#2247 ⟨
a
,
b
,
c
|
abab
=1,
bcbc
=1⟩
Up:
Monoid enumeration
Prev:
#2242
⟨
a
,
b
,
c
|
abab
=1,
accb
=1⟩
Next:
#2253
⟨
a
,
b
,
c
|
abac
=1,
abbc
=1⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-Abelian group
Element
a
has infinite order
Inverses of generators:
a
-1
=
bab
b
-1
=
aba
c
-1
=
bcb
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.
cbc
⇒
aba
[3]
2.
(
ab
)
2
⇒ 1
[1]
3.
(
ba
)
2
⇒ 1
[5]
# abc:abab=1,bcbc=1 abc - - cbc=aba abab=1 baba=1