#2599 ⟨
a
,
b
|
ababba
=
aaaa
⟩
Up:
Monoids with two generators and one relation
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#2598
⟨
a
,
b
|
ababab
=
bbaa
⟩
Next:
#2600
⟨
a
,
b
|
ababba
=
aaab
⟩
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
b
2
a
=
a
4
and
a
⋅
a
3
=
a
4
, however
ba
b
2
a
≠
a
3
Not right cancellative, because right multiplication by
a
is not injective:
aba
b
2
⋅
a
=
a
4
and
a
3
⋅
a
=
a
4
, however
aba
b
2
≠
a
3
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
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
aba
b
2
a
⇒
a
4
[1]
# ab:ababba=aaaa ab ababba=aaaa