#17109 ⟨
a
,
b
|
aaaa
=1,
aababb
=
b
⟩
Up:
Monoids with two generators and two relations
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#17105
⟨
a
,
b
|
aaaa
=1,
aabaab
=
b
⟩
Next:
#17113
⟨
a
,
b
|
aaaa
=1,
aabbab
=
b
⟩
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
⇒
ba
b
2
[3]
2.
b
(
a
b
2
)
2
⇒
b
[4]
3.
a
4
⇒ 1
[1]
# ab:aaaa=1,aababb=b b/a aab=babb babbabb=b aaaa=1