#4751 ⟨
a
,
b
|
aabbbbba
=
bba
⟩
Up:
Monoid enumeration
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#4750
⟨
a
,
b
|
aabbbbba
=
bab
⟩
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#4752
⟨
a
,
b
|
aabbbbba
=
bbb
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
c
is not injective:
a
2
bcab
⋅
c
=
c
and 1 ⋅
c
=
c
, however
a
2
bcab
≠ 1
Rewriting system
Format:
Pretty
Plain
Word:
Enter a word above to compute its normal form. Tips:
Lowercase letters stand for generators.
Spaces are ignored.
Numbers repeat the previous letter, e.g.
b90
.
Strategy:
Leftmost
Rightmost
Result:
1
1
Auxiliary generators:
c
=
bbbba
Reduction order:
Left-to-right recursive path with deg(
a
) = deg(
c
) = 0,
a
<
c
; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
b
2
a
⇒
a
2
bc
[3]
2.
b
2
c
⇒
cabc
[5]
3.
a
(
abc
)
2
⇒
c
[4]
# ab:aabbbbba=bba ac/b bbbba=c morph:5/1 bba=aabc bbc=cabc aabcabc=c