#815 ⟨a, b | aabbaaba=b⟩

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  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic 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. a2b2a2ba ⇒ b [1]
2. (a2b2)2 ⇒ bab2a2ba [2]
3. a2b2a4b3 ⇒ b3(a2ba)2 [5]
4. bab2(a2ba)2 ⇒ a2b3 [3]
5. bab2a2ba3b2 ⇒ a2b3ab2a2ba [4]
6. bab2a2ba5b3 ⇒ a2b5(a2ba)2 [6]
# ab:aabbaaba=b reversed:ab
aabbaaba=b
aabbaabb=babbaaba
aabbaaaabbb=bbbaabaaaba
babbaabaaaba=aabbb
babbaabaaabb=aabbbabbaaba
babbaabaaaaabbb=aabbbbbaabaaaba

Other submonoids of same group

3 unique, 3 total

Σ#PresentationDescriptionRelated
101774⟨a, b | abaabbaba=b⟩Infinite cancellative non-commutative monoid
102266⟨a, b | aabbaba=bab⟩Infinite cancellative non-commutative monoid
113583⟨a, b | aababaaaba=b⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

2 unique, 2 total

Σ#PresentationDescriptionRelated
91234⟨a, b | aabba=babb⟩Infinite cancellative non-commutative monoid
115376⟨a, b | ababbba=babb⟩Infinite cancellative non-commutative monoid