#10711 ⟨a, b | aaab=aba, bbbb=1⟩

Up:Monoids with two generators and two relations
Prev:#10683 ⟨a, b | aaab=aaa, bbbb=1⟩
Next:#10729 ⟨a, b | aaab=baa, abab=1⟩

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. a31 ⇒ a16 [5]
2. aba ⇒ a3b [1]
3. a3b2a ⇒ a7b2 [3]
4. a7b3a ⇒ a15b3 [4]
5. b4 ⇒ 1 [2]
# ab:aaab=aba,bbbb=1 reversed:a/b
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa=aaaaaaaaaaaaaaaa
aba=aaab
aaabba=aaaaaaabb
aaaaaaabbba=aaaaaaaaaaaaaaabbb
bbbb=1