to «6:J, 7:K». Old index = old_i = 6 | |
| After rewrite: [0:J, 1:J, 2:J, 3:J, 4:J, 5:J, 6:J, 7:K]. Using this as the new input | |
| rule is not empty, i:=old_i+1=6+1=7. max_i:=7 Reached end of the step = (i >= max_i) = (7 >= 7) = True. Proceed to next step | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 3: [0:J, 1:J, 2:J, 3:J, 4:J, 5:J, 6:J, 7:K] | |
| pos (0, 1): «0:J, 1:J». Checking whether «JJ» is among the four rules: «HJ» == «JJ»? No. «HL» == «JJ»? No. «KJ» == «JJ»? No. «KL» == «JJ»? No. Did not find a matching rule | |
| pos (1, 2): «1:J, 2:J». Checking whether «JJ» is among the four rules: «HJ» == «JJ»? No. «HL» == «JJ»? No. «KJ» == «JJ»? No. «KL» == «JJ»? No. Did not find a matching rule | |
| pos (2, 3): «2:J, 3:J». Checking whether «JJ» is among the four rules: «HJ» == «JJ»? No. «HL» == «JJ»? No. «KJ» == «JJ»? No. «KL» == «JJ»? No. Did not find a matching rule | |
| pos (3, 4): «3:J, 4:J». Checking whether «JJ» is among the four rules: «HJ» == «JJ»? No. «HL» == «JJ»? No. «KJ» == «JJ»? No. «KL» == «JJ»? No. Did not find a matching rule | |
| pos (4, 5): «4:J, 5:J». Checking whether «JJ» is among the four rules: «HJ» == «JJ»? No. «HL» == «JJ»? No. «KJ» == «JJ»? No. «KL» == «JJ»? No. Did not find a matching rule | |
| pos (5, 6): «5:J, 6:J». Checking whether «JJ» is among the four rules: «HJ» == «JJ»? No. «HL» == «JJ»? No. «KJ» == «JJ»? No. «KL» == «JJ»? No. Did not find a matching rule | |
| pos (6, 7): «6:J, 7:K». Checking whether «JK» is among the four rules: «HJ» == «JK»? No. «HL» == «JK»? No. «KJ» == «JK»? No. «KL» == «JK»? No. Did not find a matching rule | |
| In this step, we did not perform any rewrite or removal, thus stopping | |
| Final result in the internal format: [0:J, 1:J, 2:J, 3:J, 4:J, 5:J, 6:J, 7:K] | |
| P3. Translating from the internal format to original format, step by step: | |
| P3.1. As a reminder, list the translation rules from internal to original: | |
| - H -> A# | |
| - J -> #A | |
| - K -> B# | |
| - L -> #B | |
| P3.2. Translate the program back to the original format: | |
| - J -> #A | |
| - J -> #A | |
| - J -> #A | |
| - J -> #A | |
| - J -> #A | |
| - J -> #A | |
| - J -> #A | |
| - K -> B# | |
| Final result in the original format: #A #A #A #A #A #A #A B# | |
| <solution>#A #A #A #A #A #A #A B# | |
| AI-Solution: #A #A #A #A #A #A #A B# | |
| <<correct>> | |
| ## Instance 9: | |
| Term: A# A# #B #A B# B# #A B# #A #A #A #A | |
| Norm: A# A# #B #A B# B# #A B# #A #A #A #A | |
| Rwt: 18 | |
| AI-RESPONSE: | |
| - A# -> H | |
| - A# -> H | |
| - #B -> L | |
| - #A -> J | |
| - B# -> K | |
| - B# -> K | |
| - #A -> J | |
| - B# -> K | |
| - #A -> J | |
| - #A -> J | |
| - #A -> J | |
| - #A -> J | |
| Initial program in the internal format: [0:H, 1:H, 2:L, 3:J, 4:K, 5:K, 6:J, 7:K, 8:J, 9:J, 10:J, 11:J] | |
| P2: Compute the program | |
| Initial program in the internal format: [0:H, 1:H, 2:L, 3:J, 4:K, 5:K, 6:J, 7:K, 8:J, 9:J, 10:J, 11:J] | |
| pos (0, 1): «0:H, 1:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (1, 2): «1:H, 2:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «1:H, 2:L» to «1:L, 2:H». Old index = old_i = 1 | |
| After rewrite: [0:H, 1:L, 2:H, 3:J, 4:K, 5:K, 6:J, 7:K, 8:J, 9:J, 10:J, 11:J]. Using this as the new input | |
| rule is not empty, i:=old_i+1=1+1=2. max_i:=11 Reached end of the step = (i >= max_i) = (2 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (2, 3): «2:H, 3:J». Checking whether «HJ» is among the four rules: «HJ» == «HJ»? Yes. «HL» == «HJ»? No. «KJ» == «HJ»? No. «KL» == «HJ»? No. Found a matching rule | |
| Removing the pair «2:H, 3:J». Old index = old_i = 2 | |
| Before removing: [0:H, 1:L, 2:H, 3:J, 4:K, 5:K, 6:J, 7:K, 8:J, 9:J, 10:J, 11:J] | |
| Labelling the TWO elements «2:H, 3:J» to be removed: [0:H, 1:L, 2:removed, 3:removed, 4:K, 5:K, 6:J, 7:K, 8:J, 9:J, 10:J, 11:J] | |
| After removing the labelled TWO elements «2:H, 3:J» to be removed, without renumbering: [0:H, 1:L, 4:K, 5:K, 6:J, 7:K, 8:J, 9:J, 10:J, 11:J] | |
| Renumbering: [0:H, 1:L, 2:K, 3:K, 4:J, 5:K, 6:J, 7:J, 8:J, 9:J]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=2+0=2. max_i:=9 Reached end of the step = (i >= max_i) = (2 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (2, 3): «2:K, 3:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| pos (3, 4): «3:K, 4:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «3:K, 4:J» to «3:J, 4:K». Old index = old_i = 3 | |
| After rewrite: [0:H, 1:L, 2:K, 3:J, 4:K, 5:K, 6:J, 7:J, 8:J, 9:J]. Using this as the new input | |
| rule is not empty, i:=old_i+1=3+1=4. max_i:=9 Reached end of the step = (i >= max_i) = (4 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (4, 5): «4:K, 5:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| pos (5, 6): «5:K, 6:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «5:K, 6:J» to «5:J, 6:K». Old index = old_i = 5 | |
| After rewrite: [0:H, 1:L, 2:K, 3:J, 4:K, 5:J, 6:K, 7:J, 8:J, 9:J]. Using this as the new input | |
| rule is not empty, i:=old_i+1=5+1=6. max_i:=9 Reached end of the step = (i >= max_i) = (6 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (6, 7): «6:K, 7:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «6:K, 7:J» to «6:J, 7:K». Old index = old_i = 6 | |
| After rewrite: [0:H, 1:L, 2:K, 3:J, 4:K, 5:J, 6:J, 7:K, 8:J, 9:J]. Using this as the new input | |
| rule is not empty, i:=old_i+1=6+1=7. max_i:=9 Reached end of the step = (i >= max_i) = (7 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (7, 8): «7:K, 8:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «7:K, 8:J» to «7:J, 8:K». Old index = old_i = 7 | |
| After rewrite: [0:H, 1:L, 2:K, 3:J, 4:K, 5:J, 6:J, 7:J, 8:K, 9:J]. Using this as the new input | |
| rule is not empty, i:=old_i+1=7+1=8. max_i:=9 Reached end of the step = (i >= max_i) = (8 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (8, 9): «8:K, 9:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «8:K, 9:J» to «8:J, 9:K». Old index = old_i = 8 | |
| After rewrite: [0:H, 1:L, 2:K, 3:J, 4:K, 5:J, 6:J, 7:J, 8:J, 9:K]. Using this as the new input | |
| rule is not empty, i:=old_i+1=8+1=9. max_i:=9 Reached end of the step = (i >= max_i) = (9 >= 9) = True. Proceed to next step | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 1: [0:H, 1:L, 2:K, 3:J, 4:K, 5:J, 6:J, 7:J, 8:J, 9:K] | |
| pos (0, 1): «0:H, 1:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «0:H, 1:L» to «0:L, 1:H». Old index = old_i = 0 | |
| After rewrite: [0:L, 1:H, 2:K, 3:J, 4:K, 5:J, 6:J, 7:J, 8:J, 9:K]. Using this as the new input | |
| rule is not empty, i:=old_i+1=0+1=1. max_i:=9 Reached end of the step = (i >= max_i) = (1 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (1, 2): «1:H, 2:K». Checking whether «HK» is among the four rules: «HJ» == «HK»? No. «HL» == «HK»? No. «KJ» == «HK»? No. «KL» == «HK»? No. Did not find a matching rule | |
| pos (2, 3): «2:K, 3:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «2:K, 3:J» to «2:J, 3:K». Old index = old_i = 2 | |
| After rewrite: [0:L, 1:H, 2:J, 3:K, 4:K, 5:J, 6:J, 7:J, 8:J, 9:K]. Using this as the new input | |
| rule is not empty, i:=old_i+1=2+1=3. max_i:=9 Reached end of the step = (i >= max_i) = (3 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (3, 4): «3:K, 4:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| pos (4, 5): «4:K, 5:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «4:K, 5:J» to «4:J, 5:K». Old index = old_i = 4 | |
| After rewrite: [0:L, 1:H, 2:J, 3:K, 4:J, 5:K, 6:J, 7:J, 8:J, 9:K]. Using this as the new input | |
| rule is not empty, i:=old_i+1=4+1=5. max_i:=9 Reached end of the step = (i >= max_i) = (5 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (5, 6): «5:K, 6:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «5:K, 6:J» to «5:J, 6:K». Old index = old_i = 5 | |
| After rewrite: [0:L, 1:H, 2:J, 3:K, 4:J, 5:J, 6:K, 7:J, 8:J, 9:K]. Using this as the new input | |
| rule is not empty, i:=old_i+1=5+1=6. max_i:=9 Reached end of the step = (i >= max_i) = (6 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (6, 7): «6:K, 7:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «6:K, 7:J» to «6:J, 7:K». Old index = old_i = 6 | |
| After rewrite: [0:L, 1:H, 2:J, 3:K, 4:J, 5:J, 6:J, 7:K, 8:J, 9:K]. Using this as the new input | |
| rule is not empty, i:=old_i+1=6+1=7. max_i:=9 Reached end of the step = (i >= max_i) = (7 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (7, 8): «7:K, 8:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «7:K, 8:J» to «7:J, 8:K». Old index = old_i = 7 | |
| After rewrite: [0:L, 1:H, 2:J, 3:K, 4:J, 5:J, 6:J, 7:J, 8:K, 9:K]. Using this as the new input | |
| rule is not empty, i:=old_i+1=7+1=8. max_i:=9 Reached end of the step = (i >= max_i) = (8 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (8, 9): «8:K, 9:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 2: [0:L, 1:H, 2:J, 3:K, 4:J, 5:J, 6:J, 7:J, 8:K, 9:K] | |
| pos (0, 1): «0:L, 1:H». Checking whether «LH» is among the four rules: «HJ» == «LH»? No. «HL» == «LH»? No. «KJ» == «LH»? No. «KL» == «LH»? No. Did not find a matching rule | |
| pos (1, 2): «1:H, 2:J». Checking whether «HJ» is among the four rules: «HJ» == «HJ»? Yes. «HL» == «HJ»? No. «KJ» == «HJ»? No. «KL» == «HJ»? No. Found a matching rule | |
| Removing the pair «1:H, 2:J». Old index = old_i = 1 | |
| Before removing: [0:L, 1:H, 2:J, 3:K, 4:J, 5:J, 6:J, 7:J, 8:K, 9:K] | |
| Labelling the TWO elements «1:H, 2:J» to be removed: [0:L, 1:removed, 2:removed, 3:K, 4:J, 5:J, 6:J, 7:J, 8:K, 9:K] | |
| After removing the labelled TWO elements «1:H, 2:J» to be removed, without renumbering: [0:L, 3:K, 4:J, 5:J, 6:J, 7:J, 8:K, 9:K] | |
| Renumbering: [0:L, 1:K, 2:J, 3:J, 4:J, 5:J, 6:K, 7:K]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=1+0=1. max_i:=7 Reached end of the step = (i >= max_i) = (1 >= 7) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (1, 2): «1:K, 2:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «1:K, 2:J» to «1:J, 2:K». Old index = old_i = 1 | |
| After rewrite: [0:L, 1:J, 2:K, 3:J, 4:J, 5:J, 6:K, 7:K]. Using this as the new input | |
| rule is not empty, i:=old_i+1=1+1=2. max_i:=7 Reached end of the step = (i >= max_i) = (2 >= 7) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (2, 3): «2:K, 3:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «2:K, 3:J» to «2:J, 3:K». Old index = old_i = 2 | |
| After rewrite: [0:L, 1:J, 2:J, 3:K, 4:J, 5:J, 6:K, 7:K]. Using this as the new input | |
| rule is not empty, i:=old_i+1=2+1=3. max_i:=7 Reached end of the step = (i >= max_i) = (3 >= 7) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (3, 4): «3:K, 4:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «3:K, 4:J» to «3:J, 4:K». Old index = old_i = 3 | |
| After rewrite: [0:L, 1:J, 2:J, 3:J, 4:K, 5:J, 6:K, 7:K]. Using this as the new input | |
| rule is not empty, i:=old_i+1=3+1=4. max_i:=7 Reached end of the step = (i >= max_i) = (4 >= 7) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (4, 5): «4:K, 5:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «4:K, 5:J» to «4:J, 5:K». Old index = old_i = 4 | |
| After rewrite: [0:L, 1:J, 2:J, 3:J, 4:J, 5:K, 6:K, 7:K]. Using this as the new input | |
| rule is not empty, i:=old_i+1=4+1=5. max_i:=7 Reached end of the step = (i >= max_i) = (5 >= 7) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (5, 6): «5:K, 6:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| pos (6, 7): «6:K, 7:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 3: [0:L, 1:J, 2:J, 3:J, 4:J, 5:K, 6:K, 7:K] | |
| pos (0, 1): «0:L, 1:J». Checking whether «LJ» is among the four rules: «HJ» == «LJ»? No. «HL» == «LJ»? No. «KJ» == «LJ»? No. «KL» == «LJ»? No. Did not find a matching rule | |
| pos (1, 2): «1:J, 2:J». Checking whether «JJ» is among the four rules: «HJ» == «JJ»? No. «HL» == «JJ»? No. «KJ» == «JJ»? No. «KL» == «JJ»? No. Did not find a matching rule | |
| pos (2, 3): «2:J, 3:J». Checking whether «JJ» is among the four rules: «HJ» == «JJ»? No. «HL» == «JJ»? No. «KJ» == «JJ»? No. «KL» == «JJ»? No. Did not find a matching rule | |
| pos (3, 4): «3:J, 4:J». Checking whether «JJ» is among the four rules: «HJ» == «JJ»? No. «HL» == «JJ»? No. «KJ» == «JJ»? No. «KL» == «JJ»? No. Did not find a matching rule | |
| pos (4, 5): «4:J, 5:K». Checking whether «JK» is among the four rules: «HJ» == «JK»? No. «HL» == «JK»? No. «KJ» == «JK»? No. «KL» == «JK»? No. Did not find a matching rule | |
| pos (5, 6): «5:K, 6:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| pos (6, 7): «6:K, 7:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| In this step, we did not perform any rewrite or removal, thus stopping | |
| Final result in the internal format: [0:L, 1:J, 2:J, 3:J, 4:J, 5:K, 6:K, 7:K] | |
| P3. Translating from the internal format to original format, step by step: | |
| P3.1. As a reminder, list the translation rules from internal to original: | |
| - H -> A# | |
| - J -> #A | |
| - K -> B# | |
| - L -> #B | |
| P3.2. Translate the program back to the original format: | |
| - L -> #B | |
| - J -> #A | |
| - J -> #A | |
| - J -> #A | |
| - J -> #A | |
| - K -> B# | |
| - K -> B# | |
| - K -> B# | |
| Final result in the original format: #B #A #A #A #A B# B# B# | |
| <solution>#B #A #A #A #A B# B# B# | |
| AI-Solution: #B #A #A #A #A B# B# B# | |
| <<correct>> | |
| ## Instance 10: | |
| Term: B# #A B# B# B# #A #A #B #A #A #A #B | |
| Norm: B# #A B# B# B# #A #A #B #A #A #A #B | |
| Rwt: 20 | |
| AI-RESPONSE: | |
| - B# -> K | |
| - #A -> J | |
| - B# -> K | |
| - B# -> K | |
| - B# -> K | |
| - #A -> J | |
| - #A -> J | |
| - #B -> L | |
| - #A -> J | |
| - #A -> J | |
| - #A -> J | |
| - #B -> L | |
| Initial program in the internal format: [0:K, 1:J, 2:K, 3:K, 4:K, 5:J, 6:J, 7:L, 8:J, 9:J, 10:J, 11:L] | |
| P2: Compute the program | |
| Step 0: [0:K, 1:J, 2:K, 3:K, 4:K, 5:J, 6:J, 7:L, 8:J, 9:J, 10:J, 11:L] | |
| pos (0, 1): «0:K, 1:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «0:K, 1:J» to «0:J, 1:K». Old index = old_i = 0 | |
| After rewrite: [0:J, 1:K, 2:K, 3:K, 4:K, 5:J, 6:J, 7:L, 8:J, 9:J, 10:J, 11:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=0+1=1. max_i:=11 Reached end of the step = (i >= max_i) = (1 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (1, 2): «1:K, 2:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| pos (2, 3): «2:K, 3:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| pos (3, 4): «3:K, 4:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| pos (4, 5): «4:K, 5:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «4:K, 5:J» to «4:J, 5:K». Old index = old_i = 4 | |
| After rewrite: [0:J, 1:K, 2:K, 3:K, 4:J, 5:K, 6:J, 7:L, 8:J, 9:J, 10:J, 11:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=4+1=5. max_i:=11 Reached end of the step = (i >= max_i) = (5 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (5, 6): «5:K, 6:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «5:K, 6:J» to «5:J, 6:K». Old index = old_i = 5 | |
| After rewrite: [0:J, 1:K, 2:K, 3:K, 4:J, 5:J, 6:K, 7:L, 8:J, 9:J, 10:J, 11:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=5+1=6. max_i:=11 Reached end of the step = (i >= max_i) = (6 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (6, 7): «6:K, 7:L». Checking whether «KL» is among the four rules: «HJ» == «KL»? No. «HL» == «KL»? No. «KJ» == «KL»? No. «KL» == «KL»? Yes. Found a matching rule | |
| Removing the pair «6:K, 7:L». Old index = old_i = 6 | |
| Before removing: [0:J, 1:K, 2:K, 3:K, 4:J, 5:J, 6:K, 7:L, 8:J, 9:J, 10:J, 11:L] | |
| Labelling the TWO elements «6:K, 7:L» to be removed: [0:J, 1:K, 2:K, 3:K, 4:J, 5:J, 6:removed, 7:removed, 8:J, 9:J, 10:J, 11:L] | |
| After removing the labelled TWO elements «6:K, 7:L» to be removed, without renumbering: [0:J, 1:K, 2:K, 3:K, 4:J, 5:J, 8:J, 9:J, 10:J, 11:L] | |
| Renumbering: [0:J, 1:K, 2:K, 3:K, 4:J, 5:J, 6:J, 7:J, 8:J, 9:L]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=6+0=6. max_i:=9 Reached end of the step = (i >= max_i) = (6 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (7, 8): «7:J, 8:J». Checking whether «JJ» is among the four rules: «HJ» == «JJ»? No. «HL» == «JJ»? No. «KJ» == «JJ»? No. «KL» == «JJ»? No. Did not find a matching rule | |
| pos (8, 9): «8:J, 9:L». Checking whether «JL» is among the four rules: «HJ» == «JL»? No. «HL» == «JL»? No. «KJ» == «JL»? No. «KL» == «JL»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 1: [0:J, 1:K, 2:K, 3:K, 4:J, 5:J, 6:J, 7:J, 8:J, 9:L] | |
| pos (0, 1): «0:J, 1:K». Checking whether «JK» is among the four rules: «HJ» == «JK»? No. «HL» == «JK»? No. «KJ» == «JK»? No. «KL» == «JK»? No. Did not find a matching rule | |
| pos (1, 2): «1:K, 2:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| pos (2, 3): «2:K, 3:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| pos (3, 4): «3:K, 4:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «3:K, 4:J» to «3:J, 4:K». Old index = old_i = 3 | |
| After rewrite: [0:J, 1:K, 2:K, 3:J, 4:K, 5:J, 6:J, 7:J, 8:J, 9:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=3+1=4. max_i:=9 Reached end of the step = (i >= max_i) = (4 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (4, 5): «4:K, 5:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «4:K, 5:J» to «4:J, 5:K». Old index = old_i = 4 | |
| After rewrite: [0:J, 1:K, 2:K, 3:J, 4:J, 5:K, 6:J, 7:J, 8:J, 9:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=4+1=5. max_i:=9 Reached end of the step = (i >= max_i) = (5 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (5, 6): «5:K, 6:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «5:K, 6:J» to «5:J, 6:K». Old index = old_i = 5 | |
| After rewrite: [0:J, 1:K, 2:K, 3:J, 4:J, 5:J, 6:K, 7:J, 8:J, 9:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=5+1=6. max_i:=9 Reached end of the step = (i >= max_i) = (6 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (6, 7): «6:K, 7:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «6:K, 7:J» to «6:J, 7:K». Old index = old_i = 6 | |
| After rewrite: [0:J, 1:K, 2:K, 3:J, 4:J, 5:J, 6:J, 7:K, 8:J, 9:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=6+1=7. max_i:=9 Reached end of the step = (i >= max_i) = (7 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (7, 8): «7:K, 8:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «7:K, 8:J» to «7:J, 8:K». Old index = old_i = 7 | |
| After rewrite: [0:J, 1:K, 2:K, 3:J, 4:J, 5:J, 6:J, 7:J, 8:K, 9:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=7+1=8. max_i:=9 Reached end of the step = (i >= max_i) = (8 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (8, 9): «8:K, 9:L». Checking whether «KL» is among the four rules: «HJ» == «KL»? No. «HL» == «KL»? No. «KJ» == «KL»? No. «KL» == «KL»? Yes. Found a matching rule | |
| Removing the pair «8:K, 9:L». Old index = old_i = 8 | |
| Before removing: [0:J, 1:K, 2:K, 3:J, 4:J, 5:J, 6:J, 7:J, 8:K, 9:L] | |
| Labelling the TWO elements «8:K, 9:L» to be removed: [0:J, 1:K, 2:K, 3:J, 4:J, 5:J, 6:J, 7:J, 8:removed, 9:removed] | |
| After removing the labelled TWO elements «8:K, 9:L» to be removed, without renumbering: [0:J, 1:K, 2:K, 3:J, 4:J, 5:J, 6:J, 7:J] | |
| Renumbering: [0:J, 1:K, 2:K, 3:J, 4:J, 5:J, 6:J, 7:J]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=8+0=8. max_i:=7 Reached end of the step = (i >= max_i) = (8 >= 7) = True. Proceed to next step | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 2: [0:J, 1:K, 2:K, 3:J, 4:J, 5:J, 6:J, 7:J] | |
| pos (0, 1): «0:J, 1:K». Checking whether «JK» is among the four rules: «HJ» == «JK»? No. «HL» == «JK»? No. «KJ» == «JK»? No. «KL» == «JK»? No. Did not find a matching rule | |
| pos (1, 2): «1:K, 2:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| pos (2, 3): «2:K, 3:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «2:K, 3:J» to «2:J, 3:K». Old index = old_i = 2 | |
| After rewrite: [0:J, 1:K, 2:J, 3:K, 4:J, 5:J, 6:J, 7:J]. Using this as the new input | |
| rule is not empty, i:=old_i+1=2+1=3. max_i:=7 Reached end of the step = (i >= max_i) = (3 >= 7) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (3, 4): «3:K, 4:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «3:K, 4:J» to «3:J, 4:K». Old index = old_i = 3 | |
| After rewrite: [0:J, 1:K, 2:J, 3:J, 4:K, 5:J, 6:J, 7:J]. Using this as the new input | |
| rule is not empty, i:=old_i+1=3+1=4. max_i:=7 Reached end of the step = (i >= max_i) = (4 >= 7) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (4, 5): «4:K, 5:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «4:K, 5:J» to «4:J, 5:K». Old index = old_i = 4 | |
| After rewrite: [0:J, 1:K, 2:J, 3:J, 4:J, 5:K, 6:J, 7:J]. Using this as the new input | |
| rule is not empty, i:=old_i+1=4+1=5. max_i:=7 Reached end of the step = (i >= max_i) = (5 >= 7) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (5, 6): «5:K, 6:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «5:K, 6:J» to «5:J, 6:K». Old index = old_i = 5 | |
| After rewrite: [0:J, 1:K, 2:J, 3:J, 4:J, 5:J, 6:K, 7:J]. Using this as the new input | |
| rule is not empty, i:=old_i+1=5+1=6. max_i:=7 Reached end of the step = (i >= max_i) = (6 >= 7) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (6, 7): «6:K, 7:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «6:K, 7:J» to «6:J, 7:K». Old index = old_i = 6 | |
| After rewrite: [0:J, 1:K, 2:J, 3:J, 4:J, 5:J, 6:J, 7:K]. Using this as the new input | |
| rule is not empty, i:=old_i+1=6+1=7. max_i:=7 Reached end of the step = (i >= max_i) = (7 >= 7) = True. Proceed to next step | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 3: [0:J, 1:K, 2:J, 3:J, 4:J, 5:J, 6:J, 7:K] | |
| pos (0, 1): «0:J, 1:K». Checking whether «JK» is among the four rules: «HJ» == «JK»? No. «HL» == «JK»? No. «KJ» == «JK»? No. «KL» == «JK»? No. Did not find a matching rule | |
| pos (1, 2): «1:K, 2:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «1:K, 2:J» to «1:J, 2:K». Old index = old_i = 1 | |
| After rewrite: [0:J, 1:J, 2:K, 3:J, 4:J, 5:J, 6:J, 7:K]. Using this as the new input | |
| rule is not empty, i:=old_i+1=1+1=2. max_i:=7 Reached end of the step = (i >= max_i) = (2 >= 7) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (2, 3): «2:K, 3:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «2:K, 3:J» to «2:J, 3:K». Old index = old_i = 2 | |
| After rewrite: [0:J, 1:J, 2:J, 3:K, 4:J, 5:J, 6:J, 7:K]. Using this as the new input | |
| rule is not empty, i:=old_i+1=2+1=3. max_i:=7 Reached end of the step = (i >= max_i) = (3 >= 7) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (3, 4): «3:K, 4:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «3:K, 4:J» to «3:J, 4:K». Old index = old_i = 3 | |
| After rewrite: [0:J, 1:J, 2:J, 3:J, 4:K, 5:J, 6:J, 7:K]. Using this as the new input | |
| rule is not empty, i:=old_i+1=3+1=4. max_i:=7 Reached end of the step = (i >= max_i) = (4 >= 7) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (4, 5): «4:K, 5:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «4:K, 5:J» to «4:J, 5:K». Old index = old_i = 4 | |
| After rewrite: [0:J, 1:J, 2:J, 3:J, 4:J, 5:K, 6:J, 7:K]. Using this as the new input | |
| rule is not empty, i:=old_i+1=4+1=5. max_i:=7 Reached end of the step = (i >= max_i) = (5 >= 7) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (5, 6): «5:K, 6:J». Checking whether «KJ» is among the four rules: «HJ» == «KJ»? No. «HL» == «KJ»? No. «KJ» == «KJ»? Yes. «KL» == «KJ»? No. Found a matching rule | |
| Rewrite the pair «5:K, 6:J» to «5:J, 6:K». Old index = old_i = 5 | |
| After rewrite: [0:J, 1:J, 2:J, 3:J, 4:J, 5:J, 6:K, 7:K]. Using this as the new input | |
| rule is not empty, i:=old_i+1=5+1=6. max_i:=7 Reached end of the step = (i >= max_i) = (6 >= 7) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (6, 7): «6:K, 7:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 4: [0:J, 1:J, 2:J, 3:J, 4:J, 5:J, 6:K, 7:K] | |
| pos (0, 1): «0:J, 1:J». Checking whether «JJ» is among the four rules: «HJ» == «JJ»? No. «HL» == «JJ»? No. «KJ» == «JJ»? No. «KL» == «JJ»? No. Did not find a matching rule | |
| pos (1, 2): «1:J, 2:J». Checking whether «JJ» is among the four rules: «HJ» == «JJ»? No. «HL» == «JJ»? No. «KJ» == «JJ»? No. «KL» == «JJ»? No. Did not find a matching rule | |
| pos (2, 3): «2:J, 3:J». Checking whether «JJ» is among the four rules: «HJ» == «JJ»? No. «HL» == «JJ»? No. «KJ» == «JJ»? No. «KL» == «JJ»? No. Did not find a matching rule | |
| pos (3, 4): «3:J, 4:J». Checking whether «JJ» is among the four rules: «HJ» == «JJ»? No. «HL» == «JJ»? No. «KJ» == «JJ»? No. «KL» == «JJ»? No. Did not find a matching rule | |
| pos (4, 5): «4:J, 5:J». Checking whether «JJ» is among the four rules: «HJ» == «JJ»? No. «HL» == «JJ»? No. «KJ» == «JJ»? No. «KL» == «JJ»? No. Did not find a matching rule | |
| pos (5, 6): «5:J, 6:K». Checking whether «JK» is among the four rules: «HJ» == «JK»? No. «HL» == «JK»? No. «KJ» == «JK»? No. «KL» == «JK»? No. Did not find a matching rule | |
| pos (6, 7): «6:K, 7:K». Checking whether «KK» is among the four rules: «HJ» == «KK»? No. «HL» == «KK»? No. «KJ» == «KK»? No. «KL» == «KK»? No. Did not find a matching rule | |
| In this step, we did not perform any rewrite or removal, thus stopping | |
| Final result in the internal format: [0:J, 1:J, 2:J, 3:J, 4:J, 5:J, 6:K, 7:K] | |
| P3. Translating from the internal format to original format, step by step: | |
| P3.1. As a reminder, list the translation rules from internal to original: | |
| - H -> A# | |
| - J -> #A | |
| - K -> B# | |
| - L -> #B | |
| P3.2. Translate the program back to the original format: | |
| - J -> #A | |
| - J -> #A | |
| - J -> #A | |
| - J -> #A | |
| - J -> #A | |
| - J -> #A | |
| - K -> B# | |
| - K -> B# | |
| Final result in the original format: #A #A #A #A #A #A B# B# | |
| <solution>#A #A #A #A #A #A B# B# | |
| AI-Solution: #A #A #A #A #A #A B# B# | |
| <<correct>> | |
| ## Instance 11: | |
| Term: B# A# A# A# A# A# #B A# #A #B #B #B | |
| Norm: B# A# A# A# A# A# #B A# #A #B #B #B | |
| Rwt: 22 | |
| AI-RESPONSE: | |
| - B# -> K | |
| - A# -> H | |
| - A# -> H | |
| - A# -> H | |
| - A# -> H | |
| - A# -> H | |
| - #B -> L | |
| - A# -> H | |
| - #A -> J | |
| - #B -> L | |
| - #B -> L | |
| - #B -> L | |
| P2: Compute the program | |
| Initial program in the internal format: [0:K, 1:H, 2:H, 3:H, 4:H, 5:H, 6:L, 7:H, 8:J, 9:L, 10:L, 11:L] | |
| pos (0, 1): «0:K, 1:H». Checking whether «KH» is among the four rules: «HJ» == «KH»? No. «HL» == «KH»? No. «KJ» == «KH»? No. «KL» == «KH»? No. Did not find a matching rule | |
| pos (1, 2): «1:H, 2:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (2, 3): «2:H, 3:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (3, 4): «3:H, 4:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (4, 5): «4:H, 5:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (5, 6): «5:H, 6:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «5:H, 6:L» to «5:L, 6:H». Old index = old_i = 5 | |
| After rewrite: [0:K, 1:H, 2:H, 3:H, 4:H, 5:L, 6:H, 7:H, 8:J, 9:L, 10:L, 11:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=5+1=6. max_i:=11 Reached end of the step = (i >= max_i) = (6 >= 11) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (6, 7): «6:H, 7:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (7, 8): «7:H, 8:J». Checking whether «HJ» is among the four rules: «HJ» == «HJ»? Yes. «HL» == «HJ»? No. «KJ» == «HJ»? No. «KL» == «HJ»? No. Found a matching rule | |
| Removing the pair «7:H, 8:J». Old index = old_i = 7 | |
| Before removing: [0:K, 1:H, 2:H, 3:H, 4:H, 5:L, 6:H, 7:H, 8:J, 9:L, 10:L, 11:L] | |
| Labelling the TWO elements «7:H, 8:J» to be removed: [0:K, 1:H, 2:H, 3:H, 4:H, 5:L, 6:H, 7:removed, 8:removed, 9:L, 10:L, 11:L] | |
| After removing the labelled TWO elements «7:H, 8:J» to be removed, without renumbering: [0:K, 1:H, 2:H, 3:H, 4:H, 5:L, 6:H, 9:L, 10:L, 11:L] | |
| Renumbering: [0:K, 1:H, 2:H, 3:H, 4:H, 5:L, 6:H, 7:L, 8:L, 9:L]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=7+0=7. max_i:=9 Reached end of the step = (i >= max_i) = (7 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (7, 8): «7:L, 8:L». Checking whether «LL» is among the four rules: «HJ» == «LL»? No. «HL» == «LL»? No. «KJ» == «LL»? No. «KL» == «LL»? No. Did not find a matching rule | |
| pos (8, 9): «8:L, 9:L». Checking whether «LL» is among the four rules: «HJ» == «LL»? No. «HL» == «LL»? No. «KJ» == «LL»? No. «KL» == «LL»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 1: [0:K, 1:H, 2:H, 3:H, 4:H, 5:L, 6:H, 7:L, 8:L, 9:L] | |
| pos (0, 1): «0:K, 1:H». Checking whether «KH» is among the four rules: «HJ» == «KH»? No. «HL» == «KH»? No. «KJ» == «KH»? No. «KL» == «KH»? No. Did not find a matching rule | |
| pos (1, 2): «1:H, 2:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (2, 3): «2:H, 3:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (3, 4): «3:H, 4:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (4, 5): «4:H, 5:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «4:H, 5:L» to «4:L, 5:H». Old index = old_i = 4 | |
| After rewrite: [0:K, 1:H, 2:H, 3:H, 4:L, 5:H, 6:H, 7:L, 8:L, 9:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=4+1=5. max_i:=9 Reached end of the step = (i >= max_i) = (5 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (5, 6): «5:H, 6:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (6, 7): «6:H, 7:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «6:H, 7:L» to «6:L, 7:H». Old index = old_i = 6 | |
| After rewrite: [0:K, 1:H, 2:H, 3:H, 4:L, 5:H, 6:L, 7:H, 8:L, 9:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=6+1=7. max_i:=9 Reached end of the step = (i >= max_i) = (7 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (7, 8): «7:H, 8:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «7:H, 8:L» to «7:L, 8:H». Old index = old_i = 7 | |
| After rewrite: [0:K, 1:H, 2:H, 3:H, 4:L, 5:H, 6:L, 7:L, 8:H, 9:L]. Using this as the new input | |
| rule is not empty, i:=old_i+1=7+1=8. max_i:=9 Reached end of the step = (i >= max_i) = (8 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (8, 9): «8:H, 9:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «8:H, 9:L» to «8:L, 9:H». Old index = old_i = 8 | |
| After rewrite: [0:K, 1:H, 2:H, 3:H, 4:L, 5:H, 6:L, 7:L, 8:L, 9:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=8+1=9. max_i:=9 Reached end of the step = (i >= max_i) = (9 >= 9) = True. Proceed to next step | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 2: [0:K, 1:H, 2:H, 3:H, 4:L, 5:H, 6:L, 7:L, 8:L, 9:H] | |
| pos (0, 1): «0:K, 1:H». Checking whether «KH» is among the four rules: «HJ» == «KH»? No. «HL» == «KH»? No. «KJ» == «KH»? No. «KL» == «KH»? No. Did not find a matching rule | |
| pos (1, 2): «1:H, 2:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (2, 3): «2:H, 3:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (3, 4): «3:H, 4:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «3:H, 4:L» to «3:L, 4:H». Old index = old_i = 3 | |
| After rewrite: [0:K, 1:H, 2:H, 3:L, 4:H, 5:H, 6:L, 7:L, 8:L, 9:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=3+1=4. max_i:=9 Reached end of the step = (i >= max_i) = (4 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (4, 5): «4:H, 5:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (5, 6): «5:H, 6:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «5:H, 6:L» to «5:L, 6:H». Old index = old_i = 5 | |
| After rewrite: [0:K, 1:H, 2:H, 3:L, 4:H, 5:L, 6:H, 7:L, 8:L, 9:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=5+1=6. max_i:=9 Reached end of the step = (i >= max_i) = (6 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (6, 7): «6:H, 7:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «6:H, 7:L» to «6:L, 7:H». Old index = old_i = 6 | |
| After rewrite: [0:K, 1:H, 2:H, 3:L, 4:H, 5:L, 6:L, 7:H, 8:L, 9:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=6+1=7. max_i:=9 Reached end of the step = (i >= max_i) = (7 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (7, 8): «7:H, 8:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «7:H, 8:L» to «7:L, 8:H». Old index = old_i = 7 | |
| After rewrite: [0:K, 1:H, 2:H, 3:L, 4:H, 5:L, 6:L, 7:L, 8:H, 9:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=7+1=8. max_i:=9 Reached end of the step = (i >= max_i) = (8 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (8, 9): «8:H, 9:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 3: [0:K, 1:H, 2:H, 3:L, 4:H, 5:L, 6:L, 7:L, 8:H, 9:H] | |
| pos (0, 1): «0:K, 1:H». Checking whether «KH» is among the four rules: «HJ» == «KH»? No. «HL» == «KH»? No. «KJ» == «KH»? No. «KL» == «KH»? No. Did not find a matching rule | |
| pos (1, 2): «1:H, 2:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (2, 3): «2:H, 3:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «2:H, 3:L» to «2:L, 3:H». Old index = old_i = 2 | |
| After rewrite: [0:K, 1:H, 2:L, 3:H, 4:H, 5:L, 6:L, 7:L, 8:H, 9:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=2+1=3. max_i:=9 Reached end of the step = (i >= max_i) = (3 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (3, 4): «3:H, 4:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (4, 5): «4:H, 5:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «4:H, 5:L» to «4:L, 5:H». Old index = old_i = 4 | |
| After rewrite: [0:K, 1:H, 2:L, 3:H, 4:L, 5:H, 6:L, 7:L, 8:H, 9:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=4+1=5. max_i:=9 Reached end of the step = (i >= max_i) = (5 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (5, 6): «5:H, 6:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «5:H, 6:L» to «5:L, 6:H». Old index = old_i = 5 | |
| After rewrite: [0:K, 1:H, 2:L, 3:H, 4:L, 5:L, 6:H, 7:L, 8:H, 9:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=5+1=6. max_i:=9 Reached end of the step = (i >= max_i) = (6 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (6, 7): «6:H, 7:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «6:H, 7:L» to «6:L, 7:H». Old index = old_i = 6 | |
| After rewrite: [0:K, 1:H, 2:L, 3:H, 4:L, 5:L, 6:L, 7:H, 8:H, 9:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=6+1=7. max_i:=9 Reached end of the step = (i >= max_i) = (7 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (7, 8): «7:H, 8:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (8, 9): «8:H, 9:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 4: [0:K, 1:H, 2:L, 3:H, 4:L, 5:L, 6:L, 7:H, 8:H, 9:H] | |
| pos (0, 1): «0:K, 1:H». Checking whether «KH» is among the four rules: «HJ» == «KH»? No. «HL» == «KH»? No. «KJ» == «KH»? No. «KL» == «KH»? No. Did not find a matching rule | |
| pos (1, 2): «1:H, 2:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «1:H, 2:L» to «1:L, 2:H». Old index = old_i = 1 | |
| After rewrite: [0:K, 1:L, 2:H, 3:H, 4:L, 5:L, 6:L, 7:H, 8:H, 9:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=1+1=2. max_i:=9 Reached end of the step = (i >= max_i) = (2 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (2, 3): «2:H, 3:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (3, 4): «3:H, 4:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «3:H, 4:L» to «3:L, 4:H». Old index = old_i = 3 | |
| After rewrite: [0:K, 1:L, 2:H, 3:L, 4:H, 5:L, 6:L, 7:H, 8:H, 9:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=3+1=4. max_i:=9 Reached end of the step = (i >= max_i) = (4 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (4, 5): «4:H, 5:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «4:H, 5:L» to «4:L, 5:H». Old index = old_i = 4 | |
| After rewrite: [0:K, 1:L, 2:H, 3:L, 4:L, 5:H, 6:L, 7:H, 8:H, 9:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=4+1=5. max_i:=9 Reached end of the step = (i >= max_i) = (5 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (5, 6): «5:H, 6:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «5:H, 6:L» to «5:L, 6:H». Old index = old_i = 5 | |
| After rewrite: [0:K, 1:L, 2:H, 3:L, 4:L, 5:L, 6:H, 7:H, 8:H, 9:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=5+1=6. max_i:=9 Reached end of the step = (i >= max_i) = (6 >= 9) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (6, 7): «6:H, 7:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (7, 8): «7:H, 8:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (8, 9): «8:H, 9:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 5: [0:K, 1:L, 2:H, 3:L, 4:L, 5:L, 6:H, 7:H, 8:H, 9:H] | |
| pos (0, 1): «0:K, 1:L». Checking whether «KL» is among the four rules: «HJ» == «KL»? No. «HL» == «KL»? No. «KJ» == «KL»? No. «KL» == «KL»? Yes. Found a matching rule | |
| Removing the pair «0:K, 1:L». Old index = old_i = 0 | |
| Before removing: [0:K, 1:L, 2:H, 3:L, 4:L, 5:L, 6:H, 7:H, 8:H, 9:H] | |
| Labelling the TWO elements «0:K, 1:L» to be removed: [0:removed, 1:removed, 2:H, 3:L, 4:L, 5:L, 6:H, 7:H, 8:H, 9:H] | |
| After removing the labelled TWO elements «0:K, 1:L» to be removed, without renumbering: [2:H, 3:L, 4:L, 5:L, 6:H, 7:H, 8:H, 9:H] | |
| Renumbering: [0:H, 1:L, 2:L, 3:L, 4:H, 5:H, 6:H, 7:H]. USING THIS AS THE NEW PROGRAM | |
| rule is empty, i:=old_i+0=0+0=0. max_i:=7 Reached end of the step = (i >= max_i) = (0 >= 7) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (0, 1): «0:H, 1:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «0:H, 1:L» to «0:L, 1:H». Old index = old_i = 0 | |
| After rewrite: [0:L, 1:H, 2:L, 3:L, 4:H, 5:H, 6:H, 7:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=0+1=1. max_i:=7 Reached end of the step = (i >= max_i) = (1 >= 7) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (1, 2): «1:H, 2:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «1:H, 2:L» to «1:L, 2:H». Old index = old_i = 1 | |
| After rewrite: [0:L, 1:L, 2:H, 3:L, 4:H, 5:H, 6:H, 7:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=1+1=2. max_i:=7 Reached end of the step = (i >= max_i) = (2 >= 7) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (2, 3): «2:H, 3:L». Checking whether «HL» is among the four rules: «HJ» == «HL»? No. «HL» == «HL»? Yes. «KJ» == «HL»? No. «KL» == «HL»? No. Found a matching rule | |
| Rewrite the pair «2:H, 3:L» to «2:L, 3:H». Old index = old_i = 2 | |
| After rewrite: [0:L, 1:L, 2:L, 3:H, 4:H, 5:H, 6:H, 7:H]. Using this as the new input | |
| rule is not empty, i:=old_i+1=2+1=3. max_i:=7 Reached end of the step = (i >= max_i) = (3 >= 7) = False. Proceed to check next pair | |
| Performed a rewrite or removal IN THIS STEP!!! | |
| pos (3, 4): «3:H, 4:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (4, 5): «4:H, 5:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (5, 6): «5:H, 6:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (6, 7): «6:H, 7:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| In this step, we performed rewrite or removal, thus starting next step of checking | |
| Step 6: [0:L, 1:L, 2:L, 3:H, 4:H, 5:H, 6:H, 7:H] | |
| pos (0, 1): «0:L, 1:L». Checking whether «LL» is among the four rules: «HJ» == «LL»? No. «HL» == «LL»? No. «KJ» == «LL»? No. «KL» == «LL»? No. Did not find a matching rule | |
| pos (1, 2): «1:L, 2:L». Checking whether «LL» is among the four rules: «HJ» == «LL»? No. «HL» == «LL»? No. «KJ» == «LL»? No. «KL» == «LL»? No. Did not find a matching rule | |
| pos (2, 3): «2:L, 3:H». Checking whether «LH» is among the four rules: «HJ» == «LH»? No. «HL» == «LH»? No. «KJ» == «LH»? No. «KL» == «LH»? No. Did not find a matching rule | |
| pos (3, 4): «3:H, 4:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (4, 5): «4:H, 5:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (5, 6): «5:H, 6:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| pos (6, 7): «6:H, 7:H». Checking whether «HH» is among the four rules: «HJ» == «HH»? No. «HL» == «HH»? No. «KJ» == «HH»? No. «KL» == «HH»? No. Did not find a matching rule | |
| In this step, we did not perform any rewrite or removal, thus stopping | |
| Final result in the internal format: [0:L, 1:L, 2:L, 3:H, 4:H, 5:H, 6:H, 7:H] | |
| P3. Translating from the internal format to original format, step by step: | |
| P3.1. As a reminder, list the translation rules from internal to original: | |
| - H -> A# | |
| - J -> #A | |
| - K -> B# | |
| - L -> #B | |
| P3.2. Translate the program back to the original format: | |
| - L -> #B | |
| - L -> #B | |
| - L -> #B | |
| - H -> A# | |
| - H -> A# | |
| - H -> A# | |
| - H -> A# | |
| Final result in the original format: #B #B #B A# A# A# A# | |
| <solution>#B #B #B A# A# A# A# | |
| AI-Solution: #B #B #B A# A# A# A# | |
| <<incorrect>> | |
| Final score: 11 / 12 |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment