#4272 ⟨
a
,
b
,
c
|
aab
=1,
bcbb
=
c
⟩
Up:
Monoid enumeration
Prev:
#4271
⟨
a
,
b
,
c
|
aab
=1,
bcbb
=
b
⟩
Next:
#4275
⟨
a
,
b
,
c
|
aab
=1,
bcbc
=
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
⋅
aba
=
a
and
a
⋅ 1 =
a
, however
aba
≠ 1
Not right cancellative, because right multiplication by
ab
is not injective:
aba
⋅
ab
=
ab
and 1 ⋅
ab
=
ab
, however
aba
≠ 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
b
<
c
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
b
⇒ 1
[1]
2.
a
2
c
⇒
c
b
2
[3]
3.
bc
b
2
⇒
c
[2]
4.
c
2
b
2
⇒ (
bc
)
2
[4]
# abc:aab=1,bcbb=c bca - - aab=1 aac=cbb bcbb=c ccbb=bcbc