#2469 ⟨
a
,
b
,
c
|
aab
=
b
,
ccaa
=1⟩
Up:
Monoid enumeration
Prev:
#2467
⟨
a
,
b
,
c
|
aab
=
b
,
cbcb
=1⟩
Next:
#2470
⟨
a
,
b
,
c
|
aab
=
b
,
ccab
=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
c
is not injective:
c
⋅
c
a
2
c
=
c
and
c
⋅ 1 =
c
, however
c
a
2
c
≠ 1
Not right cancellative, because right multiplication by
b
is not injective:
a
2
⋅
b
=
b
and 1 ⋅
b
=
b
, however
a
2
≠ 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
a
<
b
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
b
⇒
b
[1]
2.
c
2
b
⇒
b
[3]
3.
c
2
a
2
⇒ 1
[2]
4.
c
2
ab
⇒
ab
[4]
# abc:aab=b,ccaa=1 abc - - aab=b ccb=b ccaa=1 ccab=ab