#10342 ⟨
a
,
b
|
aa
=1,
bbbbb
=
bab
⟩
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Monoid enumeration
Prev:
#10337
⟨
a
,
b
|
aa
=1,
bbabb
=
bbb
⟩
Next:
#10343
⟨
a
,
b
|
aa
=1,
bbbbb
=
bbb
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element
b
has infinite order
Not left cancellative, because left multiplication by
b
is not injective:
b
⋅
ab
=
b
5
and
b
⋅
b
4
=
b
5
, however
ab
≠
b
4
Not right cancellative, because right multiplication by
b
is not injective:
ba
⋅
b
=
b
5
and
b
4
⋅
b
=
b
5
, however
ba
≠
b
4
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.
bab
⇒
b
5
[2]
2.
a
2
⇒ 1
[1]
# ab:aa=1,bbbbb=bab b/a - - bab=bbbbb aa=1