#68 ⟨a, b | aa=1, abab=1⟩

Up:Monoids with two generators and two relations
Prev:#64 ⟨a, b | aa=1, aaaa=1⟩
Next:#73 ⟨a, b | aa=1, bbbb=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. a2 ⇒ 1
  2. bab ⇒ a 
# ab:aa=1,abab=1 ab
aa=1
bab=a

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.

63 total

Σ#PresentationMapping
692⟨a, b | aa=1, bab=a⟩φ(a) = a, φ(b) = b
8495⟨a, b | aaa=a, abab=1⟩φ(a) = a, φ(b) = b
8532⟨a, b | aab=b, abab=1⟩φ(a) = a, φ(b) = b
8537⟨a, b | aab=b, baba=1⟩φ(a) = a, φ(b) = b
8557⟨a, b | aba=b, abab=1⟩φ(a) = b, φ(b) = a
81029⟨a, b | aa=1, aaabab=1⟩φ(a) = a, φ(b) = b
81033⟨a, b | aa=1, aababa=1⟩φ(a) = a, φ(b) = b
81039⟨a, b | aa=1, abaaab=1⟩φ(a) = a, φ(b) = b
81106⟨a, b | aa=1, aabab=a⟩φ(a) = a, φ(b) = b
81114⟨a, b | aa=1, ababa=a⟩φ(a) = a, φ(b) = b
81124⟨a, b | aa=1, baaab=a⟩φ(a) = a, φ(b) = b
81183⟨a, b | aa=1, abab=aa⟩φ(a) = a, φ(b) = b
81248⟨a, b | aa=1, bab=aaa⟩φ(a) = a, φ(b) = b
103747⟨a, b | aaaa=aa, abab=1⟩φ(a) = a, φ(b) = b
103794⟨a, b | aaab=ab, abab=1⟩φ(a) = a, φ(b) = b
103799⟨a, b | aaab=ab, baba=1⟩φ(a) = a, φ(b) = b
103848⟨a, b | aaba=ab, abab=1⟩φ(a) = b, φ(b) = a
103853⟨a, b | aaba=ab, baba=1⟩φ(a) = b, φ(b) = a
103861⟨a, b | aaba=ba, abab=1⟩φ(a) = a, φ(b) = b
103866⟨a, b | aaba=ba, baba=1⟩φ(a) = a, φ(b) = b
103891⟨a, b | aabb=aa, baba=1⟩φ(a) = b, φ(b) = a
103926⟨a, b | abab=aa, baba=1⟩φ(a) = a, φ(b) = b
103955⟨a, b | abba=aa, baba=1⟩φ(a) = b, φ(b) = a
105627⟨a, b | abab=1, aaabab=1⟩φ(a) = a, φ(b) = b
105631⟨a, b | abab=1, aabaab=1⟩φ(a) = b, φ(b) = a
105632⟨a, b | abab=1, aababa=1⟩φ(a) = a, φ(b) = b
105638⟨a, b | abab=1, abaaab=1⟩φ(a) = a, φ(b) = b
105639⟨a, b | abab=1, abaaba=1⟩φ(a) = b, φ(b) = a
105640⟨a, b | abab=1, ababaa=1⟩φ(a) = a, φ(b) = b
105649⟨a, b | abab=1, baaaba=1⟩φ(a) = a, φ(b) = b
105650⟨a, b | abab=1, baabaa=1⟩φ(a) = b, φ(b) = a
105652⟨a, b | abab=1, babaaa=1⟩φ(a) = a, φ(b) = b
105971⟨a, b | aaa=a, aaabab=1⟩φ(a) = a, φ(b) = b
105975⟨a, b | aaa=a, aababa=1⟩φ(a) = a, φ(b) = b
105981⟨a, b | aaa=a, abaaab=1⟩φ(a) = a, φ(b) = b
106107⟨a, b | aab=b, aaabab=1⟩φ(a) = a, φ(b) = b
106112⟨a, b | aab=b, aababa=1⟩φ(a) = a, φ(b) = b
106119⟨a, b | aab=b, abaaab=1⟩φ(a) = a, φ(b) = b
106122⟨a, b | aab=b, ababaa=1⟩φ(a) = a, φ(b) = b
106136⟨a, b | aab=b, baaaba=1⟩φ(a) = a, φ(b) = b
106142⟨a, b | aab=b, babaaa=1⟩φ(a) = a, φ(b) = b
106210⟨a, b | aba=b, aabaab=1⟩φ(a) = b, φ(b) = a
106218⟨a, b | aba=b, abaaba=1⟩φ(a) = b, φ(b) = a
109389⟨a, b | aa=1, aaaaabab=1⟩φ(a) = a, φ(b) = b
109394⟨a, b | aa=1, aaaababa=1⟩φ(a) = a, φ(b) = b
109400⟨a, b | aa=1, aaabaaab=1⟩φ(a) = a, φ(b) = b
109403⟨a, b | aa=1, aaababaa=1⟩φ(a) = a, φ(b) = b
109416⟨a, b | aa=1, aabaaaba=1⟩φ(a) = a, φ(b) = b
109442⟨a, b | aa=1, abaaaaab=1⟩φ(a) = a, φ(b) = b
109666⟨a, b | aa=1, aaaabab=a⟩φ(a) = a, φ(b) = b
109676⟨a, b | aa=1, aaababa=a⟩φ(a) = a, φ(b) = b
109688⟨a, b | aa=1, aabaaab=a⟩φ(a) = a, φ(b) = b
109694⟨a, b | aa=1, aababaa=a⟩φ(a) = a, φ(b) = b
109718⟨a, b | aa=1, abaaaba=a⟩φ(a) = a, φ(b) = b
109760⟨a, b | aa=1, baaaaab=a⟩φ(a) = a, φ(b) = b
109947⟨a, b | aa=1, aaabab=aa⟩φ(a) = a, φ(b) = b
109963⟨a, b | aa=1, aababa=aa⟩φ(a) = a, φ(b) = b
109986⟨a, b | aa=1, abaaab=aa⟩φ(a) = a, φ(b) = b
1010204⟨a, b | aa=1, aaaaa=bab⟩φ(a) = a, φ(b) = b
1010236⟨a, b | aa=1, aabab=aaa⟩φ(a) = a, φ(b) = b
1010268⟨a, b | aa=1, ababa=aaa⟩φ(a) = a, φ(b) = b
1010304⟨a, b | aa=1, baaab=aaa⟩φ(a) = a, φ(b) = b
1010481⟨a, b | aa=1, abab=aaaa⟩φ(a) = a, φ(b) = b