#3522 ⟨
a
,
b
,
c
|
bb
=
ac
,
baa
=
a
⟩
Up:
Monoid enumeration
Prev:
#3521
⟨
a
,
b
,
c
|
bb
=
ac
,
acb
=
c
⟩
Next:
#3523
⟨
a
,
b
,
c
|
bb
=
ac
,
baa
=
b
⟩
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
b
is not injective:
b
⋅
a
b
2
=
b
2
and
b
⋅
b
=
b
2
, however
a
b
2
≠
b
Not right cancellative, because right multiplication by
a
is not injective:
ba
⋅
a
=
a
and 1 ⋅
a
=
a
, however
ba
≠ 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
b
<
a
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ac
⇒
b
2
[1]
2.
b
a
2
⇒
a
[2]
3.
ba
b
2
⇒
b
2
[3]
4.
(
ba
)
2
⇒
ba
[4]
# abc:bb=ac,baa=a bac - - ac=bb baa=a babb=bb baba=ba