#27649 ⟨a, b | aa=1, ababba=bbb⟩

Up:Monoids with two generators and two relations
Prev:#27647 ⟨a, b | aa=1, ababba=bab⟩
Next:#27655 ⟨a, b | aa=1, ababbb=bab⟩

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. b3a ⇒ abab2
  3. bab2a ⇒ ab3
  4. b(ba)2b2 ⇒ (ab)3b2
  5. (ba)3b2 ⇒ ab2ab3 
# ab:aa=1,ababba=bbb reversed:a/b
aa=1
bbba=ababb
babba=abbb
bbababb=abababbb
babababb=abbabbb

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
1128180⟨a, b | aa=1, ababb=bbba⟩φ(a) = a, φ(b) = b
1128206⟨a, b | aa=1, abbba=babb⟩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
1128196⟨a, b | aa=1, abbab=bbba⟩φ(a) = a, φ(b) = b