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

Other submonoids of same group

5 unique, 5 total

Σ#PresentationDescriptionRelated
8490⟨a, b | aaaaa=bbb⟩Infinite cancellative non-commutative monoid
91264⟨a, b | ababa=bbbb⟩Infinite cancellative non-commutative monoid
102356⟨a, b | abbabba=bbb⟩Infinite cancellative non-commutative monoid
114301⟨a, b | ababababa=bb⟩Infinite cancellative non-commutative monoid
114357⟨a, b | abbbabbba=bb⟩Infinite cancellative non-commutative monoid

Isomorphic instances

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

7 total

Σ#PresentationMapping
8296⟨a, b | aaabbbaa=1⟩φ(a) = a, φ(b) = b
8320⟨a, b | aabbbbba=1⟩φ(a) = b, φ(b) = a
112819⟨a, b | aaaaabababa=1⟩φ(a) = a, φ(b) = aaaadb
112859⟨a, b | aaaabababaa=1⟩φ(a) = a, φ(b) = aaaadb
112934⟨a, b | aaabababaaa=1⟩φ(a) = a, φ(b) = aaaadb
113171⟨a, b | abaaaaaabab=1⟩φ(a) = a, φ(b) = aaaadb
113227⟨a, b | ababaaaaaab=1⟩φ(a) = a, φ(b) = aaaadb