#5504 ⟨
a
,
b
,
c
|
ab
=
c
,
aaca
=
c
⟩
Up:
Monoid enumeration
Prev:
#5493
⟨
a
,
b
,
c
|
ab
=
c
,
aaac
=
c
⟩
Next:
#5507
⟨
a
,
b
,
c
|
ab
=
c
,
aacb
=
c
⟩
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
⋅
b
= (
ca
)
2
and
c
⋅
aca
= (
ca
)
2
, however
b
≠
aca
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(
c
) = deg(
a
) = 0,
c
<
a
; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
c
2
⇒ (
ca
)
2
[4]
2.
a
2
ca
⇒
c
[2]
3.
cb
⇒ (
ca
)
2
[5]
4.
ab
⇒
c
[1]
# abc:ab=c,aaca=c ca/b - - aacc=caca aaca=c cb=caca ab=c