#182 ⟨a, b | aabbaa=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. b3a2 ⇒ a2b3 [2]
2. a2b2a2 ⇒ b [1]
3. bab2a2 ⇒ a2b2ab [3]
# ab:aabbaa=b ab
bbbaa=aabbb
aabbaa=b
babbaa=aabbab

Other submonoids of same group

11 unique, 22 total

Σ#PresentationDescriptionRelated
7214⟨a, b | aabaa=bb⟩Infinite cancellative non-commutative monoid
8378⟨a, b | aababaa=b⟩Infinite cancellative non-commutative monoid
8519⟨a, b | aabaa=bab⟩Infinite cancellative non-commutative monoid
9672⟨a, b | aababbaba=1⟩Infinite non-Abelian group10 iso
9796⟨a, b | aabaabaa=b⟩Infinite cancellative non-commutative monoid
9854⟨a, b | ababbaba=b⟩Infinite cancellative non-commutative monoid1 iso
91204⟨a, b | aabaa=baab⟩Infinite cancellative non-commutative monoid
101670⟨a, b | aabaaabaa=b⟩Infinite cancellative non-commutative monoid
102743⟨a, b | baaab=aabaa⟩Infinite cancellative non-commutative monoid
114843⟨a, b | ababbaba=bab⟩Infinite cancellative non-commutative monoid
115943⟨a, b | abbbba=bbabb⟩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
113540⟨a, b | aabaaaabaa=b⟩φ(a) = a, φ(b) = bb