#1818 ⟨
a
,
b
,
c
|
aba
=
ab
,
cac
=1⟩
Up:
Monoid enumeration
Prev:
#1815
⟨
a
,
b
,
c
|
aba
=
ab
,
bcc
=1⟩
Next:
#1820
⟨
a
,
b
,
c
|
aba
=
ab
,
cbb
=1⟩
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
b
is not injective:
b
⋅
a
=
b
and
b
⋅ 1 =
b
, however
a
≠ 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 shortlex with
a
<
b
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ba
⇒
b
[6]
2.
ca
⇒
ac
[3]
3.
a
c
2
⇒ 1
[4]
4.
b
c
2
⇒
b
[7]
# abc:aba=ab,cac=1 abc - - ba=b ca=ac acc=1 bcc=b