#1579 ⟨
a
,
b
,
c
|
aaa
=
bb
,
ccc
=1⟩
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Monoid enumeration
Prev:
#1578
⟨
a
,
b
,
c
|
aaa
=
bb
,
cbc
=1⟩
Next:
#1581
⟨
a
,
b
,
c
|
aaa
=
bc
,
aac
=1⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-commutative monoid
Element
aba
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.
a
3
⇒
b
2
[1]
2.
b
2
a
⇒
a
b
2
[3]
3.
c
3
⇒ 1
[2]
# abc:aaa=bb,ccc=1 abc - - aaa=bb bba=abb ccc=1