#298 ⟨a, b | aaabbbba=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 [5]
2. cb ⇒ bc [13]
3. cd ⇒ 1 [9]
4. da ⇒ ad [11]
5. db ⇒ bd [6]
6. dc ⇒ 1 [12]
7. a4 ⇒ c [2]
8. b4 ⇒ d [3]
# ab:aaabbbba=1 abcd aaaa=c,bbbb=d magic:0
ca=ac
cb=bc
cd=1
da=ad
db=bd
dc=1
aaaa=c
bbbb=d

Other submonoids of same group

2 unique, 2 total

Σ#PresentationDescriptionRelated
8594⟨a, b | bbbb=aaaa⟩Infinite cancellative non-commutative monoid
102334⟨a, b | abababa=bbb⟩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
8318⟨a, b | aabbbbaa=1⟩φ(a) = a, φ(b) = b