#12128 ⟨
a
,
b
|
abba
=
bb
,
aaaaa
=1⟩
Up:
Monoid enumeration
Prev:
#12095
⟨
a
,
b
|
abba
=
aa
,
bbbbb
=1⟩
Next:
#12149
⟨
a
,
b
|
aaaa
=
aa
,
aaab
=
b
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-commutative monoid
Element
a
3
ba
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 recursive path with deg(
a
) = 0; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
5
⇒ 1
[2]
2.
a
b
2
⇒
b
2
a
4
[3]
# ab:abba=bb,aaaaa=1 a/b - - aaaaa=1 abb=bbaaaa