#3450 ⟨
a
,
b
,
c
|
ba
=
ac
,
abc
=
b
⟩
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Monoid enumeration
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#3449
⟨
a
,
b
,
c
|
ba
=
ac
,
abc
=
a
⟩
Next:
#3451
⟨
a
,
b
,
c
|
ba
=
ac
,
abc
=
c
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-commutative monoid
Element
a
has infinite order
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
Reduction order:
Left-to-right shortlex with
b
<
a
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ac
⇒
ba
[1]
2.
abc
⇒
b
[2]
# abc:ba=ac,abc=b bac - - ac=ba abc=b