#5938 ⟨
a
,
b
|
abbbba
=
abbbb
⟩
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Monoids with two generators and one relation
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#5937
⟨
a
,
b
|
abbbba
=
abbba
⟩
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#5939
⟨
a
,
b
|
abbbba
=
baaab
⟩
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
4
a
=
a
b
4
and
a
⋅
b
4
=
a
b
4
, however
b
4
a
≠
b
4
Enveloping group is isomorphic to ℤ
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
=
abbbb
Reduction order:
Left-to-right shortlex with
a
<
b
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ca
⇒
c
[4]
2.
a
b
4
⇒
c
[2]
3.
c
b
4
⇒
c
2
[5]
# ab:abbbba=abbbb abc abbbb=c magic:0 ca=c abbbb=c cbbbb=cc