#4955 ⟨
a
,
b
|
aaaabaa
=
baaa
⟩
Up:
Monoid enumeration
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#4954
⟨
a
,
b
|
aaaabaa
=
abbb
⟩
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#4956
⟨
a
,
b
|
aaaabaa
=
baab
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
a
is not injective:
a
4
ba
⋅
a
=
b
a
3
and
b
a
2
⋅
a
=
b
a
3
, however
a
4
ba
≠
b
a
2
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:
Right-to-left recursive path with deg(
a
) = 0; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
a
3
⇒
a
4
b
a
2
[1]
# ab:aaaabaa=baaa reversed:a/b - - baaa=aaaabaa