#4288 ⟨
a
,
b
|
ababaabab
=
ab
⟩
Up:
Monoids with two generators and one relation
Prev:
#4287
⟨
a
,
b
|
ababaabab
=
aa
⟩
Next:
#4289
⟨
a
,
b
|
ababaabab
=
ba
⟩
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
Reduction order:
Left-to-right shortlex with
b
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
(
aba
)
2
b
⇒ (
ab
)
2
a
2
b
[2]
2.
(
ab
)
3
a
2
b
⇒
ab
[3]
# ab:ababaabab=ab ba abaabab=ababaab abababaab=ab