#1066 ⟨
a
,
b
|
aabaab
=
bab
⟩
Up:
Monoid enumeration
Prev:
#1065
⟨
a
,
b
|
aabaab
=
baa
⟩
Next:
#1067
⟨
a
,
b
|
aabaab
=
bba
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
b
is not injective:
a
2
b
a
2
⋅
b
=
bab
and
ba
⋅
b
=
bab
, however
a
2
b
a
2
≠
ba
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
b
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
b
2
ab
⇒
bab
a
2
b
[2]
2.
(
a
2
b
)
2
⇒
bab
[1]
# ab:aabaab=bab ba - - aabbab=babaab aabaab=bab