#15531 ⟨a, b | aaa=bb, abbbb=a⟩

Up:Monoids with two generators and two relations
Prev:#15526 ⟨a, b | aaa=bb, ababb=b⟩
Next:#15532 ⟨a, b | aaa=bb, abbbb=b⟩

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. a3 ⇒ b2 [1]
2. b2a ⇒ ab2 [3]
3. ab4 ⇒ a [2]
4. b6 ⇒ b2 [4]
# ab:aaa=bb,abbbb=a ab
aaa=bb
bba=abb
abbbb=a
bbbbbb=bb

Isomorphic instances

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

1 total

Σ#PresentationMapping
1115541⟨a, b | aaa=bb, bbabb=a⟩φ(a) = a, φ(b) = b