#16168 ⟨
a
,
b
|
aab
=
ab
,
abab
=
bb
⟩
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Monoid enumeration
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#16167
⟨
a
,
b
|
aab
=
ab
,
abab
=
ba
⟩
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#16169
⟨
a
,
b
|
aab
=
ab
,
abba
=
aa
⟩
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
⋅
ab
=
ab
and
a
⋅
b
=
ab
, however
ab
≠
b
Not right cancellative, because right multiplication by
b
is not injective:
a
2
⋅
b
=
ab
and
a
⋅
b
=
ab
, however
a
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
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
b
⇒
ab
[1]
2.
a
b
2
⇒
b
2
[3]
3.
(
ab
)
2
⇒
b
2
[2]
4.
b
2
ab
⇒
b
3
[4]
# ab:aab=ab,abab=bb ab - - aab=ab abb=bb abab=bb bbab=bbb