#2580 ⟨
a
,
b
|
abaaba
=
aaab
⟩
Up:
Monoids with two generators and one relation
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#2579
⟨
a
,
b
|
abaaba
=
aaaa
⟩
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#2581
⟨
a
,
b
|
abaaba
=
aaba
⟩
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
a
2
ba
=
a
3
b
and
a
⋅
a
2
b
=
a
3
b
, however
b
a
2
ba
≠
a
2
b
Enveloping group: ⟨
a
,
b
|
aabba
-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
Auxiliary generators:
c
=
ab
Reduction order:
Right-to-left recursive path with deg(
b
) = deg(
c
) = 0,
b
<
c
; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
ab
⇒
c
[2]
2.
a
2
c
⇒ (
ca
)
2
[4]
# ab:abaaba=aaab reversed:bc/a ab=c morph:2/1 ab=c aac=caca