#22843 ⟨
a
,
b
|
aaa
=1,
babab
=
bbb
⟩
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Monoids with two generators and two relations
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#22842
⟨
a
,
b
|
aaa
=1,
babab
=
bab
⟩
Next:
#22847
⟨
a
,
b
|
aaa
=1,
babbb
=
abb
⟩
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
3
⇒ 1
[1]
2.
b
(
ab
)
2
⇒
b
3
[2]
3.
b
3
ab
⇒
ba
b
3
[3]
# ab:aaa=1,babab=bbb ab aaa=1 babab=bbb bbbab=babbb