#6081 ⟨
a
,
b
,
c
|
ab
=
c
,
bbc
=
cb
⟩
Up:
Monoid enumeration
Prev:
#6077
⟨
a
,
b
,
c
|
ab
=
c
,
bbc
=
ba
⟩
Next:
#6082
⟨
a
,
b
,
c
|
ab
=
c
,
bbc
=
cc
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
b
is not injective:
ab
⋅
b
=
b
2
ab
and
b
2
a
⋅
b
=
b
2
ab
, however
ab
≠
b
2
a
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:
Right-to-left recursive path with deg(
b
) = 0; deg(
a
) = deg(
c
) = 1,
a
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
b
2
⇒
b
2
ab
[2]
2.
c
⇒
ab
[1]
# abc:ab=c,bbc=cb reversed:b/ac - - abb=bbab c=ab