#2326 ⟨
a
,
b
|
ababaab
=
bab
⟩
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Monoid enumeration
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#2325
⟨
a
,
b
|
ababaab
=
baa
⟩
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#2327
⟨
a
,
b
|
ababaab
=
bba
⟩
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
2
a
⋅
c
=
c
2
and
c
⋅
c
=
c
2
, however
a
c
2
a
≠
c
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:
Right-to-left 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
c
2
ac
⇒
c
2
[5]
2.
a
c
4
⇒
c
3
ac
[6]
3.
ab
⇒
c
[2]
4.
bc
⇒
c
2
ac
[4]
# ab:ababaab=bab reversed:ac/b ab=c morph:2/0 accac=cc acccc=cccac ab=c bc=ccac