#5126 ⟨
a
,
b
|
aab
=
ab
,
aaaa
=
a
⟩
Up:
Monoids with two generators and two relations
Prev:
#5125
⟨
a
,
b
|
aab
=
aa
,
bbbb
=
b
⟩
Next:
#5143
⟨
a
,
b
|
aab
=
ab
,
baaa
=
b
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 10
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
b
⇒
ab
[1]
2.
a
4
⇒
a
[2]
# ab:aab=ab,aaaa=a ab aab=ab aaaa=a