#2305 ⟨
a
,
b
|
abaabab
=
aaa
⟩
Up:
Monoids with two generators and one relation
Prev:
#2304
⟨
a
,
b
|
abaaaba
=
bbb
⟩
Next:
#2306
⟨
a
,
b
|
abaabab
=
aab
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 10
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
ba
(
ab
)
2
=
a
3
and
a
⋅
a
2
=
a
3
, however
ba
(
ab
)
2
≠
a
2
Enveloping group: ⟨
a
,
b
|
aaabba
-1
b
⟩
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
b
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
(
aba
)
2
b
⇒
a
3
[1]
2.
a
5
bab
⇒
ab
a
2
b
a
3
[2]
# ab:abaabab=aaa ba abaabab=aaa aaaaabab=abaabaaa