#1694 ⟨a, b | aabababaa=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. b(ba)3a ⇒ a(ab)3b [2]
2. a(ab)3a2 ⇒ b [1]
3. (ba)4a ⇒ a(ab)4 [3]
# ab:aabababaa=b ab
bbababaa=aabababb
aabababaa=b
babababaa=aabababab

Other submonoids of same group

5 unique, 8 total

Σ#PresentationDescriptionRelated
8388⟨a, b | aabbbaa=b⟩Infinite cancellative non-commutative monoid
8520⟨a, b | aabaa=bbb⟩Infinite cancellative non-commutative monoid
101360⟨a, b | aaababbaba=1⟩Infinite non-Abelian group3 iso
102066⟨a, b | ababbaba=bb⟩Infinite cancellative non-commutative monoid
102766⟨a, b | babab=aabaa⟩Infinite cancellative non-commutative monoid