#27125 ⟨a, b | aa=1, ababbba=bb⟩

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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. b6 ⇒ b2
  2. b2ab4 ⇒ b2a
  3. b4a ⇒ ab4
  4. a2 ⇒ 1
  5. abab2 ⇒ b2ab3
  6. ab2a ⇒ bab3
  7. ab3a ⇒ b3ab2
  8. b(ba)2 ⇒ ab5 
# ab:aa=1,ababbba=bb b/a
bbbbbb=bb
bbabbbb=bba
bbbba=abbbb
aa=1
ababb=bbabbb
abba=babbb
abbba=bbbabb
bbaba=abbbbb

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.

2 total

Σ#PresentationMapping
1127656⟨a, b | aa=1, ababbb=bba⟩φ(a) = a, φ(b) = b
1128266⟨a, b | aa=1, babbb=abba⟩φ(a) = a, φ(b) = b

Other anti-isomorphic instances

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

1 total

Σ#PresentationMapping
1127680⟨a, b | aa=1, abbbab=bba⟩φ(a) = a, φ(b) = b