#10767 ⟨a, b | aaab=bba, bbbb=1⟩

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Properties

Element profile

Complete 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
  1. a9 ⇒ a
  2. aba8 ⇒ ab
  3. b2a ⇒ a3b
  4. ab2 ⇒ a4ba7
  5. (ab)2 ⇒ a6ba6
  6. aba2b ⇒ a7
  7. aba3b ⇒ a3ba3
  8. aba4b ⇒ a2ba5
  9. aba5b ⇒ a7ba
  10. aba6b ⇒ a5ba4
  11. aba7b ⇒ a8ba2
  12. b4 ⇒ 1 
# ab:aaab=bba,bbbb=1 a/b
aaaaaaaaa=a
abaaaaaaaa=ab
bba=aaab
abb=aaaabaaaaaaa
abab=aaaaaabaaaaaa
abaab=aaaaaaa
abaaab=aaabaaa
abaaaab=aabaaaaa
abaaaaab=aaaaaaaba
abaaaaaab=aaaaabaaaa
abaaaaaaab=aaaaaaaabaa
bbbb=1

Right Cayley graph

Left Cayley graph

Others with same cardinality

1 unique, 1 total

Σ#PresentationDescriptionRelated
1114354⟨a, b | aaaa=a, abbba=b⟩Finite non-commutative monoid with 148 elements

Other isomorphic instances

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

2 total

Σ#PresentationMapping
1117115⟨a, b | aaaa=1, aabbba=b⟩φ(a) = b, φ(b) = a
1117644⟨a, b | aaaa=1, aabbb=ba⟩φ(a) = b, φ(b) = ab

Other anti-isomorphic instances

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

1 total

Σ#PresentationMapping
1111088⟨a, b | babb=aaa, bbbb=1⟩φ(a) = a, φ(b) = bbb