#5705 ⟨
a
,
b
,
c
|
aa
=
b
,
acb
=
bb
⟩
Up:
Monoid enumeration
Prev:
#5702
⟨
a
,
b
,
c
|
aa
=
b
,
acb
=
ab
⟩
Next:
#5706
⟨
a
,
b
,
c
|
aa
=
b
,
acb
=
bc
⟩
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
⋅
c
a
2
=
a
4
and
a
⋅
a
3
=
a
4
, however
c
a
2
≠
a
3
Not right cancellative, because right multiplication by
a
is not injective:
aca
⋅
a
=
a
4
and
a
3
⋅
a
=
a
4
, however
aca
≠
a
3
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 recursive path with deg(
a
) = deg(
c
) = 0,
a
<
c
; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ac
a
2
⇒
a
4
[2]
2.
b
⇒
a
2
[1]
# abc:aa=b,acb=bb ac/b - - acaa=aaaa b=aa