#6104 ⟨
a
,
b
,
c
|
ab
=
c
,
cac
=
ca
⟩
Up:
Monoid enumeration
Prev:
#6103
⟨
a
,
b
,
c
|
ab
=
c
,
cac
=
bc
⟩
Next:
#6105
⟨
a
,
b
,
c
|
ab
=
c
,
cac
=
cb
⟩
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
d
is not injective:
d
⋅
c
=
d
and
d
⋅ 1 =
d
, however
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
Auxiliary generators:
d
=
ca
Reduction order:
Left-to-right recursive path with deg(
d
) = deg(
a
) = deg(
c
) = 0,
d
<
a
<
c
; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
da
⇒
d
2
[6]
2.
dc
⇒
d
[5]
3.
ca
⇒
d
[3]
4.
db
⇒
c
2
[7]
5.
ab
⇒
c
[1]
# abc:ab=c,cac=ca dac/b ca=d morph:2/1 da=dd dc=d ca=d db=cc ab=c