#3634 ⟨
a
,
b
|
aabbaabaab
=
b
⟩
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Monoid enumeration
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#3633
⟨
a
,
b
|
aabbaabaab
=
a
⟩
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#3635
⟨
a
,
b
|
aabbaababa
=
a
⟩
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
b
is not injective:
a
2
b
(
b
a
2
)
2
⋅
b
=
b
and 1 ⋅
b
=
b
, however
a
2
b
(
b
a
2
)
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
=
aab
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.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
cb
c
2
⇒
b
[3]
2.
a
2
b
⇒
c
[2]
3.
c
b
2
⇒
b
2
c
4
[5]
4.
(
cb
)
2
⇒
b
2
c
2
[4]
# ab:aabbaabaab=b ac/b aab=c morph:3/0 cbcc=b aab=c cbb=bbcccc cbcb=bbcc