#2360 ⟨
a
,
b
|
abbbbba
=
abb
⟩
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Monoid enumeration
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#2359
⟨
a
,
b
|
abbbbba
=
aba
⟩
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#2361
⟨
a
,
b
|
abbbbba
=
bab
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
c
is not injective:
c
⋅
bcba
=
c
and
c
⋅ 1 =
c
, however
bcba
≠ 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
=
abbbb
Reduction order:
Left-to-right shortlex with
c
<
b
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
c
b
2
⇒
cbc
[5]
2.
a
b
2
⇒
cba
[3]
3.
(
cb
)
2
a
⇒
c
[4]
# ab:abbbbba=abb cba abbbb=c morph:5/1 cbb=cbc abb=cba cbcba=c