#27647 ⟨a, b | aa=1, ababba=bab⟩

Up:Monoids with two generators and two relations
Prev:#27641 ⟨a, b | aa=1, ababab=bbb⟩
Next:#27649 ⟨a, b | aa=1, ababba=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. a2 ⇒ 1
  2. (ba)2 ⇒ (ab)2
  3. bab2 ⇒ bab
  4. b2ab ⇒ bab 
# ab:aa=1,ababba=bab ab
aa=1
baba=abab
babb=bab
bbab=bab

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.

3 total

Σ#PresentationMapping
1128164⟨a, b | aa=1, ababa=babb⟩φ(a) = a, φ(b) = b
1128176⟨a, b | aa=1, ababb=baba⟩φ(a) = a, φ(b) = b
1128192⟨a, b | aa=1, abbab=baba⟩φ(a) = a, φ(b) = b