#479 ⟨a, b | abbaab=aa⟩

Up:Monoids with two generators and one relation
Prev:#478 ⟨a, b | ababba=bb⟩
Next:#480 ⟨a, b | abbaab=ab⟩

Quick links

  1. Properties
  2. Rewriting system

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. ab2 ⇒ c [2]
2. a2b ⇒ cac [4]
3. c2ac ⇒ a2 [6]
4. cacb ⇒ ac [5]
5. a(ac)2 ⇒ c2a3 [8]
6. a3cb ⇒ c2a2c [7]
# ab:abbaab=aa bca abb=c morph:3/2
abb=c
aab=cac
ccac=aa
cacb=ac
aacac=ccaaa
aaacb=ccaac