#1252 ⟨
a
,
b
|
abaab
=
bbab
⟩
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Monoid enumeration
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#1251
⟨
a
,
b
|
abaab
=
bbaa
⟩
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#1253
⟨
a
,
b
|
abaab
=
bbba
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
c
is not injective:
b
2
⋅
c
=
cac
and
ca
⋅
c
=
cac
, however
b
2
≠
ca
Rewriting system
Format:
Pretty
Plain
Word:
Enter a word above to compute its normal form. Tips:
Lowercase letters stand for generators.
Spaces are ignored.
Numbers repeat the previous letter, e.g.
b90
.
Strategy:
Leftmost
Rightmost
Result:
1
1
Auxiliary generators:
c
=
ab
Reduction order:
Left-to-right shortlex with
c
<
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
ab
⇒
c
[2]
2.
b
2
c
⇒
cac
[4]
3.
(
ac
)
2
⇒
cbc
[5]
4.
a
c
2
bc
⇒
cbcac
[6]
# ab:abaab=bbab cab ab=c morph:2/1 ab=c bbc=cac acac=cbc accbc=cbcac