#16262 ⟨
a
,
b
|
aab
=
ba
,
bbab
=
ab
⟩
Up:
Monoids with two generators and two relations
Prev:
#16261
⟨
a
,
b
|
aab
=
ba
,
bbab
=
aa
⟩
Next:
#16263
⟨
a
,
b
|
aab
=
ba
,
bbab
=
ba
⟩
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.
b
a
4
⇒
ba
[8]
2.
ab
⇒
b
a
2
[9]
3.
b
3
a
⇒
ba
[3]
# ab:aab=ba,bbab=ab a/b baaaa=ba ab=baa bbba=ba