#4411 ⟨
a
,
b
,
c
|
aba
=1,
acbb
=
c
⟩
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Monoid enumeration
Prev:
#4408
⟨
a
,
b
,
c
|
aba
=1,
acac
=
c
⟩
Next:
#4414
⟨
a
,
b
,
c
|
aba
=1,
acbc
=
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.
ab
⇒
ba
[3]
2.
b
a
2
⇒ 1
[4]
3.
c
b
2
⇒
bac
[5]
4.
c
a
2
⇒
acb
[6]
# abc:aba=1,acbb=c bac - - ab=ba baa=1 cbb=bac caa=acb