#5379 ⟨
a
,
b
|
ababbba
=
bbba
⟩
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Monoids with two generators and one relation
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#5378
⟨
a
,
b
|
ababbba
=
bbab
⟩
Next:
#5380
⟨
a
,
b
|
ababbba
=
bbbb
⟩
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 shortlex with
a
<
c
<
b
Auxiliary generators:
bbba
=
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
abac
⇒
c
[4]
2.
b
3
a
⇒
c
[2]
3.
b
3
c
⇒
cbac
[5]
# ab:ababbba=bbba acb bbba=c magic:0 abac=c bbba=c bbbc=cbac