#6072 ⟨
a
,
b
,
c
|
ab
=
c
,
bac
=
cb
⟩
Up:
Monoid enumeration
Prev:
#6071
⟨
a
,
b
,
c
|
ab
=
c
,
bac
=
ca
⟩
Next:
#6073
⟨
a
,
b
,
c
|
ab
=
c
,
bac
=
cc
⟩
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
⋅
b
=
b
a
2
b
and
b
a
2
⋅
b
=
b
a
2
b
, however
ab
≠
b
a
2
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
) = 0; deg(
b
) = deg(
c
) = 1,
b
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
c
⇒
ab
[1]
2.
a
b
2
⇒
b
a
2
b
[2]
# abc:ab=c,bac=cb a/bc - - c=ab abb=baab