#22272 ⟨
a
,
b
|
aaa
=1,
ababbb
=
bb
⟩
Up:
Monoids with two generators and two relations
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#22271
⟨
a
,
b
|
aaa
=1,
ababbb
=
ba
⟩
Next:
#22276
⟨
a
,
b
|
aaa
=1,
abbaab
=
bb
⟩
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 recursive path with deg(
b
) = 0; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
b
2
⇒
ba
b
3
[3]
2.
aba
b
3
⇒
b
2
[2]
3.
a
3
⇒ 1
[1]
# ab:aaa=1,ababbb=bb b/a aabb=babbb ababbb=bb aaa=1