#1784 ⟨
a
,
b
|
abababaab
=
b
⟩
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Monoid enumeration
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#1783
⟨
a
,
b
|
abababaab
=
a
⟩
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#1785
⟨
a
,
b
|
ababababa
=
a
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
c
is not injective:
a
c
3
a
⋅
c
=
c
and 1 ⋅
c
=
c
, however
a
c
3
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
Auxiliary generators:
c
=
ab
Reduction order:
Left-to-right recursive path with deg(
c
) = deg(
a
) = 0,
c
<
a
; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
a
c
4
⇒
c
3
ac
[5]
2.
a
c
3
ac
⇒
c
[4]
3.
b
⇒
c
3
ac
[3]
# ab:abababaab=b ca/b ab=c morph:2/0 acccc=cccac acccac=c b=cccac