#1046 ⟨a, b | aa=1, abbabb=1⟩

Up:Monoids with two generators and two relations
Prev:#1042 ⟨a, b | aa=1, ababab=1⟩
Next:#1059 ⟨a, b | aa=1, bbbbbb=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. cac ⇒ a
  3. cb ⇒ bc
  4. cab ⇒ abaca
  5. b2 ⇒ c 
# ab:aa=1,abbabb=1 ac/b bb=c frequency:2/0
aa=1
cac=a
cb=bc
cab=abaca
bb=c

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.

22 total

Σ#PresentationMapping
81055⟨a, b | aa=1, babbab=1⟩φ(a) = a, φ(b) = b
81132⟨a, b | aa=1, bbabb=a⟩φ(a) = a, φ(b) = b
105988⟨a, b | aaa=a, abbabb=1⟩φ(a) = a, φ(b) = b
105997⟨a, b | aaa=a, babbab=1⟩φ(a) = a, φ(b) = b
106129⟨a, b | aab=b, abbabb=1⟩φ(a) = a, φ(b) = b
106147⟨a, b | aab=b, babbab=1⟩φ(a) = a, φ(b) = b
109410⟨a, b | aa=1, aaabbabb=1⟩φ(a) = a, φ(b) = b
109426⟨a, b | aa=1, aababbab=1⟩φ(a) = a, φ(b) = b
109450⟨a, b | aa=1, abaababb=1⟩φ(a) = a, φ(b) = b
109460⟨a, b | aa=1, ababbaba=1⟩φ(a) = a, φ(b) = b
109466⟨a, b | aa=1, abbaaabb=1⟩φ(a) = a, φ(b) = b
109470⟨a, b | aa=1, abbabaab=1⟩φ(a) = a, φ(b) = b
109490⟨a, b | aa=1, baaabbab=1⟩φ(a) = a, φ(b) = b
109500⟨a, b | aa=1, babaabab=1⟩φ(a) = a, φ(b) = b
109706⟨a, b | aa=1, aabbabb=a⟩φ(a) = a, φ(b) = b
109734⟨a, b | aa=1, ababbab=a⟩φ(a) = a, φ(b) = b
109746⟨a, b | aa=1, abbabba=a⟩φ(a) = a, φ(b) = b
109770⟨a, b | aa=1, baababb=a⟩φ(a) = a, φ(b) = b
109788⟨a, b | aa=1, bbaaabb=a⟩φ(a) = a, φ(b) = b
1010013⟨a, b | aa=1, abbabb=aa⟩φ(a) = a, φ(b) = b
1010047⟨a, b | aa=1, babbab=aa⟩φ(a) = a, φ(b) = b
1010332⟨a, b | aa=1, bbabb=aaa⟩φ(a) = a, φ(b) = b

Other anti-isomorphic instances

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

2 total

Σ#PresentationMapping
106156⟨a, b | aab=b, bbabba=1⟩φ(a) = a, φ(b) = b
109433⟨a, b | aa=1, aabbabba=1⟩φ(a) = a, φ(b) = b