#1824 ⟨
a
,
b
,
c
|
aba
=
ab
,
ccc
=1⟩
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Monoid enumeration
Prev:
#1823
⟨
a
,
b
,
c
|
aba
=
ab
,
ccb
=1⟩
Next:
#1825
⟨
a
,
b
,
c
|
aba
=
ac
,
abb
=1⟩
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
=
ab
Reduction order:
Left-to-right shortlex with
d
<
b
<
a
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
db
⇒
d
2
[6]
2.
da
⇒
d
[5]
3.
ab
⇒
d
[3]
4.
c
3
⇒ 1
[2]
# abc:aba=ab,ccc=1 dbac ab=d morph:2/1 db=dd da=d ab=d ccc=1