#1211 ⟨
a
,
b
|
aabab
=
abaa
⟩
Up:
Monoids with two generators and one relation
Prev:
#1210
⟨
a
,
b
|
aabab
=
aabb
⟩
Next:
#1212
⟨
a
,
b
|
aabab
=
abab
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 9
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅ (
ab
)
2
=
ab
a
2
and
a
⋅
b
a
2
=
ab
a
2
, however (
ab
)
2
≠
b
a
2
Enveloping group: ⟨
a
,
b
|
aabba
-1
b
-1
⟩
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
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
(
ab
)
2
⇒
ab
a
2
[1]
# ab:aabab=abaa ab aabab=abaa