#7232 ⟨
a
,
b
,
c
|
aa
=1,
bacc
=
ba
⟩
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Monoid enumeration
Prev:
#7228
⟨
a
,
b
,
c
|
aa
=1,
bacb
=
cc
⟩
Next:
#7233
⟨
a
,
b
,
c
|
aa
=1,
bacc
=
bb
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
ab
has infinite order
Not left cancellative, because left multiplication by
b
is not injective:
b
⋅
a
c
2
=
ba
and
b
⋅
a
=
ba
, however
a
c
2
≠
a
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
Reduction order:
Left-to-right shortlex with
a
<
b
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
⇒ 1
[1]
2.
ba
c
2
⇒
ba
[2]
# abc:aa=1,bacc=ba abc - - aa=1 bacc=ba