#16133 ⟨
a
,
b
|
aab
=
aa
,
bbab
=
aa
⟩
Up:
Monoid enumeration
Prev:
#16132
⟨
a
,
b
|
aab
=
aa
,
bbaa
=
bb
⟩
Next:
#16134
⟨
a
,
b
|
aab
=
aa
,
bbab
=
ab
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
ba
has infinite order
Not left cancellative, because left multiplication by
b
is not injective:
b
⋅
ba
b
2
=
b
2
ab
and
b
⋅
bab
=
b
2
ab
, however
ba
b
2
≠
bab
Not right cancellative, because right multiplication by
b
is not injective:
b
2
ab
⋅
b
=
b
2
ab
and
b
2
a
⋅
b
=
b
2
ab
, however
b
2
ab
≠
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 recursive path with deg(
b
) = 0; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
2
a
b
2
⇒
b
2
ab
[4]
2.
a
2
⇒
b
2
ab
[2]
3.
b
(
ba
)
2
⇒
a
b
2
ab
[5]
# ab:aab=aa,bbab=aa b/a - - bbabb=bbab aa=bbab bbaba=abbab