#2086 ⟨
a
,
b
|
abbbaaab
=
ab
⟩
Up:
Monoids with two generators and one relation
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#2085
⟨
a
,
b
|
abbbaaab
=
aa
⟩
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#2087
⟨
a
,
b
|
abbbaaab
=
ba
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 10
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
b
3
a
3
b
=
ab
and
a
⋅
b
=
ab
, however
b
3
a
3
b
≠
b
Not right cancellative, because right multiplication by
b
is not injective:
a
b
3
a
3
⋅
b
=
ab
and
a
⋅
b
=
ab
, however
a
b
3
a
3
≠
a
Enveloping group: ⟨
a
,
b
|
aaabbb
⟩
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
b
3
a
3
b
⇒
ab
[1]
# ab:abbbaaab=ab ab abbbaaab=ab