#20720 ⟨a, b | ab=aa, aaaaa=aa⟩

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Properties

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. ab ⇒ a2
  2. a5 ⇒ a2 
# ab:ab=aa,aaaaa=aa ab
ab=aa
aaaaa=aa

Right Cayley graph (truncated)

Left Cayley graph (truncated)

Other isomorphic instances

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

31 total

Σ#PresentationMapping
1120721⟨a, b | ab=aa, aaaaa=ab⟩φ(a) = a, φ(b) = b
1120724⟨a, b | ab=aa, aaaab=aa⟩φ(a) = a, φ(b) = b
1120725⟨a, b | ab=aa, aaaab=ab⟩φ(a) = a, φ(b) = b
1120728⟨a, b | ab=aa, aaaba=aa⟩φ(a) = a, φ(b) = b
1120729⟨a, b | ab=aa, aaaba=ab⟩φ(a) = a, φ(b) = b
1120732⟨a, b | ab=aa, aaabb=aa⟩φ(a) = a, φ(b) = b
1120733⟨a, b | ab=aa, aaabb=ab⟩φ(a) = a, φ(b) = b
1120736⟨a, b | ab=aa, aabaa=aa⟩φ(a) = a, φ(b) = b
1120737⟨a, b | ab=aa, aabaa=ab⟩φ(a) = a, φ(b) = b
1120740⟨a, b | ab=aa, aabab=aa⟩φ(a) = a, φ(b) = b
1120741⟨a, b | ab=aa, aabab=ab⟩φ(a) = a, φ(b) = b
1120744⟨a, b | ab=aa, aabba=aa⟩φ(a) = a, φ(b) = b
1120745⟨a, b | ab=aa, aabba=ab⟩φ(a) = a, φ(b) = b
1120748⟨a, b | ab=aa, aabbb=aa⟩φ(a) = a, φ(b) = b
1120749⟨a, b | ab=aa, aabbb=ab⟩φ(a) = a, φ(b) = b
1120752⟨a, b | ab=aa, abaaa=aa⟩φ(a) = a, φ(b) = b
1120753⟨a, b | ab=aa, abaaa=ab⟩φ(a) = a, φ(b) = b
1120756⟨a, b | ab=aa, abaab=aa⟩φ(a) = a, φ(b) = b
1120757⟨a, b | ab=aa, abaab=ab⟩φ(a) = a, φ(b) = b
1120760⟨a, b | ab=aa, ababa=aa⟩φ(a) = a, φ(b) = b
1120761⟨a, b | ab=aa, ababa=ab⟩φ(a) = a, φ(b) = b
1120764⟨a, b | ab=aa, ababb=aa⟩φ(a) = a, φ(b) = b
1120765⟨a, b | ab=aa, ababb=ab⟩φ(a) = a, φ(b) = b
1120768⟨a, b | ab=aa, abbaa=aa⟩φ(a) = a, φ(b) = b
1120769⟨a, b | ab=aa, abbaa=ab⟩φ(a) = a, φ(b) = b
1120772⟨a, b | ab=aa, abbab=aa⟩φ(a) = a, φ(b) = b
1120773⟨a, b | ab=aa, abbab=ab⟩φ(a) = a, φ(b) = b
1120776⟨a, b | ab=aa, abbba=aa⟩φ(a) = a, φ(b) = b
1120777⟨a, b | ab=aa, abbba=ab⟩φ(a) = a, φ(b) = b
1120780⟨a, b | ab=aa, abbbb=aa⟩φ(a) = a, φ(b) = b
1120781⟨a, b | ab=aa, abbbb=ab⟩φ(a) = a, φ(b) = b