#9153 ⟨a, b | aa=a, abba=abb⟩

Up:Monoids with two generators and two relations
Prev:#9152 ⟨a, b | aa=a, abba=aba⟩
Next:#9154 ⟨a, b | aa=a, abba=bab⟩

Quick links

  1. Properties
  2. Rewriting system
  3. Isomorphic instances
  4. Anti-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. a2 ⇒ a [1]
2. ac ⇒ c [6]
3. ab ⇒ c [3]
4. cba ⇒ cb [5]
5. cb2 ⇒ cbc [7]
# ab:aa=a,abba=abb acb ab=c morph:2/1
aa=a
ac=c
ab=c
cba=cb
cbb=cbc

Isomorphic instances

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

2 total

Σ#PresentationMapping
1125163⟨a, b | aa=a, aabba=abb⟩φ(a) = a, φ(b) = b
1125677⟨a, b | aa=a, abba=aabb⟩φ(a) = a, φ(b) = b

Anti-isomorphic instances

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

1 total

Σ#PresentationMapping
1125166⟨a, b | aa=a, aabba=bba⟩φ(a) = a, φ(b) = b