#5119 ⟨
a
,
b
|
aabaaab
=
aaba
⟩
Up:
Monoid enumeration
Prev:
#5118
⟨
a
,
b
|
aabaaab
=
aaab
⟩
Next:
#5120
⟨
a
,
b
|
aabaaab
=
aabb
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
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
2
and
c
⋅
c
=
c
2
, however
a
≠
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:
Right-to-left shortlex with
c
<
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ca
⇒
c
2
[6]
2.
c
2
ba
⇒
a
2
bc
[8]
3.
a
2
ba
⇒
c
[2]
4.
c
3
b
⇒
c
[7]
# ab:aabaaab=aaba reversed:cab aaba=c magic:0 ca=cc ccba=aabc aaba=c cccb=c