#678 ⟨a, b | aabbaaabb=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. dc ⇒ 1 [17]
2. cd ⇒ 1 [15]
3. ca ⇒ ac [5]
4. da ⇒ ad [19]
5. c5b ⇒ bc5 [37]
6. db ⇒ c4bd5 [40]
7. ba ⇒ ac3bd3 [41]
8. cb2 ⇒ b2c [22]
9. a3 ⇒ c [2]
10. b4 ⇒ ad2 [24]
# ab:aabbaaabb=1 c/d/ab aaa=c,bbaabb=d magic:0
dc=1
cd=1
ca=ac
da=ad
cccccb=bccccc
db=ccccbddddd
ba=acccbddd
cbb=bbc
aaa=c
bbbb=add

Other submonoids of same group

2 unique, 3 total

Σ#PresentationDescriptionRelated
9860⟨a, b | abbaabba=b⟩Infinite cancellative non-commutative monoid1 iso
114865⟨a, b | abbaabba=bab⟩Infinite cancellative non-commutative monoid

Isomorphic instances

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

12 total

Σ#PresentationMapping
9680⟨a, b | aabbaabba=1⟩φ(a) = a, φ(b) = b
9722⟨a, b | abbaaabba=1⟩φ(a) = a, φ(b) = b
9724⟨a, b | abbaabbba=1⟩φ(a) = b, φ(b) = a
113056⟨a, b | aababaaabba=1⟩φ(a) = aad, φ(b) = aaba
113101⟨a, b | aabbaaababa=1⟩φ(a) = aad, φ(b) = aaba
113107⟨a, b | aabbaabaabb=1⟩φ(a) = aabbcb, φ(b) = bba
113110⟨a, b | aabbaabbaab=1⟩φ(a) = aabbcb, φ(b) = bba
113193⟨a, b | abaaabbaaab=1⟩φ(a) = aad, φ(b) = aaba
113216⟨a, b | abaabbaabba=1⟩φ(a) = aabbcb, φ(b) = bab
113278⟨a, b | abbaabaabba=1⟩φ(a) = aabbcb, φ(b) = bab
113282⟨a, b | abbaabbabba=1⟩φ(a) = bab, φ(b) = aabbcb
113300⟨a, b | abbbababbba=1⟩φ(a) = abaa, φ(b) = aad