#5203 ⟨
a
,
b
|
aababba
=
bbaa
⟩
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Monoids with two generators and one relation
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#5202
⟨
a
,
b
|
aababba
=
babb
⟩
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#5204
⟨
a
,
b
|
aababba
=
bbab
⟩
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(
a
) = deg(
c
) = 0,
a
<
c
; deg(
b
) = 1
Auxiliary generators:
ba
=
c
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
ba
⇒
c
[2]
2.
bca
⇒
a
2
cbc
[4]
# ab:aababba=bbaa reversed:ac/b ba=c morph:2/2 ba=c bca=aacbc