#5586 ⟨
a
,
b
|
aaabab
=
babab
⟩
Up:
Monoids with two generators and one relation
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#5585
⟨
a
,
b
|
aaabab
=
babaa
⟩
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#5587
⟨
a
,
b
|
aaabab
=
babba
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 11
Infinite non-cancellative non-commutative monoid
Not right cancellative, because right multiplication by
b
is not injective:
a
3
ba
⋅
b
=
b
(
ab
)
2
and (
ba
)
2
⋅
b
=
b
(
ab
)
2
, however
a
3
ba
≠ (
ba
)
2
Enveloping group is isomorphic to ℤ
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
3
bab
⇒
b
(
ab
)
2
[1]
# ab:aaabab=babab ab aaabab=babab