#5604 ⟨
a
,
b
,
c
|
ab
=
c
,
cbac
=
a
⟩
Up:
Monoid enumeration
Prev:
#5603
⟨
a
,
b
,
c
|
ab
=
c
,
cacc
=
c
⟩
Next:
#5605
⟨
a
,
b
,
c
|
ab
=
c
,
cbac
=
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
a
is not injective:
a
⋅
b
2
a
2
b
=
a
and
a
⋅ 1 =
a
, however
b
2
a
2
b
≠ 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(
b
) = deg(
a
) = 0,
b
<
a
; deg(
c
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
3
b
⇒
ab
a
2
[4]
2.
ab
a
2
b
⇒
a
b
2
a
2
[3]
3.
a
b
2
a
2
b
⇒
a
[2]
4.
c
⇒
ab
[1]
# abc:ab=c,cbac=a ba/c - - aaab=abaa abaab=abbaa abbaab=a c=ab