#27125 ⟨a, b | aa=1, ababbba=bb

Quick links

  1. Properties
  2. Rewriting system
  3. Isomorphic instances
  4. Anti-isomorphic instances

Properties

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
#RuleProof
1. b6 ⇒ b2 [23]
2. b2ab4 ⇒ b2a [20]
3. b4a ⇒ ab4 [27]
4. a2 ⇒ 1 [1]
5. abab2 ⇒ b2ab3 [21]
6. ab2a ⇒ bab3 [5]
7. ab3a ⇒ b3ab2 [26]
8. b(ba)2 ⇒ ab5 [25]
# ab:aa=1,ababbba=bb b/a
bbbbbb=bb
bbabbbb=bba
bbbba=abbbb
aa=1
ababb=bbabbb
abba=babbb
abbba=bbbabb
bbaba=abbbbb

Isomorphic instances

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

2 total

Σ#PresentationMapping
1127656a, b | aa=1, ababbb=bbaφ(a) = a, φ(b) = b
1128266a, b | aa=1, babbb=abbaφ(a) = a, φ(b) = b

Anti-isomorphic instances

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

1 total

Σ#PresentationMapping
1127680a, b | aa=1, abbbab=bbaφ(a) = a, φ(b) = b