#1732 ⟨a, b | aabbbaaba=b⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group

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. a2b3a2ba ⇒ b [1]
2. a2b3a2b2 ⇒ bab3a2ba [2]
3. a2b3a4b4 ⇒ b3(ba2ba)2 [5]
4. bab2(ba2ba)2 ⇒ a2b4 [3]
5. bab3a(ab)2a2b2 ⇒ a2b4ab3a2ba [4]
6. bab3a(ab)2a4b4 ⇒ a2b6(ba2ba)2 [6]
# ab:aabbbaaba=b reversed:ab
aabbbaaba=b
aabbbaabb=babbbaaba
aabbbaaaabbbb=bbbbaababaaba
babbbaababaaba=aabbbb
babbbaababaabb=aabbbbabbbaaba
babbbaababaaaabbbb=aabbbbbbbaababaaba

Other submonoids of same group

1 unique, 1 total

Σ#PresentationDescriptionRelated
114278⟨a, b | abaabbaba=bb⟩Infinite cancellative non-commutative monoid