#16390 ⟨
a
,
b
|
aba
=
ab
,
abaa
=
ab
⟩
Up:
Monoids with two generators and two relations
Prev:
#16388
⟨
a
,
b
|
aba
=
ab
,
aabb
=
bb
⟩
Next:
#16394
⟨
a
,
b
|
aba
=
ab
,
abab
=
ab
⟩
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
Auxiliary generators:
c
=
ab
Reduction order:
Left-to-right shortlex with
a
<
c
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
ab
⇒
c
[2]
2.
ca
⇒
c
[4]
3.
cb
⇒
c
2
[5]
# ab:aba=ab,abaa=ab acb ab=c morph:2/1 ab=c ca=c cb=cc