#3096 ⟨
a
,
b
,
c
|
ab
=
aa
,
bacc
=1⟩
Up:
Monoid enumeration
Prev:
#3095
⟨
a
,
b
,
c
|
ab
=
aa
,
bacb
=1⟩
Next:
#3097
⟨
a
,
b
,
c
|
ab
=
aa
,
bbac
=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
⋅
b
=
a
2
and
a
⋅
a
=
a
2
, however
b
≠
a
Not right cancellative, because right multiplication by
a
c
2
is not injective:
a
c
2
b
⋅
a
c
2
=
a
c
2
and 1 ⋅
a
c
2
=
a
c
2
, however
a
c
2
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
a
<
b
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ab
⇒
a
2
[1]
2.
ba
c
2
⇒ 1
[2]
3.
a
3
c
2
⇒
a
[3]
# abc:ab=aa,bacc=1 abc - - ab=aa bacc=1 aaacc=a