#13295 ⟨a, b | aaaaa=1, abbabb=1⟩

Up:Monoids with two generators and two relations
Prev:#13293 ⟨a, b | aaaaa=1, ababbb=1⟩
Next:#13308 ⟨a, b | aaaaa=1, bbbbbb=1⟩

Quick links

  1. Properties
  2. Rewriting system
  3. 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. a5 ⇒ 1 [1]
2. bab2a ⇒ ab2ab [6]
3. b2ab2 ⇒ a4 [3]
4. b2aba4 ⇒ a4bab2 [4]
# ab:aaaaa=1,abbabb=1 ab
aaaaa=1
babba=abbab
bbabb=aaaa
bbabaaaa=aaaababb

Isomorphic instances

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

1 total

Σ#PresentationMapping
1113304⟨a, b | aaaaa=1, babbab=1⟩φ(a) = a, φ(b) = b