#5697 ⟨
a
,
b
,
c
|
aa
=
b
,
aca
=
ac
⟩
Up:
Monoid enumeration
Prev:
#5693
⟨
a
,
b
,
c
|
aa
=
b
,
abc
=
cb
⟩
Next:
#5698
⟨
a
,
b
,
c
|
aa
=
b
,
aca
=
bb
⟩
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
d
is not injective:
d
⋅
a
=
d
and
d
⋅ 1 =
d
, 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
=
ac
Reduction order:
Left-to-right recursive path with deg(
d
) = deg(
c
) = deg(
a
) = 0,
d
<
c
<
a
; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
dc
⇒
d
2
[6]
2.
da
⇒
d
[5]
3.
ac
⇒
d
[3]
4.
b
⇒
a
2
[1]
# abc:aa=b,aca=ac dca/b ac=d morph:2/1 dc=dd da=d ac=d b=aa