#13119 ⟨a, b | bbb=aaa, abba=b⟩

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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. a21 ⇒ a3
  2. ba18 ⇒ b
  3. a3b ⇒ ba3
  4. b2 ⇒ a2ba14
  5. bab ⇒ aba7
  6. ba2b ⇒ a7 
# ab:bbb=aaa,abba=b a/b
aaaaaaaaaaaaaaaaaaaaa=aaa
baaaaaaaaaaaaaaaaaa=b
aaab=baaa
bb=aabaaaaaaaaaaaaaa
bab=abaaaaaaa
baab=aaaaaaa

Right Cayley graph

Left Cayley graph

Others with same cardinality

1 unique, 1 total

Σ#PresentationDescriptionRelated
1116549⟨a, b | aba=bb, bab=aaa⟩Finite non-commutative monoid with 75 elements

Other isomorphic instances

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

1 total

Σ#PresentationMapping
1115524⟨a, b | aaa=bb, ababa=b⟩φ(a) = a, φ(b) = aabaaaaaaaaaaaaaaa