#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⟩

Properties

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

Right Cayley graph (truncated)

Left Cayley graph (truncated)