#1206 ⟨a, b | aabaa=bbbb⟩

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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. a2ba2 ⇒ b4 [1]
2. b5a2 ⇒ a2b5 [2]
3. b4aba2 ⇒ a2bab4 [3]
# ab:aabaa=bbbb ab
aabaa=bbbb
bbbbbaa=aabbbbb
bbbbabaa=aababbbb

Other submonoids of same group

3 unique, 6 total

Σ#PresentationDescriptionRelated
9826⟨a, b | aabbbbaa=b⟩Infinite cancellative non-commutative monoid
112865⟨a, b | aaaababbaba=1⟩Infinite non-Abelian group3 iso
114844⟨a, b | ababbaba=bbb⟩Infinite cancellative non-commutative monoid