#2354 ⟨
a
,
b
|
abbabba
=
abb
⟩
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Monoids with two generators and one relation
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#2353
⟨
a
,
b
|
abbabba
=
aba
⟩
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#2355
⟨
a
,
b
|
abbabba
=
bab
⟩
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
⋅ (
b
2
a
)
2
=
a
b
2
and
a
⋅
b
2
=
a
b
2
, however (
b
2
a
)
2
≠
b
2
Enveloping group: ⟨
a
,
b
|
aabb
⟩
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
Auxiliary generators:
c
=
abb
Reduction order:
Left-to-right shortlex with
a
<
c
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
b
2
⇒
c
[2]
2.
c
2
a
⇒
c
[4]
3.
c
b
2
⇒
c
3
[5]
# ab:abbabba=abb acb abb=c magic:0 abb=c cca=c cbb=ccc