#6070 ⟨
a
,
b
,
c
|
ab
=
c
,
bac
=
bc
⟩
Up:
Monoid enumeration
Prev:
#6068
⟨
a
,
b
,
c
|
ab
=
c
,
bac
=
ba
⟩
Next:
#6071
⟨
a
,
b
,
c
|
ab
=
c
,
bac
=
ca
⟩
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
⋅
a
2
b
=
bab
and
b
⋅
ab
=
bab
, however
a
2
b
≠
ab
Not right cancellative, because right multiplication by
b
is not injective:
b
a
2
⋅
b
=
bab
and
ba
⋅
b
=
bab
, however
b
a
2
≠
ba
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(
a
) = deg(
b
) = 0,
a
<
b
; deg(
c
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
a
2
b
⇒
bab
[2]
2.
c
⇒
ab
[1]
# abc:ab=c,bac=bc ab/c - - baab=bab c=ab