#2210 ⟨
a
,
b
|
aabaaab
=
abb
⟩
Up:
Monoids with two generators and one relation
Prev:
#2209
⟨
a
,
b
|
aabaaab
=
aba
⟩
Next:
#2211
⟨
a
,
b
|
aabaaab
=
baa
⟩
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
⋅
ab
a
3
b
=
a
b
2
and
a
⋅
b
2
=
a
b
2
, however
ab
a
3
b
≠
b
2
Not right cancellative, because right multiplication by
b
is not injective:
a
2
b
a
3
⋅
b
=
a
b
2
and
ab
⋅
b
=
a
b
2
, however
a
2
b
a
3
≠
ab
Enveloping group: ⟨
a
,
b
|
aaabab
-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
b
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
(
a
2
b
)
2
b
⇒
a
b
2
a
3
b
[2]
2.
a
2
b
a
3
b
⇒
a
b
2
[1]
# ab:aabaaab=abb ba aabaabb=abbaaab aabaaab=abb