#2284 ⟨
a
,
b
|
aabbbba
=
aab
⟩
Up:
Monoids with two generators and one relation
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#2283
⟨
a
,
b
|
aabbbba
=
aaa
⟩
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#2285
⟨
a
,
b
|
aabbbba
=
aba
⟩
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
⋅
a
b
4
a
=
a
2
b
and
a
⋅
ab
=
a
2
b
, however
a
b
4
a
≠
ab
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
=
aab
Reduction order:
Left-to-right recursive path with deg(
b
) = deg(
c
) = 0,
b
<
c
; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
cab
⇒
c
b
3
c
[5]
2.
c
b
3
a
⇒
c
[4]
3.
a
2
b
⇒
c
[2]
# ab:aabbbba=aab bc/a aab=c magic:0 cab=cbbbc cbbba=c aab=c