#4754 ⟨
a
,
b
|
abaaaaab
=
aab
⟩
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Monoid enumeration
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#4753
⟨
a
,
b
|
abaaaaab
=
aaa
⟩
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#4755
⟨
a
,
b
|
abaaaaab
=
aba
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
ab
=
abc
and
a
⋅
bc
=
abc
, however
ab
≠
bc
Not right cancellative, because right multiplication by
c
is not injective:
a
⋅
c
=
c
2
and
c
⋅
c
=
c
2
, however
a
≠
c
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
=
aaaaab
Reduction order:
Left-to-right shortlex with
b
<
c
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
ac
⇒
c
2
[5]
2.
a
2
b
⇒
abc
[3]
3.
ab
c
4
⇒
c
[4]
# ab:abaaaaab=aab bca aaaaab=c morph:6/1 ac=cc aab=abc abcccc=c