#645 ⟨a, b | aaabbabba=1⟩

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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. ad ⇒ da [10]
2. da3 ⇒ 1 [11]
3. cd ⇒ dc [12]
4. ca3 ⇒ a3c [18]
5. cac ⇒ d2a2 [15]
6. cb ⇒ bc [5]
7. cab ⇒ d2a2ba4ca [20]
8. b2 ⇒ c [2]
# ab:aaabbabba=1 reversed:ad/cb bb=c,acac=d morph:2/0,4/0
ad=da
daaa=1
cd=dc
caaa=aaac
cac=ddaa
cb=bc
cab=ddaabaaaaca
bb=c

Other submonoids of same group

3 unique, 3 total

Σ#PresentationDescriptionRelated
91116⟨a, b | abaaba=bbb⟩Infinite cancellative non-commutative monoid
114262⟨a, b | abaabaaba=bb⟩Infinite cancellative non-commutative monoid
114346⟨a, b | abbababba=bb⟩Infinite cancellative non-commutative monoid

Isomorphic instances

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

8 total

Σ#PresentationMapping
9683⟨a, b | aabbabbaa=1⟩φ(a) = a, φ(b) = b
9690⟨a, b | aabbbbaab=1⟩φ(a) = b, φ(b) = a
9709⟨a, b | abaabbbba=1⟩φ(a) = b, φ(b) = a
113047⟨a, b | aabaabbbaab=1⟩φ(a) = baaaaca, φ(b) = bba
113128⟨a, b | aabbabbabba=1⟩φ(a) = bab, φ(b) = baaaaca
113139⟨a, b | aabbbaabaab=1⟩φ(a) = baaaaca, φ(b) = bba
113206⟨a, b | abaabaabbba=1⟩φ(a) = baaaaca, φ(b) = bab
113221⟨a, b | abaabbbaaba=1⟩φ(a) = baaaaca, φ(b) = bab