#16547 ⟨
a
,
b
|
aba
=
bb
,
baa
=
aab
⟩
Up:
Monoid enumeration
Prev:
#16545
⟨
a
,
b
|
aba
=
bb
,
abb
=
aaa
⟩
Next:
#16548
⟨
a
,
b
|
aba
=
bb
,
baa
=
aba
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-commutative monoid
Element
a
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
2
b
⇒
b
a
2
[2]
2.
b
2
⇒
aba
[1]
3.
(
ab
)
2
⇒ (
ba
)
2
[3]
# ab:aba=bb,baa=aab a/b - - aab=baa bb=aba abab=baba