#21200 ⟨a, b | aaa=1, ababbbbb=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. b72 ⇒ 1
  2. b4a ⇒ ab4
  3. a2 ⇒ bab5
  4. aba ⇒ b67
  5. ab2a ⇒ b3ab59
  6. bab3a ⇒ ab3ab55 
# ab:aaa=1,ababbbbb=1 b/a
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=1
bbbba=abbbb
aa=babbbbb
aba=bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
abba=bbbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
babbba=abbbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Right Cayley graph

Left Cayley graph

Other isomorphic instances

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

3 total

Σ#PresentationMapping
1121217⟨a, b | aaa=1, abbbbbab=1⟩φ(a) = a, φ(b) = b
1121240⟨a, b | aaa=1, bababbbb=1⟩φ(a) = a, φ(b) = b
1121250⟨a, b | aaa=1, bbababbb=1⟩φ(a) = a, φ(b) = b