#13214 ⟨
a
,
b
|
abb
=
aba
,
bba
=
aa
⟩
Up:
Monoid enumeration
Prev:
#13213
⟨
a
,
b
|
abb
=
aba
,
bab
=
bb
⟩
Next:
#13215
⟨
a
,
b
|
abb
=
aba
,
bba
=
ab
⟩
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
a
is not injective:
a
⋅
ba
=
a
b
2
and
a
⋅
b
2
=
a
b
2
, however
ba
≠
b
2
Not right cancellative, because right multiplication by
a
is not injective:
b
2
⋅
a
=
a
2
and
a
⋅
a
=
a
2
, however
b
2
≠
a
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.
b
2
a
⇒
a
2
[2]
2.
aba
⇒
a
b
2
[1]
3.
a
b
4
⇒
a
3
[3]
4.
a
3
b
2
⇒
a
4
[4]
# ab:abb=aba,bba=aa ba - - bba=aa aba=abb abbbb=aaa aaabb=aaaa