#26183 ⟨
a
,
b
|
aa
=1,
bbbbbbbbb
=1⟩
Up:
Monoid enumeration
Prev:
#26090
⟨
a
,
b
|
aa
=1,
abbabbabb
=1⟩
Next:
#26599
⟨
a
,
b
|
aa
=1,
ababbbba
=
b
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Isomorphic to ℤ
2
∗ ℤ
9
Infinite non-Abelian group
Element
ba
has infinite order
Inverses of generators:
a
-1
=
a
b
-1
=
b
8
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
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
⇒ 1
[1]
2.
b
9
⇒ 1
[2]
# ab:aa=1,bbbbbbbbb=1 ab - - aa=1 bbbbbbbbb=1