#4090 ⟨
a
,
b
|
aabaababa
=
ba
⟩
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Monoid enumeration
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#4089
⟨
a
,
b
|
aabaababa
=
ab
⟩
Next:
#4091
⟨
a
,
b
|
aabaababa
=
bb
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
c
is not injective:
a
(
ac
)
2
⋅
c
=
c
and 1 ⋅
c
=
c
, however
a
(
ac
)
2
≠ 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
=
ba
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.
a
2
ca
c
2
⇒
c
[4]
2.
ba
⇒
c
[2]
3.
bc
⇒ (
ca
)
2
c
2
[5]
# ab:aabaababa=ba ac/b ba=c magic:0 aacacc=c ba=c bc=cacacc