#4453 ⟨
a
,
b
,
c
|
aba
=1,
bcac
=
c
⟩
Up:
Monoid enumeration
Prev:
#4450
⟨
a
,
b
,
c
|
aba
=1,
bbcc
=
c
⟩
Next:
#4456
⟨
a
,
b
,
c
|
aba
=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 right cancellative, because right multiplication by
c
is not injective:
bca
⋅
c
=
c
and 1 ⋅
c
=
c
, however
bca
≠ 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
c
<
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ba
⇒
ab
[3]
2.
a
2
c
⇒
cac
[5]
3.
a
2
b
⇒ 1
[4]
4.
bcac
⇒
c
[2]
# abc:aba=1,bcac=c cab - - ba=ab aac=cac aab=1 bcac=c