#6040 ⟨
a
,
b
,
c
|
ab
=
c
,
aca
=
cc
⟩
Up:
Monoid enumeration
Prev:
#6039
⟨
a
,
b
,
c
|
ab
=
c
,
aca
=
cb
⟩
Next:
#6045
⟨
a
,
b
,
c
|
ab
=
c
,
acb
=
bc
⟩
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
a
<
b
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ab
⇒
c
[1]
2.
aca
⇒
c
2
[2]
3.
c
2
b
⇒
a
c
2
[3]
4.
c
3
a
⇒
a
c
3
[4]
# abc:ab=c,aca=cc abc - - ab=c aca=cc ccb=acc ccca=accc