#5849 ⟨
a
,
b
|
abaaba
=
abaab
⟩
Up:
Monoids with two generators and one relation
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#5848
⟨
a
,
b
|
abaaba
=
aabbb
⟩
Next:
#5850
⟨
a
,
b
|
abaaba
=
ababa
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 11
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
b
a
2
ba
=
ab
a
2
b
and
a
⋅
b
a
2
b
=
ab
a
2
b
, however
b
a
2
ba
≠
b
a
2
b
Enveloping group is isomorphic to ℤ
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
=
abaab
Reduction order:
Left-to-right recursive path with deg(
a
) = deg(
c
) = 0,
a
<
c
; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ca
⇒
c
[4]
2.
cb
⇒
abac
[5]
3.
ab
a
2
b
⇒
c
[2]
# ab:abaaba=abaab ac/b abaab=c magic:0 ca=c cb=abac abaab=c