#6103 ⟨
a
,
b
,
c
|
ab
=
c
,
cac
=
bc
⟩
Up:
Monoid enumeration
Prev:
#6102
⟨
a
,
b
,
c
|
ab
=
c
,
cac
=
bb
⟩
Next:
#6104
⟨
a
,
b
,
c
|
ab
=
c
,
cac
=
ca
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
c
is not injective:
aca
⋅
c
=
c
2
and
c
⋅
c
=
c
2
, however
aca
≠
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
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
c
3
⇒
c
2
ac
[4]
2.
(
ac
)
2
⇒
c
2
[3]
3.
bc
⇒
cac
[2]
4.
ab
⇒
c
[1]
# abc:ab=c,cac=bc ca/b - - accc=ccac acac=cc bc=cac ab=c