#4091 ⟨
a
,
b
|
aabaababa
=
bb
⟩
Up:
Monoids with two generators and one relation
Prev:
#4090
⟨
a
,
b
|
aabaababa
=
ba
⟩
Next:
#4092
⟨
a
,
b
|
aabaababb
=
aa
⟩
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
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
(
a
2
b
)
2
aba
⇒
b
2
[1]
2.
b
2
(
aba
)
2
ba
⇒ (
a
2
b
)
2
a
b
3
[2]
# ab:aabaababa=bb ab aabaababa=bb bbabaababa=aabaababbb