#5798 ⟨
a
,
b
|
aabbba
=
babab
⟩
Up:
Monoids with two generators and one relation
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#5797
⟨
a
,
b
|
aabbba
=
babaa
⟩
Next:
#5799
⟨
a
,
b
|
aabbba
=
babba
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 11
Infinite cancellative non-commutative monoid
Submonoid of enveloping group: ⟨
a
,
b
|
aaba
-1
ba
-1
b
-1
b
-1
a
-1
b
⟩
Embedding:
φ
(
a
) =
ba
-1
,
φ
(
b
) =
b
-1
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.
a
2
b
3
a
⇒
b
(
ab
)
2
[1]
2.
a
2
b
4
(
ab
)
2
⇒ (
ba
)
3
b
3
a
[2]
# ab:aabbba=babab ba aabbba=babab aabbbbabab=babababbba