#27671 ⟨a, b | aa=1, abbabb=bab⟩

Up:Monoids with two generators and two relations
Prev:#27657 ⟨a, b | aa=1, ababbb=bbb⟩
Next:#27673 ⟨a, b | aa=1, abbabb=bbb⟩

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. bab5 ⇒ bab
  2. b5ab ⇒ bab
  3. a2 ⇒ 1
  4. (ab)2 ⇒ b2ab2
  5. ab2ab ⇒ bab4
  6. ab3ab ⇒ b3ab3
  7. bab4ab ⇒ ab4ab2 
# ab:aa=1,abbabb=bab b/a
babbbbb=bab
bbbbbab=bab
aa=1
abab=bbabb
abbab=babbbb
abbbab=bbbabbb
babbbbab=abbbbabb

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.

1 total

Σ#PresentationMapping
1128280⟨a, b | aa=1, bbabb=abab⟩φ(a) = a, φ(b) = b