#1281 ⟨a, b | aaaaaaabba=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. b2 ⇒ d [3]
2. ca ⇒ ac [6]
3. cb ⇒ bc [15]
4. cd ⇒ 1 [9]
5. da ⇒ ad [13]
6. db ⇒ bd [5]
7. dc ⇒ 1 [14]
8. a8 ⇒ c [2]
# ab:aaaaaaabba=1 abcd aaaaaaaa=c,bb=d magic:0
bb=d
ca=ac
cb=bc
cd=1
da=ad
db=bd
dc=1
aaaaaaaa=c

Other submonoids of same group

8 unique, 8 total

Σ#PresentationDescriptionRelated
101818⟨a, b | abbbbbbba=b⟩Infinite cancellative non-commutative monoid
101821⟨a, b | aaaaaaaa=bb⟩Infinite cancellative non-commutative monoid
102090⟨a, b | abbbbbba=bb⟩Infinite cancellative non-commutative monoid
102095⟨a, b | aaaaaaa=bab⟩Infinite cancellative non-commutative monoid
102362⟨a, b | abbbbba=bbb⟩Infinite cancellative non-commutative monoid
102370⟨a, b | aaaaaa=baab⟩Infinite cancellative non-commutative monoid
102634⟨a, b | abbbba=bbbb⟩Infinite cancellative non-commutative monoid
102741⟨a, b | baaab=aaaaa⟩Infinite cancellative non-commutative monoid

Isomorphic instances

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

4 total

Σ#PresentationMapping
101287⟨a, b | aaaaaabbaa=1⟩φ(a) = a, φ(b) = b
101299⟨a, b | aaaaabbaaa=1⟩φ(a) = a, φ(b) = b
101322⟨a, b | aaaabbaaaa=1⟩φ(a) = a, φ(b) = b
101546⟨a, b | abbbbbbbba=1⟩φ(a) = b, φ(b) = a