#3473 ⟨
a
,
b
,
c
|
ba
=
ac
,
cab
=
b
⟩
Up:
Monoid enumeration
Prev:
#3472
⟨
a
,
b
,
c
|
ba
=
ac
,
cab
=
a
⟩
Next:
#3474
⟨
a
,
b
,
c
|
ba
=
ac
,
cbb
=
a
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
d
is not injective:
cd
⋅
d
=
d
and 1 ⋅
d
=
d
, however
cd
≠ 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
=
aab
Reduction order:
Right-to-left recursive path with deg(
c
) = deg(
d
) = 0,
c
<
d
; deg(
b
) = 1; deg(
a
) = 2
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
c
d
2
⇒
d
[8]
2.
b
⇒
c
2
d
[11]
3.
ac
⇒
c
2
da
[12]
4.
ad
⇒
d
2
[7]
# abc:ba=ac,cab=b reversed:cd/b/a aab=d morph:3/1 cdd=d b=ccd ac=ccda ad=dd