#28273 ⟨
a
,
b
|
aa
=1,
babbb
=
bbab
⟩
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Monoid enumeration
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#28271
⟨
a
,
b
|
aa
=1,
babbb
=
babb
⟩
Next:
#28275
⟨
a
,
b
|
aa
=1,
babbb
=
bbbb
⟩
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
⋅
a
b
3
=
b
2
ab
and
b
⋅
bab
=
b
2
ab
, however
a
b
3
≠
bab
Not right cancellative, because right multiplication by
b
is not injective:
ba
b
2
⋅
b
=
b
2
ab
and
b
2
a
⋅
b
=
b
2
ab
, however
ba
b
2
≠
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
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
⇒ 1
[1]
2.
ba
b
3
⇒
b
2
ab
[2]
# ab:aa=1,babbb=bbab ab - - aa=1 babbb=bbab