#2143 ⟨
a
,
b
|
aaaabba
=
bba
⟩
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Monoids with two generators and one relation
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#2142
⟨
a
,
b
|
aaaabba
=
bab
⟩
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#2144
⟨
a
,
b
|
aaaabba
=
bbb
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 10
Infinite non-cancellative non-commutative monoid
Not right cancellative, because right multiplication by
a
is not injective:
a
4
b
2
⋅
a
=
b
2
a
and
b
2
⋅
a
=
b
2
a
, however
a
4
b
2
≠
b
2
Enveloping group is isomorphic to ℤ
4
∗ 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
=
bba
Reduction order:
Left-to-right recursive path with deg(
a
) = deg(
c
) = 0,
a
<
c
; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
4
c
⇒
c
[4]
2.
b
2
a
⇒
c
[2]
3.
b
2
c
⇒
c
a
3
c
[5]
# ab:aaaabba=bba ac/b bba=c magic:0 aaaac=c bba=c bbc=caaac