#16543 ⟨
a
,
b
|
aba
=
ab
,
bbb
=
aba
⟩
Up:
Monoids with two generators and two relations
Prev:
#16540
⟨
a
,
b
|
aba
=
ab
,
bba
=
aaa
⟩
Next:
#16544
⟨
a
,
b
|
aba
=
ba
,
baa
=
aba
⟩
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(
b
) = 0; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
6
⇒
b
4
[5]
2.
ab
⇒
b
3
[2]
3.
b
3
a
⇒
b
3
[4]
# ab:aba=ab,bbb=aba b/a bbbbbb=bbbb ab=bbb bbba=bbb