#1801 ⟨
a
,
b
,
c
|
aba
=
aa
,
bcb
=1⟩
Up:
Monoid enumeration
Prev:
#1800
⟨
a
,
b
,
c
|
aba
=
aa
,
bbc
=1⟩
Next:
#1802
⟨
a
,
b
,
c
|
aba
=
aa
,
bcc
=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
⋅
ba
=
a
2
and
a
⋅
a
=
a
2
, however
ba
≠
a
Not right cancellative, because right multiplication by
a
is not injective:
ab
⋅
a
=
a
2
and
a
⋅
a
=
a
2
, however
ab
≠
a
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.
cb
⇒
bc
[3]
2.
aba
⇒
a
2
[1]
3.
b
2
c
⇒ 1
[4]
# abc:aba=aa,bcb=1 abc - - cb=bc aba=aa bbc=1