#3483 ⟨
a
,
b
,
c
|
bb
=
aa
,
abc
=
a
⟩
Up:
Monoid enumeration
Prev:
#3481
⟨
a
,
b
,
c
|
bb
=
aa
,
aac
=
c
⟩
Next:
#3484
⟨
a
,
b
,
c
|
bb
=
aa
,
abc
=
b
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
ba
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
bc
=
a
and
a
⋅ 1 =
a
, however
bc
≠ 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 recursive path with deg(
b
) = deg(
c
) = 0,
b
<
c
; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
3
c
⇒
b
2
[4]
2.
abc
⇒
a
[2]
3.
b
2
a
⇒
a
b
2
[3]
4.
a
2
⇒
b
2
[1]
# abc:bb=aa,abc=a bc/a - - bbbc=bb abc=a bba=abb aa=bb