#91 ⟨a, b | ababa=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. b2a ⇒ ab2 [2]
2. a(ba)2 ⇒ b [1]
# ab:ababa=b ab
bba=abb
ababa=b

Other submonoids of same group

12 unique, 52 total

Σ#PresentationDescriptionRelated
530⟨a, b | aabba=1⟩Infinite non-Abelian group40 iso
543⟨a, b | abba=b⟩Infinite cancellative non-commutative monoid
546⟨a, b | aaa=bb⟩Infinite cancellative non-commutative monoid
553⟨a, b | aba=bb⟩Infinite cancellative non-commutative monoid
6123⟨a, b | bab=aba⟩Infinite cancellative non-commutative monoid
7267⟨a, b | abba=bab⟩Infinite cancellative non-commutative monoid
8555⟨a, b | abbba=bab⟩Infinite cancellative non-commutative monoid
91137⟨a, b | abbbba=bab⟩Infinite cancellative non-commutative monoid
91262⟨a, b | ababa=baab⟩Infinite cancellative non-commutative monoid
102361⟨a, b | abbbbba=bab⟩Infinite cancellative non-commutative monoid
114887⟨a, b | abbbbbba=bab⟩Infinite cancellative non-commutative monoid
115855⟨a, b | abaaba=baaab⟩Infinite cancellative non-commutative monoid

Isomorphic instances

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

5 total

Σ#PresentationMapping
7190⟨a, b | abaaba=b⟩φ(a) = a, φ(b) = abab
8396⟨a, b | abaaaba=b⟩φ(a) = a, φ(b) = bab
9834⟨a, b | abaaaaba=b⟩φ(a) = a, φ(b) = baabab
101750⟨a, b | abaaaaaba=b⟩φ(a) = a, φ(b) = abaabaabaabab
113700⟨a, b | abaaaaaaba=b⟩φ(a) = a, φ(b) = baabaabaabab