#13171 ⟨
a
,
b
|
aba
=
aab
,
bba
=
ab
⟩
Up:
Monoids with two generators and two relations
Prev:
#13170
⟨
a
,
b
|
aba
=
aab
,
bba
=
aa
⟩
Next:
#13172
⟨
a
,
b
|
aba
=
aab
,
bba
=
ba
⟩
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:
Right-to-left recursive path with deg(
b
) = 0; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ab
⇒
b
2
a
[2]
2.
b
4
a
2
⇒
b
2
a
2
[4]
# ab:aba=aab,bba=ab reversed:b/a ab=bba bbbbaa=bbaa