#5068 ⟨a, b | aaa=ab, bbab=a⟩

Up:Monoids with two generators and two relations
Prev:#5066 ⟨a, b | aaa=ab, bbaa=a⟩
Next:#5070 ⟨a, b | aaa=ab, bbba=a⟩

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. a7 ⇒ a [5]
2. ab ⇒ a3 [1]
3. b2a ⇒ a5 [6]
# ab:aaa=ab,bbab=a a/b
aaaaaaa=a
ab=aaa
bba=aaaaa

Isomorphic instances

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

8 total

Σ#PresentationMapping
1114616⟨a, b | aaba=b, aabbb=b⟩φ(a) = b, φ(b) = a
1114640⟨a, b | aaba=b, baabb=b⟩φ(a) = b, φ(b) = a
1114644⟨a, b | aaba=b, babab=b⟩φ(a) = b, φ(b) = a
1114646⟨a, b | aaba=b, babba=b⟩φ(a) = b, φ(b) = a
1114652⟨a, b | aaba=b, bbaab=b⟩φ(a) = b, φ(b) = a
1114654⟨a, b | aaba=b, bbaba=b⟩φ(a) = b, φ(b) = a
1114658⟨a, b | aaba=b, bbbaa=b⟩φ(a) = b, φ(b) = a
1115489⟨a, b | aaa=ab, bbaaa=a⟩φ(a) = a, φ(b) = b