#25252 ⟨
a
,
b
|
aa
=
a
,
bbabb
=
bab
⟩
Up:
Monoids with two generators and two relations
Prev:
#25251
⟨
a
,
b
|
aa
=
a
,
bbabb
=
abb
⟩
Next:
#25253
⟨
a
,
b
|
aa
=
a
,
bbabb
=
bbb
⟩
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 shortlex with
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
⇒
a
[1]
2.
b
2
a
b
2
⇒
bab
[2]
3.
b
2
(
ab
)
2
⇒ (
ba
)
2
b
2
[3]
# ab:aa=a,bbabb=bab ab aa=a bbabb=bab bbabab=bababb