#1930 ⟨
a
,
b
,
c
|
abc
=
ab
,
aca
=1⟩
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Monoid enumeration
Prev:
#1929
⟨
a
,
b
,
c
|
abc
=
aa
,
ccc
=1⟩
Next:
#1931
⟨
a
,
b
,
c
|
abc
=
ab
,
acb
=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
b
is not injective:
b
⋅
c
=
b
and
b
⋅ 1 =
b
, however
c
≠ 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
Reduction order:
Left-to-right shortlex with
c
<
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ac
⇒
ca
[3]
2.
bc
⇒
b
[5]
3.
c
a
2
⇒ 1
[4]
4.
b
a
2
⇒
b
[6]
# abc:abc=ab,aca=1 cab - - ac=ca bc=b caa=1 baa=b