#3406 ⟨
a
,
b
,
c
|
ac
=
ab
,
bca
=
c
⟩
Up:
Monoid enumeration
Prev:
#3404
⟨
a
,
b
,
c
|
ac
=
ab
,
bca
=
a
⟩
Next:
#3407
⟨
a
,
b
,
c
|
ac
=
ab
,
bcb
=
a
⟩
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
a
is not injective:
a
⋅
b
=
ac
and
a
⋅
c
=
ac
, however
b
≠
c
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
<
c
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ab
⇒
ac
[1]
2.
cb
⇒
c
2
[4]
3.
bca
⇒
c
[2]
4.
a
c
2
a
⇒
ac
[3]
5.
c
3
a
⇒
c
2
[5]
# abc:ac=ab,bca=c acb - - ab=ac cb=cc bca=c acca=ac ccca=cc