#1116 ⟨a, b | abaaba=bbb⟩

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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. (aba)2 ⇒ b3 [1]
2. b3aba ⇒ abab3 [2]
3. b4a2ba ⇒ aba2b4 [3]
# ab:abaaba=bbb ab
abaaba=bbb
bbbaba=ababbb
bbbbaaba=abaabbbb

Other submonoids of same group

3 unique, 11 total

Σ#PresentationDescriptionRelated
9645⟨a, b | aaabbabba=1⟩Infinite non-Abelian group8 iso
114262⟨a, b | abaabaaba=bb⟩Infinite cancellative non-commutative monoid
114346⟨a, b | abbababba=bb⟩Infinite cancellative non-commutative monoid