#5019 ⟨
a
,
b
|
aaabaaa
=
babb
⟩
Up:
Monoids with two generators and one relation
Prev:
#5018
⟨
a
,
b
|
aaabaaa
=
baab
⟩
Next:
#5020
⟨
a
,
b
|
aaabaaa
=
bbbb
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 11
Infinite non-commutative monoid
Rewriting system
Format:
Pretty
Plain
Word to reduce:
Tips:
Lowercase letters stand for generators.
Spaces are ignored.
Numbers repeat the previous letter, e.g.
b90
.
Reduction strategy:
Leftmost
Rightmost
Path to normal form:
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.
ba
b
2
⇒
a
3
b
a
3
[1]
2.
a
3
b
a
4
b
2
⇒
ba
(
b
a
3
)
2
[2]
# ab:aaabaaa=babb a/b babb=aaabaaa aaabaaaabb=babaaabaaa