#364 ⟨
a
,
b
,
c
|
aba
=
b
,
caa
=1⟩
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Monoid enumeration
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#363
⟨
a
,
b
,
c
|
aba
=
b
,
bcc
=1⟩
Next:
#365
⟨
a
,
b
,
c
|
aba
=
b
,
cac
=1⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 7
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
=
c
and
c
⋅ 1 =
c
, however
a
2
c
≠ 1
Not right cancellative, because right multiplication by
a
2
is not injective:
a
2
c
⋅
a
2
=
a
2
and 1 ⋅
a
2
=
a
2
, however
a
2
c
≠ 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
Reduction order:
Left-to-right recursive path with deg(
a
) = deg(
b
) = 0,
a
<
b
; deg(
c
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
aba
⇒
b
[1]
2.
b
2
a
⇒
a
b
2
[3]
3.
cb
⇒
b
a
2
[5]
4.
c
a
2
⇒ 1
[2]
5.
cab
⇒
ba
[4]
# abc:aba=b,caa=1 ab/c - - aba=b bba=abb cb=baa caa=1 cab=ba