#456 ⟨a, b | aabbaa=bb⟩

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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 ⇒ b2 [1]
2. b4a2 ⇒ a2b4 [2]
3. (b2a)2a ⇒ a(ab2)2 [3]
# ab:aabbaa=bb ab
aabbaa=bb
bbbbaa=aabbbb
bbabbaa=aabbabb

Other submonoids of same group

2 unique, 2 total

Σ#PresentationDescriptionRelated
101796⟨a, b | ababbbaba=b⟩Infinite cancellative non-commutative monoid
102235⟨a, b | aababaa=bab⟩Infinite cancellative non-commutative monoid