#7688 ⟨
a
,
b
,
c
|
aa
=1,
bcb
=
bbb
⟩
Up:
Monoid enumeration
Prev:
#7687
⟨
a
,
b
,
c
|
aa
=1,
bcb
=
bac
⟩
Next:
#7689
⟨
a
,
b
,
c
|
aa
=1,
bcb
=
bbc
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
ba
has infinite order
Not left cancellative, because left multiplication by
b
is not injective:
b
⋅
cb
=
b
3
and
b
⋅
b
2
=
b
3
, however
cb
≠
b
2
Not right cancellative, because right multiplication by
b
is not injective:
bc
⋅
b
=
b
3
and
b
2
⋅
b
=
b
3
, however
bc
≠
b
2
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.
a
2
⇒ 1
[1]
2.
bcb
⇒
b
3
[2]
# abc:aa=1,bcb=bbb abc - - aa=1 bcb=bbb