#1199 ⟨
a
,
b
|
aabaa
=
aaba
⟩
Up:
Monoid enumeration
Prev:
#1198
⟨
a
,
b
|
aabaa
=
aaab
⟩
Next:
#1200
⟨
a
,
b
|
aabaa
=
aabb
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
c
is not injective:
c
⋅
a
=
c
and
c
⋅ 1 =
c
, however
a
≠ 1
Not right cancellative, because right multiplication by
c
is not injective:
a
2
b
⋅
c
=
c
2
and
c
⋅
c
=
c
2
, however
a
2
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
Auxiliary generators:
c
=
aaba
Reduction order:
Left-to-right shortlex with
a
<
c
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ca
⇒
c
[4]
2.
cba
⇒
c
2
[6]
3.
cbc
⇒
c
3
[7]
4.
a
2
ba
⇒
c
[2]
5.
a
2
bc
⇒
c
2
[8]
# ab:aabaa=aaba acb aaba=c magic:0 ca=c cba=cc cbc=ccc aaba=c aabc=cc