#5228 ⟨
a
,
b
|
aba
=
aa
,
aabb
=
a
⟩
Up:
Monoids with two generators and two relations
Prev:
#5222
⟨
a
,
b
|
aba
=
aa
,
aaaa
=
a
⟩
Next:
#5232
⟨
a
,
b
|
aba
=
aa
,
abba
=
a
⟩
Properties
Presentation has sum-of-sides 10
Infinite non-commutative monoid
Complete rewriting system
Format:
Pretty
Plain
Word to reduce:
Tips:
Lowercase letters stand for generators.
Spaces are ignored.
Numbers repeat the previous letter, e.g.
b90
.
Reduction strategy:
Leftmost
Rightmost
Path to normal form:
1
1
Reduction order:
Left-to-right shortlex with
a
<
b
aba
⇒
a
2
a
2
b
2
⇒
a
# ab:aba=aa,aabb=a ab aba=aa aabb=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.
1 total
Σ
#
Presentation
Mapping
11
15821
⟨
a
,
b
|
aba
=
aa
,
ababb
=
a
⟩
φ
(
a
) =
a
,
φ
(
b
) =
b
