#1685 ⟨a, b | aba=bb, bbb=b⟩

Up:Monoids with two generators and two relations
Prev:#1682 ⟨a, b | aba=bb, bab=a⟩
Next:#1686 ⟨a, b | abb=aa, bbb=a⟩

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. ba ⇒ ab
  2. a2b ⇒ b2
  3. b3 ⇒ b 
# ab:aba=bb,bbb=b ab
ba=ab
aab=bb
bbb=b

Staircase diagram

Right Cayley graph (truncated)

Other isomorphic instances

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

25 total

Σ#PresentationMapping
91994⟨a, b | aaa=a, baab=a⟩φ(a) = b, φ(b) = a
105203⟨a, b | aab=bb, abba=b⟩φ(a) = a, φ(b) = b
105281⟨a, b | aba=bb, aabb=b⟩φ(a) = a, φ(b) = b
105283⟨a, b | aba=bb, abab=b⟩φ(a) = a, φ(b) = b
105289⟨a, b | aba=bb, baab=b⟩φ(a) = a, φ(b) = b
1112160⟨a, b | aaaa=aa, baab=a⟩φ(a) = b, φ(b) = a
1112256⟨a, b | aaab=ab, baab=a⟩φ(a) = b, φ(b) = a
1112272⟨a, b | aaab=ba, aabb=a⟩φ(a) = b, φ(b) = a
1112276⟨a, b | aaab=ba, abab=a⟩φ(a) = b, φ(b) = a
1112278⟨a, b | aaab=ba, abba=a⟩φ(a) = b, φ(b) = a
1112284⟨a, b | aaab=ba, baab=a⟩φ(a) = b, φ(b) = a
1112286⟨a, b | aaab=ba, baba=a⟩φ(a) = b, φ(b) = a
1112290⟨a, b | aaab=ba, bbaa=a⟩φ(a) = b, φ(b) = a
1112366⟨a, b | aaba=ab, baba=a⟩φ(a) = b, φ(b) = a
1112382⟨a, b | aaba=ba, abab=a⟩φ(a) = b, φ(b) = a
1112390⟨a, b | aaba=ba, baab=a⟩φ(a) = b, φ(b) = a
1114711⟨a, b | aabb=a, babbb=a⟩φ(a) = b, φ(b) = a
1114775⟨a, b | abab=a, babbb=a⟩φ(a) = b, φ(b) = a
1114838⟨a, b | abba=b, aaaba=b⟩φ(a) = a, φ(b) = b
1115742⟨a, b | aab=bb, aaaba=b⟩φ(a) = a, φ(b) = b
1115910⟨a, b | aba=bb, aaaba=b⟩φ(a) = a, φ(b) = b
1118740⟨a, b | aaa=a, baaaab=a⟩φ(a) = b, φ(b) = a
1119284⟨a, b | aaa=a, baaab=aa⟩φ(a) = b, φ(b) = a
1119780⟨a, b | aaa=a, aaaa=bab⟩φ(a) = b, φ(b) = a
1119828⟨a, b | aaa=a, baab=aaa⟩φ(a) = b, φ(b) = a