#2996 ⟨
a
,
b
,
c
|
aab
=
c
,
cac
=
a
⟩
Up:
Monoid enumeration
Prev:
#2995
⟨
a
,
b
,
c
|
aab
=
c
,
cab
=
c
⟩
Next:
#2998
⟨
a
,
b
,
c
|
aab
=
c
,
cac
=
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
⋅
ab
a
3
b
=
a
and
a
⋅ 1 =
a
, however
ab
a
3
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
4
b
⇒
a
2
b
a
2
[3]
2.
a
2
b
a
3
b
⇒
a
[2]
3.
c
⇒
a
2
b
[1]
# abc:aab=c,cac=a ba/c - - aaaab=aabaa aabaaab=a c=aab