#660 ⟨
a
,
b
|
ab
=
aa
,
bb
=
aa
⟩
Up:
Monoids with two generators and two relations
Prev:
#658
⟨
a
,
b
|
ab
=
aa
,
ba
=
aa
⟩
Next:
#662
⟨
a
,
b
|
ab
=
aa
,
bb
=
ba
⟩
Properties
Presentation has sum-of-sides 8
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
ab
⇒
a
2
b
2
⇒
a
2
b
a
2
⇒
a
3
# ab:ab=aa,bb=aa ab ab=aa bb=aa baa=aaa
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
8
661
⟨
a
,
b
|
ab
=
aa
,
bb
=
ab
⟩
φ
(
a
) =
a
,
φ
(
b
) =
b
