#157 ⟨
a
,
b
|
ab
=
aa
,
ba
=
a
⟩
Up:
Monoids with two generators and two relations
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#151
⟨
a
,
b
|
ba
=
ab
,
aaa
=1⟩
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#158
⟨
a
,
b
|
ab
=
aa
,
ba
=
b
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 7
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.
ab
⇒
a
2
[1]
2.
ba
⇒
a
[2]
3.
a
3
⇒
a
2
[3]
# ab:ab=aa,ba=a ab ab=aa ba=a aaa=aa