#5911 ⟨
a
,
b
|
abbaab
=
aaaba
⟩
Up:
Monoids with two generators and one relation
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#5910
⟨
a
,
b
|
abbaab
=
aaaab
⟩
Next:
#5912
⟨
a
,
b
|
abbaab
=
aaabb
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 11
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
b
2
a
2
b
=
a
3
ba
and
a
⋅
a
2
ba
=
a
3
ba
, however
b
2
a
2
b
≠
a
2
ba
Enveloping group: ⟨
a
,
b
|
aabaabbab
-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
b
2
a
2
b
⇒
a
3
ba
[1]
2.
a
3
bab
a
2
b
⇒
a
b
2
a
4
ba
[2]
# ab:abbaab=aaaba ba abbaab=aaaba aaababaab=abbaaaaba