#1623 ⟨
a
,
b
,
c
|
aab
=
ab
,
caa
=1⟩
Up:
Monoid enumeration
Prev:
#1622
⟨
a
,
b
,
c
|
aab
=
ab
,
bcc
=1⟩
Next:
#1624
⟨
a
,
b
,
c
|
aab
=
ab
,
cab
=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
c
is not injective:
c
⋅
a
2
c
=
c
and
c
⋅ 1 =
c
, however
a
2
c
≠ 1
Not right cancellative, because right multiplication by
b
is not injective:
a
⋅
b
=
b
and 1 ⋅
b
=
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.
ab
⇒
b
[4]
2.
cb
⇒
b
[5]
3.
c
a
2
⇒ 1
[2]
# abc:aab=ab,caa=1 abc - - ab=b cb=b caa=1