#2595 ⟨
a
,
b
|
aaa
=1,
bbbb
=
bb
⟩
Up:
Monoids with two generators and two relations
Prev:
#2592
⟨
a
,
b
|
aaa
=1,
babb
=
bb
⟩
Next:
#2755
⟨
a
,
b
|
aa
=
a
,
bbbbbb
=1⟩
Properties
Presentation has sum-of-sides 9
Isomorphic to ℤ
3
∗ ℕ
(4 = 2)
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
a
3
⇒ 1
b
4
⇒
b
2
# ab:aaa=1,bbbb=bb ab aaa=1 bbbb=bb
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
22819
⟨
a
,
b
|
aaa
=1,
abbbb
=
abb
⟩
φ
(
a
) =
a
,
φ
(
b
) =
b
