#326 ⟨a, b | aa=1, aabb=b⟩

Up:Monoids with two generators and two relations
Prev:#322 ⟨a, b | aa=1, aaab=b⟩
Next:#330 ⟨a, b | aa=1, abba=b⟩

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. a2 ⇒ 1
  2. b2 ⇒ b 
# ab:aa=1,aabb=b ab
aa=1
bb=b

Right Cayley graph (truncated)

Left Cayley graph (truncated)

Other isomorphic instances

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

55 total

Σ#PresentationMapping
7334⟨a, b | aa=1, baab=b⟩φ(a) = a, φ(b) = b
7361⟨a, b | aa=1, aab=bb⟩φ(a) = a, φ(b) = b
7366⟨a, b | aa=1, abb=ab⟩φ(a) = a, φ(b) = b
93343⟨a, b | aa=1, aaaabb=b⟩φ(a) = a, φ(b) = b
93353⟨a, b | aa=1, aabaab=b⟩φ(a) = a, φ(b) = b
93359⟨a, b | aa=1, aabbaa=b⟩φ(a) = a, φ(b) = b
93389⟨a, b | aa=1, baaaab=b⟩φ(a) = a, φ(b) = b
93478⟨a, b | aa=1, aaaab=bb⟩φ(a) = a, φ(b) = b
93484⟨a, b | aa=1, aaabb=ab⟩φ(a) = a, φ(b) = b
93489⟨a, b | aa=1, aabaa=bb⟩φ(a) = a, φ(b) = b
93496⟨a, b | aa=1, aabba=ba⟩φ(a) = a, φ(b) = b
93503⟨a, b | aa=1, abaab=ab⟩φ(a) = a, φ(b) = b
93617⟨a, b | aa=1, aaab=abb⟩φ(a) = a, φ(b) = b
93628⟨a, b | aa=1, aaba=bba⟩φ(a) = a, φ(b) = b
93631⟨a, b | aa=1, aabb=aab⟩φ(a) = a, φ(b) = b
93634⟨a, b | aa=1, aabb=baa⟩φ(a) = a, φ(b) = b
93648⟨a, b | aa=1, abba=aba⟩φ(a) = a, φ(b) = b
93661⟨a, b | aa=1, baab=aab⟩φ(a) = a, φ(b) = b
1126447⟨a, b | aa=1, aaaaaabb=b⟩φ(a) = a, φ(b) = b
1126459⟨a, b | aa=1, aaaabaab=b⟩φ(a) = a, φ(b) = b
1126465⟨a, b | aa=1, aaaabbaa=b⟩φ(a) = a, φ(b) = b
1126503⟨a, b | aa=1, aabaaaab=b⟩φ(a) = a, φ(b) = b
1126509⟨a, b | aa=1, aabaabaa=b⟩φ(a) = a, φ(b) = b
1126641⟨a, b | aa=1, baaaaaab=b⟩φ(a) = a, φ(b) = b
1126974⟨a, b | aa=1, aaaaaab=bb⟩φ(a) = a, φ(b) = b
1126980⟨a, b | aa=1, aaaaabb=ab⟩φ(a) = a, φ(b) = b
1126986⟨a, b | aa=1, aaaabaa=bb⟩φ(a) = a, φ(b) = b
1126993⟨a, b | aa=1, aaaabba=ba⟩φ(a) = a, φ(b) = b
1127003⟨a, b | aa=1, aaabaab=ab⟩φ(a) = a, φ(b) = b
1127015⟨a, b | aa=1, aaabbaa=ab⟩φ(a) = a, φ(b) = b
1127036⟨a, b | aa=1, aabaaba=ba⟩φ(a) = a, φ(b) = b
1127085⟨a, b | aa=1, abaaaab=ab⟩φ(a) = a, φ(b) = b
1127505⟨a, b | aa=1, aaaaab=abb⟩φ(a) = a, φ(b) = b
1127516⟨a, b | aa=1, aaaaba=bba⟩φ(a) = a, φ(b) = b
1127519⟨a, b | aa=1, aaaabb=aab⟩φ(a) = a, φ(b) = b
1127522⟨a, b | aa=1, aaaabb=baa⟩φ(a) = a, φ(b) = b
1127529⟨a, b | aa=1, aaabaa=abb⟩φ(a) = a, φ(b) = b
1127544⟨a, b | aa=1, aaabba=aba⟩φ(a) = a, φ(b) = b
1127559⟨a, b | aa=1, aabaab=aab⟩φ(a) = a, φ(b) = b
1127562⟨a, b | aa=1, aabaab=baa⟩φ(a) = a, φ(b) = b
1127583⟨a, b | aa=1, aabbaa=aab⟩φ(a) = a, φ(b) = b
1127622⟨a, b | aa=1, abaaba=aba⟩φ(a) = a, φ(b) = b
1127697⟨a, b | aa=1, baaaab=aab⟩φ(a) = a, φ(b) = b
1128037⟨a, b | aa=1, aaaab=aabb⟩φ(a) = a, φ(b) = b
1128043⟨a, b | aa=1, aaaab=baab⟩φ(a) = a, φ(b) = b
1128046⟨a, b | aa=1, aaaab=bbaa⟩φ(a) = a, φ(b) = b
1128056⟨a, b | aa=1, aaaba=abba⟩φ(a) = a, φ(b) = b
1128067⟨a, b | aa=1, aaabb=aaab⟩φ(a) = a, φ(b) = b
1128070⟨a, b | aa=1, aaabb=abaa⟩φ(a) = a, φ(b) = b
1128085⟨a, b | aa=1, aabaa=aabb⟩φ(a) = a, φ(b) = b
1128089⟨a, b | aa=1, aabaa=baab⟩φ(a) = a, φ(b) = b
1128110⟨a, b | aa=1, aabba=aaba⟩φ(a) = a, φ(b) = b
1128116⟨a, b | aa=1, aabba=baaa⟩φ(a) = a, φ(b) = b
1128141⟨a, b | aa=1, abaab=aaab⟩φ(a) = a, φ(b) = b
1128144⟨a, b | aa=1, abaab=abaa⟩φ(a) = a, φ(b) = b