#6102 ⟨
a
,
b
,
c
|
ab
=
c
,
cac
=
bb
⟩
Up:
Monoid enumeration
Prev:
#6101
⟨
a
,
b
,
c
|
ab
=
c
,
cac
=
ba
⟩
Next:
#6103
⟨
a
,
b
,
c
|
ab
=
c
,
cac
=
bc
⟩
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:
ab
a
2
⋅
b
=
b
2
and
b
⋅
b
=
b
2
, however
ab
a
2
≠
b
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(
b
) = deg(
a
) = 0,
b
<
a
; deg(
c
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
aba
b
2
⇒
b
2
a
2
b
[3]
2.
ab
a
2
b
⇒
b
2
[2]
3.
c
⇒
ab
[1]
# abc:ab=c,cac=bb ba/c - - ababb=bbaab abaab=bb c=ab