#410 ⟨a, b | abbabba=b⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Isomorphic instances

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. b3a ⇒ ab3 [2]
2. a(b2a)2 ⇒ b [1]
# ab:abbabba=b ab
bbba=abbb
abbabba=b

Other submonoids of same group

5 unique, 13 total

Σ#PresentationDescriptionRelated
667⟨a, b | aabbba=1⟩Infinite non-Abelian group8 iso
6124⟨a, b | bbb=aaa⟩Infinite cancellative non-commutative monoid
7229⟨a, b | ababa=bb⟩Infinite cancellative non-commutative monoid
91115⟨a, b | abaaba=bab⟩Infinite cancellative non-commutative monoid
115304⟨a, b | abaaaba=baab⟩Infinite cancellative non-commutative monoid

Isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

1 total

Σ#PresentationMapping
113764⟨a, b | ababaababa=b⟩φ(a) = a, φ(b) = abbabb