#4510 ⟨
a
,
b
,
c
|
abc
=1,
abab
=
a
⟩
Up:
Monoid enumeration
Prev:
#4508
⟨
a
,
b
,
c
|
abc
=1,
abaa
=
b
⟩
Next:
#4513
⟨
a
,
b
,
c
|
abc
=1,
abac
=
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
⋅
c
=
ab
and
a
⋅
b
=
ab
, however
c
≠
b
Not right cancellative, because right multiplication by
bc
is not injective:
bca
⋅
bc
=
bc
and 1 ⋅
bc
=
bc
, however
bca
≠ 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 shortlex with
a
<
b
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ac
⇒
ab
[3]
2.
aba
⇒
a
2
b
[4]
3.
abc
⇒ 1
[1]
4.
a
2
b
2
⇒
a
[5]
# abc:abc=1,abab=a abc - - ac=ab aba=aab abc=1 aabb=a