#3043 ⟨
a
,
b
,
c
|
aba
=
b
,
cbc
=
b
⟩
Up:
Monoid enumeration
Prev:
#3042
⟨
a
,
b
,
c
|
aba
=
b
,
cbc
=
a
⟩
Next:
#3045
⟨
a
,
b
,
c
|
aba
=
c
,
abc
=
b
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite cancellative 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
a
<
c
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
aba
⇒
b
[1]
2.
cbc
⇒
b
[2]
3.
b
2
a
⇒
a
b
2
[3]
4.
b
2
c
⇒
c
b
2
[4]
# abc:aba=b,cbc=b acb - - aba=b cbc=b bba=abb bbc=cbb