#4127 ⟨
a
,
b
,
c
|
aaa
=1,
abcc
=
c
⟩
Up:
Monoid enumeration
Prev:
#4126
⟨
a
,
b
,
c
|
aaa
=1,
abcc
=
b
⟩
Next:
#4129
⟨
a
,
b
,
c
|
aaa
=1,
baac
=
a
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
aba
has infinite order
Not right cancellative, because right multiplication by
c
is not injective:
bc
⋅
c
=
a
2
c
and
a
2
⋅
c
=
a
2
c
, however
bc
≠
a
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
3
⇒ 1
[1]
2.
b
c
2
⇒
a
2
c
[3]
# abc:aaa=1,abcc=c abc - - aaa=1 bcc=aac