#5666 ⟨
a
,
b
|
aabaab
=
babab
⟩
Up:
Monoids with two generators and one relation
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#5665
⟨
a
,
b
|
aabaab
=
babaa
⟩
Next:
#5667
⟨
a
,
b
|
aabaab
=
babba
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 11
Infinite non-cancellative non-commutative monoid
Not right cancellative, because right multiplication by
b
is not injective:
a
2
b
a
2
⋅
b
=
b
(
ab
)
2
and (
ba
)
2
⋅
b
=
b
(
ab
)
2
, however
a
2
b
a
2
≠ (
ba
)
2
Enveloping group: ⟨
a
,
b
|
aabab
-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
b
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
(
a
2
b
)
2
⇒
b
(
ab
)
2
[1]
2.
a
2
b
2
(
ab
)
2
⇒ (
ba
)
3
ab
[2]
# ab:aabaab=babab ba aabaab=babab aabbabab=bababaab