#4824 ⟨a, b | abababba=aab⟩

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  1. Properties
  2. Rewriting system

Properties

Rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
#RuleProof
1. (ab)3ba ⇒ a2b [1]
2. a(ab)4 ⇒ a3(b2a)2 [4]
3. a2b(ba)2b2a ⇒ a(ab)2 [2]
4. a3(b2a)2ba ⇒ (a2b)2 [7]
5. a2ba2(b2a)2 ⇒ a3(b2a)2ab [5]
6. a2(bab2a)2 ⇒ a(ab)3 [3]
7. a3b2(ab2a)2 ⇒ a(ab)2a2b [8]
8. a(ab)2a2(b2a)2 ⇒ a3(b2a)2(ab)2 [6]
9. a3(b2a)2abab2a ⇒ a(ab)3a2b [9]
10. a(ab)3a2(b2a)2 ⇒ a3(b2a)2(ab)3 [10]
# ab:abababba=aab ab
abababba=aab
aabababab=aaabbabba
aabbababba=aabab
aaabbabbaba=aabaab
aabaabbabba=aaabbabbaab
aababbababba=aababab
aaabbabbaabba=aababaab
aababaabbabba=aaabbabbaabab
aaabbabbaababba=aabababaab
aabababaabbabba=aaabbabbaababab