#1086 ⟨a, b | aabbaa=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. a2b2a2 ⇒ b3 [1]
2. b5a2 ⇒ a2b5 [2]
3. b3ab2a2 ⇒ a2b2ab3 [3]
# ab:aabbaa=bbb ab
aabbaa=bbb
bbbbbaa=aabbbbb
bbbabbaa=aabbabbb

Other submonoids of same group

3 unique, 3 total

Σ#PresentationDescriptionRelated
9958⟨a, b | aabbbaa=bb⟩Infinite cancellative non-commutative monoid
113794⟨a, b | ababbbbaba=b⟩Infinite cancellative non-commutative monoid
114320⟨a, b | ababbbaba=bb⟩Infinite cancellative non-commutative monoid