#188 ⟨
a
,
b
|
abaaab
=
b
⟩
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Monoid enumeration
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#187
⟨
a
,
b
|
abaaab
=
a
⟩
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#189
⟨
a
,
b
|
abaaba
=
a
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
b
is not injective:
ab
a
3
⋅
b
=
b
and 1 ⋅
b
=
b
, however
ab
a
3
≠ 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.
bab
⇒
a
b
2
[4]
2.
b
a
2
b
⇒
a
2
b
2
[7]
3.
b
a
3
b
⇒
a
3
b
2
[6]
4.
a
4
b
2
⇒
b
[5]
# ab:abaaab=b ab - - bab=abb baab=aabb baaab=aaabb aaaabb=b