#553 ⟨
a
,
b
,
c
|
bb
=
ac
,
ca
=
a
⟩
Up:
Monoid enumeration
Prev:
#552
⟨
a
,
b
,
c
|
bb
=
ac
,
bc
=
c
⟩
Next:
#554
⟨
a
,
b
,
c
|
bb
=
ac
,
ca
=
b
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
a
is not injective:
c
⋅
a
=
a
and 1 ⋅
a
=
a
, 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 recursive path with deg(
c
) = 0; deg(
a
) = deg(
b
) = 1,
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ca
⇒
a
[2]
2.
bac
⇒
acb
[3]
3.
b
2
⇒
ac
[1]
4.
b
a
2
⇒
acba
[4]
# abc:bb=ac,ca=a c/ab - - ca=a bac=acb bb=ac baa=acba