#131 ⟨a, b | aaaabba=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. a5 ⇒ c [2]
# ab:aaaabba=1 abcd aaaaa=c,bb=d magic:0
bb=d
ca=ac
cb=bc
cd=1
da=ad
db=bd
dc=1
aaaaa=c

Other submonoids of same group

7 unique, 7 total

Σ#PresentationDescriptionRelated
7196⟨a, b | abbbba=b⟩Infinite cancellative non-commutative monoid
7199⟨a, b | aaaaa=bb⟩Infinite cancellative non-commutative monoid
7232⟨a, b | abbba=bb⟩Infinite cancellative non-commutative monoid
7237⟨a, b | aaaa=bab⟩Infinite cancellative non-commutative monoid
7268⟨a, b | abba=bbb⟩Infinite cancellative non-commutative monoid
102333⟨a, b | abababa=bab⟩Infinite cancellative non-commutative monoid
102767⟨a, b | babab=ababa⟩Infinite cancellative non-commutative monoid

Isomorphic instances

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

11 total

Σ#PresentationMapping
7137⟨a, b | aaabbaa=1⟩φ(a) = a, φ(b) = b
7160⟨a, b | abbbbba=1⟩φ(a) = b, φ(b) = a
9605⟨a, b | aaaaababa=1⟩φ(a) = a, φ(b) = aaaadb
9615⟨a, b | aaaababaa=1⟩φ(a) = a, φ(b) = aaaadb
9633⟨a, b | aaababaaa=1⟩φ(a) = a, φ(b) = aaaadb
9695⟨a, b | abaaaaaab=1⟩φ(a) = a, φ(b) = aaaadb
112795⟨a, b | aaaaaabaaba=1⟩φ(a) = a, φ(b) = aaaadbaaaad
112813⟨a, b | aaaaabaabaa=1⟩φ(a) = a, φ(b) = aaaadbaaaad
112847⟨a, b | aaaabaabaaa=1⟩φ(a) = a, φ(b) = aaaadbaaaad
113005⟨a, b | aabaaaaaaab=1⟩φ(a) = a, φ(b) = aaaadaaaadb
113170⟨a, b | abaaaaaaaba=1⟩φ(a) = a, φ(b) = aaaadbaaaad