#1062 ⟨
a
,
b
,
c
|
ab
=
c
,
bb
=
ab
⟩
Up:
Monoid enumeration
Prev:
#1049
⟨
a
,
b
,
c
|
ab
=
c
,
ccc
=
c
⟩
Next:
#1063
⟨
a
,
b
,
c
|
ab
=
c
,
bc
=
ab
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
b
is not injective:
a
⋅
b
=
b
2
and
b
⋅
b
=
b
2
, however
a
≠
b
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
Reduction order:
Left-to-right recursive path with deg(
b
) = deg(
a
) = 0,
b
<
a
; deg(
c
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ab
⇒
b
2
[2]
2.
c
⇒
b
2
[3]
# abc:ab=c,bb=ab ba/c - - ab=bb c=bb