#5400 ⟨
a
,
b
|
abbabba
=
aabb
⟩
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Monoid enumeration
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#5399
⟨
a
,
b
|
abbabba
=
aaba
⟩
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#5401
⟨
a
,
b
|
abbabba
=
abab
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅ (
b
2
a
)
2
=
a
2
b
2
and
a
⋅
a
b
2
=
a
2
b
2
, however (
b
2
a
)
2
≠
a
b
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
=
abb
Reduction order:
Right-to-left recursive path with deg(
b
) = deg(
c
) = 0,
b
<
c
; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
ac
⇒
c
2
a
[4]
2.
a
b
2
⇒
c
[2]
# ab:abbabba=aabb reversed:bc/a abb=c morph:3/0 ac=cca abb=c