#4829 ⟨
a
,
b
|
abababba
=
bba
⟩
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Monoid enumeration
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#4828
⟨
a
,
b
|
abababba
=
bab
⟩
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#4830
⟨
a
,
b
|
abababba
=
bbb
⟩
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
c
is not injective:
a
c
2
b
⋅
c
=
bc
and
b
⋅
c
=
bc
, however
a
c
2
b
≠
b
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
Auxiliary generators:
c
=
ba
Reduction order:
Left-to-right recursive path with deg(
c
) = 0; deg(
a
) = deg(
b
) = 1,
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
a
c
2
bc
⇒
bc
[4]
2.
ba
⇒
c
[2]
3.
b
2
c
⇒
c
3
bc
[5]
# ab:abababba=bba c/ab ba=c morph:2/1 accbc=bc ba=c bbc=cccbc