#2503 ⟨
a
,
b
|
aababa
=
baaa
⟩
Up:
Monoids with two generators and one relation
Prev:
#2502
⟨
a
,
b
|
aababa
=
abbb
⟩
Next:
#2504
⟨
a
,
b
|
aababa
=
baab
⟩
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
a
is not injective:
a
(
ab
)
2
⋅
a
=
b
a
3
and
b
a
2
⋅
a
=
b
a
3
, however
a
(
ab
)
2
≠
b
a
2
Enveloping group: ⟨
a
,
b
|
aabba
-1
a
-1
b
-1
⟩
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
Auxiliary generators:
c
=
ba
Reduction order:
Left-to-right recursive path with deg(
b
) = deg(
c
) = 0,
b
<
c
; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
ba
⇒
c
[2]
2.
c
a
2
⇒
a
2
c
2
[4]
# ab:aababa=baaa bc/a ba=c morph:2/1 ba=c caa=aacc