#22268 ⟨
a
,
b
|
aaa
=1,
ababba
=
bb
⟩
Up:
Monoid enumeration
Prev:
#22264
⟨
a
,
b
|
aaa
=1,
ababab
=
bb
⟩
Next:
#22271
⟨
a
,
b
|
aaa
=1,
ababbb
=
ba
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-commutative monoid
Element
b
a
2
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:
Right-to-left recursive path with deg(
b
) = 0; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
b
2
⇒
ba
b
2
a
[3]
2.
aba
b
2
⇒
b
2
a
2
[4]
3.
a
3
⇒ 1
[1]
# ab:aaa=1,ababba=bb reversed:b/a - - aabb=babba ababb=bbaa aaa=1