#22823 ⟨
a
,
b
|
aaa
=1,
abbbb
=
bbb
⟩
Up:
Monoids with two generators and two relations
Prev:
#22822
⟨
a
,
b
|
aaa
=1,
abbbb
=
bba
⟩
Next:
#22833
⟨
a
,
b
|
aaa
=1,
baabb
=
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 recursive path with deg(
b
) = 0; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
6
⇒
b
3
[5]
2.
a
b
3
⇒
b
5
[4]
3.
a
3
⇒ 1
[1]
# ab:aaa=1,abbbb=bbb b/a bbbbbb=bbb abbb=bbbbb aaa=1