#1433 ⟨
a
,
b
,
c
|
aa
=1,
bcb
=
bc
⟩
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Monoid enumeration
Prev:
#1432
⟨
a
,
b
,
c
|
aa
=1,
bcb
=
bb
⟩
Next:
#1434
⟨
a
,
b
,
c
|
aa
=1,
bcb
=
cc
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element
ba
has infinite order
Not left cancellative, because left multiplication by
d
is not injective:
d
⋅
b
=
d
and
d
⋅ 1 =
d
, however
b
≠ 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
⇒ 1
[1]
2.
dc
⇒
d
2
[6]
3.
db
⇒
d
[5]
4.
bc
⇒
d
[3]
# abc:aa=1,bcb=bc adcb bc=d morph:2/1 aa=1 dc=dd db=d bc=d