#516 ⟨
a
,
b
|
aabaa
=
aab
⟩
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Monoid enumeration
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#515
⟨
a
,
b
|
aabaa
=
aaa
⟩
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#517
⟨
a
,
b
|
aabaa
=
aba
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
c
is not injective:
c
⋅
a
2
=
c
and
c
⋅ 1 =
c
, however
a
2
≠ 1
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
=
aab
Reduction order:
Left-to-right shortlex with
a
<
c
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
cb
⇒
c
2
[5]
2.
a
2
b
⇒
c
[2]
3.
c
a
2
⇒
c
[4]
4.
cab
⇒
cac
[6]
# ab:aabaa=aab acb aab=c magic:0 cb=cc aab=c caa=c cab=cac