#5664 ⟨
a
,
b
|
aabaab
=
baabb
⟩
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Monoid enumeration
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#5663
⟨
a
,
b
|
aabaab
=
baaba
⟩
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#5665
⟨
a
,
b
|
aabaab
=
babaa
⟩
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
a
2
⋅
b
=
b
a
2
b
2
and
b
a
2
b
⋅
b
=
b
a
2
b
2
, however
a
2
b
a
2
≠
b
a
2
b
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 shortlex with
a
<
c
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
a
2
b
⇒
c
[2]
2.
bcb
⇒
c
2
[4]
3.
a
2
c
2
⇒
c
2
b
[5]
4.
b
c
3
⇒
c
3
b
[6]
# ab:aabaab=baabb acb aab=c morph:3/0 aab=c bcb=cc aacc=ccb bccc=cccb