#2063 ⟨
a
,
b
|
ababbaab
=
bb
⟩
Up:
Monoids with two generators and one relation
Prev:
#2062
⟨
a
,
b
|
ababbaab
=
ba
⟩
Next:
#2064
⟨
a
,
b
|
ababbaba
=
aa
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 10
Infinite non-cancellative non-commutative monoid
Not right cancellative, because right multiplication by
b
is not injective:
aba
b
2
a
2
⋅
b
=
b
2
and
b
⋅
b
=
b
2
, however
aba
b
2
a
2
≠
b
Enveloping group: ⟨
a
,
b
|
aababa
-1
bb
⟩
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
b
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ab
(
a
b
2
)
2
⇒ (
b
2
a
)
2
ab
[2]
2.
aba
b
2
a
2
b
⇒
b
2
[1]
# ab:ababbaab=bb ba ababbabb=bbabbaab ababbaab=bb