#923 ⟨
a
,
b
|
aaabbba
=
ba
⟩
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Monoid enumeration
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#922
⟨
a
,
b
|
aaabbba
=
ab
⟩
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#924
⟨
a
,
b
|
aaabbba
=
bb
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
c
is not injective:
b
⋅
c
=
c
a
2
c
and
c
a
2
⋅
c
=
c
a
2
c
, however
b
≠
c
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
Auxiliary generators:
c
=
bbba
Reduction order:
Left-to-right recursive path with deg(
a
) = deg(
c
) = 0,
a
<
c
; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
a
(
a
2
c
)
3
⇒
c
[4]
2.
ba
⇒
a
3
c
[3]
3.
bc
⇒
c
a
2
c
[5]
# ab:aaabbba=ba ac/b bbba=c morph:4/1 aaacaacaac=c ba=aaac bc=caac