#1615 ⟨
a
,
b
,
c
|
aab
=
ab
,
aca
=1⟩
Up:
Monoid enumeration
Prev:
#1613
⟨
a
,
b
,
c
|
aab
=
ab
,
aac
=1⟩
Next:
#1616
⟨
a
,
b
,
c
|
aab
=
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 right cancellative, because right multiplication by
b
is not injective:
a
⋅
b
=
b
and 1 ⋅
b
=
b
, 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
Reduction order:
Left-to-right shortlex with
a
<
b
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ab
⇒
b
[4]
2.
ca
⇒
ac
[3]
3.
cb
⇒
b
[6]
4.
a
2
c
⇒ 1
[7]
# abc:aab=ab,aca=1 abc - - ab=b ca=ac cb=b aac=1