#18416 ⟨
a
,
b
|
aab
=
b
,
aaaaaaa
=1⟩
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Monoid enumeration
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#18415
⟨
a
,
b
|
aab
=
a
,
bbbbbbb
=1⟩
Next:
#18615
⟨
a
,
b
|
aba
=
a
,
bbbbbbb
=1⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
b
has infinite order
Not right cancellative, because right multiplication by
b
is not injective:
a
⋅
b
=
b
and 1 ⋅
b
=
b
, however
a
≠ 1
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.
ab
⇒
b
[3]
2.
a
7
⇒ 1
[2]
# ab:aab=b,aaaaaaa=1 ab - - ab=b aaaaaaa=1