#5659 ⟨
a
,
b
,
c
|
aa
=
a
,
bcb
=
bc
⟩
Up:
Monoid enumeration
Prev:
#5658
⟨
a
,
b
,
c
|
aa
=
a
,
bcb
=
bb
⟩
Next:
#5660
⟨
a
,
b
,
c
|
aa
=
a
,
bcb
=
cc
⟩
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
⋅
a
=
a
and
a
⋅ 1 =
a
, however
a
≠ 1
Not right cancellative, because right multiplication by
a
is not injective:
a
⋅
a
=
a
and 1 ⋅
a
=
a
, however
a
≠ 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
Auxiliary generators:
d
=
bc
Reduction order:
Left-to-right shortlex with
a
<
d
<
c
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
a
2
⇒
a
[1]
2.
dc
⇒
d
2
[6]
3.
db
⇒
d
[5]
4.
bc
⇒
d
[3]
# abc:aa=a,bcb=bc adcb bc=d morph:2/1 aa=a dc=dd db=d bc=d