#254 ⟨a, b | aaba=bbb⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic group

Properties

Rewriting system

Format:
Word:
Enter a word above to compute its normal form. Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Strategy:
Result: 1 
1
#RuleProof
1. a(ab)2 ⇒ ba2ba [2]
2. b3 ⇒ a2ba [1]
# ab:aaba=bbb a/b - -
aabab=baaba
bbb=aaba

Other submonoids of same group

6 unique, 25 total

Σ#PresentationPropertiesφ
8290⟨a, b | aaababba=1⟩Grp Inf19
8478⟨a, b | ababba=bb⟩Can Inf
9863⟨a, b | abbabbba=b⟩Can Inf
91263⟨a, b | ababa=babb⟩Can Inf
114796⟨a, b | abaababa=bab⟩Can Inf
115405⟨a, b | abbabba=babb⟩Can Inf

Other submonoids of anti-isomorphic group

3 unique, 3 total

Σ#PresentationProperties
7186⟨a, b | aabbba=b⟩Can Inf
9804⟨a, b | aabababa=b⟩Can Inf
113560⟨a, b | aabaabaaba=b⟩Can Inf