#16952 ⟨
a
,
b
|
abab
=1,
aaaaaaa
=1⟩
Up:
Monoid enumeration
Prev:
#16908
⟨
a
,
b
|
aabb
=1,
aababab
=1⟩
Next:
#16955
⟨
a
,
b
|
abab
=1,
aaaaabb
=1⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-Abelian group
Element
a
4
b
a
2
has infinite order
Inverses of generators:
a
-1
=
a
6
b
-1
=
aba
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 recursive path with deg(
a
) = 0; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
7
⇒ 1
[2]
2.
bab
⇒
a
6
[3]
# ab:abab=1,aaaaaaa=1 a/b - - aaaaaaa=1 bab=aaaaaa