#5286 ⟨
a
,
b
,
c
|
ab
=
a
,
aaca
=
c
⟩
Up:
Monoid enumeration
Prev:
#5284
⟨
a
,
b
,
c
|
ab
=
a
,
aaca
=
a
⟩
Next:
#5287
⟨
a
,
b
,
c
|
ab
=
a
,
aacb
=
a
⟩
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
c
is not injective:
c
⋅
b
=
c
and
c
⋅ 1 =
c
, however
b
≠ 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.
cb
⇒
c
[3]
2.
ab
⇒
a
[1]
3.
a
2
c
2
⇒ (
ca
)
2
[4]
4.
a
2
ca
⇒
c
[2]
# abc:ab=a,aaca=c cab - - cb=c ab=a aacc=caca aaca=c