#2610 ⟨
a
,
b
,
c
|
aba
=
b
,
accc
=1⟩
Up:
Monoid enumeration
Prev:
#2609
⟨
a
,
b
,
c
|
aba
=
b
,
accb
=1⟩
Next:
#2611
⟨
a
,
b
,
c
|
aba
=
b
,
baac
=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
a
is not injective:
a
⋅
c
3
a
=
a
and
a
⋅ 1 =
a
, however
c
3
a
≠ 1
Not right cancellative, because right multiplication by
c
3
is not injective:
c
3
a
⋅
c
3
=
c
3
and 1 ⋅
c
3
=
c
3
, however
c
3
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.
aba
⇒
b
[1]
2.
b
2
a
⇒
a
b
2
[3]
3.
a
c
3
⇒ 1
[2]
4.
b
c
3
⇒
ab
[4]
# abc:aba=b,accc=1 abc - - aba=b bba=abb accc=1 bccc=ab