#609 ⟨a, b | aaaaabbba=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. ca ⇒ ac [6]
2. cb ⇒ bc [15]
3. cd ⇒ 1 [9]
4. da ⇒ ad [17]
5. db ⇒ bd [5]
6. dc ⇒ 1 [14]
7. b3 ⇒ d [3]
8. a6 ⇒ c [2]
# ab:aaaaabbba=1 abcd aaaaaa=c,bbb=d magic:0
ca=ac
cb=bc
cd=1
da=ad
db=bd
dc=1
bbb=d
aaaaaa=c

Other submonoids of same group

3 unique, 3 total

Σ#PresentationDescriptionRelated
91008⟨a, b | aaaaaa=bbb⟩Infinite cancellative non-commutative monoid
102764⟨a, b | babab=aaaaa⟩Infinite cancellative non-commutative monoid
115406⟨a, b | abbabba=bbbb⟩Infinite cancellative non-commutative monoid

Isomorphic instances

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

3 total

Σ#PresentationMapping
9623⟨a, b | aaaabbbaa=1⟩φ(a) = a, φ(b) = b
9646⟨a, b | aaabbbaaa=1⟩φ(a) = a, φ(b) = b
9694⟨a, b | aabbbbbba=1⟩φ(a) = b, φ(b) = a