#1678 ⟨
a
,
b
,
c
|
aab
=
bb
,
aca
=1⟩
Up:
Monoid enumeration
Prev:
#1676
⟨
a
,
b
,
c
|
aab
=
bb
,
aac
=1⟩
Next:
#1679
⟨
a
,
b
,
c
|
aab
=
bb
,
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:
cb
⋅
b
=
b
and 1 ⋅
b
=
b
, however
cb
≠ 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.
ca
⇒
ac
[3]
2.
a
2
b
⇒
b
2
[1]
3.
a
2
c
⇒ 1
[5]
4.
c
b
2
⇒
b
[4]
# abc:aab=bb,aca=1 abc - - ca=ac aab=bb aac=1 cbb=b