#1259 ⟨
a
,
b
|
ababa
=
abab
⟩
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Monoid enumeration
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#1258
⟨
a
,
b
|
ababa
=
aabb
⟩
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#1260
⟨
a
,
b
|
ababa
=
abba
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
c
is not injective:
c
⋅
a
=
c
and
c
⋅ 1 =
c
, however
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
=
abab
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.
#
Rule
Proof
1.
ca
⇒
c
[4]
2.
cb
⇒
abc
[5]
3.
(
ab
)
2
⇒
c
[2]
# ab:ababa=abab ac/b abab=c magic:0 ca=c cb=abc abab=c