#3586 ⟨
a
,
b
,
c
|
ba
=
ab
,
cc
=
aa
⟩
Up:
Monoid enumeration
Prev:
#3585
⟨
a
,
b
,
c
|
ba
=
ab
,
ca
=
bc
⟩
Next:
#3587
⟨
a
,
b
,
c
|
ba
=
ab
,
cc
=
ab
⟩
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
<
b
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ba
⇒
ab
[1]
2.
c
2
⇒
a
2
[2]
3.
c
a
2
⇒
a
2
c
[3]
# abc:ba=ab,cc=aa abc - - ba=ab cc=aa caa=aac